Research ArticleDesign of PI Controller for Voltage Controller ofFour-Phase Interleaved Boost Converter Using ParticleSwarm Optimization

Ittipon Laoprom and Satean Tunyasrirut

Department of Electrical Engineering Faculty of Engineering Pathumwan Institute of Technology Bangkok 10330 ailand

Correspondence should be addressed to Ittipon Laoprom oodoodkpgmailcom

Received 26 October 2019 Accepted 18 January 2020 Published 16 March 2020

Academic Editor Michela Robba

Copyright copy 2020 Ittipon Laoprom and Satean Tunyasrirut +is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution and reproduction in any medium provided theoriginal work is properly cited

+is article introduces voltage feedback controlling using the PI controller tuned gains by metaheuristic optimizations for a four-phase interleaved boost converter+emetaheuristic optimizations particle swarm optimization (PSO) genetic algorithm (GA) andTabu search (TS) are applied to find the optimal gains for the proposed control system In experiment the designed control system isimplemented on the DSP board TMS320F28335 with MATLABSimulink In this paper there are two conditions of the controlsystem in the test without load and with load+e response result of the proposed control system tuned gains by PSO is no overshootand approaches to the steady state better than GA and TS methods Moreover it is able to maintain the output voltage feedback at aconstant level according to the control signal both without load andwith load conditions As a result the four-phase interleaved boostconverter is regulated by the PI controller tuned gains with PSO which could efficiently maintain the voltage of both levels

1 Introduction

Currently the need for energy is increasing It is necessary tofind energy from other possible resources for example solarenergy wind energy and fuel energy In general to bringalternative energies to use it is necessary to increase or reducethe voltage level before the actual use +is is to make itconform with certain equipment For increasing the voltage apower electronic circuit is required+e boost converter is oneof the circuits used for increasing voltage +e boost convertercircuit is a circuit that uses less equipment and can raise thevoltage For this reason it is one of the popular circuits used toincrease the voltage for further applications [1 2]

Due to the increasing need for energies at present the useof a single energy transforming set is not enough for serving thepurpose+us devices that work together in parallel are used toserve an increasing need for energies and using only one boostconverter which requires high energymight not be possible Soit is necessary to have devices that work together in parallel inorder to share the burden of increasing need for energies

However when the boost converter works in parallel it willcreate a high ripple of input and output voltage For this reasonthe operation of each set of the boost converter connected inparallel is set for working at appropriate degrees +is is toreduce the ripple of input and output current and as a con-sequence the output voltage has less ripple +eboost converter in parallel has been applied to various workslike the use of power factor correction (PFC) in experimentrooms the application for solar energy fuel cell and DC-DCswitched-mode power converters (SMPC) [3ndash8]

However though the voltage has less ripple with nosystem to control the voltage output size to be constant whenbrought into actual use could possibly affect the stability ofthe system for example change from lower load to higherload +is will cause the reduction of output voltage tobecome smaller than the required size +e same applies tochanging from higher to lower load and this will causeoutput voltage higher than that required Because of this it isvery important to have a system to control output voltage inorder to keep the output voltage constant though there is a

HindawiJournal of Control Science and EngineeringVolume 2020 Article ID 9515160 13 pageshttpsdoiorg10115520209515160

change in output or input load For certain types of workhaving only one PI controller is sufficient for controlling theprocess to be stable and its result of controlling using the PIcontroller is acceptable

+ere are various ways to adjust the value of the Pro-portionalndashIntegral (PI) controller and currently artificialintelligence plays an important role in searching suitablevalues Examples are Tabu search (TS) genetic search (GS)and particle swarm optimization (PSO) +e PSO in par-ticular is a method to give a suitable value and has been usedwith many systems of PSO such as the DC motor controlsystem the one without carbon brush the DC-to-DCconverter circuit system the test on the electric motor driveand the multilevel inverter +e applications on theabovementioned systems gave a very satisfactory result andusing the search values with the test system also provided asatisfactory response [9ndash14]

As mentioned previously the PSO is widely applied to thePI controller for simulation system and real-world systemHowever it is usually employed in one-phase and two-phaseinterleaved boost converter circuits +ere are a few studiesconsidering the gained value PI controller for real system ofthe four-phase interleaved boost converter circuit +is re-search introduces a design of the PI controller using PSOsearch for controlling the voltage of the four-phase inter-leaved boost converter in order to control output voltage atconstant size throughout the use +e technique used was byPSO to control output voltage to have constant size accordingto the set voltage both when the load is constant and while theload is changed +e circuit keeps reducing the input andoutput voltage ripple as usual so that it is possible to be usedfor further work related to increasing voltage level

2 Theory of Boost Converter

+e boost converter circuit is a power converter circuitthat works to increase output voltage to be higher than that ofthe input +e structure of the circuit is shown in Figure 1

21eory of Four-Phase Interleaved Boost Converter Circuit+e four-phase interleaved boost converter is a circuitdesigned based on the original boost converter+e originalboost converter is designed to work in parallel while thecircuit operation is interleaved +e interleave depends onthe number of the parallel boost converters while the four-phase interleaved boost converter helps to solve theproblem of overload burden the original boost converterhas As the circuit load increases it is necessary to designlarger equipment as a result Also switch operation will geta higher load as a result Four-phase interleaved boostconverter can solve this problem +is also helped in re-ducing the ripple of input and output +e four-phaseinterleaved boost converter circuit [15ndash18] is shown inFigure 2

Operation of the four-phase interleaved boost convertercircuit is shown in Figures 3ndash6 [16ndash18]

L1

S1C

D1

RVin Vout

Figure 1 Original boost converter

Vin

L4L3L2L1

S1 S2 S3 S4

D1D2D3D4

C

Load Vout

Figure 2 Four-phase interleaved boost converter circuit

ON

ON

ON

ON

OFF

OFF

OFF

OFF OFF

OFF

OFF

S1

S2

S3

S4

IL1

IL2

IL3

IL4

Iin ΔIout

ΔIL3

ΔIL2

ΔIL1

ΔIL4

t

t

t

t

t

t

t

t

t

D middotTs

Ts

Figure 3 Switching pattern and inductor current waveform inrange of the duty ratio less than 14

2 Journal of Control Science and Engineering

22Design ofDifferent ParameterValues Design of differentparameter values can be performed as follows

+e equation for designing duty cycle for switching canbe designed using the following equations

Voutput Vinput

1 minus D (1)

D 1 minusVinput

Voutput1113890 1113891 (2)

where D is duty cycle Vinput is voltage input and Voutput isvoltage output

+e equation for designing inductance value can bederived using the following equation

L1 L2 L3 L4 VinputD

ΔILfs

(3)

where L is inductor ΔIL is induction ripple current and fS

is switching frequency+e equation for designing capacitor value can be de-

rived form the following equation

C VoutputD

RfsΔVoutput (4)

where C is capacitor R is resistor load and ΔVoutput is aripple factor of the output voltage

For designing the angle of the boost converter in eachphase the switching angle of the boost converter in eachphase can be designed to form the following equation

θ 360N

(5)

where θ is angle of switching and N is number of phases ofthe boost converter circuit

3 Algorithm of PSO

+e origin of searching the most suitable value of PSO wasdeveloped by Reynolds in 1987 [19 20] He got inspirationfrom the patterns of herd movement such as flock of birdsschool of fish and insect swarm as shown in Figure 7 +emovement is based on three main principles confrontationavoidance of swarm same speed control within the swarm

OFF

OFF

OFF

OFF

OFF

S1

S2

S3

S4

IL1

IL2

IL3

IL4

Iin ΔIout

ΔIL3

ΔIL2

ΔIL1

ΔIL4

t

t

t

t

t

t

t

t

t

ON

ON

OFF

ON

ON

DmiddotTs

Ts

Figure 4 Switching pattern and inductor current waveform inrange of duty ratio as 14

OFF

OFF

OFF

OFF

S1

S2

S3

S4

IL1

IL2

IL3

IL4

Iin ΔIout

ΔIL3

ΔIL2

ΔIL1

ΔIL4

t

t

t

t

t

t

t

t

t

ON

ON

OFF

ON

ONON

DmiddotTs

Ts

Figure 5 Switching pattern and inductor current waveform inrange of duty ratio as 12

Journal of Control Science and Engineering 3

and moving to the center of the swarm+ese principles leadto the swarm behavior in nature ie self-defense from beinghunted and searching for food resources effectively Later in

1995 Kennedy and Eberhart developed PSO as an effectivetool for solving the problem of obtaining the most suitablevalue [21]

OFF

OFF

OFF

S1

S2

S3

S4

IL1

IL2

IL3

IL4

Iin ΔIout

ΔIL3

ΔIL2

ΔIL1

ΔIL4

t

t

t

t

t

t

t

t

t

ON

ON

OFF

ON

ONON

ON

DmiddotTs

Ts

Figure 6 Switching pattern and inductor current waveform in range of duty ratio as 34

(a) (b)

(c) (d)

Figure 7 +e movement of flock of birds school of fish and insect swarm used as a guideline for particle swarm search

4 Journal of Control Science and Engineering

Algorithm of PSO has the same feature of evolutionarycalculation ie there will be a creation of population calledparticle which will move around the search space Eachparticle has a speed vector and a memory unit to be used forstoring previous good answers pbest is set as good answer inthe current search while gbest is set as global solution Allparticles will move in a similar manner and the ones closestto the target are the strongest With the particle swarmmovement principle the rest of the particles will be adjustedto have a similar movement direction as that of thosestrongest ones +is makes it possible for the whole particleswarm to move to the target effectively

Consider that the search-space is d-dimensional and atparticle i-th in the swarm It can be defined asXi (xi1 xi2 xid) and the velocity can be representedby another d-dimensional vector as Vi (vi1 vi2 vid)

and the best previously visited position of this particle bedenoted by Pi (pi1 pi2 pid) +e adjustment of particlemovement direction and the answers found are shown inequations (6) and (7) accordingly [22] Where x is a particleor answer v is speed vector showing adjusted direction w isinertia weight c1 is cognitive acceleration c2 is social ac-celeration and r1 and r2 are random numbers uniformlydistributed in the range [01]

In case of 2D space the movement of particles should beadjusted as shown in Figure 8

vn+1id wv

nid + c1r

n1 x

pbestid minus x

nid1113872 1113873 + c2r2 x

gbestid minus x

nid1113872 1113873 (6)

xn+1id x

nid + v

n+1id (7)

+e inertial weight w can be calculated from the relationas in equation (8) where wmax is the maximum weight wminis the minimum weight kmax is the number of the highestsearch round set and k is the current search round +e bestvalue suitable for use is the number of current search roundand the most suitable value of work application is c1 and c2which should be in-between 1 and 2 while wmin and wmaxshould be equal to 04 and 09 accordingly [23] Algorithm ofPSO has the following details

wi wmax minus kwmax minus wmin

kmax1113888 1113889 (8)

+e steps of designing PSO are as follows

Step 1 setting initial values which are search spacenumber of particles and maximum number of searchroundsStep 2 creating particles with normal sampling dis-tribution according to the number setStep 3 evaluating the strength of each particle usingobjective functionStep 4 adjusting the movement direction in accordancewith the strongest particle using equations (6) and (8)Step 5 calculating the particle of the current searchround using equation (7)Step 6 checking the ending condition If it is cor-related this means that the best search is obtained

+en stop the search or perform step 3 to further thenext search

4 Theory PI

+e PI controller is a combination between the proportionalcontroller P and integral controller I +e system forcontrolling PI is shown as a block diagram in Figure 9 PIcontrolling system is composed of error signal E(s) controlsignal U(s) output response signal C(s) reference signalR(s) disturbing signal D(s) and transferring signal of thesystem Gp(s) and Gc(s) +e theoretical function of the PIcontroller is stated in the following equation

Gc(s)1113868111386811138681113868PI Kp +

Ki

s

Kps + Ki

s (9)

+e PI controlling system is shown in Figure 9+e four-phase interleaved boost converter system has a

fast output response but lacks stability +e PI controller hasthe advantage of faster response times and less stable errors+erefore it is very appropriate to choose a PI controller forthis system

To obtain the value of the PI controller for the four-phaseinterleaved boost converter circuit the design of the PIcontroller uses PSO search to control four-phase interleavedboost converter voltage as shown in Figure 10

5 Digital Signal Processor Set

+is part will focus on the digital signal processor or DigitalSignal Processor (DSP) board TMS320F28335 of Texas In-struments company [24] as shown in Figure 11 for analyzingreal-time controlling +e Texas Instrument TMS320F28335consisting of a 32-bit CPU and a single-precision 32-bitfloating-point +e CPU speed is controlled by a clock signalwith the frequency of 150MHz working with MATLABSimulink [25] It produces pulse width modulation (PWM)signal for driving the four-phase interleaved boost convertercircuit switch of 25 kHz frequency as shown in Figure 12

6 Design of Four-Phase Interleaved BoostConverter Circuit

+e parameter value of the four-phase interleaved boostconverter obtained from equations (1)ndash(5) is shown inTable 1

For the design of a four-phase interleaved boost con-verter circuit to simplify circuit design the four-phase in-terleaved boost converter has parallel circuits +ereforeconsidering only one model of the circuit to make it easier todesign +e transferring function of the boost convertercircuit uses the impedance method where the analysis makesuse of switching operation while the switch is off+is can beshown as follows [26] All of the impedance value (Ztotal) isshown in the following equation

Ztotal Z1(s) + Z2(s) (10)

Z1(s) is the condition of the switch when the circuit isopen and Z2(s) is the condition of the switch when the

Journal of Control Science and Engineering 5

circuit is closed+e value of Z1(s) is shown in the followingequation and the value of Z2(s) is shown in equation (12)

Vin(s)

I(s)

RLCs2 + Ls + R

RCs + 1 (11)

Vout(s)

I(s)

R

RCs + 1 (12)

and the transferring function of the system is shown in thefollowing equation

Vout(s)

Vin

R

RLCs2 + Ls + R (13)

Where the value with parameter from Table 1 is replaced andthe transfer function of the system is obtained and it isshown in the following equation

Gp(s) 2

1173 times 10minus9s2 + 5865 times 10minus6s + 2 (14)

Asmentioned in equation(14) the term 1173 times 10minus9 s2 isa very small value considered close to zero +is systemtherefore became first order called Type 0 system+us it issuitable for the PI controller

In designing the value of PI for the four-phase inter-leaved boost converter circuit using particle swarm searchbased on Figure 8 PSO search was used for designing a PIcontroller for the four-phase interleaved boost convertercircuit system where PSO algorithm was made by MAT-LAB working with Intel(R) Core (TM) i5-3210M25 GHz +e number of particle sets is 100 where c1 c2is 20 r1 and r2 are random numbers uniformly distributedin the range [0 1] wmin is 04 wmax is 09 and kmax is 1000ie maximum iteration set as the termination criteria foreach trial

Based on comparing GA and TS the design was doneusing a PI controller for the four-phase interleaved boostconverter circuit GA and TS parameter search is designedas original Both GA and TS will be canceled when pro-cessing the construction or making a repletion of up to 1000times GA and TS will not be discussed But they show moredetails of GA in [27 28] and TS in [29ndash31] accordingly +ealgorithm of the two searches mentioned works by usingMATLAB

For designing the PI controller its parameter PI is set forsearching the following spaces Kp ranges [0 10] and Kiranges [50 100] +e processing designed for 50 experiment

xn

pbest

gbest

xn+1

v

Current motion

Figure 8 Movement of particles in 2D space

Gc(s) Gp(s)+

ndash

R(s)

D(s)

+

+

C(s)

PID Controller

E(s) U(s)

Plant

Figure 9 Operation diagram of the PI controller

KPV + (KIVs)+ ndash

+ndashParticle swarm optimization

(PSO) Vref

Plant(Four-phase interleaved

boost converter)

VrefVout

Figure 10 Operation diagram of the PI controller design using PSO search to control four-phase interleaved boost converter circuit voltage

6 Journal of Control Science and Engineering

searches starts with different search points to find the bestvalue After the search processing stops the parameter valueof the PI controller is obtained using GA TS and PSOmethods as shown in equations (15)ndash(17) accordingly +eresult of the simulation of the controller system is shown inFigure 13

Gc(s)1113868111386811138681113868PI GA 0435 +

1286s

(15)

Gc(s)1113868111386811138681113868PI TS

0325 +1256

s (16)

Gc(s)1113868111386811138681113868PI PSO

0413 +1413

s (17)

Based on Figure 11 the response of four-phase inter-leaved boost converter circuit simulation and time forsearching can be seen in Table 2 where Tr is the rise timeMpis the maximum percent overshoot Ts is the settling timeand ess is the steady state error Based on Table 2 PSO is ableto search the PI parameter value for the four-phase inter-leaved boost converter with minimum time Moreover the

DSP TMS320F28335

Load

Power supply

Four-phase interleaved boost

Figure 11 Shows the design of the PI controller using PSO for controlling Four-phase interleaved boost converter circuit voltage for theexperiment

Vin

L4

L3

L2

L1

S1 S2 S3 S4

D1

D2

D3

D4

C

Load

Vout

4-phase shi gate drive

TMS320F28335controller

S1 S2 S3 S4

Command 4-phase shi

Voltage sensor

Voltage sensor feedback

Figure 12 Diagram of designing a PI controller using PSO for controlling four-phase interleaved boost converter circuit voltage

Table 1 Summary table of the parameter value of the four-phaseinterleaved boost converter circuit

Parameter Parameter valueInput voltage 138VInductor 5865 μHCapacitor 100 μFAngle of switching 90degFrequency of switching 25 kHz

Journal of Control Science and Engineering 7

control system of the four-phase interleaved boost converteralso gives a quick response when rise time and settling timehave the best value and show the result of convergence to theanswer of PI search value using PSO as shown in Figure 14

7 Experiment Result

+e test on the PI controller with the PSO search forcontrolling voltage of the four-phase interleaved boostconverter uses 4 sets of original boost converter circuit

working in parallel +e operation is done with 90-degreeinterface and has a voltage sensor sending electrical signalsto the DSP board TMS320F28335 working with MATLABSimulink of sampling time at 00001 second

In this research the voltage level was kept at 2 levels ie20V and 24V +e result of the experiment shows thestability condition treatment of circuit voltage whilechanging load without the control system and voltagecontrol of 20V and 24V while changing load accordingly+e data collection was done using digital storage scope GWInstek GDS-3000 Series 150MHz 4 input channels

Based on the experimental results of circuit voltagetreatment while changing load without a control systemwithvoltage control of 20V and 24V as shown in Figures 15 and16 it was found that the output voltage of the circuitdropped significantly when the load was increased +efigure shows that the system was unstable to maintain theoutput voltage level to be constant

From Figure 17 the inductor current phases 1 and 2 areindicated with switch signals S1 and S2 respectively+e signalsS1 and S2 are determined to operate the inductor current in 90degree of differentiation It can be seen that when both switchesare on there will be increase in current in the load On the otherhand when both switches are off current will decrease+erefore experiment results confirm the theoretical analysisFrom Figure 18 the current of the four-phase interleaved boostconverter is investigated for every 90-degree switch signaloverlapping It can be seen that all inductor currents still appearaccording to the switch signals S1 and S2 respectively

For controlling PI controller voltage at 20V the gainedvalues of the PI controller using three optimization algo-rithms of GA TS and PSO are applied to examine theresponse and the stability of the circuit voltage +e resultsare shown in Figures 19ndash24

Figures 19 21 and 23 show the result of voltage responseand current when the gained values of the PI controller areapplied in GA TS and PSO respectively +e initial voltageinput is set at 138V and this study focused on the voltage

Table 2 System responses by the PI controller

EntrySystem responses by PI

Search time (sec)T r (sec) M p () T s (sec) e ss ()

GA 00022 000 00095 000 17614TS 0002 000 00085 000 10435PSO 000185 000 00075 000 4483

12

1

08

06

Am

plitu

de04

02

00 0002 0004 0006 0008 001

Time (seconds)

Time series plot

0012 0014 0016 0018 002

ReferenceGA

TSPSO

Figure 13 Result of response simulation of PI controller voltage with GA TS and PSO

0 10 20 30 40 50Count

60 70 80 90 100

8

7

6

5

4

Conv

erge

nt ra

te

3

2

1

Figure 14 Shows the result of convergence towards the answerwhile searching the PI value using PSO search

8 Journal of Control Science and Engineering

output controlling at 20V +ree algorithms can providegood response results and also can remain the steady state ofvoltage output instantaneously It could enter the conditionwithin less than 20milliseconds (ms) and could maintain the

output voltage both when in stable load condition and whilechanging load +e system could enter the stable conditionquickly while having a very satisfactory less changing ofvoltage Figures 20 22 and 24 illustrate the results when

Applied load Released load

Voltage output

Current output

Current input

Figure 15 Result of the four-phase interleaved boost convertercircuit at voltage of 20V without the controller

Applied load Released load

Voltage output

Current output

Current input

Figure 16 Result of the four-phase interleaved boost convertercircuit at voltage of 24V without the controller

Signal S1

Signal S2

Inductor current phase1

Inductor current phase2

Figure 17 Result of inductor current when compared to switchoperation of the four-phase interleaved boost converter circuit

Inductor current phase1 Inductor current phase2

Inductor current phase3 Inductor current phase3

Figure 18 Result of inductor current of the 4 phases of the four-phase interleaved boost converter circuit

Current input

Voltage output Vref output

Current output

Figure 19 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 20 Result of maintaining voltage stability and current whilechanging load using a PI controller with GA search

Journal of Control Science and Engineering 9

changing the load It can be seen that the stability of voltageoutput from three algorithms still remains unchanged al-though load has changed Table 3 shows the system responseby the PI controller at 20V

In summary the system response of voltage output fromthe PI controller at 20V using GA TS and PSO can beconcluded as in Table 3 Also the PI control with PSO searchhad the quickest response to reference signal when com-pared to GA and TS+e PSO establishes the lowest rise timeat 6ms and the lowest time to steady state at 8ms+ereforethe PSO is the best algorithm in controlling the voltageoutput at 20V

In order to control voltage output at 24V the same PIcontroller gained values as one for 20V are applied in GATS and PSO respectively It was found that GA TS andPSO had a quick response to reference signal and could enterthe condition in less than 20ms Figures 25ndash27 show theresult of voltage response and current when the gainedvalues of the PI controller are applied in GA TS and PSOrespectively +e initial voltage input is set at 138V In theexperiment case the voltage output is controlled at 24V

+ree optimization algorithms can provide good re-sponse results and also can remain the steady state of voltageoutput similar to the case of 20V controlling Figures 28ndash30show the results when changing the load It can be seen thatthe stability of voltage output from three algorithms stillremains unchanged although load has changed Table 4shows the system response by the PI controller at 24V

As in Table 4 the system response of voltage output bythe PI controller at 24V using GA TS and PSO can beconcluded +e GA performs at the lowest rise time of 7mswhereas GA needs 16ms in converging to steady stateHowever for PSO algorithm rise time is 72ms which isclose to the GA algorithm while the time to go to the steadystate is about 10ms which is less than GA +e PSOtherefore provides most suitable algorithm in controlling

Current output

Current input

Voltage output Vref output

Figure 21 Result of voltage response and current using a PIcontroller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 22 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Voltage output

Current output

Current input

Vref output

Figure 23 Result of voltage response and current using a PIcontroller with PSO search

Applied load Released load

Voltage output

Current output

Current input

Figure 24 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 3 System response by the PI controller at 20V

EntrySystem responses by PI

Tr (ms) Mp () Ts (ms) ess ()GA 12 000 16 000TS 14 000 17 000PSO 6 000 8 000

10 Journal of Control Science and Engineering

the voltage output at 24V compared to GA and TS as well ascontrolling voltage at 20V

+e proposed control algorithm though applied for theboost converter of 20V and 24V using PSO exhibits the bestperformance in the aspect of system response and stability+e experimental results agree with [32 33] although

Voltage output Vref output

Current output

Current input

Figure 26 Response of voltage and current using a PI controllerwith TS search

Voltage output

Current output

Current input

Vref output

Figure 27 Result of voltage response and current using a PIcontroller with PSO search

Voltage output

Current output

Vref output

Current input

Figure 25 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 28 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 29 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 30 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 4 System response by the PI controller at 24V

EntrySystem responses by PI

T r (ms) M p () T s (ms) e ss ()GA 7 000 16 000TS 72 000 15 000PSO 72 000 10 000

Journal of Control Science and Engineering 11

applied for the four-phase interleaved boost converterHowever there are no overshoot and time to steady statereaches faster than their study

8 Conclusion

In this paper the four-phase interleaved boost convertercircuit is controlled by the PI controller In order to tune thegains of the PI controller the PSO GA and TS and met-aheuristic optimizations are applied In testing the controlsystem the response of the four-phase interleaved boostconverter obtained by PSO has the rise time and setting timefaster than the GA and TS methods Additionally it is foundthat the tracing and controlling response result of outputvoltage is extremely satisfactory when load condition isconstant and while changing the load It can be concludedthat the four-phase interleaved boost converter circuit usingthe PI controller tuned gains by PSO is greatly effective forregulating the voltage in a real system

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors would like to acknowledge Department ofElectrical Engineering and Faculty of EngineeringPathumwan Institute of Technology for the financial sup-port and facilities +ey would also like to show theirgratitude to Assoc Prof Dr Decha Pungdaorueng and AsstProf Dr Wachirapond Permpoonsinsup who gave veryuseful advices and suggestions for completing this research

References

[1] C Jain and B Singh ldquoAn adjustable DC link voltage-basedcontrol of multifunctional grid interfaced solar PV systemrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 2 pp 651ndash660 2017

[2] Y A Zuniga-Ventura D Langarica-Cordoba J Leyva-Ramos L H Diaz-Saldierna and V M Ramirez-RiveraldquoAdaptive backstepping control for a fuel cellboost convertersystemrdquo IEEE Journal of Emerging and Selected Topics inPower Electronics vol 6 no 2 pp 686ndash695 2018

[3] P Mungporn P +ounthong S Sikkabut et al ldquoDifferentialflatness-based control of currentvoltage stabilization for asingle-phase PFC with multiphase interleaved boost con-verterrdquo in Proceedings of the European Conference on Elec-trical Engineering and Computer Science pp 124ndash130 AthensGreece November 2017

[4] A Marcos-Pastor E Vidal-Idiarte A Cid-Pastor andL Martinez-Salamero ldquoInterleaved digital power factorcorrection based on the sliding-mode approachrdquo IEEETransactions on Power Electronics vol 31 no 6 pp 4641ndash4653 2016

[5] D Apablaza and J Munoz ldquoLaboratory implementation of aboost interleaved converter for PV applicationsrdquo IEEE LatinAmerica Transactions vol 14 no 6 pp 2738ndash2743 2016

[6] F H Aghdam and M Abapour ldquoReliability and cost analysisof multistage boost converters connected to PV panelsrdquo IEEEJournal of Photovoltaics vol 6 no 4 pp 981ndash989 2016

[7] R Seyezhai and B L Mathur ldquoA comparison of three-phaseuncoupled and directly coupled interleaved boost converterfor fuel cell applicationsrdquo International Journal on ElectricalEngineering and Informatics vol 3 no 3 pp 394ndash407 2011

[8] S Banerjee A Ghosh and N Rana ldquoDesign and fabricationof closed loop two-phase interleaved boost converter withtype-III controllerrdquo in Proceedings of the IECON 2016mdash42ndAnnual Conference of the IEEE Industrial Electronics Societypp 3331ndash3336 Florence Italy October 2016

[9] C Kiree D Kumpanya S Tunyasrirut and D PuangdownreongldquoPSO-based optimal PI(D) controller design for brushless DCmotor speed control with back EMF detectionrdquo Journal ofElectrical Engineering and Technology vol 11 no 3 pp 715ndash7232016

[10] S Banerjee A Ghosh and N Rana ldquoAn improved interleavedboost converter with PSO-based optimal type-III[ controllerrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 1 pp 323ndash337 2017

[11] M Calvini M Carpita A Formentini and M MarchesonildquoPSO-based self-commissioning of electrical motor drivesrdquoIEEE Transactions on Industrial Electronics vol 62 no 2pp 768ndash776 2015

[12] S W Shneen A Z Salman Q A Jawad and H ShareefldquoAdvanced optimal by PSO-PI for DC motorrdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 165ndash175 2019

[13] M Rasheed R Omar M Sulaiman and W Abd Halim ldquoAmodified cascaded h-bridge multilevel inverter based onparticle swarm optimisation (PSO) techniquerdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 41ndash45 October 2019

[14] M Rasheed R Omar M Sulaiman and W A HalimldquoParticle swarm optimisation (PSO) algorithm with reducednumberof switches in multilevel inverter (MLI)rdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 14 no 3 pp 1114ndash1124 2019

[15] M Arun Devi K Valarmathi and R Mahendran ldquoRipplecurrent reduction in interleaved boost converter by usingadvanced PWM techniquesrdquo in Proceedings of the IEEE In-ternational Conference on Advanced Communication Controland Computing Technologies (lCACCCT) pp 115ndash119Ramanathapuram India May 2014

[16] S Kascak M Prazenica M Jarabicova and R KonarikldquoAnalysis of four-phase interleaved boost converterrdquo Trans-actions on Electrical Engineering vol 6 no 4 pp 110ndash1132017

[17] S Kascak M Prazenica M Jarabicova and R KonarikldquoFour-phase interleaved boost converter theory and appli-cationsrdquo WSEAS Transactions on Power Systems vol 13pp 272ndash282 2018

[18] S Kascak M Jarabicova and R Konarik ldquoFour phase in-terleaved boost converter-analysis and verificationrdquo ActaElectrotechnica et Informatica vol 18 no 1 pp 35ndash40 2018

[19] C W Reynolds ldquoFlocks herds and schools a distributedbehavioral modelrdquo ACM SIGGRAPH Computer Graphicsvol 21 no 4 pp 25ndash34 1987

[20] J Kennedy and R Eberhart Swarm Intelligence MorganKaufman Burlington MA USA 2001

12 Journal of Control Science and Engineering

[21] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceeding of IEEE International Conference Neural Networksvol IV pp 1942ndash1948 Perth Australia 1995

[22] K S Kumar K K Aggarwal and J Singh ldquoDesign of fuzzymodels through partical swarm optimizationrdquo in IntegratedIntelligent Systems for Engineering Design pp 43ndash62 IOSpress Amsterdam Netherlands 2006

[23] R Eberhart and Y Shi ldquoComparing inertial weights andconstriction factor in particle swarm optimizationrdquo in Pro-ceeding of Internationnal Congress on Evolutioning Compu-tation pp 84ndash88 La Jolla CA USA 2000

[24] Texas Instruments TMS320F28335 Digital Signal ControllerTexas Instruments Dallas TX USA 2007

[25] +e Math Works Inc MATLABSimulink Userrsquos Guide +eMath Works Inc Natick MA USA 1998

[26] V Viswanatha ldquoA complete mathematical modeling simu-lation and computational implementation of boost convertervia MATLABSimulinkrdquo International Journal of Pure andApplied Mathematics vol 114 no 10 pp 407ndash419 2017

[27] D E Goldberg Genetic Algorithm in Search Optimizationand Machine Learning Addison-Wesley Publishing BostonMA USA 1989

[28] D E Goldberg ldquoGenetic and evolutionary algorithms come ofagerdquo Communications of the ACM vol 37 no 3 pp 113ndash1191994

[29] F Glover ldquoTabu search-Part Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[30] F Glover ldquoTabu search-Part IIrdquoORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[31] F Glover ldquoParametric tabu-search for mixed integer pro-gramsrdquo Computers amp Operations Research vol 33 no 9pp 2449ndash2494 2006

[32] A Ghosh and S Banerjee ldquoControl of switched-mode boostconverter by using classical and optimized type controllersrdquoCEAI vol 17 no 4 pp 114ndash125 2015

[33] A Ghosh S Banerjee M K Sarkar and P Dutta ldquoDesign andimplementation of type-II and type-III controller for DC-DCswitched-mode boost converter by using K-factor approachand optimisation techniquesrdquo IET Power Electronics vol 9no 5 pp 938ndash950 2016

Journal of Control Science and Engineering 13

22Design ofDifferent ParameterValues Design of differentparameter values can be performed as follows

+e equation for designing duty cycle for switching canbe designed using the following equations

Voutput Vinput

1 minus D (1)

D 1 minusVinput

Voutput1113890 1113891 (2)

where D is duty cycle Vinput is voltage input and Voutput isvoltage output

+e equation for designing inductance value can bederived using the following equation

L1 L2 L3 L4 VinputD

ΔILfs

(3)

where L is inductor ΔIL is induction ripple current and fS

is switching frequency+e equation for designing capacitor value can be de-

rived form the following equation

C VoutputD

RfsΔVoutput (4)

where C is capacitor R is resistor load and ΔVoutput is aripple factor of the output voltage

For designing the angle of the boost converter in eachphase the switching angle of the boost converter in eachphase can be designed to form the following equation

θ 360N

(5)

where θ is angle of switching and N is number of phases ofthe boost converter circuit

3 Algorithm of PSO

+e origin of searching the most suitable value of PSO wasdeveloped by Reynolds in 1987 [19 20] He got inspirationfrom the patterns of herd movement such as flock of birdsschool of fish and insect swarm as shown in Figure 7 +emovement is based on three main principles confrontationavoidance of swarm same speed control within the swarm

OFF

OFF

OFF

OFF

OFF

S1

S2

S3

S4

IL1

IL2

IL3

IL4

Iin ΔIout

ΔIL3

ΔIL2

ΔIL1

ΔIL4

t

t

t

t

t

t

t

t

t

ON

ON

OFF

ON

ON

DmiddotTs

Ts

Figure 4 Switching pattern and inductor current waveform inrange of duty ratio as 14

OFF

OFF

OFF

OFF

S1

S2

S3

S4

IL1

IL2

IL3

IL4

Iin ΔIout

ΔIL3

ΔIL2

ΔIL1

ΔIL4

t

t

t

t

t

t

t

t

t

ON

ON

OFF

ON

ONON

DmiddotTs

Ts

Figure 5 Switching pattern and inductor current waveform inrange of duty ratio as 12

Journal of Control Science and Engineering 3

and moving to the center of the swarm+ese principles leadto the swarm behavior in nature ie self-defense from beinghunted and searching for food resources effectively Later in

1995 Kennedy and Eberhart developed PSO as an effectivetool for solving the problem of obtaining the most suitablevalue [21]

OFF

OFF

OFF

S1

S2

S3

S4

IL1

IL2

IL3

IL4

Iin ΔIout

ΔIL3

ΔIL2

ΔIL1

ΔIL4

t

t

t

t

t

t

t

t

t

ON

ON

OFF

ON

ONON

ON

DmiddotTs

Ts

Figure 6 Switching pattern and inductor current waveform in range of duty ratio as 34

(a) (b)

(c) (d)

Figure 7 +e movement of flock of birds school of fish and insect swarm used as a guideline for particle swarm search

4 Journal of Control Science and Engineering

Algorithm of PSO has the same feature of evolutionarycalculation ie there will be a creation of population calledparticle which will move around the search space Eachparticle has a speed vector and a memory unit to be used forstoring previous good answers pbest is set as good answer inthe current search while gbest is set as global solution Allparticles will move in a similar manner and the ones closestto the target are the strongest With the particle swarmmovement principle the rest of the particles will be adjustedto have a similar movement direction as that of thosestrongest ones +is makes it possible for the whole particleswarm to move to the target effectively

Consider that the search-space is d-dimensional and atparticle i-th in the swarm It can be defined asXi (xi1 xi2 xid) and the velocity can be representedby another d-dimensional vector as Vi (vi1 vi2 vid)

and the best previously visited position of this particle bedenoted by Pi (pi1 pi2 pid) +e adjustment of particlemovement direction and the answers found are shown inequations (6) and (7) accordingly [22] Where x is a particleor answer v is speed vector showing adjusted direction w isinertia weight c1 is cognitive acceleration c2 is social ac-celeration and r1 and r2 are random numbers uniformlydistributed in the range [01]

In case of 2D space the movement of particles should beadjusted as shown in Figure 8

vn+1id wv

nid + c1r

n1 x

pbestid minus x

nid1113872 1113873 + c2r2 x

gbestid minus x

nid1113872 1113873 (6)

xn+1id x

nid + v

n+1id (7)

+e inertial weight w can be calculated from the relationas in equation (8) where wmax is the maximum weight wminis the minimum weight kmax is the number of the highestsearch round set and k is the current search round +e bestvalue suitable for use is the number of current search roundand the most suitable value of work application is c1 and c2which should be in-between 1 and 2 while wmin and wmaxshould be equal to 04 and 09 accordingly [23] Algorithm ofPSO has the following details

wi wmax minus kwmax minus wmin

kmax1113888 1113889 (8)

+e steps of designing PSO are as follows

Step 1 setting initial values which are search spacenumber of particles and maximum number of searchroundsStep 2 creating particles with normal sampling dis-tribution according to the number setStep 3 evaluating the strength of each particle usingobjective functionStep 4 adjusting the movement direction in accordancewith the strongest particle using equations (6) and (8)Step 5 calculating the particle of the current searchround using equation (7)Step 6 checking the ending condition If it is cor-related this means that the best search is obtained

+en stop the search or perform step 3 to further thenext search

4 Theory PI

+e PI controller is a combination between the proportionalcontroller P and integral controller I +e system forcontrolling PI is shown as a block diagram in Figure 9 PIcontrolling system is composed of error signal E(s) controlsignal U(s) output response signal C(s) reference signalR(s) disturbing signal D(s) and transferring signal of thesystem Gp(s) and Gc(s) +e theoretical function of the PIcontroller is stated in the following equation

Gc(s)1113868111386811138681113868PI Kp +

Ki

s

Kps + Ki

s (9)

+e PI controlling system is shown in Figure 9+e four-phase interleaved boost converter system has a

fast output response but lacks stability +e PI controller hasthe advantage of faster response times and less stable errors+erefore it is very appropriate to choose a PI controller forthis system

To obtain the value of the PI controller for the four-phaseinterleaved boost converter circuit the design of the PIcontroller uses PSO search to control four-phase interleavedboost converter voltage as shown in Figure 10

5 Digital Signal Processor Set

+is part will focus on the digital signal processor or DigitalSignal Processor (DSP) board TMS320F28335 of Texas In-struments company [24] as shown in Figure 11 for analyzingreal-time controlling +e Texas Instrument TMS320F28335consisting of a 32-bit CPU and a single-precision 32-bitfloating-point +e CPU speed is controlled by a clock signalwith the frequency of 150MHz working with MATLABSimulink [25] It produces pulse width modulation (PWM)signal for driving the four-phase interleaved boost convertercircuit switch of 25 kHz frequency as shown in Figure 12

6 Design of Four-Phase Interleaved BoostConverter Circuit

+e parameter value of the four-phase interleaved boostconverter obtained from equations (1)ndash(5) is shown inTable 1

For the design of a four-phase interleaved boost con-verter circuit to simplify circuit design the four-phase in-terleaved boost converter has parallel circuits +ereforeconsidering only one model of the circuit to make it easier todesign +e transferring function of the boost convertercircuit uses the impedance method where the analysis makesuse of switching operation while the switch is off+is can beshown as follows [26] All of the impedance value (Ztotal) isshown in the following equation

Ztotal Z1(s) + Z2(s) (10)

Z1(s) is the condition of the switch when the circuit isopen and Z2(s) is the condition of the switch when the

Journal of Control Science and Engineering 5

circuit is closed+e value of Z1(s) is shown in the followingequation and the value of Z2(s) is shown in equation (12)

Vin(s)

I(s)

RLCs2 + Ls + R

RCs + 1 (11)

Vout(s)

I(s)

R

RCs + 1 (12)

and the transferring function of the system is shown in thefollowing equation

Vout(s)

Vin

R

RLCs2 + Ls + R (13)

Where the value with parameter from Table 1 is replaced andthe transfer function of the system is obtained and it isshown in the following equation

Gp(s) 2

1173 times 10minus9s2 + 5865 times 10minus6s + 2 (14)

Asmentioned in equation(14) the term 1173 times 10minus9 s2 isa very small value considered close to zero +is systemtherefore became first order called Type 0 system+us it issuitable for the PI controller

In designing the value of PI for the four-phase inter-leaved boost converter circuit using particle swarm searchbased on Figure 8 PSO search was used for designing a PIcontroller for the four-phase interleaved boost convertercircuit system where PSO algorithm was made by MAT-LAB working with Intel(R) Core (TM) i5-3210M25 GHz +e number of particle sets is 100 where c1 c2is 20 r1 and r2 are random numbers uniformly distributedin the range [0 1] wmin is 04 wmax is 09 and kmax is 1000ie maximum iteration set as the termination criteria foreach trial

Based on comparing GA and TS the design was doneusing a PI controller for the four-phase interleaved boostconverter circuit GA and TS parameter search is designedas original Both GA and TS will be canceled when pro-cessing the construction or making a repletion of up to 1000times GA and TS will not be discussed But they show moredetails of GA in [27 28] and TS in [29ndash31] accordingly +ealgorithm of the two searches mentioned works by usingMATLAB

For designing the PI controller its parameter PI is set forsearching the following spaces Kp ranges [0 10] and Kiranges [50 100] +e processing designed for 50 experiment

xn

pbest

gbest

xn+1

v

Current motion

Figure 8 Movement of particles in 2D space

Gc(s) Gp(s)+

ndash

R(s)

D(s)

+

+

C(s)

PID Controller

E(s) U(s)

Plant

Figure 9 Operation diagram of the PI controller

KPV + (KIVs)+ ndash

+ndashParticle swarm optimization

(PSO) Vref

Plant(Four-phase interleaved

boost converter)

VrefVout

Figure 10 Operation diagram of the PI controller design using PSO search to control four-phase interleaved boost converter circuit voltage

6 Journal of Control Science and Engineering

searches starts with different search points to find the bestvalue After the search processing stops the parameter valueof the PI controller is obtained using GA TS and PSOmethods as shown in equations (15)ndash(17) accordingly +eresult of the simulation of the controller system is shown inFigure 13

Gc(s)1113868111386811138681113868PI GA 0435 +

1286s

(15)

Gc(s)1113868111386811138681113868PI TS

0325 +1256

s (16)

Gc(s)1113868111386811138681113868PI PSO

0413 +1413

s (17)

Based on Figure 11 the response of four-phase inter-leaved boost converter circuit simulation and time forsearching can be seen in Table 2 where Tr is the rise timeMpis the maximum percent overshoot Ts is the settling timeand ess is the steady state error Based on Table 2 PSO is ableto search the PI parameter value for the four-phase inter-leaved boost converter with minimum time Moreover the

DSP TMS320F28335

Load

Power supply

Four-phase interleaved boost

Figure 11 Shows the design of the PI controller using PSO for controlling Four-phase interleaved boost converter circuit voltage for theexperiment

Vin

L4

L3

L2

L1

S1 S2 S3 S4

D1

D2

D3

D4

C

Load

Vout

4-phase shi gate drive

TMS320F28335controller

S1 S2 S3 S4

Command 4-phase shi

Voltage sensor

Voltage sensor feedback

Figure 12 Diagram of designing a PI controller using PSO for controlling four-phase interleaved boost converter circuit voltage

Table 1 Summary table of the parameter value of the four-phaseinterleaved boost converter circuit

Parameter Parameter valueInput voltage 138VInductor 5865 μHCapacitor 100 μFAngle of switching 90degFrequency of switching 25 kHz

Journal of Control Science and Engineering 7

control system of the four-phase interleaved boost converteralso gives a quick response when rise time and settling timehave the best value and show the result of convergence to theanswer of PI search value using PSO as shown in Figure 14

7 Experiment Result

+e test on the PI controller with the PSO search forcontrolling voltage of the four-phase interleaved boostconverter uses 4 sets of original boost converter circuit

working in parallel +e operation is done with 90-degreeinterface and has a voltage sensor sending electrical signalsto the DSP board TMS320F28335 working with MATLABSimulink of sampling time at 00001 second

In this research the voltage level was kept at 2 levels ie20V and 24V +e result of the experiment shows thestability condition treatment of circuit voltage whilechanging load without the control system and voltagecontrol of 20V and 24V while changing load accordingly+e data collection was done using digital storage scope GWInstek GDS-3000 Series 150MHz 4 input channels

Based on the experimental results of circuit voltagetreatment while changing load without a control systemwithvoltage control of 20V and 24V as shown in Figures 15 and16 it was found that the output voltage of the circuitdropped significantly when the load was increased +efigure shows that the system was unstable to maintain theoutput voltage level to be constant

From Figure 17 the inductor current phases 1 and 2 areindicated with switch signals S1 and S2 respectively+e signalsS1 and S2 are determined to operate the inductor current in 90degree of differentiation It can be seen that when both switchesare on there will be increase in current in the load On the otherhand when both switches are off current will decrease+erefore experiment results confirm the theoretical analysisFrom Figure 18 the current of the four-phase interleaved boostconverter is investigated for every 90-degree switch signaloverlapping It can be seen that all inductor currents still appearaccording to the switch signals S1 and S2 respectively

For controlling PI controller voltage at 20V the gainedvalues of the PI controller using three optimization algo-rithms of GA TS and PSO are applied to examine theresponse and the stability of the circuit voltage +e resultsare shown in Figures 19ndash24

Figures 19 21 and 23 show the result of voltage responseand current when the gained values of the PI controller areapplied in GA TS and PSO respectively +e initial voltageinput is set at 138V and this study focused on the voltage

Table 2 System responses by the PI controller

EntrySystem responses by PI

Search time (sec)T r (sec) M p () T s (sec) e ss ()

GA 00022 000 00095 000 17614TS 0002 000 00085 000 10435PSO 000185 000 00075 000 4483

12

1

08

06

Am

plitu

de04

02

00 0002 0004 0006 0008 001

Time (seconds)

Time series plot

0012 0014 0016 0018 002

ReferenceGA

TSPSO

Figure 13 Result of response simulation of PI controller voltage with GA TS and PSO

0 10 20 30 40 50Count

60 70 80 90 100

8

7

6

5

4

Conv

erge

nt ra

te

3

2

1

Figure 14 Shows the result of convergence towards the answerwhile searching the PI value using PSO search

8 Journal of Control Science and Engineering

output controlling at 20V +ree algorithms can providegood response results and also can remain the steady state ofvoltage output instantaneously It could enter the conditionwithin less than 20milliseconds (ms) and could maintain the

output voltage both when in stable load condition and whilechanging load +e system could enter the stable conditionquickly while having a very satisfactory less changing ofvoltage Figures 20 22 and 24 illustrate the results when

Applied load Released load

Voltage output

Current output

Current input

Figure 15 Result of the four-phase interleaved boost convertercircuit at voltage of 20V without the controller

Applied load Released load

Voltage output

Current output

Current input

Figure 16 Result of the four-phase interleaved boost convertercircuit at voltage of 24V without the controller

Signal S1

Signal S2

Inductor current phase1

Inductor current phase2

Figure 17 Result of inductor current when compared to switchoperation of the four-phase interleaved boost converter circuit

Inductor current phase1 Inductor current phase2

Inductor current phase3 Inductor current phase3

Figure 18 Result of inductor current of the 4 phases of the four-phase interleaved boost converter circuit

Current input

Voltage output Vref output

Current output

Figure 19 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 20 Result of maintaining voltage stability and current whilechanging load using a PI controller with GA search

Journal of Control Science and Engineering 9

changing the load It can be seen that the stability of voltageoutput from three algorithms still remains unchanged al-though load has changed Table 3 shows the system responseby the PI controller at 20V

In summary the system response of voltage output fromthe PI controller at 20V using GA TS and PSO can beconcluded as in Table 3 Also the PI control with PSO searchhad the quickest response to reference signal when com-pared to GA and TS+e PSO establishes the lowest rise timeat 6ms and the lowest time to steady state at 8ms+ereforethe PSO is the best algorithm in controlling the voltageoutput at 20V

In order to control voltage output at 24V the same PIcontroller gained values as one for 20V are applied in GATS and PSO respectively It was found that GA TS andPSO had a quick response to reference signal and could enterthe condition in less than 20ms Figures 25ndash27 show theresult of voltage response and current when the gainedvalues of the PI controller are applied in GA TS and PSOrespectively +e initial voltage input is set at 138V In theexperiment case the voltage output is controlled at 24V

+ree optimization algorithms can provide good re-sponse results and also can remain the steady state of voltageoutput similar to the case of 20V controlling Figures 28ndash30show the results when changing the load It can be seen thatthe stability of voltage output from three algorithms stillremains unchanged although load has changed Table 4shows the system response by the PI controller at 24V

As in Table 4 the system response of voltage output bythe PI controller at 24V using GA TS and PSO can beconcluded +e GA performs at the lowest rise time of 7mswhereas GA needs 16ms in converging to steady stateHowever for PSO algorithm rise time is 72ms which isclose to the GA algorithm while the time to go to the steadystate is about 10ms which is less than GA +e PSOtherefore provides most suitable algorithm in controlling

Current output

Current input

Voltage output Vref output

Figure 21 Result of voltage response and current using a PIcontroller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 22 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Voltage output

Current output

Current input

Vref output

Figure 23 Result of voltage response and current using a PIcontroller with PSO search

Applied load Released load

Voltage output

Current output

Current input

Figure 24 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 3 System response by the PI controller at 20V

EntrySystem responses by PI

Tr (ms) Mp () Ts (ms) ess ()GA 12 000 16 000TS 14 000 17 000PSO 6 000 8 000

10 Journal of Control Science and Engineering

the voltage output at 24V compared to GA and TS as well ascontrolling voltage at 20V

+e proposed control algorithm though applied for theboost converter of 20V and 24V using PSO exhibits the bestperformance in the aspect of system response and stability+e experimental results agree with [32 33] although

Voltage output Vref output

Current output

Current input

Figure 26 Response of voltage and current using a PI controllerwith TS search

Voltage output

Current output

Current input

Vref output

Figure 27 Result of voltage response and current using a PIcontroller with PSO search

Voltage output

Current output

Vref output

Current input

Figure 25 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 28 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 29 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 30 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 4 System response by the PI controller at 24V

EntrySystem responses by PI

T r (ms) M p () T s (ms) e ss ()GA 7 000 16 000TS 72 000 15 000PSO 72 000 10 000

Journal of Control Science and Engineering 11

applied for the four-phase interleaved boost converterHowever there are no overshoot and time to steady statereaches faster than their study

8 Conclusion

In this paper the four-phase interleaved boost convertercircuit is controlled by the PI controller In order to tune thegains of the PI controller the PSO GA and TS and met-aheuristic optimizations are applied In testing the controlsystem the response of the four-phase interleaved boostconverter obtained by PSO has the rise time and setting timefaster than the GA and TS methods Additionally it is foundthat the tracing and controlling response result of outputvoltage is extremely satisfactory when load condition isconstant and while changing the load It can be concludedthat the four-phase interleaved boost converter circuit usingthe PI controller tuned gains by PSO is greatly effective forregulating the voltage in a real system

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors would like to acknowledge Department ofElectrical Engineering and Faculty of EngineeringPathumwan Institute of Technology for the financial sup-port and facilities +ey would also like to show theirgratitude to Assoc Prof Dr Decha Pungdaorueng and AsstProf Dr Wachirapond Permpoonsinsup who gave veryuseful advices and suggestions for completing this research

References

[1] C Jain and B Singh ldquoAn adjustable DC link voltage-basedcontrol of multifunctional grid interfaced solar PV systemrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 2 pp 651ndash660 2017

[2] Y A Zuniga-Ventura D Langarica-Cordoba J Leyva-Ramos L H Diaz-Saldierna and V M Ramirez-RiveraldquoAdaptive backstepping control for a fuel cellboost convertersystemrdquo IEEE Journal of Emerging and Selected Topics inPower Electronics vol 6 no 2 pp 686ndash695 2018

[3] P Mungporn P +ounthong S Sikkabut et al ldquoDifferentialflatness-based control of currentvoltage stabilization for asingle-phase PFC with multiphase interleaved boost con-verterrdquo in Proceedings of the European Conference on Elec-trical Engineering and Computer Science pp 124ndash130 AthensGreece November 2017

[4] A Marcos-Pastor E Vidal-Idiarte A Cid-Pastor andL Martinez-Salamero ldquoInterleaved digital power factorcorrection based on the sliding-mode approachrdquo IEEETransactions on Power Electronics vol 31 no 6 pp 4641ndash4653 2016

[5] D Apablaza and J Munoz ldquoLaboratory implementation of aboost interleaved converter for PV applicationsrdquo IEEE LatinAmerica Transactions vol 14 no 6 pp 2738ndash2743 2016

[6] F H Aghdam and M Abapour ldquoReliability and cost analysisof multistage boost converters connected to PV panelsrdquo IEEEJournal of Photovoltaics vol 6 no 4 pp 981ndash989 2016

[7] R Seyezhai and B L Mathur ldquoA comparison of three-phaseuncoupled and directly coupled interleaved boost converterfor fuel cell applicationsrdquo International Journal on ElectricalEngineering and Informatics vol 3 no 3 pp 394ndash407 2011

[8] S Banerjee A Ghosh and N Rana ldquoDesign and fabricationof closed loop two-phase interleaved boost converter withtype-III controllerrdquo in Proceedings of the IECON 2016mdash42ndAnnual Conference of the IEEE Industrial Electronics Societypp 3331ndash3336 Florence Italy October 2016

[9] C Kiree D Kumpanya S Tunyasrirut and D PuangdownreongldquoPSO-based optimal PI(D) controller design for brushless DCmotor speed control with back EMF detectionrdquo Journal ofElectrical Engineering and Technology vol 11 no 3 pp 715ndash7232016

[10] S Banerjee A Ghosh and N Rana ldquoAn improved interleavedboost converter with PSO-based optimal type-III[ controllerrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 1 pp 323ndash337 2017

[11] M Calvini M Carpita A Formentini and M MarchesonildquoPSO-based self-commissioning of electrical motor drivesrdquoIEEE Transactions on Industrial Electronics vol 62 no 2pp 768ndash776 2015

[12] S W Shneen A Z Salman Q A Jawad and H ShareefldquoAdvanced optimal by PSO-PI for DC motorrdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 165ndash175 2019

[13] M Rasheed R Omar M Sulaiman and W Abd Halim ldquoAmodified cascaded h-bridge multilevel inverter based onparticle swarm optimisation (PSO) techniquerdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 41ndash45 October 2019

[14] M Rasheed R Omar M Sulaiman and W A HalimldquoParticle swarm optimisation (PSO) algorithm with reducednumberof switches in multilevel inverter (MLI)rdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 14 no 3 pp 1114ndash1124 2019

[15] M Arun Devi K Valarmathi and R Mahendran ldquoRipplecurrent reduction in interleaved boost converter by usingadvanced PWM techniquesrdquo in Proceedings of the IEEE In-ternational Conference on Advanced Communication Controland Computing Technologies (lCACCCT) pp 115ndash119Ramanathapuram India May 2014

[16] S Kascak M Prazenica M Jarabicova and R KonarikldquoAnalysis of four-phase interleaved boost converterrdquo Trans-actions on Electrical Engineering vol 6 no 4 pp 110ndash1132017

[17] S Kascak M Prazenica M Jarabicova and R KonarikldquoFour-phase interleaved boost converter theory and appli-cationsrdquo WSEAS Transactions on Power Systems vol 13pp 272ndash282 2018

[18] S Kascak M Jarabicova and R Konarik ldquoFour phase in-terleaved boost converter-analysis and verificationrdquo ActaElectrotechnica et Informatica vol 18 no 1 pp 35ndash40 2018

[19] C W Reynolds ldquoFlocks herds and schools a distributedbehavioral modelrdquo ACM SIGGRAPH Computer Graphicsvol 21 no 4 pp 25ndash34 1987

[20] J Kennedy and R Eberhart Swarm Intelligence MorganKaufman Burlington MA USA 2001

12 Journal of Control Science and Engineering

[21] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceeding of IEEE International Conference Neural Networksvol IV pp 1942ndash1948 Perth Australia 1995

[22] K S Kumar K K Aggarwal and J Singh ldquoDesign of fuzzymodels through partical swarm optimizationrdquo in IntegratedIntelligent Systems for Engineering Design pp 43ndash62 IOSpress Amsterdam Netherlands 2006

[23] R Eberhart and Y Shi ldquoComparing inertial weights andconstriction factor in particle swarm optimizationrdquo in Pro-ceeding of Internationnal Congress on Evolutioning Compu-tation pp 84ndash88 La Jolla CA USA 2000

[24] Texas Instruments TMS320F28335 Digital Signal ControllerTexas Instruments Dallas TX USA 2007

[25] +e Math Works Inc MATLABSimulink Userrsquos Guide +eMath Works Inc Natick MA USA 1998

[26] V Viswanatha ldquoA complete mathematical modeling simu-lation and computational implementation of boost convertervia MATLABSimulinkrdquo International Journal of Pure andApplied Mathematics vol 114 no 10 pp 407ndash419 2017

[27] D E Goldberg Genetic Algorithm in Search Optimizationand Machine Learning Addison-Wesley Publishing BostonMA USA 1989

[28] D E Goldberg ldquoGenetic and evolutionary algorithms come ofagerdquo Communications of the ACM vol 37 no 3 pp 113ndash1191994

[29] F Glover ldquoTabu search-Part Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[30] F Glover ldquoTabu search-Part IIrdquoORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[31] F Glover ldquoParametric tabu-search for mixed integer pro-gramsrdquo Computers amp Operations Research vol 33 no 9pp 2449ndash2494 2006

[32] A Ghosh and S Banerjee ldquoControl of switched-mode boostconverter by using classical and optimized type controllersrdquoCEAI vol 17 no 4 pp 114ndash125 2015

[33] A Ghosh S Banerjee M K Sarkar and P Dutta ldquoDesign andimplementation of type-II and type-III controller for DC-DCswitched-mode boost converter by using K-factor approachand optimisation techniquesrdquo IET Power Electronics vol 9no 5 pp 938ndash950 2016

Journal of Control Science and Engineering 13

and moving to the center of the swarm+ese principles leadto the swarm behavior in nature ie self-defense from beinghunted and searching for food resources effectively Later in

1995 Kennedy and Eberhart developed PSO as an effectivetool for solving the problem of obtaining the most suitablevalue [21]

OFF

OFF

OFF

S1

S2

S3

S4

IL1

IL2

IL3

IL4

Iin ΔIout

ΔIL3

ΔIL2

ΔIL1

ΔIL4

t

t

t

t

t

t

t

t

t

ON

ON

OFF

ON

ONON

ON

DmiddotTs

Ts

Figure 6 Switching pattern and inductor current waveform in range of duty ratio as 34

(a) (b)

(c) (d)

Figure 7 +e movement of flock of birds school of fish and insect swarm used as a guideline for particle swarm search

4 Journal of Control Science and Engineering

Algorithm of PSO has the same feature of evolutionarycalculation ie there will be a creation of population calledparticle which will move around the search space Eachparticle has a speed vector and a memory unit to be used forstoring previous good answers pbest is set as good answer inthe current search while gbest is set as global solution Allparticles will move in a similar manner and the ones closestto the target are the strongest With the particle swarmmovement principle the rest of the particles will be adjustedto have a similar movement direction as that of thosestrongest ones +is makes it possible for the whole particleswarm to move to the target effectively

Consider that the search-space is d-dimensional and atparticle i-th in the swarm It can be defined asXi (xi1 xi2 xid) and the velocity can be representedby another d-dimensional vector as Vi (vi1 vi2 vid)

and the best previously visited position of this particle bedenoted by Pi (pi1 pi2 pid) +e adjustment of particlemovement direction and the answers found are shown inequations (6) and (7) accordingly [22] Where x is a particleor answer v is speed vector showing adjusted direction w isinertia weight c1 is cognitive acceleration c2 is social ac-celeration and r1 and r2 are random numbers uniformlydistributed in the range [01]

In case of 2D space the movement of particles should beadjusted as shown in Figure 8

vn+1id wv

nid + c1r

n1 x

pbestid minus x

nid1113872 1113873 + c2r2 x

gbestid minus x

nid1113872 1113873 (6)

xn+1id x

nid + v

n+1id (7)

+e inertial weight w can be calculated from the relationas in equation (8) where wmax is the maximum weight wminis the minimum weight kmax is the number of the highestsearch round set and k is the current search round +e bestvalue suitable for use is the number of current search roundand the most suitable value of work application is c1 and c2which should be in-between 1 and 2 while wmin and wmaxshould be equal to 04 and 09 accordingly [23] Algorithm ofPSO has the following details

wi wmax minus kwmax minus wmin

kmax1113888 1113889 (8)

+e steps of designing PSO are as follows

Step 1 setting initial values which are search spacenumber of particles and maximum number of searchroundsStep 2 creating particles with normal sampling dis-tribution according to the number setStep 3 evaluating the strength of each particle usingobjective functionStep 4 adjusting the movement direction in accordancewith the strongest particle using equations (6) and (8)Step 5 calculating the particle of the current searchround using equation (7)Step 6 checking the ending condition If it is cor-related this means that the best search is obtained

+en stop the search or perform step 3 to further thenext search

4 Theory PI

+e PI controller is a combination between the proportionalcontroller P and integral controller I +e system forcontrolling PI is shown as a block diagram in Figure 9 PIcontrolling system is composed of error signal E(s) controlsignal U(s) output response signal C(s) reference signalR(s) disturbing signal D(s) and transferring signal of thesystem Gp(s) and Gc(s) +e theoretical function of the PIcontroller is stated in the following equation

Gc(s)1113868111386811138681113868PI Kp +

Ki

s

Kps + Ki

s (9)

+e PI controlling system is shown in Figure 9+e four-phase interleaved boost converter system has a

fast output response but lacks stability +e PI controller hasthe advantage of faster response times and less stable errors+erefore it is very appropriate to choose a PI controller forthis system

To obtain the value of the PI controller for the four-phaseinterleaved boost converter circuit the design of the PIcontroller uses PSO search to control four-phase interleavedboost converter voltage as shown in Figure 10

5 Digital Signal Processor Set

+is part will focus on the digital signal processor or DigitalSignal Processor (DSP) board TMS320F28335 of Texas In-struments company [24] as shown in Figure 11 for analyzingreal-time controlling +e Texas Instrument TMS320F28335consisting of a 32-bit CPU and a single-precision 32-bitfloating-point +e CPU speed is controlled by a clock signalwith the frequency of 150MHz working with MATLABSimulink [25] It produces pulse width modulation (PWM)signal for driving the four-phase interleaved boost convertercircuit switch of 25 kHz frequency as shown in Figure 12

6 Design of Four-Phase Interleaved BoostConverter Circuit

+e parameter value of the four-phase interleaved boostconverter obtained from equations (1)ndash(5) is shown inTable 1

For the design of a four-phase interleaved boost con-verter circuit to simplify circuit design the four-phase in-terleaved boost converter has parallel circuits +ereforeconsidering only one model of the circuit to make it easier todesign +e transferring function of the boost convertercircuit uses the impedance method where the analysis makesuse of switching operation while the switch is off+is can beshown as follows [26] All of the impedance value (Ztotal) isshown in the following equation

Ztotal Z1(s) + Z2(s) (10)

Z1(s) is the condition of the switch when the circuit isopen and Z2(s) is the condition of the switch when the

Journal of Control Science and Engineering 5

circuit is closed+e value of Z1(s) is shown in the followingequation and the value of Z2(s) is shown in equation (12)

Vin(s)

I(s)

RLCs2 + Ls + R

RCs + 1 (11)

Vout(s)

I(s)

R

RCs + 1 (12)

and the transferring function of the system is shown in thefollowing equation

Vout(s)

Vin

R

RLCs2 + Ls + R (13)

Where the value with parameter from Table 1 is replaced andthe transfer function of the system is obtained and it isshown in the following equation

Gp(s) 2

1173 times 10minus9s2 + 5865 times 10minus6s + 2 (14)

Asmentioned in equation(14) the term 1173 times 10minus9 s2 isa very small value considered close to zero +is systemtherefore became first order called Type 0 system+us it issuitable for the PI controller

In designing the value of PI for the four-phase inter-leaved boost converter circuit using particle swarm searchbased on Figure 8 PSO search was used for designing a PIcontroller for the four-phase interleaved boost convertercircuit system where PSO algorithm was made by MAT-LAB working with Intel(R) Core (TM) i5-3210M25 GHz +e number of particle sets is 100 where c1 c2is 20 r1 and r2 are random numbers uniformly distributedin the range [0 1] wmin is 04 wmax is 09 and kmax is 1000ie maximum iteration set as the termination criteria foreach trial

Based on comparing GA and TS the design was doneusing a PI controller for the four-phase interleaved boostconverter circuit GA and TS parameter search is designedas original Both GA and TS will be canceled when pro-cessing the construction or making a repletion of up to 1000times GA and TS will not be discussed But they show moredetails of GA in [27 28] and TS in [29ndash31] accordingly +ealgorithm of the two searches mentioned works by usingMATLAB

For designing the PI controller its parameter PI is set forsearching the following spaces Kp ranges [0 10] and Kiranges [50 100] +e processing designed for 50 experiment

xn

pbest

gbest

xn+1

v

Current motion

Figure 8 Movement of particles in 2D space

Gc(s) Gp(s)+

ndash

R(s)

D(s)

+

+

C(s)

PID Controller

E(s) U(s)

Plant

Figure 9 Operation diagram of the PI controller

KPV + (KIVs)+ ndash

+ndashParticle swarm optimization

(PSO) Vref

Plant(Four-phase interleaved

boost converter)

VrefVout

Figure 10 Operation diagram of the PI controller design using PSO search to control four-phase interleaved boost converter circuit voltage

6 Journal of Control Science and Engineering

searches starts with different search points to find the bestvalue After the search processing stops the parameter valueof the PI controller is obtained using GA TS and PSOmethods as shown in equations (15)ndash(17) accordingly +eresult of the simulation of the controller system is shown inFigure 13

Gc(s)1113868111386811138681113868PI GA 0435 +

1286s

(15)

Gc(s)1113868111386811138681113868PI TS

0325 +1256

s (16)

Gc(s)1113868111386811138681113868PI PSO

0413 +1413

s (17)

Based on Figure 11 the response of four-phase inter-leaved boost converter circuit simulation and time forsearching can be seen in Table 2 where Tr is the rise timeMpis the maximum percent overshoot Ts is the settling timeand ess is the steady state error Based on Table 2 PSO is ableto search the PI parameter value for the four-phase inter-leaved boost converter with minimum time Moreover the

DSP TMS320F28335

Load

Power supply

Four-phase interleaved boost

Figure 11 Shows the design of the PI controller using PSO for controlling Four-phase interleaved boost converter circuit voltage for theexperiment

Vin

L4

L3

L2

L1

S1 S2 S3 S4

D1

D2

D3

D4

C

Load

Vout

4-phase shi gate drive

TMS320F28335controller

S1 S2 S3 S4

Command 4-phase shi

Voltage sensor

Voltage sensor feedback

Figure 12 Diagram of designing a PI controller using PSO for controlling four-phase interleaved boost converter circuit voltage

Table 1 Summary table of the parameter value of the four-phaseinterleaved boost converter circuit

Parameter Parameter valueInput voltage 138VInductor 5865 μHCapacitor 100 μFAngle of switching 90degFrequency of switching 25 kHz

Journal of Control Science and Engineering 7

control system of the four-phase interleaved boost converteralso gives a quick response when rise time and settling timehave the best value and show the result of convergence to theanswer of PI search value using PSO as shown in Figure 14

7 Experiment Result

+e test on the PI controller with the PSO search forcontrolling voltage of the four-phase interleaved boostconverter uses 4 sets of original boost converter circuit

working in parallel +e operation is done with 90-degreeinterface and has a voltage sensor sending electrical signalsto the DSP board TMS320F28335 working with MATLABSimulink of sampling time at 00001 second

In this research the voltage level was kept at 2 levels ie20V and 24V +e result of the experiment shows thestability condition treatment of circuit voltage whilechanging load without the control system and voltagecontrol of 20V and 24V while changing load accordingly+e data collection was done using digital storage scope GWInstek GDS-3000 Series 150MHz 4 input channels

Based on the experimental results of circuit voltagetreatment while changing load without a control systemwithvoltage control of 20V and 24V as shown in Figures 15 and16 it was found that the output voltage of the circuitdropped significantly when the load was increased +efigure shows that the system was unstable to maintain theoutput voltage level to be constant

From Figure 17 the inductor current phases 1 and 2 areindicated with switch signals S1 and S2 respectively+e signalsS1 and S2 are determined to operate the inductor current in 90degree of differentiation It can be seen that when both switchesare on there will be increase in current in the load On the otherhand when both switches are off current will decrease+erefore experiment results confirm the theoretical analysisFrom Figure 18 the current of the four-phase interleaved boostconverter is investigated for every 90-degree switch signaloverlapping It can be seen that all inductor currents still appearaccording to the switch signals S1 and S2 respectively

For controlling PI controller voltage at 20V the gainedvalues of the PI controller using three optimization algo-rithms of GA TS and PSO are applied to examine theresponse and the stability of the circuit voltage +e resultsare shown in Figures 19ndash24

Figures 19 21 and 23 show the result of voltage responseand current when the gained values of the PI controller areapplied in GA TS and PSO respectively +e initial voltageinput is set at 138V and this study focused on the voltage

Table 2 System responses by the PI controller

EntrySystem responses by PI

Search time (sec)T r (sec) M p () T s (sec) e ss ()

GA 00022 000 00095 000 17614TS 0002 000 00085 000 10435PSO 000185 000 00075 000 4483

12

1

08

06

Am

plitu

de04

02

00 0002 0004 0006 0008 001

Time (seconds)

Time series plot

0012 0014 0016 0018 002

ReferenceGA

TSPSO

Figure 13 Result of response simulation of PI controller voltage with GA TS and PSO

0 10 20 30 40 50Count

60 70 80 90 100

8

7

6

5

4

Conv

erge

nt ra

te

3

2

1

Figure 14 Shows the result of convergence towards the answerwhile searching the PI value using PSO search

8 Journal of Control Science and Engineering

output controlling at 20V +ree algorithms can providegood response results and also can remain the steady state ofvoltage output instantaneously It could enter the conditionwithin less than 20milliseconds (ms) and could maintain the

output voltage both when in stable load condition and whilechanging load +e system could enter the stable conditionquickly while having a very satisfactory less changing ofvoltage Figures 20 22 and 24 illustrate the results when

Applied load Released load

Voltage output

Current output

Current input

Figure 15 Result of the four-phase interleaved boost convertercircuit at voltage of 20V without the controller

Applied load Released load

Voltage output

Current output

Current input

Figure 16 Result of the four-phase interleaved boost convertercircuit at voltage of 24V without the controller

Signal S1

Signal S2

Inductor current phase1

Inductor current phase2

Figure 17 Result of inductor current when compared to switchoperation of the four-phase interleaved boost converter circuit

Inductor current phase1 Inductor current phase2

Inductor current phase3 Inductor current phase3

Figure 18 Result of inductor current of the 4 phases of the four-phase interleaved boost converter circuit

Current input

Voltage output Vref output

Current output

Figure 19 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 20 Result of maintaining voltage stability and current whilechanging load using a PI controller with GA search

Journal of Control Science and Engineering 9

changing the load It can be seen that the stability of voltageoutput from three algorithms still remains unchanged al-though load has changed Table 3 shows the system responseby the PI controller at 20V

In summary the system response of voltage output fromthe PI controller at 20V using GA TS and PSO can beconcluded as in Table 3 Also the PI control with PSO searchhad the quickest response to reference signal when com-pared to GA and TS+e PSO establishes the lowest rise timeat 6ms and the lowest time to steady state at 8ms+ereforethe PSO is the best algorithm in controlling the voltageoutput at 20V

In order to control voltage output at 24V the same PIcontroller gained values as one for 20V are applied in GATS and PSO respectively It was found that GA TS andPSO had a quick response to reference signal and could enterthe condition in less than 20ms Figures 25ndash27 show theresult of voltage response and current when the gainedvalues of the PI controller are applied in GA TS and PSOrespectively +e initial voltage input is set at 138V In theexperiment case the voltage output is controlled at 24V

+ree optimization algorithms can provide good re-sponse results and also can remain the steady state of voltageoutput similar to the case of 20V controlling Figures 28ndash30show the results when changing the load It can be seen thatthe stability of voltage output from three algorithms stillremains unchanged although load has changed Table 4shows the system response by the PI controller at 24V

As in Table 4 the system response of voltage output bythe PI controller at 24V using GA TS and PSO can beconcluded +e GA performs at the lowest rise time of 7mswhereas GA needs 16ms in converging to steady stateHowever for PSO algorithm rise time is 72ms which isclose to the GA algorithm while the time to go to the steadystate is about 10ms which is less than GA +e PSOtherefore provides most suitable algorithm in controlling

Current output

Current input

Voltage output Vref output

Figure 21 Result of voltage response and current using a PIcontroller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 22 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Voltage output

Current output

Current input

Vref output

Figure 23 Result of voltage response and current using a PIcontroller with PSO search

Applied load Released load

Voltage output

Current output

Current input

Figure 24 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 3 System response by the PI controller at 20V

EntrySystem responses by PI

Tr (ms) Mp () Ts (ms) ess ()GA 12 000 16 000TS 14 000 17 000PSO 6 000 8 000

10 Journal of Control Science and Engineering

the voltage output at 24V compared to GA and TS as well ascontrolling voltage at 20V

+e proposed control algorithm though applied for theboost converter of 20V and 24V using PSO exhibits the bestperformance in the aspect of system response and stability+e experimental results agree with [32 33] although

Voltage output Vref output

Current output

Current input

Figure 26 Response of voltage and current using a PI controllerwith TS search

Voltage output

Current output

Current input

Vref output

Figure 27 Result of voltage response and current using a PIcontroller with PSO search

Voltage output

Current output

Vref output

Current input

Figure 25 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 28 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 29 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 30 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 4 System response by the PI controller at 24V

EntrySystem responses by PI

T r (ms) M p () T s (ms) e ss ()GA 7 000 16 000TS 72 000 15 000PSO 72 000 10 000

Journal of Control Science and Engineering 11

applied for the four-phase interleaved boost converterHowever there are no overshoot and time to steady statereaches faster than their study

8 Conclusion

In this paper the four-phase interleaved boost convertercircuit is controlled by the PI controller In order to tune thegains of the PI controller the PSO GA and TS and met-aheuristic optimizations are applied In testing the controlsystem the response of the four-phase interleaved boostconverter obtained by PSO has the rise time and setting timefaster than the GA and TS methods Additionally it is foundthat the tracing and controlling response result of outputvoltage is extremely satisfactory when load condition isconstant and while changing the load It can be concludedthat the four-phase interleaved boost converter circuit usingthe PI controller tuned gains by PSO is greatly effective forregulating the voltage in a real system

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors would like to acknowledge Department ofElectrical Engineering and Faculty of EngineeringPathumwan Institute of Technology for the financial sup-port and facilities +ey would also like to show theirgratitude to Assoc Prof Dr Decha Pungdaorueng and AsstProf Dr Wachirapond Permpoonsinsup who gave veryuseful advices and suggestions for completing this research

References

[1] C Jain and B Singh ldquoAn adjustable DC link voltage-basedcontrol of multifunctional grid interfaced solar PV systemrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 2 pp 651ndash660 2017

[2] Y A Zuniga-Ventura D Langarica-Cordoba J Leyva-Ramos L H Diaz-Saldierna and V M Ramirez-RiveraldquoAdaptive backstepping control for a fuel cellboost convertersystemrdquo IEEE Journal of Emerging and Selected Topics inPower Electronics vol 6 no 2 pp 686ndash695 2018

[3] P Mungporn P +ounthong S Sikkabut et al ldquoDifferentialflatness-based control of currentvoltage stabilization for asingle-phase PFC with multiphase interleaved boost con-verterrdquo in Proceedings of the European Conference on Elec-trical Engineering and Computer Science pp 124ndash130 AthensGreece November 2017

[4] A Marcos-Pastor E Vidal-Idiarte A Cid-Pastor andL Martinez-Salamero ldquoInterleaved digital power factorcorrection based on the sliding-mode approachrdquo IEEETransactions on Power Electronics vol 31 no 6 pp 4641ndash4653 2016

[5] D Apablaza and J Munoz ldquoLaboratory implementation of aboost interleaved converter for PV applicationsrdquo IEEE LatinAmerica Transactions vol 14 no 6 pp 2738ndash2743 2016

[6] F H Aghdam and M Abapour ldquoReliability and cost analysisof multistage boost converters connected to PV panelsrdquo IEEEJournal of Photovoltaics vol 6 no 4 pp 981ndash989 2016

[7] R Seyezhai and B L Mathur ldquoA comparison of three-phaseuncoupled and directly coupled interleaved boost converterfor fuel cell applicationsrdquo International Journal on ElectricalEngineering and Informatics vol 3 no 3 pp 394ndash407 2011

[8] S Banerjee A Ghosh and N Rana ldquoDesign and fabricationof closed loop two-phase interleaved boost converter withtype-III controllerrdquo in Proceedings of the IECON 2016mdash42ndAnnual Conference of the IEEE Industrial Electronics Societypp 3331ndash3336 Florence Italy October 2016

[9] C Kiree D Kumpanya S Tunyasrirut and D PuangdownreongldquoPSO-based optimal PI(D) controller design for brushless DCmotor speed control with back EMF detectionrdquo Journal ofElectrical Engineering and Technology vol 11 no 3 pp 715ndash7232016

[10] S Banerjee A Ghosh and N Rana ldquoAn improved interleavedboost converter with PSO-based optimal type-III[ controllerrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 1 pp 323ndash337 2017

[11] M Calvini M Carpita A Formentini and M MarchesonildquoPSO-based self-commissioning of electrical motor drivesrdquoIEEE Transactions on Industrial Electronics vol 62 no 2pp 768ndash776 2015

[12] S W Shneen A Z Salman Q A Jawad and H ShareefldquoAdvanced optimal by PSO-PI for DC motorrdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 165ndash175 2019

[13] M Rasheed R Omar M Sulaiman and W Abd Halim ldquoAmodified cascaded h-bridge multilevel inverter based onparticle swarm optimisation (PSO) techniquerdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 41ndash45 October 2019

[14] M Rasheed R Omar M Sulaiman and W A HalimldquoParticle swarm optimisation (PSO) algorithm with reducednumberof switches in multilevel inverter (MLI)rdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 14 no 3 pp 1114ndash1124 2019

[15] M Arun Devi K Valarmathi and R Mahendran ldquoRipplecurrent reduction in interleaved boost converter by usingadvanced PWM techniquesrdquo in Proceedings of the IEEE In-ternational Conference on Advanced Communication Controland Computing Technologies (lCACCCT) pp 115ndash119Ramanathapuram India May 2014

[16] S Kascak M Prazenica M Jarabicova and R KonarikldquoAnalysis of four-phase interleaved boost converterrdquo Trans-actions on Electrical Engineering vol 6 no 4 pp 110ndash1132017

[17] S Kascak M Prazenica M Jarabicova and R KonarikldquoFour-phase interleaved boost converter theory and appli-cationsrdquo WSEAS Transactions on Power Systems vol 13pp 272ndash282 2018

[18] S Kascak M Jarabicova and R Konarik ldquoFour phase in-terleaved boost converter-analysis and verificationrdquo ActaElectrotechnica et Informatica vol 18 no 1 pp 35ndash40 2018

[19] C W Reynolds ldquoFlocks herds and schools a distributedbehavioral modelrdquo ACM SIGGRAPH Computer Graphicsvol 21 no 4 pp 25ndash34 1987

[20] J Kennedy and R Eberhart Swarm Intelligence MorganKaufman Burlington MA USA 2001

12 Journal of Control Science and Engineering

[21] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceeding of IEEE International Conference Neural Networksvol IV pp 1942ndash1948 Perth Australia 1995

[22] K S Kumar K K Aggarwal and J Singh ldquoDesign of fuzzymodels through partical swarm optimizationrdquo in IntegratedIntelligent Systems for Engineering Design pp 43ndash62 IOSpress Amsterdam Netherlands 2006

[23] R Eberhart and Y Shi ldquoComparing inertial weights andconstriction factor in particle swarm optimizationrdquo in Pro-ceeding of Internationnal Congress on Evolutioning Compu-tation pp 84ndash88 La Jolla CA USA 2000

[24] Texas Instruments TMS320F28335 Digital Signal ControllerTexas Instruments Dallas TX USA 2007

[25] +e Math Works Inc MATLABSimulink Userrsquos Guide +eMath Works Inc Natick MA USA 1998

[26] V Viswanatha ldquoA complete mathematical modeling simu-lation and computational implementation of boost convertervia MATLABSimulinkrdquo International Journal of Pure andApplied Mathematics vol 114 no 10 pp 407ndash419 2017

[27] D E Goldberg Genetic Algorithm in Search Optimizationand Machine Learning Addison-Wesley Publishing BostonMA USA 1989

[28] D E Goldberg ldquoGenetic and evolutionary algorithms come ofagerdquo Communications of the ACM vol 37 no 3 pp 113ndash1191994

[29] F Glover ldquoTabu search-Part Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[30] F Glover ldquoTabu search-Part IIrdquoORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[31] F Glover ldquoParametric tabu-search for mixed integer pro-gramsrdquo Computers amp Operations Research vol 33 no 9pp 2449ndash2494 2006

[32] A Ghosh and S Banerjee ldquoControl of switched-mode boostconverter by using classical and optimized type controllersrdquoCEAI vol 17 no 4 pp 114ndash125 2015

[33] A Ghosh S Banerjee M K Sarkar and P Dutta ldquoDesign andimplementation of type-II and type-III controller for DC-DCswitched-mode boost converter by using K-factor approachand optimisation techniquesrdquo IET Power Electronics vol 9no 5 pp 938ndash950 2016

Journal of Control Science and Engineering 13

Algorithm of PSO has the same feature of evolutionarycalculation ie there will be a creation of population calledparticle which will move around the search space Eachparticle has a speed vector and a memory unit to be used forstoring previous good answers pbest is set as good answer inthe current search while gbest is set as global solution Allparticles will move in a similar manner and the ones closestto the target are the strongest With the particle swarmmovement principle the rest of the particles will be adjustedto have a similar movement direction as that of thosestrongest ones +is makes it possible for the whole particleswarm to move to the target effectively

Consider that the search-space is d-dimensional and atparticle i-th in the swarm It can be defined asXi (xi1 xi2 xid) and the velocity can be representedby another d-dimensional vector as Vi (vi1 vi2 vid)

and the best previously visited position of this particle bedenoted by Pi (pi1 pi2 pid) +e adjustment of particlemovement direction and the answers found are shown inequations (6) and (7) accordingly [22] Where x is a particleor answer v is speed vector showing adjusted direction w isinertia weight c1 is cognitive acceleration c2 is social ac-celeration and r1 and r2 are random numbers uniformlydistributed in the range [01]

In case of 2D space the movement of particles should beadjusted as shown in Figure 8

vn+1id wv

nid + c1r

n1 x

pbestid minus x

nid1113872 1113873 + c2r2 x

gbestid minus x

nid1113872 1113873 (6)

xn+1id x

nid + v

n+1id (7)

+e inertial weight w can be calculated from the relationas in equation (8) where wmax is the maximum weight wminis the minimum weight kmax is the number of the highestsearch round set and k is the current search round +e bestvalue suitable for use is the number of current search roundand the most suitable value of work application is c1 and c2which should be in-between 1 and 2 while wmin and wmaxshould be equal to 04 and 09 accordingly [23] Algorithm ofPSO has the following details

wi wmax minus kwmax minus wmin

kmax1113888 1113889 (8)

+e steps of designing PSO are as follows

Step 1 setting initial values which are search spacenumber of particles and maximum number of searchroundsStep 2 creating particles with normal sampling dis-tribution according to the number setStep 3 evaluating the strength of each particle usingobjective functionStep 4 adjusting the movement direction in accordancewith the strongest particle using equations (6) and (8)Step 5 calculating the particle of the current searchround using equation (7)Step 6 checking the ending condition If it is cor-related this means that the best search is obtained

+en stop the search or perform step 3 to further thenext search

4 Theory PI

+e PI controller is a combination between the proportionalcontroller P and integral controller I +e system forcontrolling PI is shown as a block diagram in Figure 9 PIcontrolling system is composed of error signal E(s) controlsignal U(s) output response signal C(s) reference signalR(s) disturbing signal D(s) and transferring signal of thesystem Gp(s) and Gc(s) +e theoretical function of the PIcontroller is stated in the following equation

Gc(s)1113868111386811138681113868PI Kp +

Ki

s

Kps + Ki

s (9)

+e PI controlling system is shown in Figure 9+e four-phase interleaved boost converter system has a

fast output response but lacks stability +e PI controller hasthe advantage of faster response times and less stable errors+erefore it is very appropriate to choose a PI controller forthis system

To obtain the value of the PI controller for the four-phaseinterleaved boost converter circuit the design of the PIcontroller uses PSO search to control four-phase interleavedboost converter voltage as shown in Figure 10

5 Digital Signal Processor Set

+is part will focus on the digital signal processor or DigitalSignal Processor (DSP) board TMS320F28335 of Texas In-struments company [24] as shown in Figure 11 for analyzingreal-time controlling +e Texas Instrument TMS320F28335consisting of a 32-bit CPU and a single-precision 32-bitfloating-point +e CPU speed is controlled by a clock signalwith the frequency of 150MHz working with MATLABSimulink [25] It produces pulse width modulation (PWM)signal for driving the four-phase interleaved boost convertercircuit switch of 25 kHz frequency as shown in Figure 12

6 Design of Four-Phase Interleaved BoostConverter Circuit

+e parameter value of the four-phase interleaved boostconverter obtained from equations (1)ndash(5) is shown inTable 1

For the design of a four-phase interleaved boost con-verter circuit to simplify circuit design the four-phase in-terleaved boost converter has parallel circuits +ereforeconsidering only one model of the circuit to make it easier todesign +e transferring function of the boost convertercircuit uses the impedance method where the analysis makesuse of switching operation while the switch is off+is can beshown as follows [26] All of the impedance value (Ztotal) isshown in the following equation

Ztotal Z1(s) + Z2(s) (10)

Z1(s) is the condition of the switch when the circuit isopen and Z2(s) is the condition of the switch when the

Journal of Control Science and Engineering 5

circuit is closed+e value of Z1(s) is shown in the followingequation and the value of Z2(s) is shown in equation (12)

Vin(s)

I(s)

RLCs2 + Ls + R

RCs + 1 (11)

Vout(s)

I(s)

R

RCs + 1 (12)

and the transferring function of the system is shown in thefollowing equation

Vout(s)

Vin

R

RLCs2 + Ls + R (13)

Where the value with parameter from Table 1 is replaced andthe transfer function of the system is obtained and it isshown in the following equation

Gp(s) 2

1173 times 10minus9s2 + 5865 times 10minus6s + 2 (14)

Asmentioned in equation(14) the term 1173 times 10minus9 s2 isa very small value considered close to zero +is systemtherefore became first order called Type 0 system+us it issuitable for the PI controller

In designing the value of PI for the four-phase inter-leaved boost converter circuit using particle swarm searchbased on Figure 8 PSO search was used for designing a PIcontroller for the four-phase interleaved boost convertercircuit system where PSO algorithm was made by MAT-LAB working with Intel(R) Core (TM) i5-3210M25 GHz +e number of particle sets is 100 where c1 c2is 20 r1 and r2 are random numbers uniformly distributedin the range [0 1] wmin is 04 wmax is 09 and kmax is 1000ie maximum iteration set as the termination criteria foreach trial

Based on comparing GA and TS the design was doneusing a PI controller for the four-phase interleaved boostconverter circuit GA and TS parameter search is designedas original Both GA and TS will be canceled when pro-cessing the construction or making a repletion of up to 1000times GA and TS will not be discussed But they show moredetails of GA in [27 28] and TS in [29ndash31] accordingly +ealgorithm of the two searches mentioned works by usingMATLAB

For designing the PI controller its parameter PI is set forsearching the following spaces Kp ranges [0 10] and Kiranges [50 100] +e processing designed for 50 experiment

xn

pbest

gbest

xn+1

v

Current motion

Figure 8 Movement of particles in 2D space

Gc(s) Gp(s)+

ndash

R(s)

D(s)

+

+

C(s)

PID Controller

E(s) U(s)

Plant

Figure 9 Operation diagram of the PI controller

KPV + (KIVs)+ ndash

+ndashParticle swarm optimization

(PSO) Vref

Plant(Four-phase interleaved

boost converter)

VrefVout

Figure 10 Operation diagram of the PI controller design using PSO search to control four-phase interleaved boost converter circuit voltage

6 Journal of Control Science and Engineering

searches starts with different search points to find the bestvalue After the search processing stops the parameter valueof the PI controller is obtained using GA TS and PSOmethods as shown in equations (15)ndash(17) accordingly +eresult of the simulation of the controller system is shown inFigure 13

Gc(s)1113868111386811138681113868PI GA 0435 +

1286s

(15)

Gc(s)1113868111386811138681113868PI TS

0325 +1256

s (16)

Gc(s)1113868111386811138681113868PI PSO

0413 +1413

s (17)

Based on Figure 11 the response of four-phase inter-leaved boost converter circuit simulation and time forsearching can be seen in Table 2 where Tr is the rise timeMpis the maximum percent overshoot Ts is the settling timeand ess is the steady state error Based on Table 2 PSO is ableto search the PI parameter value for the four-phase inter-leaved boost converter with minimum time Moreover the

DSP TMS320F28335

Load

Power supply

Four-phase interleaved boost

Figure 11 Shows the design of the PI controller using PSO for controlling Four-phase interleaved boost converter circuit voltage for theexperiment

Vin

L4

L3

L2

L1

S1 S2 S3 S4

D1

D2

D3

D4

C

Load

Vout

4-phase shi gate drive

TMS320F28335controller

S1 S2 S3 S4

Command 4-phase shi

Voltage sensor

Voltage sensor feedback

Figure 12 Diagram of designing a PI controller using PSO for controlling four-phase interleaved boost converter circuit voltage

Table 1 Summary table of the parameter value of the four-phaseinterleaved boost converter circuit

Parameter Parameter valueInput voltage 138VInductor 5865 μHCapacitor 100 μFAngle of switching 90degFrequency of switching 25 kHz

Journal of Control Science and Engineering 7

control system of the four-phase interleaved boost converteralso gives a quick response when rise time and settling timehave the best value and show the result of convergence to theanswer of PI search value using PSO as shown in Figure 14

7 Experiment Result

+e test on the PI controller with the PSO search forcontrolling voltage of the four-phase interleaved boostconverter uses 4 sets of original boost converter circuit

working in parallel +e operation is done with 90-degreeinterface and has a voltage sensor sending electrical signalsto the DSP board TMS320F28335 working with MATLABSimulink of sampling time at 00001 second

In this research the voltage level was kept at 2 levels ie20V and 24V +e result of the experiment shows thestability condition treatment of circuit voltage whilechanging load without the control system and voltagecontrol of 20V and 24V while changing load accordingly+e data collection was done using digital storage scope GWInstek GDS-3000 Series 150MHz 4 input channels

Based on the experimental results of circuit voltagetreatment while changing load without a control systemwithvoltage control of 20V and 24V as shown in Figures 15 and16 it was found that the output voltage of the circuitdropped significantly when the load was increased +efigure shows that the system was unstable to maintain theoutput voltage level to be constant

From Figure 17 the inductor current phases 1 and 2 areindicated with switch signals S1 and S2 respectively+e signalsS1 and S2 are determined to operate the inductor current in 90degree of differentiation It can be seen that when both switchesare on there will be increase in current in the load On the otherhand when both switches are off current will decrease+erefore experiment results confirm the theoretical analysisFrom Figure 18 the current of the four-phase interleaved boostconverter is investigated for every 90-degree switch signaloverlapping It can be seen that all inductor currents still appearaccording to the switch signals S1 and S2 respectively

For controlling PI controller voltage at 20V the gainedvalues of the PI controller using three optimization algo-rithms of GA TS and PSO are applied to examine theresponse and the stability of the circuit voltage +e resultsare shown in Figures 19ndash24

Figures 19 21 and 23 show the result of voltage responseand current when the gained values of the PI controller areapplied in GA TS and PSO respectively +e initial voltageinput is set at 138V and this study focused on the voltage

Table 2 System responses by the PI controller

EntrySystem responses by PI

Search time (sec)T r (sec) M p () T s (sec) e ss ()

GA 00022 000 00095 000 17614TS 0002 000 00085 000 10435PSO 000185 000 00075 000 4483

12

1

08

06

Am

plitu

de04

02

00 0002 0004 0006 0008 001

Time (seconds)

Time series plot

0012 0014 0016 0018 002

ReferenceGA

TSPSO

Figure 13 Result of response simulation of PI controller voltage with GA TS and PSO

0 10 20 30 40 50Count

60 70 80 90 100

8

7

6

5

4

Conv

erge

nt ra

te

3

2

1

Figure 14 Shows the result of convergence towards the answerwhile searching the PI value using PSO search

8 Journal of Control Science and Engineering

output controlling at 20V +ree algorithms can providegood response results and also can remain the steady state ofvoltage output instantaneously It could enter the conditionwithin less than 20milliseconds (ms) and could maintain the

output voltage both when in stable load condition and whilechanging load +e system could enter the stable conditionquickly while having a very satisfactory less changing ofvoltage Figures 20 22 and 24 illustrate the results when

Applied load Released load

Voltage output

Current output

Current input

Figure 15 Result of the four-phase interleaved boost convertercircuit at voltage of 20V without the controller

Applied load Released load

Voltage output

Current output

Current input

Figure 16 Result of the four-phase interleaved boost convertercircuit at voltage of 24V without the controller

Signal S1

Signal S2

Inductor current phase1

Inductor current phase2

Figure 17 Result of inductor current when compared to switchoperation of the four-phase interleaved boost converter circuit

Inductor current phase1 Inductor current phase2

Inductor current phase3 Inductor current phase3

Figure 18 Result of inductor current of the 4 phases of the four-phase interleaved boost converter circuit

Current input

Voltage output Vref output

Current output

Figure 19 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 20 Result of maintaining voltage stability and current whilechanging load using a PI controller with GA search

Journal of Control Science and Engineering 9

changing the load It can be seen that the stability of voltageoutput from three algorithms still remains unchanged al-though load has changed Table 3 shows the system responseby the PI controller at 20V

In summary the system response of voltage output fromthe PI controller at 20V using GA TS and PSO can beconcluded as in Table 3 Also the PI control with PSO searchhad the quickest response to reference signal when com-pared to GA and TS+e PSO establishes the lowest rise timeat 6ms and the lowest time to steady state at 8ms+ereforethe PSO is the best algorithm in controlling the voltageoutput at 20V

In order to control voltage output at 24V the same PIcontroller gained values as one for 20V are applied in GATS and PSO respectively It was found that GA TS andPSO had a quick response to reference signal and could enterthe condition in less than 20ms Figures 25ndash27 show theresult of voltage response and current when the gainedvalues of the PI controller are applied in GA TS and PSOrespectively +e initial voltage input is set at 138V In theexperiment case the voltage output is controlled at 24V

+ree optimization algorithms can provide good re-sponse results and also can remain the steady state of voltageoutput similar to the case of 20V controlling Figures 28ndash30show the results when changing the load It can be seen thatthe stability of voltage output from three algorithms stillremains unchanged although load has changed Table 4shows the system response by the PI controller at 24V

As in Table 4 the system response of voltage output bythe PI controller at 24V using GA TS and PSO can beconcluded +e GA performs at the lowest rise time of 7mswhereas GA needs 16ms in converging to steady stateHowever for PSO algorithm rise time is 72ms which isclose to the GA algorithm while the time to go to the steadystate is about 10ms which is less than GA +e PSOtherefore provides most suitable algorithm in controlling

Current output

Current input

Voltage output Vref output

Figure 21 Result of voltage response and current using a PIcontroller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 22 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Voltage output

Current output

Current input

Vref output

Figure 23 Result of voltage response and current using a PIcontroller with PSO search

Applied load Released load

Voltage output

Current output

Current input

Figure 24 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 3 System response by the PI controller at 20V

EntrySystem responses by PI

Tr (ms) Mp () Ts (ms) ess ()GA 12 000 16 000TS 14 000 17 000PSO 6 000 8 000

10 Journal of Control Science and Engineering

the voltage output at 24V compared to GA and TS as well ascontrolling voltage at 20V

+e proposed control algorithm though applied for theboost converter of 20V and 24V using PSO exhibits the bestperformance in the aspect of system response and stability+e experimental results agree with [32 33] although

Voltage output Vref output

Current output

Current input

Figure 26 Response of voltage and current using a PI controllerwith TS search

Voltage output

Current output

Current input

Vref output

Figure 27 Result of voltage response and current using a PIcontroller with PSO search

Voltage output

Current output

Vref output

Current input

Figure 25 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 28 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 29 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 30 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 4 System response by the PI controller at 24V

EntrySystem responses by PI

T r (ms) M p () T s (ms) e ss ()GA 7 000 16 000TS 72 000 15 000PSO 72 000 10 000

Journal of Control Science and Engineering 11

applied for the four-phase interleaved boost converterHowever there are no overshoot and time to steady statereaches faster than their study

8 Conclusion

In this paper the four-phase interleaved boost convertercircuit is controlled by the PI controller In order to tune thegains of the PI controller the PSO GA and TS and met-aheuristic optimizations are applied In testing the controlsystem the response of the four-phase interleaved boostconverter obtained by PSO has the rise time and setting timefaster than the GA and TS methods Additionally it is foundthat the tracing and controlling response result of outputvoltage is extremely satisfactory when load condition isconstant and while changing the load It can be concludedthat the four-phase interleaved boost converter circuit usingthe PI controller tuned gains by PSO is greatly effective forregulating the voltage in a real system

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors would like to acknowledge Department ofElectrical Engineering and Faculty of EngineeringPathumwan Institute of Technology for the financial sup-port and facilities +ey would also like to show theirgratitude to Assoc Prof Dr Decha Pungdaorueng and AsstProf Dr Wachirapond Permpoonsinsup who gave veryuseful advices and suggestions for completing this research

References

[1] C Jain and B Singh ldquoAn adjustable DC link voltage-basedcontrol of multifunctional grid interfaced solar PV systemrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 2 pp 651ndash660 2017

[2] Y A Zuniga-Ventura D Langarica-Cordoba J Leyva-Ramos L H Diaz-Saldierna and V M Ramirez-RiveraldquoAdaptive backstepping control for a fuel cellboost convertersystemrdquo IEEE Journal of Emerging and Selected Topics inPower Electronics vol 6 no 2 pp 686ndash695 2018

[3] P Mungporn P +ounthong S Sikkabut et al ldquoDifferentialflatness-based control of currentvoltage stabilization for asingle-phase PFC with multiphase interleaved boost con-verterrdquo in Proceedings of the European Conference on Elec-trical Engineering and Computer Science pp 124ndash130 AthensGreece November 2017

[4] A Marcos-Pastor E Vidal-Idiarte A Cid-Pastor andL Martinez-Salamero ldquoInterleaved digital power factorcorrection based on the sliding-mode approachrdquo IEEETransactions on Power Electronics vol 31 no 6 pp 4641ndash4653 2016

[5] D Apablaza and J Munoz ldquoLaboratory implementation of aboost interleaved converter for PV applicationsrdquo IEEE LatinAmerica Transactions vol 14 no 6 pp 2738ndash2743 2016

[6] F H Aghdam and M Abapour ldquoReliability and cost analysisof multistage boost converters connected to PV panelsrdquo IEEEJournal of Photovoltaics vol 6 no 4 pp 981ndash989 2016

[7] R Seyezhai and B L Mathur ldquoA comparison of three-phaseuncoupled and directly coupled interleaved boost converterfor fuel cell applicationsrdquo International Journal on ElectricalEngineering and Informatics vol 3 no 3 pp 394ndash407 2011

[8] S Banerjee A Ghosh and N Rana ldquoDesign and fabricationof closed loop two-phase interleaved boost converter withtype-III controllerrdquo in Proceedings of the IECON 2016mdash42ndAnnual Conference of the IEEE Industrial Electronics Societypp 3331ndash3336 Florence Italy October 2016

[9] C Kiree D Kumpanya S Tunyasrirut and D PuangdownreongldquoPSO-based optimal PI(D) controller design for brushless DCmotor speed control with back EMF detectionrdquo Journal ofElectrical Engineering and Technology vol 11 no 3 pp 715ndash7232016

[10] S Banerjee A Ghosh and N Rana ldquoAn improved interleavedboost converter with PSO-based optimal type-III[ controllerrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 1 pp 323ndash337 2017

[11] M Calvini M Carpita A Formentini and M MarchesonildquoPSO-based self-commissioning of electrical motor drivesrdquoIEEE Transactions on Industrial Electronics vol 62 no 2pp 768ndash776 2015

[12] S W Shneen A Z Salman Q A Jawad and H ShareefldquoAdvanced optimal by PSO-PI for DC motorrdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 165ndash175 2019

[13] M Rasheed R Omar M Sulaiman and W Abd Halim ldquoAmodified cascaded h-bridge multilevel inverter based onparticle swarm optimisation (PSO) techniquerdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 41ndash45 October 2019

[14] M Rasheed R Omar M Sulaiman and W A HalimldquoParticle swarm optimisation (PSO) algorithm with reducednumberof switches in multilevel inverter (MLI)rdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 14 no 3 pp 1114ndash1124 2019

[15] M Arun Devi K Valarmathi and R Mahendran ldquoRipplecurrent reduction in interleaved boost converter by usingadvanced PWM techniquesrdquo in Proceedings of the IEEE In-ternational Conference on Advanced Communication Controland Computing Technologies (lCACCCT) pp 115ndash119Ramanathapuram India May 2014

[16] S Kascak M Prazenica M Jarabicova and R KonarikldquoAnalysis of four-phase interleaved boost converterrdquo Trans-actions on Electrical Engineering vol 6 no 4 pp 110ndash1132017

[17] S Kascak M Prazenica M Jarabicova and R KonarikldquoFour-phase interleaved boost converter theory and appli-cationsrdquo WSEAS Transactions on Power Systems vol 13pp 272ndash282 2018

[18] S Kascak M Jarabicova and R Konarik ldquoFour phase in-terleaved boost converter-analysis and verificationrdquo ActaElectrotechnica et Informatica vol 18 no 1 pp 35ndash40 2018

[19] C W Reynolds ldquoFlocks herds and schools a distributedbehavioral modelrdquo ACM SIGGRAPH Computer Graphicsvol 21 no 4 pp 25ndash34 1987

[20] J Kennedy and R Eberhart Swarm Intelligence MorganKaufman Burlington MA USA 2001

12 Journal of Control Science and Engineering

[21] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceeding of IEEE International Conference Neural Networksvol IV pp 1942ndash1948 Perth Australia 1995

[22] K S Kumar K K Aggarwal and J Singh ldquoDesign of fuzzymodels through partical swarm optimizationrdquo in IntegratedIntelligent Systems for Engineering Design pp 43ndash62 IOSpress Amsterdam Netherlands 2006

[23] R Eberhart and Y Shi ldquoComparing inertial weights andconstriction factor in particle swarm optimizationrdquo in Pro-ceeding of Internationnal Congress on Evolutioning Compu-tation pp 84ndash88 La Jolla CA USA 2000

[24] Texas Instruments TMS320F28335 Digital Signal ControllerTexas Instruments Dallas TX USA 2007

[25] +e Math Works Inc MATLABSimulink Userrsquos Guide +eMath Works Inc Natick MA USA 1998

[26] V Viswanatha ldquoA complete mathematical modeling simu-lation and computational implementation of boost convertervia MATLABSimulinkrdquo International Journal of Pure andApplied Mathematics vol 114 no 10 pp 407ndash419 2017

[27] D E Goldberg Genetic Algorithm in Search Optimizationand Machine Learning Addison-Wesley Publishing BostonMA USA 1989

[28] D E Goldberg ldquoGenetic and evolutionary algorithms come ofagerdquo Communications of the ACM vol 37 no 3 pp 113ndash1191994

[29] F Glover ldquoTabu search-Part Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[30] F Glover ldquoTabu search-Part IIrdquoORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[31] F Glover ldquoParametric tabu-search for mixed integer pro-gramsrdquo Computers amp Operations Research vol 33 no 9pp 2449ndash2494 2006

[32] A Ghosh and S Banerjee ldquoControl of switched-mode boostconverter by using classical and optimized type controllersrdquoCEAI vol 17 no 4 pp 114ndash125 2015

[33] A Ghosh S Banerjee M K Sarkar and P Dutta ldquoDesign andimplementation of type-II and type-III controller for DC-DCswitched-mode boost converter by using K-factor approachand optimisation techniquesrdquo IET Power Electronics vol 9no 5 pp 938ndash950 2016

Journal of Control Science and Engineering 13

circuit is closed+e value of Z1(s) is shown in the followingequation and the value of Z2(s) is shown in equation (12)

Vin(s)

I(s)

RLCs2 + Ls + R

RCs + 1 (11)

Vout(s)

I(s)

R

RCs + 1 (12)

and the transferring function of the system is shown in thefollowing equation

Vout(s)

Vin

R

RLCs2 + Ls + R (13)

Where the value with parameter from Table 1 is replaced andthe transfer function of the system is obtained and it isshown in the following equation

Gp(s) 2

1173 times 10minus9s2 + 5865 times 10minus6s + 2 (14)

Asmentioned in equation(14) the term 1173 times 10minus9 s2 isa very small value considered close to zero +is systemtherefore became first order called Type 0 system+us it issuitable for the PI controller

In designing the value of PI for the four-phase inter-leaved boost converter circuit using particle swarm searchbased on Figure 8 PSO search was used for designing a PIcontroller for the four-phase interleaved boost convertercircuit system where PSO algorithm was made by MAT-LAB working with Intel(R) Core (TM) i5-3210M25 GHz +e number of particle sets is 100 where c1 c2is 20 r1 and r2 are random numbers uniformly distributedin the range [0 1] wmin is 04 wmax is 09 and kmax is 1000ie maximum iteration set as the termination criteria foreach trial

Based on comparing GA and TS the design was doneusing a PI controller for the four-phase interleaved boostconverter circuit GA and TS parameter search is designedas original Both GA and TS will be canceled when pro-cessing the construction or making a repletion of up to 1000times GA and TS will not be discussed But they show moredetails of GA in [27 28] and TS in [29ndash31] accordingly +ealgorithm of the two searches mentioned works by usingMATLAB

For designing the PI controller its parameter PI is set forsearching the following spaces Kp ranges [0 10] and Kiranges [50 100] +e processing designed for 50 experiment

xn

pbest

gbest

xn+1

v

Current motion

Figure 8 Movement of particles in 2D space

Gc(s) Gp(s)+

ndash

R(s)

D(s)

+

+

C(s)

PID Controller

E(s) U(s)

Plant

Figure 9 Operation diagram of the PI controller

KPV + (KIVs)+ ndash

+ndashParticle swarm optimization

(PSO) Vref

Plant(Four-phase interleaved

boost converter)

VrefVout

Figure 10 Operation diagram of the PI controller design using PSO search to control four-phase interleaved boost converter circuit voltage

6 Journal of Control Science and Engineering

searches starts with different search points to find the bestvalue After the search processing stops the parameter valueof the PI controller is obtained using GA TS and PSOmethods as shown in equations (15)ndash(17) accordingly +eresult of the simulation of the controller system is shown inFigure 13

Gc(s)1113868111386811138681113868PI GA 0435 +

1286s

(15)

Gc(s)1113868111386811138681113868PI TS

0325 +1256

s (16)

Gc(s)1113868111386811138681113868PI PSO

0413 +1413

s (17)

Based on Figure 11 the response of four-phase inter-leaved boost converter circuit simulation and time forsearching can be seen in Table 2 where Tr is the rise timeMpis the maximum percent overshoot Ts is the settling timeand ess is the steady state error Based on Table 2 PSO is ableto search the PI parameter value for the four-phase inter-leaved boost converter with minimum time Moreover the

DSP TMS320F28335

Load

Power supply

Four-phase interleaved boost

Figure 11 Shows the design of the PI controller using PSO for controlling Four-phase interleaved boost converter circuit voltage for theexperiment

Vin

L4

L3

L2

L1

S1 S2 S3 S4

D1

D2

D3

D4

C

Load

Vout

4-phase shi gate drive

TMS320F28335controller

S1 S2 S3 S4

Command 4-phase shi

Voltage sensor

Voltage sensor feedback

Figure 12 Diagram of designing a PI controller using PSO for controlling four-phase interleaved boost converter circuit voltage

Table 1 Summary table of the parameter value of the four-phaseinterleaved boost converter circuit

Parameter Parameter valueInput voltage 138VInductor 5865 μHCapacitor 100 μFAngle of switching 90degFrequency of switching 25 kHz

Journal of Control Science and Engineering 7

control system of the four-phase interleaved boost converteralso gives a quick response when rise time and settling timehave the best value and show the result of convergence to theanswer of PI search value using PSO as shown in Figure 14

7 Experiment Result

+e test on the PI controller with the PSO search forcontrolling voltage of the four-phase interleaved boostconverter uses 4 sets of original boost converter circuit

working in parallel +e operation is done with 90-degreeinterface and has a voltage sensor sending electrical signalsto the DSP board TMS320F28335 working with MATLABSimulink of sampling time at 00001 second

In this research the voltage level was kept at 2 levels ie20V and 24V +e result of the experiment shows thestability condition treatment of circuit voltage whilechanging load without the control system and voltagecontrol of 20V and 24V while changing load accordingly+e data collection was done using digital storage scope GWInstek GDS-3000 Series 150MHz 4 input channels

Based on the experimental results of circuit voltagetreatment while changing load without a control systemwithvoltage control of 20V and 24V as shown in Figures 15 and16 it was found that the output voltage of the circuitdropped significantly when the load was increased +efigure shows that the system was unstable to maintain theoutput voltage level to be constant

From Figure 17 the inductor current phases 1 and 2 areindicated with switch signals S1 and S2 respectively+e signalsS1 and S2 are determined to operate the inductor current in 90degree of differentiation It can be seen that when both switchesare on there will be increase in current in the load On the otherhand when both switches are off current will decrease+erefore experiment results confirm the theoretical analysisFrom Figure 18 the current of the four-phase interleaved boostconverter is investigated for every 90-degree switch signaloverlapping It can be seen that all inductor currents still appearaccording to the switch signals S1 and S2 respectively

For controlling PI controller voltage at 20V the gainedvalues of the PI controller using three optimization algo-rithms of GA TS and PSO are applied to examine theresponse and the stability of the circuit voltage +e resultsare shown in Figures 19ndash24

Figures 19 21 and 23 show the result of voltage responseand current when the gained values of the PI controller areapplied in GA TS and PSO respectively +e initial voltageinput is set at 138V and this study focused on the voltage

Table 2 System responses by the PI controller

EntrySystem responses by PI

Search time (sec)T r (sec) M p () T s (sec) e ss ()

GA 00022 000 00095 000 17614TS 0002 000 00085 000 10435PSO 000185 000 00075 000 4483

12

1

08

06

Am

plitu

de04

02

00 0002 0004 0006 0008 001

Time (seconds)

Time series plot

0012 0014 0016 0018 002

ReferenceGA

TSPSO

Figure 13 Result of response simulation of PI controller voltage with GA TS and PSO

0 10 20 30 40 50Count

60 70 80 90 100

8

7

6

5

4

Conv

erge

nt ra

te

3

2

1

Figure 14 Shows the result of convergence towards the answerwhile searching the PI value using PSO search

8 Journal of Control Science and Engineering

output controlling at 20V +ree algorithms can providegood response results and also can remain the steady state ofvoltage output instantaneously It could enter the conditionwithin less than 20milliseconds (ms) and could maintain the

output voltage both when in stable load condition and whilechanging load +e system could enter the stable conditionquickly while having a very satisfactory less changing ofvoltage Figures 20 22 and 24 illustrate the results when

Applied load Released load

Voltage output

Current output

Current input

Figure 15 Result of the four-phase interleaved boost convertercircuit at voltage of 20V without the controller

Applied load Released load

Voltage output

Current output

Current input

Figure 16 Result of the four-phase interleaved boost convertercircuit at voltage of 24V without the controller

Signal S1

Signal S2

Inductor current phase1

Inductor current phase2

Figure 17 Result of inductor current when compared to switchoperation of the four-phase interleaved boost converter circuit

Inductor current phase1 Inductor current phase2

Inductor current phase3 Inductor current phase3

Figure 18 Result of inductor current of the 4 phases of the four-phase interleaved boost converter circuit

Current input

Voltage output Vref output

Current output

Figure 19 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 20 Result of maintaining voltage stability and current whilechanging load using a PI controller with GA search

Journal of Control Science and Engineering 9

changing the load It can be seen that the stability of voltageoutput from three algorithms still remains unchanged al-though load has changed Table 3 shows the system responseby the PI controller at 20V

In summary the system response of voltage output fromthe PI controller at 20V using GA TS and PSO can beconcluded as in Table 3 Also the PI control with PSO searchhad the quickest response to reference signal when com-pared to GA and TS+e PSO establishes the lowest rise timeat 6ms and the lowest time to steady state at 8ms+ereforethe PSO is the best algorithm in controlling the voltageoutput at 20V

In order to control voltage output at 24V the same PIcontroller gained values as one for 20V are applied in GATS and PSO respectively It was found that GA TS andPSO had a quick response to reference signal and could enterthe condition in less than 20ms Figures 25ndash27 show theresult of voltage response and current when the gainedvalues of the PI controller are applied in GA TS and PSOrespectively +e initial voltage input is set at 138V In theexperiment case the voltage output is controlled at 24V

+ree optimization algorithms can provide good re-sponse results and also can remain the steady state of voltageoutput similar to the case of 20V controlling Figures 28ndash30show the results when changing the load It can be seen thatthe stability of voltage output from three algorithms stillremains unchanged although load has changed Table 4shows the system response by the PI controller at 24V

As in Table 4 the system response of voltage output bythe PI controller at 24V using GA TS and PSO can beconcluded +e GA performs at the lowest rise time of 7mswhereas GA needs 16ms in converging to steady stateHowever for PSO algorithm rise time is 72ms which isclose to the GA algorithm while the time to go to the steadystate is about 10ms which is less than GA +e PSOtherefore provides most suitable algorithm in controlling

Current output

Current input

Voltage output Vref output

Figure 21 Result of voltage response and current using a PIcontroller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 22 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Voltage output

Current output

Current input

Vref output

Figure 23 Result of voltage response and current using a PIcontroller with PSO search

Applied load Released load

Voltage output

Current output

Current input

Figure 24 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 3 System response by the PI controller at 20V

EntrySystem responses by PI

Tr (ms) Mp () Ts (ms) ess ()GA 12 000 16 000TS 14 000 17 000PSO 6 000 8 000

10 Journal of Control Science and Engineering

the voltage output at 24V compared to GA and TS as well ascontrolling voltage at 20V

+e proposed control algorithm though applied for theboost converter of 20V and 24V using PSO exhibits the bestperformance in the aspect of system response and stability+e experimental results agree with [32 33] although

Voltage output Vref output

Current output

Current input

Figure 26 Response of voltage and current using a PI controllerwith TS search

Voltage output

Current output

Current input

Vref output

Figure 27 Result of voltage response and current using a PIcontroller with PSO search

Voltage output

Current output

Vref output

Current input

Figure 25 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 28 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 29 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 30 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 4 System response by the PI controller at 24V

EntrySystem responses by PI

T r (ms) M p () T s (ms) e ss ()GA 7 000 16 000TS 72 000 15 000PSO 72 000 10 000

Journal of Control Science and Engineering 11

applied for the four-phase interleaved boost converterHowever there are no overshoot and time to steady statereaches faster than their study

8 Conclusion

In this paper the four-phase interleaved boost convertercircuit is controlled by the PI controller In order to tune thegains of the PI controller the PSO GA and TS and met-aheuristic optimizations are applied In testing the controlsystem the response of the four-phase interleaved boostconverter obtained by PSO has the rise time and setting timefaster than the GA and TS methods Additionally it is foundthat the tracing and controlling response result of outputvoltage is extremely satisfactory when load condition isconstant and while changing the load It can be concludedthat the four-phase interleaved boost converter circuit usingthe PI controller tuned gains by PSO is greatly effective forregulating the voltage in a real system

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors would like to acknowledge Department ofElectrical Engineering and Faculty of EngineeringPathumwan Institute of Technology for the financial sup-port and facilities +ey would also like to show theirgratitude to Assoc Prof Dr Decha Pungdaorueng and AsstProf Dr Wachirapond Permpoonsinsup who gave veryuseful advices and suggestions for completing this research

References

[1] C Jain and B Singh ldquoAn adjustable DC link voltage-basedcontrol of multifunctional grid interfaced solar PV systemrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 2 pp 651ndash660 2017

[2] Y A Zuniga-Ventura D Langarica-Cordoba J Leyva-Ramos L H Diaz-Saldierna and V M Ramirez-RiveraldquoAdaptive backstepping control for a fuel cellboost convertersystemrdquo IEEE Journal of Emerging and Selected Topics inPower Electronics vol 6 no 2 pp 686ndash695 2018

[3] P Mungporn P +ounthong S Sikkabut et al ldquoDifferentialflatness-based control of currentvoltage stabilization for asingle-phase PFC with multiphase interleaved boost con-verterrdquo in Proceedings of the European Conference on Elec-trical Engineering and Computer Science pp 124ndash130 AthensGreece November 2017

[4] A Marcos-Pastor E Vidal-Idiarte A Cid-Pastor andL Martinez-Salamero ldquoInterleaved digital power factorcorrection based on the sliding-mode approachrdquo IEEETransactions on Power Electronics vol 31 no 6 pp 4641ndash4653 2016

[5] D Apablaza and J Munoz ldquoLaboratory implementation of aboost interleaved converter for PV applicationsrdquo IEEE LatinAmerica Transactions vol 14 no 6 pp 2738ndash2743 2016

[6] F H Aghdam and M Abapour ldquoReliability and cost analysisof multistage boost converters connected to PV panelsrdquo IEEEJournal of Photovoltaics vol 6 no 4 pp 981ndash989 2016

[7] R Seyezhai and B L Mathur ldquoA comparison of three-phaseuncoupled and directly coupled interleaved boost converterfor fuel cell applicationsrdquo International Journal on ElectricalEngineering and Informatics vol 3 no 3 pp 394ndash407 2011

[8] S Banerjee A Ghosh and N Rana ldquoDesign and fabricationof closed loop two-phase interleaved boost converter withtype-III controllerrdquo in Proceedings of the IECON 2016mdash42ndAnnual Conference of the IEEE Industrial Electronics Societypp 3331ndash3336 Florence Italy October 2016

[9] C Kiree D Kumpanya S Tunyasrirut and D PuangdownreongldquoPSO-based optimal PI(D) controller design for brushless DCmotor speed control with back EMF detectionrdquo Journal ofElectrical Engineering and Technology vol 11 no 3 pp 715ndash7232016

[10] S Banerjee A Ghosh and N Rana ldquoAn improved interleavedboost converter with PSO-based optimal type-III[ controllerrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 1 pp 323ndash337 2017

[11] M Calvini M Carpita A Formentini and M MarchesonildquoPSO-based self-commissioning of electrical motor drivesrdquoIEEE Transactions on Industrial Electronics vol 62 no 2pp 768ndash776 2015

[12] S W Shneen A Z Salman Q A Jawad and H ShareefldquoAdvanced optimal by PSO-PI for DC motorrdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 165ndash175 2019

[13] M Rasheed R Omar M Sulaiman and W Abd Halim ldquoAmodified cascaded h-bridge multilevel inverter based onparticle swarm optimisation (PSO) techniquerdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 41ndash45 October 2019

[14] M Rasheed R Omar M Sulaiman and W A HalimldquoParticle swarm optimisation (PSO) algorithm with reducednumberof switches in multilevel inverter (MLI)rdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 14 no 3 pp 1114ndash1124 2019

[15] M Arun Devi K Valarmathi and R Mahendran ldquoRipplecurrent reduction in interleaved boost converter by usingadvanced PWM techniquesrdquo in Proceedings of the IEEE In-ternational Conference on Advanced Communication Controland Computing Technologies (lCACCCT) pp 115ndash119Ramanathapuram India May 2014

[16] S Kascak M Prazenica M Jarabicova and R KonarikldquoAnalysis of four-phase interleaved boost converterrdquo Trans-actions on Electrical Engineering vol 6 no 4 pp 110ndash1132017

[17] S Kascak M Prazenica M Jarabicova and R KonarikldquoFour-phase interleaved boost converter theory and appli-cationsrdquo WSEAS Transactions on Power Systems vol 13pp 272ndash282 2018

[18] S Kascak M Jarabicova and R Konarik ldquoFour phase in-terleaved boost converter-analysis and verificationrdquo ActaElectrotechnica et Informatica vol 18 no 1 pp 35ndash40 2018

[19] C W Reynolds ldquoFlocks herds and schools a distributedbehavioral modelrdquo ACM SIGGRAPH Computer Graphicsvol 21 no 4 pp 25ndash34 1987

[20] J Kennedy and R Eberhart Swarm Intelligence MorganKaufman Burlington MA USA 2001

12 Journal of Control Science and Engineering

[21] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceeding of IEEE International Conference Neural Networksvol IV pp 1942ndash1948 Perth Australia 1995

[22] K S Kumar K K Aggarwal and J Singh ldquoDesign of fuzzymodels through partical swarm optimizationrdquo in IntegratedIntelligent Systems for Engineering Design pp 43ndash62 IOSpress Amsterdam Netherlands 2006

[23] R Eberhart and Y Shi ldquoComparing inertial weights andconstriction factor in particle swarm optimizationrdquo in Pro-ceeding of Internationnal Congress on Evolutioning Compu-tation pp 84ndash88 La Jolla CA USA 2000

[24] Texas Instruments TMS320F28335 Digital Signal ControllerTexas Instruments Dallas TX USA 2007

[25] +e Math Works Inc MATLABSimulink Userrsquos Guide +eMath Works Inc Natick MA USA 1998

[26] V Viswanatha ldquoA complete mathematical modeling simu-lation and computational implementation of boost convertervia MATLABSimulinkrdquo International Journal of Pure andApplied Mathematics vol 114 no 10 pp 407ndash419 2017

[27] D E Goldberg Genetic Algorithm in Search Optimizationand Machine Learning Addison-Wesley Publishing BostonMA USA 1989

[28] D E Goldberg ldquoGenetic and evolutionary algorithms come ofagerdquo Communications of the ACM vol 37 no 3 pp 113ndash1191994

[29] F Glover ldquoTabu search-Part Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[30] F Glover ldquoTabu search-Part IIrdquoORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[31] F Glover ldquoParametric tabu-search for mixed integer pro-gramsrdquo Computers amp Operations Research vol 33 no 9pp 2449ndash2494 2006

[32] A Ghosh and S Banerjee ldquoControl of switched-mode boostconverter by using classical and optimized type controllersrdquoCEAI vol 17 no 4 pp 114ndash125 2015

[33] A Ghosh S Banerjee M K Sarkar and P Dutta ldquoDesign andimplementation of type-II and type-III controller for DC-DCswitched-mode boost converter by using K-factor approachand optimisation techniquesrdquo IET Power Electronics vol 9no 5 pp 938ndash950 2016

Journal of Control Science and Engineering 13

searches starts with different search points to find the bestvalue After the search processing stops the parameter valueof the PI controller is obtained using GA TS and PSOmethods as shown in equations (15)ndash(17) accordingly +eresult of the simulation of the controller system is shown inFigure 13

Gc(s)1113868111386811138681113868PI GA 0435 +

1286s

(15)

Gc(s)1113868111386811138681113868PI TS

0325 +1256

s (16)

Gc(s)1113868111386811138681113868PI PSO

0413 +1413

s (17)

Based on Figure 11 the response of four-phase inter-leaved boost converter circuit simulation and time forsearching can be seen in Table 2 where Tr is the rise timeMpis the maximum percent overshoot Ts is the settling timeand ess is the steady state error Based on Table 2 PSO is ableto search the PI parameter value for the four-phase inter-leaved boost converter with minimum time Moreover the

DSP TMS320F28335

Load

Power supply

Four-phase interleaved boost

Figure 11 Shows the design of the PI controller using PSO for controlling Four-phase interleaved boost converter circuit voltage for theexperiment

Vin

L4

L3

L2

L1

S1 S2 S3 S4

D1

D2

D3

D4

C

Load

Vout

4-phase shi gate drive

TMS320F28335controller

S1 S2 S3 S4

Command 4-phase shi

Voltage sensor

Voltage sensor feedback

Figure 12 Diagram of designing a PI controller using PSO for controlling four-phase interleaved boost converter circuit voltage

Table 1 Summary table of the parameter value of the four-phaseinterleaved boost converter circuit

Parameter Parameter valueInput voltage 138VInductor 5865 μHCapacitor 100 μFAngle of switching 90degFrequency of switching 25 kHz

Journal of Control Science and Engineering 7

control system of the four-phase interleaved boost converteralso gives a quick response when rise time and settling timehave the best value and show the result of convergence to theanswer of PI search value using PSO as shown in Figure 14

7 Experiment Result

+e test on the PI controller with the PSO search forcontrolling voltage of the four-phase interleaved boostconverter uses 4 sets of original boost converter circuit

working in parallel +e operation is done with 90-degreeinterface and has a voltage sensor sending electrical signalsto the DSP board TMS320F28335 working with MATLABSimulink of sampling time at 00001 second

In this research the voltage level was kept at 2 levels ie20V and 24V +e result of the experiment shows thestability condition treatment of circuit voltage whilechanging load without the control system and voltagecontrol of 20V and 24V while changing load accordingly+e data collection was done using digital storage scope GWInstek GDS-3000 Series 150MHz 4 input channels

Based on the experimental results of circuit voltagetreatment while changing load without a control systemwithvoltage control of 20V and 24V as shown in Figures 15 and16 it was found that the output voltage of the circuitdropped significantly when the load was increased +efigure shows that the system was unstable to maintain theoutput voltage level to be constant

From Figure 17 the inductor current phases 1 and 2 areindicated with switch signals S1 and S2 respectively+e signalsS1 and S2 are determined to operate the inductor current in 90degree of differentiation It can be seen that when both switchesare on there will be increase in current in the load On the otherhand when both switches are off current will decrease+erefore experiment results confirm the theoretical analysisFrom Figure 18 the current of the four-phase interleaved boostconverter is investigated for every 90-degree switch signaloverlapping It can be seen that all inductor currents still appearaccording to the switch signals S1 and S2 respectively

For controlling PI controller voltage at 20V the gainedvalues of the PI controller using three optimization algo-rithms of GA TS and PSO are applied to examine theresponse and the stability of the circuit voltage +e resultsare shown in Figures 19ndash24

Figures 19 21 and 23 show the result of voltage responseand current when the gained values of the PI controller areapplied in GA TS and PSO respectively +e initial voltageinput is set at 138V and this study focused on the voltage

Table 2 System responses by the PI controller

EntrySystem responses by PI

Search time (sec)T r (sec) M p () T s (sec) e ss ()

GA 00022 000 00095 000 17614TS 0002 000 00085 000 10435PSO 000185 000 00075 000 4483

12

1

08

06

Am

plitu

de04

02

00 0002 0004 0006 0008 001

Time (seconds)

Time series plot

0012 0014 0016 0018 002

ReferenceGA

TSPSO

Figure 13 Result of response simulation of PI controller voltage with GA TS and PSO

0 10 20 30 40 50Count

60 70 80 90 100

8

7

6

5

4

Conv

erge

nt ra

te

3

2

1

Figure 14 Shows the result of convergence towards the answerwhile searching the PI value using PSO search

8 Journal of Control Science and Engineering

output controlling at 20V +ree algorithms can providegood response results and also can remain the steady state ofvoltage output instantaneously It could enter the conditionwithin less than 20milliseconds (ms) and could maintain the

output voltage both when in stable load condition and whilechanging load +e system could enter the stable conditionquickly while having a very satisfactory less changing ofvoltage Figures 20 22 and 24 illustrate the results when

Applied load Released load

Voltage output

Current output

Current input

Figure 15 Result of the four-phase interleaved boost convertercircuit at voltage of 20V without the controller

Applied load Released load

Voltage output

Current output

Current input

Figure 16 Result of the four-phase interleaved boost convertercircuit at voltage of 24V without the controller

Signal S1

Signal S2

Inductor current phase1

Inductor current phase2

Figure 17 Result of inductor current when compared to switchoperation of the four-phase interleaved boost converter circuit

Inductor current phase1 Inductor current phase2

Inductor current phase3 Inductor current phase3

Figure 18 Result of inductor current of the 4 phases of the four-phase interleaved boost converter circuit

Current input

Voltage output Vref output

Current output

Figure 19 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 20 Result of maintaining voltage stability and current whilechanging load using a PI controller with GA search

Journal of Control Science and Engineering 9

changing the load It can be seen that the stability of voltageoutput from three algorithms still remains unchanged al-though load has changed Table 3 shows the system responseby the PI controller at 20V

In summary the system response of voltage output fromthe PI controller at 20V using GA TS and PSO can beconcluded as in Table 3 Also the PI control with PSO searchhad the quickest response to reference signal when com-pared to GA and TS+e PSO establishes the lowest rise timeat 6ms and the lowest time to steady state at 8ms+ereforethe PSO is the best algorithm in controlling the voltageoutput at 20V

In order to control voltage output at 24V the same PIcontroller gained values as one for 20V are applied in GATS and PSO respectively It was found that GA TS andPSO had a quick response to reference signal and could enterthe condition in less than 20ms Figures 25ndash27 show theresult of voltage response and current when the gainedvalues of the PI controller are applied in GA TS and PSOrespectively +e initial voltage input is set at 138V In theexperiment case the voltage output is controlled at 24V

+ree optimization algorithms can provide good re-sponse results and also can remain the steady state of voltageoutput similar to the case of 20V controlling Figures 28ndash30show the results when changing the load It can be seen thatthe stability of voltage output from three algorithms stillremains unchanged although load has changed Table 4shows the system response by the PI controller at 24V

As in Table 4 the system response of voltage output bythe PI controller at 24V using GA TS and PSO can beconcluded +e GA performs at the lowest rise time of 7mswhereas GA needs 16ms in converging to steady stateHowever for PSO algorithm rise time is 72ms which isclose to the GA algorithm while the time to go to the steadystate is about 10ms which is less than GA +e PSOtherefore provides most suitable algorithm in controlling

Current output

Current input

Voltage output Vref output

Figure 21 Result of voltage response and current using a PIcontroller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 22 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Voltage output

Current output

Current input

Vref output

Figure 23 Result of voltage response and current using a PIcontroller with PSO search

Applied load Released load

Voltage output

Current output

Current input

Figure 24 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 3 System response by the PI controller at 20V

EntrySystem responses by PI

Tr (ms) Mp () Ts (ms) ess ()GA 12 000 16 000TS 14 000 17 000PSO 6 000 8 000

10 Journal of Control Science and Engineering

the voltage output at 24V compared to GA and TS as well ascontrolling voltage at 20V

+e proposed control algorithm though applied for theboost converter of 20V and 24V using PSO exhibits the bestperformance in the aspect of system response and stability+e experimental results agree with [32 33] although

Voltage output Vref output

Current output

Current input

Figure 26 Response of voltage and current using a PI controllerwith TS search

Voltage output

Current output

Current input

Vref output

Figure 27 Result of voltage response and current using a PIcontroller with PSO search

Voltage output

Current output

Vref output

Current input

Figure 25 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 28 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 29 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 30 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 4 System response by the PI controller at 24V

EntrySystem responses by PI

T r (ms) M p () T s (ms) e ss ()GA 7 000 16 000TS 72 000 15 000PSO 72 000 10 000

Journal of Control Science and Engineering 11

applied for the four-phase interleaved boost converterHowever there are no overshoot and time to steady statereaches faster than their study

8 Conclusion

In this paper the four-phase interleaved boost convertercircuit is controlled by the PI controller In order to tune thegains of the PI controller the PSO GA and TS and met-aheuristic optimizations are applied In testing the controlsystem the response of the four-phase interleaved boostconverter obtained by PSO has the rise time and setting timefaster than the GA and TS methods Additionally it is foundthat the tracing and controlling response result of outputvoltage is extremely satisfactory when load condition isconstant and while changing the load It can be concludedthat the four-phase interleaved boost converter circuit usingthe PI controller tuned gains by PSO is greatly effective forregulating the voltage in a real system

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors would like to acknowledge Department ofElectrical Engineering and Faculty of EngineeringPathumwan Institute of Technology for the financial sup-port and facilities +ey would also like to show theirgratitude to Assoc Prof Dr Decha Pungdaorueng and AsstProf Dr Wachirapond Permpoonsinsup who gave veryuseful advices and suggestions for completing this research

References

[1] C Jain and B Singh ldquoAn adjustable DC link voltage-basedcontrol of multifunctional grid interfaced solar PV systemrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 2 pp 651ndash660 2017

[2] Y A Zuniga-Ventura D Langarica-Cordoba J Leyva-Ramos L H Diaz-Saldierna and V M Ramirez-RiveraldquoAdaptive backstepping control for a fuel cellboost convertersystemrdquo IEEE Journal of Emerging and Selected Topics inPower Electronics vol 6 no 2 pp 686ndash695 2018

[3] P Mungporn P +ounthong S Sikkabut et al ldquoDifferentialflatness-based control of currentvoltage stabilization for asingle-phase PFC with multiphase interleaved boost con-verterrdquo in Proceedings of the European Conference on Elec-trical Engineering and Computer Science pp 124ndash130 AthensGreece November 2017

[4] A Marcos-Pastor E Vidal-Idiarte A Cid-Pastor andL Martinez-Salamero ldquoInterleaved digital power factorcorrection based on the sliding-mode approachrdquo IEEETransactions on Power Electronics vol 31 no 6 pp 4641ndash4653 2016

[5] D Apablaza and J Munoz ldquoLaboratory implementation of aboost interleaved converter for PV applicationsrdquo IEEE LatinAmerica Transactions vol 14 no 6 pp 2738ndash2743 2016

[6] F H Aghdam and M Abapour ldquoReliability and cost analysisof multistage boost converters connected to PV panelsrdquo IEEEJournal of Photovoltaics vol 6 no 4 pp 981ndash989 2016

[7] R Seyezhai and B L Mathur ldquoA comparison of three-phaseuncoupled and directly coupled interleaved boost converterfor fuel cell applicationsrdquo International Journal on ElectricalEngineering and Informatics vol 3 no 3 pp 394ndash407 2011

[8] S Banerjee A Ghosh and N Rana ldquoDesign and fabricationof closed loop two-phase interleaved boost converter withtype-III controllerrdquo in Proceedings of the IECON 2016mdash42ndAnnual Conference of the IEEE Industrial Electronics Societypp 3331ndash3336 Florence Italy October 2016

[9] C Kiree D Kumpanya S Tunyasrirut and D PuangdownreongldquoPSO-based optimal PI(D) controller design for brushless DCmotor speed control with back EMF detectionrdquo Journal ofElectrical Engineering and Technology vol 11 no 3 pp 715ndash7232016

[10] S Banerjee A Ghosh and N Rana ldquoAn improved interleavedboost converter with PSO-based optimal type-III[ controllerrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 1 pp 323ndash337 2017

[11] M Calvini M Carpita A Formentini and M MarchesonildquoPSO-based self-commissioning of electrical motor drivesrdquoIEEE Transactions on Industrial Electronics vol 62 no 2pp 768ndash776 2015

[12] S W Shneen A Z Salman Q A Jawad and H ShareefldquoAdvanced optimal by PSO-PI for DC motorrdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 165ndash175 2019

[13] M Rasheed R Omar M Sulaiman and W Abd Halim ldquoAmodified cascaded h-bridge multilevel inverter based onparticle swarm optimisation (PSO) techniquerdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 41ndash45 October 2019

[14] M Rasheed R Omar M Sulaiman and W A HalimldquoParticle swarm optimisation (PSO) algorithm with reducednumberof switches in multilevel inverter (MLI)rdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 14 no 3 pp 1114ndash1124 2019

[15] M Arun Devi K Valarmathi and R Mahendran ldquoRipplecurrent reduction in interleaved boost converter by usingadvanced PWM techniquesrdquo in Proceedings of the IEEE In-ternational Conference on Advanced Communication Controland Computing Technologies (lCACCCT) pp 115ndash119Ramanathapuram India May 2014

[16] S Kascak M Prazenica M Jarabicova and R KonarikldquoAnalysis of four-phase interleaved boost converterrdquo Trans-actions on Electrical Engineering vol 6 no 4 pp 110ndash1132017

[17] S Kascak M Prazenica M Jarabicova and R KonarikldquoFour-phase interleaved boost converter theory and appli-cationsrdquo WSEAS Transactions on Power Systems vol 13pp 272ndash282 2018

[18] S Kascak M Jarabicova and R Konarik ldquoFour phase in-terleaved boost converter-analysis and verificationrdquo ActaElectrotechnica et Informatica vol 18 no 1 pp 35ndash40 2018

[19] C W Reynolds ldquoFlocks herds and schools a distributedbehavioral modelrdquo ACM SIGGRAPH Computer Graphicsvol 21 no 4 pp 25ndash34 1987

[20] J Kennedy and R Eberhart Swarm Intelligence MorganKaufman Burlington MA USA 2001

12 Journal of Control Science and Engineering

[21] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceeding of IEEE International Conference Neural Networksvol IV pp 1942ndash1948 Perth Australia 1995

[22] K S Kumar K K Aggarwal and J Singh ldquoDesign of fuzzymodels through partical swarm optimizationrdquo in IntegratedIntelligent Systems for Engineering Design pp 43ndash62 IOSpress Amsterdam Netherlands 2006

[23] R Eberhart and Y Shi ldquoComparing inertial weights andconstriction factor in particle swarm optimizationrdquo in Pro-ceeding of Internationnal Congress on Evolutioning Compu-tation pp 84ndash88 La Jolla CA USA 2000

[24] Texas Instruments TMS320F28335 Digital Signal ControllerTexas Instruments Dallas TX USA 2007

[25] +e Math Works Inc MATLABSimulink Userrsquos Guide +eMath Works Inc Natick MA USA 1998

[26] V Viswanatha ldquoA complete mathematical modeling simu-lation and computational implementation of boost convertervia MATLABSimulinkrdquo International Journal of Pure andApplied Mathematics vol 114 no 10 pp 407ndash419 2017

[27] D E Goldberg Genetic Algorithm in Search Optimizationand Machine Learning Addison-Wesley Publishing BostonMA USA 1989

[28] D E Goldberg ldquoGenetic and evolutionary algorithms come ofagerdquo Communications of the ACM vol 37 no 3 pp 113ndash1191994

[29] F Glover ldquoTabu search-Part Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[30] F Glover ldquoTabu search-Part IIrdquoORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[31] F Glover ldquoParametric tabu-search for mixed integer pro-gramsrdquo Computers amp Operations Research vol 33 no 9pp 2449ndash2494 2006

[32] A Ghosh and S Banerjee ldquoControl of switched-mode boostconverter by using classical and optimized type controllersrdquoCEAI vol 17 no 4 pp 114ndash125 2015

[33] A Ghosh S Banerjee M K Sarkar and P Dutta ldquoDesign andimplementation of type-II and type-III controller for DC-DCswitched-mode boost converter by using K-factor approachand optimisation techniquesrdquo IET Power Electronics vol 9no 5 pp 938ndash950 2016

Journal of Control Science and Engineering 13

control system of the four-phase interleaved boost converteralso gives a quick response when rise time and settling timehave the best value and show the result of convergence to theanswer of PI search value using PSO as shown in Figure 14

7 Experiment Result

+e test on the PI controller with the PSO search forcontrolling voltage of the four-phase interleaved boostconverter uses 4 sets of original boost converter circuit

working in parallel +e operation is done with 90-degreeinterface and has a voltage sensor sending electrical signalsto the DSP board TMS320F28335 working with MATLABSimulink of sampling time at 00001 second

In this research the voltage level was kept at 2 levels ie20V and 24V +e result of the experiment shows thestability condition treatment of circuit voltage whilechanging load without the control system and voltagecontrol of 20V and 24V while changing load accordingly+e data collection was done using digital storage scope GWInstek GDS-3000 Series 150MHz 4 input channels

Based on the experimental results of circuit voltagetreatment while changing load without a control systemwithvoltage control of 20V and 24V as shown in Figures 15 and16 it was found that the output voltage of the circuitdropped significantly when the load was increased +efigure shows that the system was unstable to maintain theoutput voltage level to be constant

From Figure 17 the inductor current phases 1 and 2 areindicated with switch signals S1 and S2 respectively+e signalsS1 and S2 are determined to operate the inductor current in 90degree of differentiation It can be seen that when both switchesare on there will be increase in current in the load On the otherhand when both switches are off current will decrease+erefore experiment results confirm the theoretical analysisFrom Figure 18 the current of the four-phase interleaved boostconverter is investigated for every 90-degree switch signaloverlapping It can be seen that all inductor currents still appearaccording to the switch signals S1 and S2 respectively

For controlling PI controller voltage at 20V the gainedvalues of the PI controller using three optimization algo-rithms of GA TS and PSO are applied to examine theresponse and the stability of the circuit voltage +e resultsare shown in Figures 19ndash24

Figures 19 21 and 23 show the result of voltage responseand current when the gained values of the PI controller areapplied in GA TS and PSO respectively +e initial voltageinput is set at 138V and this study focused on the voltage

Table 2 System responses by the PI controller

EntrySystem responses by PI

Search time (sec)T r (sec) M p () T s (sec) e ss ()

GA 00022 000 00095 000 17614TS 0002 000 00085 000 10435PSO 000185 000 00075 000 4483

12

1

08

06

Am

plitu

de04

02

00 0002 0004 0006 0008 001

Time (seconds)

Time series plot

0012 0014 0016 0018 002

ReferenceGA

TSPSO

Figure 13 Result of response simulation of PI controller voltage with GA TS and PSO

0 10 20 30 40 50Count

60 70 80 90 100

8

7

6

5

4

Conv

erge

nt ra

te

3

2

1

Figure 14 Shows the result of convergence towards the answerwhile searching the PI value using PSO search

8 Journal of Control Science and Engineering

output controlling at 20V +ree algorithms can providegood response results and also can remain the steady state ofvoltage output instantaneously It could enter the conditionwithin less than 20milliseconds (ms) and could maintain the

output voltage both when in stable load condition and whilechanging load +e system could enter the stable conditionquickly while having a very satisfactory less changing ofvoltage Figures 20 22 and 24 illustrate the results when

Applied load Released load

Voltage output

Current output

Current input

Figure 15 Result of the four-phase interleaved boost convertercircuit at voltage of 20V without the controller

Applied load Released load

Voltage output

Current output

Current input

Figure 16 Result of the four-phase interleaved boost convertercircuit at voltage of 24V without the controller

Signal S1

Signal S2

Inductor current phase1

Inductor current phase2

Figure 17 Result of inductor current when compared to switchoperation of the four-phase interleaved boost converter circuit

Inductor current phase1 Inductor current phase2

Inductor current phase3 Inductor current phase3

Figure 18 Result of inductor current of the 4 phases of the four-phase interleaved boost converter circuit

Current input

Voltage output Vref output

Current output

Figure 19 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 20 Result of maintaining voltage stability and current whilechanging load using a PI controller with GA search

Journal of Control Science and Engineering 9

changing the load It can be seen that the stability of voltageoutput from three algorithms still remains unchanged al-though load has changed Table 3 shows the system responseby the PI controller at 20V

In summary the system response of voltage output fromthe PI controller at 20V using GA TS and PSO can beconcluded as in Table 3 Also the PI control with PSO searchhad the quickest response to reference signal when com-pared to GA and TS+e PSO establishes the lowest rise timeat 6ms and the lowest time to steady state at 8ms+ereforethe PSO is the best algorithm in controlling the voltageoutput at 20V

In order to control voltage output at 24V the same PIcontroller gained values as one for 20V are applied in GATS and PSO respectively It was found that GA TS andPSO had a quick response to reference signal and could enterthe condition in less than 20ms Figures 25ndash27 show theresult of voltage response and current when the gainedvalues of the PI controller are applied in GA TS and PSOrespectively +e initial voltage input is set at 138V In theexperiment case the voltage output is controlled at 24V

+ree optimization algorithms can provide good re-sponse results and also can remain the steady state of voltageoutput similar to the case of 20V controlling Figures 28ndash30show the results when changing the load It can be seen thatthe stability of voltage output from three algorithms stillremains unchanged although load has changed Table 4shows the system response by the PI controller at 24V

As in Table 4 the system response of voltage output bythe PI controller at 24V using GA TS and PSO can beconcluded +e GA performs at the lowest rise time of 7mswhereas GA needs 16ms in converging to steady stateHowever for PSO algorithm rise time is 72ms which isclose to the GA algorithm while the time to go to the steadystate is about 10ms which is less than GA +e PSOtherefore provides most suitable algorithm in controlling

Current output

Current input

Voltage output Vref output

Figure 21 Result of voltage response and current using a PIcontroller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 22 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Voltage output

Current output

Current input

Vref output

Figure 23 Result of voltage response and current using a PIcontroller with PSO search

Applied load Released load

Voltage output

Current output

Current input

Figure 24 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 3 System response by the PI controller at 20V

EntrySystem responses by PI

Tr (ms) Mp () Ts (ms) ess ()GA 12 000 16 000TS 14 000 17 000PSO 6 000 8 000

10 Journal of Control Science and Engineering

the voltage output at 24V compared to GA and TS as well ascontrolling voltage at 20V

+e proposed control algorithm though applied for theboost converter of 20V and 24V using PSO exhibits the bestperformance in the aspect of system response and stability+e experimental results agree with [32 33] although

Voltage output Vref output

Current output

Current input

Figure 26 Response of voltage and current using a PI controllerwith TS search

Voltage output

Current output

Current input

Vref output

Figure 27 Result of voltage response and current using a PIcontroller with PSO search

Voltage output

Current output

Vref output

Current input

Figure 25 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 28 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 29 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 30 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 4 System response by the PI controller at 24V

EntrySystem responses by PI

T r (ms) M p () T s (ms) e ss ()GA 7 000 16 000TS 72 000 15 000PSO 72 000 10 000

Journal of Control Science and Engineering 11

applied for the four-phase interleaved boost converterHowever there are no overshoot and time to steady statereaches faster than their study

8 Conclusion

In this paper the four-phase interleaved boost convertercircuit is controlled by the PI controller In order to tune thegains of the PI controller the PSO GA and TS and met-aheuristic optimizations are applied In testing the controlsystem the response of the four-phase interleaved boostconverter obtained by PSO has the rise time and setting timefaster than the GA and TS methods Additionally it is foundthat the tracing and controlling response result of outputvoltage is extremely satisfactory when load condition isconstant and while changing the load It can be concludedthat the four-phase interleaved boost converter circuit usingthe PI controller tuned gains by PSO is greatly effective forregulating the voltage in a real system

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors would like to acknowledge Department ofElectrical Engineering and Faculty of EngineeringPathumwan Institute of Technology for the financial sup-port and facilities +ey would also like to show theirgratitude to Assoc Prof Dr Decha Pungdaorueng and AsstProf Dr Wachirapond Permpoonsinsup who gave veryuseful advices and suggestions for completing this research

References

[1] C Jain and B Singh ldquoAn adjustable DC link voltage-basedcontrol of multifunctional grid interfaced solar PV systemrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 2 pp 651ndash660 2017

[2] Y A Zuniga-Ventura D Langarica-Cordoba J Leyva-Ramos L H Diaz-Saldierna and V M Ramirez-RiveraldquoAdaptive backstepping control for a fuel cellboost convertersystemrdquo IEEE Journal of Emerging and Selected Topics inPower Electronics vol 6 no 2 pp 686ndash695 2018

[3] P Mungporn P +ounthong S Sikkabut et al ldquoDifferentialflatness-based control of currentvoltage stabilization for asingle-phase PFC with multiphase interleaved boost con-verterrdquo in Proceedings of the European Conference on Elec-trical Engineering and Computer Science pp 124ndash130 AthensGreece November 2017

[4] A Marcos-Pastor E Vidal-Idiarte A Cid-Pastor andL Martinez-Salamero ldquoInterleaved digital power factorcorrection based on the sliding-mode approachrdquo IEEETransactions on Power Electronics vol 31 no 6 pp 4641ndash4653 2016

[5] D Apablaza and J Munoz ldquoLaboratory implementation of aboost interleaved converter for PV applicationsrdquo IEEE LatinAmerica Transactions vol 14 no 6 pp 2738ndash2743 2016

[6] F H Aghdam and M Abapour ldquoReliability and cost analysisof multistage boost converters connected to PV panelsrdquo IEEEJournal of Photovoltaics vol 6 no 4 pp 981ndash989 2016

[7] R Seyezhai and B L Mathur ldquoA comparison of three-phaseuncoupled and directly coupled interleaved boost converterfor fuel cell applicationsrdquo International Journal on ElectricalEngineering and Informatics vol 3 no 3 pp 394ndash407 2011

[8] S Banerjee A Ghosh and N Rana ldquoDesign and fabricationof closed loop two-phase interleaved boost converter withtype-III controllerrdquo in Proceedings of the IECON 2016mdash42ndAnnual Conference of the IEEE Industrial Electronics Societypp 3331ndash3336 Florence Italy October 2016

[9] C Kiree D Kumpanya S Tunyasrirut and D PuangdownreongldquoPSO-based optimal PI(D) controller design for brushless DCmotor speed control with back EMF detectionrdquo Journal ofElectrical Engineering and Technology vol 11 no 3 pp 715ndash7232016

[10] S Banerjee A Ghosh and N Rana ldquoAn improved interleavedboost converter with PSO-based optimal type-III[ controllerrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 1 pp 323ndash337 2017

[11] M Calvini M Carpita A Formentini and M MarchesonildquoPSO-based self-commissioning of electrical motor drivesrdquoIEEE Transactions on Industrial Electronics vol 62 no 2pp 768ndash776 2015

[12] S W Shneen A Z Salman Q A Jawad and H ShareefldquoAdvanced optimal by PSO-PI for DC motorrdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 165ndash175 2019

[13] M Rasheed R Omar M Sulaiman and W Abd Halim ldquoAmodified cascaded h-bridge multilevel inverter based onparticle swarm optimisation (PSO) techniquerdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 41ndash45 October 2019

[14] M Rasheed R Omar M Sulaiman and W A HalimldquoParticle swarm optimisation (PSO) algorithm with reducednumberof switches in multilevel inverter (MLI)rdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 14 no 3 pp 1114ndash1124 2019

[15] M Arun Devi K Valarmathi and R Mahendran ldquoRipplecurrent reduction in interleaved boost converter by usingadvanced PWM techniquesrdquo in Proceedings of the IEEE In-ternational Conference on Advanced Communication Controland Computing Technologies (lCACCCT) pp 115ndash119Ramanathapuram India May 2014

[16] S Kascak M Prazenica M Jarabicova and R KonarikldquoAnalysis of four-phase interleaved boost converterrdquo Trans-actions on Electrical Engineering vol 6 no 4 pp 110ndash1132017

[17] S Kascak M Prazenica M Jarabicova and R KonarikldquoFour-phase interleaved boost converter theory and appli-cationsrdquo WSEAS Transactions on Power Systems vol 13pp 272ndash282 2018

[18] S Kascak M Jarabicova and R Konarik ldquoFour phase in-terleaved boost converter-analysis and verificationrdquo ActaElectrotechnica et Informatica vol 18 no 1 pp 35ndash40 2018

[19] C W Reynolds ldquoFlocks herds and schools a distributedbehavioral modelrdquo ACM SIGGRAPH Computer Graphicsvol 21 no 4 pp 25ndash34 1987

[20] J Kennedy and R Eberhart Swarm Intelligence MorganKaufman Burlington MA USA 2001

12 Journal of Control Science and Engineering

[21] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceeding of IEEE International Conference Neural Networksvol IV pp 1942ndash1948 Perth Australia 1995

[22] K S Kumar K K Aggarwal and J Singh ldquoDesign of fuzzymodels through partical swarm optimizationrdquo in IntegratedIntelligent Systems for Engineering Design pp 43ndash62 IOSpress Amsterdam Netherlands 2006

[23] R Eberhart and Y Shi ldquoComparing inertial weights andconstriction factor in particle swarm optimizationrdquo in Pro-ceeding of Internationnal Congress on Evolutioning Compu-tation pp 84ndash88 La Jolla CA USA 2000

[24] Texas Instruments TMS320F28335 Digital Signal ControllerTexas Instruments Dallas TX USA 2007

[25] +e Math Works Inc MATLABSimulink Userrsquos Guide +eMath Works Inc Natick MA USA 1998

[26] V Viswanatha ldquoA complete mathematical modeling simu-lation and computational implementation of boost convertervia MATLABSimulinkrdquo International Journal of Pure andApplied Mathematics vol 114 no 10 pp 407ndash419 2017

[27] D E Goldberg Genetic Algorithm in Search Optimizationand Machine Learning Addison-Wesley Publishing BostonMA USA 1989

[28] D E Goldberg ldquoGenetic and evolutionary algorithms come ofagerdquo Communications of the ACM vol 37 no 3 pp 113ndash1191994

[29] F Glover ldquoTabu search-Part Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[30] F Glover ldquoTabu search-Part IIrdquoORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[31] F Glover ldquoParametric tabu-search for mixed integer pro-gramsrdquo Computers amp Operations Research vol 33 no 9pp 2449ndash2494 2006

[32] A Ghosh and S Banerjee ldquoControl of switched-mode boostconverter by using classical and optimized type controllersrdquoCEAI vol 17 no 4 pp 114ndash125 2015

[33] A Ghosh S Banerjee M K Sarkar and P Dutta ldquoDesign andimplementation of type-II and type-III controller for DC-DCswitched-mode boost converter by using K-factor approachand optimisation techniquesrdquo IET Power Electronics vol 9no 5 pp 938ndash950 2016

Journal of Control Science and Engineering 13

output controlling at 20V +ree algorithms can providegood response results and also can remain the steady state ofvoltage output instantaneously It could enter the conditionwithin less than 20milliseconds (ms) and could maintain the

output voltage both when in stable load condition and whilechanging load +e system could enter the stable conditionquickly while having a very satisfactory less changing ofvoltage Figures 20 22 and 24 illustrate the results when

Applied load Released load

Voltage output

Current output

Current input

Figure 15 Result of the four-phase interleaved boost convertercircuit at voltage of 20V without the controller

Applied load Released load

Voltage output

Current output

Current input

Figure 16 Result of the four-phase interleaved boost convertercircuit at voltage of 24V without the controller

Signal S1

Signal S2

Inductor current phase1

Inductor current phase2

Figure 17 Result of inductor current when compared to switchoperation of the four-phase interleaved boost converter circuit

Inductor current phase1 Inductor current phase2

Inductor current phase3 Inductor current phase3

Figure 18 Result of inductor current of the 4 phases of the four-phase interleaved boost converter circuit

Current input

Voltage output Vref output

Current output

Figure 19 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 20 Result of maintaining voltage stability and current whilechanging load using a PI controller with GA search

Journal of Control Science and Engineering 9

changing the load It can be seen that the stability of voltageoutput from three algorithms still remains unchanged al-though load has changed Table 3 shows the system responseby the PI controller at 20V

In summary the system response of voltage output fromthe PI controller at 20V using GA TS and PSO can beconcluded as in Table 3 Also the PI control with PSO searchhad the quickest response to reference signal when com-pared to GA and TS+e PSO establishes the lowest rise timeat 6ms and the lowest time to steady state at 8ms+ereforethe PSO is the best algorithm in controlling the voltageoutput at 20V

In order to control voltage output at 24V the same PIcontroller gained values as one for 20V are applied in GATS and PSO respectively It was found that GA TS andPSO had a quick response to reference signal and could enterthe condition in less than 20ms Figures 25ndash27 show theresult of voltage response and current when the gainedvalues of the PI controller are applied in GA TS and PSOrespectively +e initial voltage input is set at 138V In theexperiment case the voltage output is controlled at 24V

+ree optimization algorithms can provide good re-sponse results and also can remain the steady state of voltageoutput similar to the case of 20V controlling Figures 28ndash30show the results when changing the load It can be seen thatthe stability of voltage output from three algorithms stillremains unchanged although load has changed Table 4shows the system response by the PI controller at 24V

As in Table 4 the system response of voltage output bythe PI controller at 24V using GA TS and PSO can beconcluded +e GA performs at the lowest rise time of 7mswhereas GA needs 16ms in converging to steady stateHowever for PSO algorithm rise time is 72ms which isclose to the GA algorithm while the time to go to the steadystate is about 10ms which is less than GA +e PSOtherefore provides most suitable algorithm in controlling

Current output

Current input

Voltage output Vref output

Figure 21 Result of voltage response and current using a PIcontroller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 22 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Voltage output

Current output

Current input

Vref output

Figure 23 Result of voltage response and current using a PIcontroller with PSO search

Applied load Released load

Voltage output

Current output

Current input

Figure 24 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 3 System response by the PI controller at 20V

EntrySystem responses by PI

Tr (ms) Mp () Ts (ms) ess ()GA 12 000 16 000TS 14 000 17 000PSO 6 000 8 000

10 Journal of Control Science and Engineering

the voltage output at 24V compared to GA and TS as well ascontrolling voltage at 20V

+e proposed control algorithm though applied for theboost converter of 20V and 24V using PSO exhibits the bestperformance in the aspect of system response and stability+e experimental results agree with [32 33] although

Voltage output Vref output

Current output

Current input

Figure 26 Response of voltage and current using a PI controllerwith TS search

Voltage output

Current output

Current input

Vref output

Figure 27 Result of voltage response and current using a PIcontroller with PSO search

Voltage output

Current output

Vref output

Current input

Figure 25 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 28 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 29 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 30 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 4 System response by the PI controller at 24V

EntrySystem responses by PI

T r (ms) M p () T s (ms) e ss ()GA 7 000 16 000TS 72 000 15 000PSO 72 000 10 000

Journal of Control Science and Engineering 11

applied for the four-phase interleaved boost converterHowever there are no overshoot and time to steady statereaches faster than their study

8 Conclusion

In this paper the four-phase interleaved boost convertercircuit is controlled by the PI controller In order to tune thegains of the PI controller the PSO GA and TS and met-aheuristic optimizations are applied In testing the controlsystem the response of the four-phase interleaved boostconverter obtained by PSO has the rise time and setting timefaster than the GA and TS methods Additionally it is foundthat the tracing and controlling response result of outputvoltage is extremely satisfactory when load condition isconstant and while changing the load It can be concludedthat the four-phase interleaved boost converter circuit usingthe PI controller tuned gains by PSO is greatly effective forregulating the voltage in a real system

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors would like to acknowledge Department ofElectrical Engineering and Faculty of EngineeringPathumwan Institute of Technology for the financial sup-port and facilities +ey would also like to show theirgratitude to Assoc Prof Dr Decha Pungdaorueng and AsstProf Dr Wachirapond Permpoonsinsup who gave veryuseful advices and suggestions for completing this research

References

[1] C Jain and B Singh ldquoAn adjustable DC link voltage-basedcontrol of multifunctional grid interfaced solar PV systemrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 2 pp 651ndash660 2017

[2] Y A Zuniga-Ventura D Langarica-Cordoba J Leyva-Ramos L H Diaz-Saldierna and V M Ramirez-RiveraldquoAdaptive backstepping control for a fuel cellboost convertersystemrdquo IEEE Journal of Emerging and Selected Topics inPower Electronics vol 6 no 2 pp 686ndash695 2018

[3] P Mungporn P +ounthong S Sikkabut et al ldquoDifferentialflatness-based control of currentvoltage stabilization for asingle-phase PFC with multiphase interleaved boost con-verterrdquo in Proceedings of the European Conference on Elec-trical Engineering and Computer Science pp 124ndash130 AthensGreece November 2017

[4] A Marcos-Pastor E Vidal-Idiarte A Cid-Pastor andL Martinez-Salamero ldquoInterleaved digital power factorcorrection based on the sliding-mode approachrdquo IEEETransactions on Power Electronics vol 31 no 6 pp 4641ndash4653 2016

[5] D Apablaza and J Munoz ldquoLaboratory implementation of aboost interleaved converter for PV applicationsrdquo IEEE LatinAmerica Transactions vol 14 no 6 pp 2738ndash2743 2016

[6] F H Aghdam and M Abapour ldquoReliability and cost analysisof multistage boost converters connected to PV panelsrdquo IEEEJournal of Photovoltaics vol 6 no 4 pp 981ndash989 2016

[7] R Seyezhai and B L Mathur ldquoA comparison of three-phaseuncoupled and directly coupled interleaved boost converterfor fuel cell applicationsrdquo International Journal on ElectricalEngineering and Informatics vol 3 no 3 pp 394ndash407 2011

[8] S Banerjee A Ghosh and N Rana ldquoDesign and fabricationof closed loop two-phase interleaved boost converter withtype-III controllerrdquo in Proceedings of the IECON 2016mdash42ndAnnual Conference of the IEEE Industrial Electronics Societypp 3331ndash3336 Florence Italy October 2016

[9] C Kiree D Kumpanya S Tunyasrirut and D PuangdownreongldquoPSO-based optimal PI(D) controller design for brushless DCmotor speed control with back EMF detectionrdquo Journal ofElectrical Engineering and Technology vol 11 no 3 pp 715ndash7232016

[10] S Banerjee A Ghosh and N Rana ldquoAn improved interleavedboost converter with PSO-based optimal type-III[ controllerrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 1 pp 323ndash337 2017

[11] M Calvini M Carpita A Formentini and M MarchesonildquoPSO-based self-commissioning of electrical motor drivesrdquoIEEE Transactions on Industrial Electronics vol 62 no 2pp 768ndash776 2015

[12] S W Shneen A Z Salman Q A Jawad and H ShareefldquoAdvanced optimal by PSO-PI for DC motorrdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 165ndash175 2019

[13] M Rasheed R Omar M Sulaiman and W Abd Halim ldquoAmodified cascaded h-bridge multilevel inverter based onparticle swarm optimisation (PSO) techniquerdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 41ndash45 October 2019

[14] M Rasheed R Omar M Sulaiman and W A HalimldquoParticle swarm optimisation (PSO) algorithm with reducednumberof switches in multilevel inverter (MLI)rdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 14 no 3 pp 1114ndash1124 2019

[15] M Arun Devi K Valarmathi and R Mahendran ldquoRipplecurrent reduction in interleaved boost converter by usingadvanced PWM techniquesrdquo in Proceedings of the IEEE In-ternational Conference on Advanced Communication Controland Computing Technologies (lCACCCT) pp 115ndash119Ramanathapuram India May 2014

[16] S Kascak M Prazenica M Jarabicova and R KonarikldquoAnalysis of four-phase interleaved boost converterrdquo Trans-actions on Electrical Engineering vol 6 no 4 pp 110ndash1132017

[17] S Kascak M Prazenica M Jarabicova and R KonarikldquoFour-phase interleaved boost converter theory and appli-cationsrdquo WSEAS Transactions on Power Systems vol 13pp 272ndash282 2018

[18] S Kascak M Jarabicova and R Konarik ldquoFour phase in-terleaved boost converter-analysis and verificationrdquo ActaElectrotechnica et Informatica vol 18 no 1 pp 35ndash40 2018

[19] C W Reynolds ldquoFlocks herds and schools a distributedbehavioral modelrdquo ACM SIGGRAPH Computer Graphicsvol 21 no 4 pp 25ndash34 1987

[20] J Kennedy and R Eberhart Swarm Intelligence MorganKaufman Burlington MA USA 2001

12 Journal of Control Science and Engineering

[21] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceeding of IEEE International Conference Neural Networksvol IV pp 1942ndash1948 Perth Australia 1995

[22] K S Kumar K K Aggarwal and J Singh ldquoDesign of fuzzymodels through partical swarm optimizationrdquo in IntegratedIntelligent Systems for Engineering Design pp 43ndash62 IOSpress Amsterdam Netherlands 2006

[23] R Eberhart and Y Shi ldquoComparing inertial weights andconstriction factor in particle swarm optimizationrdquo in Pro-ceeding of Internationnal Congress on Evolutioning Compu-tation pp 84ndash88 La Jolla CA USA 2000

[24] Texas Instruments TMS320F28335 Digital Signal ControllerTexas Instruments Dallas TX USA 2007

[25] +e Math Works Inc MATLABSimulink Userrsquos Guide +eMath Works Inc Natick MA USA 1998

[26] V Viswanatha ldquoA complete mathematical modeling simu-lation and computational implementation of boost convertervia MATLABSimulinkrdquo International Journal of Pure andApplied Mathematics vol 114 no 10 pp 407ndash419 2017

[27] D E Goldberg Genetic Algorithm in Search Optimizationand Machine Learning Addison-Wesley Publishing BostonMA USA 1989

[28] D E Goldberg ldquoGenetic and evolutionary algorithms come ofagerdquo Communications of the ACM vol 37 no 3 pp 113ndash1191994

[29] F Glover ldquoTabu search-Part Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[30] F Glover ldquoTabu search-Part IIrdquoORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[31] F Glover ldquoParametric tabu-search for mixed integer pro-gramsrdquo Computers amp Operations Research vol 33 no 9pp 2449ndash2494 2006

[32] A Ghosh and S Banerjee ldquoControl of switched-mode boostconverter by using classical and optimized type controllersrdquoCEAI vol 17 no 4 pp 114ndash125 2015

[33] A Ghosh S Banerjee M K Sarkar and P Dutta ldquoDesign andimplementation of type-II and type-III controller for DC-DCswitched-mode boost converter by using K-factor approachand optimisation techniquesrdquo IET Power Electronics vol 9no 5 pp 938ndash950 2016

Journal of Control Science and Engineering 13

changing the load It can be seen that the stability of voltageoutput from three algorithms still remains unchanged al-though load has changed Table 3 shows the system responseby the PI controller at 20V

In summary the system response of voltage output fromthe PI controller at 20V using GA TS and PSO can beconcluded as in Table 3 Also the PI control with PSO searchhad the quickest response to reference signal when com-pared to GA and TS+e PSO establishes the lowest rise timeat 6ms and the lowest time to steady state at 8ms+ereforethe PSO is the best algorithm in controlling the voltageoutput at 20V

In order to control voltage output at 24V the same PIcontroller gained values as one for 20V are applied in GATS and PSO respectively It was found that GA TS andPSO had a quick response to reference signal and could enterthe condition in less than 20ms Figures 25ndash27 show theresult of voltage response and current when the gainedvalues of the PI controller are applied in GA TS and PSOrespectively +e initial voltage input is set at 138V In theexperiment case the voltage output is controlled at 24V

+ree optimization algorithms can provide good re-sponse results and also can remain the steady state of voltageoutput similar to the case of 20V controlling Figures 28ndash30show the results when changing the load It can be seen thatthe stability of voltage output from three algorithms stillremains unchanged although load has changed Table 4shows the system response by the PI controller at 24V

As in Table 4 the system response of voltage output bythe PI controller at 24V using GA TS and PSO can beconcluded +e GA performs at the lowest rise time of 7mswhereas GA needs 16ms in converging to steady stateHowever for PSO algorithm rise time is 72ms which isclose to the GA algorithm while the time to go to the steadystate is about 10ms which is less than GA +e PSOtherefore provides most suitable algorithm in controlling

Current output

Current input

Voltage output Vref output

Figure 21 Result of voltage response and current using a PIcontroller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 22 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Voltage output

Current output

Current input

Vref output

Figure 23 Result of voltage response and current using a PIcontroller with PSO search

Applied load Released load

Voltage output

Current output

Current input

Figure 24 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 3 System response by the PI controller at 20V

EntrySystem responses by PI

Tr (ms) Mp () Ts (ms) ess ()GA 12 000 16 000TS 14 000 17 000PSO 6 000 8 000

10 Journal of Control Science and Engineering

the voltage output at 24V compared to GA and TS as well ascontrolling voltage at 20V

+e proposed control algorithm though applied for theboost converter of 20V and 24V using PSO exhibits the bestperformance in the aspect of system response and stability+e experimental results agree with [32 33] although

Voltage output Vref output

Current output

Current input

Figure 26 Response of voltage and current using a PI controllerwith TS search

Voltage output

Current output

Current input

Vref output

Figure 27 Result of voltage response and current using a PIcontroller with PSO search

Voltage output

Current output

Vref output

Current input

Figure 25 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 28 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 29 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 30 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 4 System response by the PI controller at 24V

EntrySystem responses by PI

T r (ms) M p () T s (ms) e ss ()GA 7 000 16 000TS 72 000 15 000PSO 72 000 10 000

Journal of Control Science and Engineering 11

applied for the four-phase interleaved boost converterHowever there are no overshoot and time to steady statereaches faster than their study

8 Conclusion

In this paper the four-phase interleaved boost convertercircuit is controlled by the PI controller In order to tune thegains of the PI controller the PSO GA and TS and met-aheuristic optimizations are applied In testing the controlsystem the response of the four-phase interleaved boostconverter obtained by PSO has the rise time and setting timefaster than the GA and TS methods Additionally it is foundthat the tracing and controlling response result of outputvoltage is extremely satisfactory when load condition isconstant and while changing the load It can be concludedthat the four-phase interleaved boost converter circuit usingthe PI controller tuned gains by PSO is greatly effective forregulating the voltage in a real system

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors would like to acknowledge Department ofElectrical Engineering and Faculty of EngineeringPathumwan Institute of Technology for the financial sup-port and facilities +ey would also like to show theirgratitude to Assoc Prof Dr Decha Pungdaorueng and AsstProf Dr Wachirapond Permpoonsinsup who gave veryuseful advices and suggestions for completing this research

References

[1] C Jain and B Singh ldquoAn adjustable DC link voltage-basedcontrol of multifunctional grid interfaced solar PV systemrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 2 pp 651ndash660 2017

[2] Y A Zuniga-Ventura D Langarica-Cordoba J Leyva-Ramos L H Diaz-Saldierna and V M Ramirez-RiveraldquoAdaptive backstepping control for a fuel cellboost convertersystemrdquo IEEE Journal of Emerging and Selected Topics inPower Electronics vol 6 no 2 pp 686ndash695 2018

[3] P Mungporn P +ounthong S Sikkabut et al ldquoDifferentialflatness-based control of currentvoltage stabilization for asingle-phase PFC with multiphase interleaved boost con-verterrdquo in Proceedings of the European Conference on Elec-trical Engineering and Computer Science pp 124ndash130 AthensGreece November 2017

[4] A Marcos-Pastor E Vidal-Idiarte A Cid-Pastor andL Martinez-Salamero ldquoInterleaved digital power factorcorrection based on the sliding-mode approachrdquo IEEETransactions on Power Electronics vol 31 no 6 pp 4641ndash4653 2016

[5] D Apablaza and J Munoz ldquoLaboratory implementation of aboost interleaved converter for PV applicationsrdquo IEEE LatinAmerica Transactions vol 14 no 6 pp 2738ndash2743 2016

[6] F H Aghdam and M Abapour ldquoReliability and cost analysisof multistage boost converters connected to PV panelsrdquo IEEEJournal of Photovoltaics vol 6 no 4 pp 981ndash989 2016

[7] R Seyezhai and B L Mathur ldquoA comparison of three-phaseuncoupled and directly coupled interleaved boost converterfor fuel cell applicationsrdquo International Journal on ElectricalEngineering and Informatics vol 3 no 3 pp 394ndash407 2011

[8] S Banerjee A Ghosh and N Rana ldquoDesign and fabricationof closed loop two-phase interleaved boost converter withtype-III controllerrdquo in Proceedings of the IECON 2016mdash42ndAnnual Conference of the IEEE Industrial Electronics Societypp 3331ndash3336 Florence Italy October 2016

[9] C Kiree D Kumpanya S Tunyasrirut and D PuangdownreongldquoPSO-based optimal PI(D) controller design for brushless DCmotor speed control with back EMF detectionrdquo Journal ofElectrical Engineering and Technology vol 11 no 3 pp 715ndash7232016

[10] S Banerjee A Ghosh and N Rana ldquoAn improved interleavedboost converter with PSO-based optimal type-III[ controllerrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 1 pp 323ndash337 2017

[11] M Calvini M Carpita A Formentini and M MarchesonildquoPSO-based self-commissioning of electrical motor drivesrdquoIEEE Transactions on Industrial Electronics vol 62 no 2pp 768ndash776 2015

[12] S W Shneen A Z Salman Q A Jawad and H ShareefldquoAdvanced optimal by PSO-PI for DC motorrdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 165ndash175 2019

[13] M Rasheed R Omar M Sulaiman and W Abd Halim ldquoAmodified cascaded h-bridge multilevel inverter based onparticle swarm optimisation (PSO) techniquerdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 41ndash45 October 2019

[14] M Rasheed R Omar M Sulaiman and W A HalimldquoParticle swarm optimisation (PSO) algorithm with reducednumberof switches in multilevel inverter (MLI)rdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 14 no 3 pp 1114ndash1124 2019

[15] M Arun Devi K Valarmathi and R Mahendran ldquoRipplecurrent reduction in interleaved boost converter by usingadvanced PWM techniquesrdquo in Proceedings of the IEEE In-ternational Conference on Advanced Communication Controland Computing Technologies (lCACCCT) pp 115ndash119Ramanathapuram India May 2014

[16] S Kascak M Prazenica M Jarabicova and R KonarikldquoAnalysis of four-phase interleaved boost converterrdquo Trans-actions on Electrical Engineering vol 6 no 4 pp 110ndash1132017

[17] S Kascak M Prazenica M Jarabicova and R KonarikldquoFour-phase interleaved boost converter theory and appli-cationsrdquo WSEAS Transactions on Power Systems vol 13pp 272ndash282 2018

[18] S Kascak M Jarabicova and R Konarik ldquoFour phase in-terleaved boost converter-analysis and verificationrdquo ActaElectrotechnica et Informatica vol 18 no 1 pp 35ndash40 2018

[19] C W Reynolds ldquoFlocks herds and schools a distributedbehavioral modelrdquo ACM SIGGRAPH Computer Graphicsvol 21 no 4 pp 25ndash34 1987

[20] J Kennedy and R Eberhart Swarm Intelligence MorganKaufman Burlington MA USA 2001

12 Journal of Control Science and Engineering

[21] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceeding of IEEE International Conference Neural Networksvol IV pp 1942ndash1948 Perth Australia 1995

[22] K S Kumar K K Aggarwal and J Singh ldquoDesign of fuzzymodels through partical swarm optimizationrdquo in IntegratedIntelligent Systems for Engineering Design pp 43ndash62 IOSpress Amsterdam Netherlands 2006

[23] R Eberhart and Y Shi ldquoComparing inertial weights andconstriction factor in particle swarm optimizationrdquo in Pro-ceeding of Internationnal Congress on Evolutioning Compu-tation pp 84ndash88 La Jolla CA USA 2000

[24] Texas Instruments TMS320F28335 Digital Signal ControllerTexas Instruments Dallas TX USA 2007

[25] +e Math Works Inc MATLABSimulink Userrsquos Guide +eMath Works Inc Natick MA USA 1998

[26] V Viswanatha ldquoA complete mathematical modeling simu-lation and computational implementation of boost convertervia MATLABSimulinkrdquo International Journal of Pure andApplied Mathematics vol 114 no 10 pp 407ndash419 2017

[27] D E Goldberg Genetic Algorithm in Search Optimizationand Machine Learning Addison-Wesley Publishing BostonMA USA 1989

[28] D E Goldberg ldquoGenetic and evolutionary algorithms come ofagerdquo Communications of the ACM vol 37 no 3 pp 113ndash1191994

[29] F Glover ldquoTabu search-Part Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[30] F Glover ldquoTabu search-Part IIrdquoORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[31] F Glover ldquoParametric tabu-search for mixed integer pro-gramsrdquo Computers amp Operations Research vol 33 no 9pp 2449ndash2494 2006

[32] A Ghosh and S Banerjee ldquoControl of switched-mode boostconverter by using classical and optimized type controllersrdquoCEAI vol 17 no 4 pp 114ndash125 2015

[33] A Ghosh S Banerjee M K Sarkar and P Dutta ldquoDesign andimplementation of type-II and type-III controller for DC-DCswitched-mode boost converter by using K-factor approachand optimisation techniquesrdquo IET Power Electronics vol 9no 5 pp 938ndash950 2016

Journal of Control Science and Engineering 13

the voltage output at 24V compared to GA and TS as well ascontrolling voltage at 20V

+e proposed control algorithm though applied for theboost converter of 20V and 24V using PSO exhibits the bestperformance in the aspect of system response and stability+e experimental results agree with [32 33] although

Voltage output Vref output

Current output

Current input

Figure 26 Response of voltage and current using a PI controllerwith TS search

Voltage output

Current output

Current input

Vref output

Figure 27 Result of voltage response and current using a PIcontroller with PSO search

Voltage output

Current output

Vref output

Current input

Figure 25 Result of voltage response and current using a PIcontroller with GA search

Applied load Released load

Voltage output

Current output

Current input

Figure 28 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 29 Result of maintaining voltage stability and current whilechanging load using a PI controller with TS search

Applied load Released load

Voltage output

Current output

Current input

Figure 30 Result of maintaining voltage stability and current whilechanging load using a PI controller with PSO search

Table 4 System response by the PI controller at 24V

EntrySystem responses by PI

T r (ms) M p () T s (ms) e ss ()GA 7 000 16 000TS 72 000 15 000PSO 72 000 10 000

Journal of Control Science and Engineering 11

applied for the four-phase interleaved boost converterHowever there are no overshoot and time to steady statereaches faster than their study

8 Conclusion

In this paper the four-phase interleaved boost convertercircuit is controlled by the PI controller In order to tune thegains of the PI controller the PSO GA and TS and met-aheuristic optimizations are applied In testing the controlsystem the response of the four-phase interleaved boostconverter obtained by PSO has the rise time and setting timefaster than the GA and TS methods Additionally it is foundthat the tracing and controlling response result of outputvoltage is extremely satisfactory when load condition isconstant and while changing the load It can be concludedthat the four-phase interleaved boost converter circuit usingthe PI controller tuned gains by PSO is greatly effective forregulating the voltage in a real system

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors would like to acknowledge Department ofElectrical Engineering and Faculty of EngineeringPathumwan Institute of Technology for the financial sup-port and facilities +ey would also like to show theirgratitude to Assoc Prof Dr Decha Pungdaorueng and AsstProf Dr Wachirapond Permpoonsinsup who gave veryuseful advices and suggestions for completing this research

References

[1] C Jain and B Singh ldquoAn adjustable DC link voltage-basedcontrol of multifunctional grid interfaced solar PV systemrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 2 pp 651ndash660 2017

[2] Y A Zuniga-Ventura D Langarica-Cordoba J Leyva-Ramos L H Diaz-Saldierna and V M Ramirez-RiveraldquoAdaptive backstepping control for a fuel cellboost convertersystemrdquo IEEE Journal of Emerging and Selected Topics inPower Electronics vol 6 no 2 pp 686ndash695 2018

[3] P Mungporn P +ounthong S Sikkabut et al ldquoDifferentialflatness-based control of currentvoltage stabilization for asingle-phase PFC with multiphase interleaved boost con-verterrdquo in Proceedings of the European Conference on Elec-trical Engineering and Computer Science pp 124ndash130 AthensGreece November 2017

[4] A Marcos-Pastor E Vidal-Idiarte A Cid-Pastor andL Martinez-Salamero ldquoInterleaved digital power factorcorrection based on the sliding-mode approachrdquo IEEETransactions on Power Electronics vol 31 no 6 pp 4641ndash4653 2016

[5] D Apablaza and J Munoz ldquoLaboratory implementation of aboost interleaved converter for PV applicationsrdquo IEEE LatinAmerica Transactions vol 14 no 6 pp 2738ndash2743 2016

[6] F H Aghdam and M Abapour ldquoReliability and cost analysisof multistage boost converters connected to PV panelsrdquo IEEEJournal of Photovoltaics vol 6 no 4 pp 981ndash989 2016

[7] R Seyezhai and B L Mathur ldquoA comparison of three-phaseuncoupled and directly coupled interleaved boost converterfor fuel cell applicationsrdquo International Journal on ElectricalEngineering and Informatics vol 3 no 3 pp 394ndash407 2011

[8] S Banerjee A Ghosh and N Rana ldquoDesign and fabricationof closed loop two-phase interleaved boost converter withtype-III controllerrdquo in Proceedings of the IECON 2016mdash42ndAnnual Conference of the IEEE Industrial Electronics Societypp 3331ndash3336 Florence Italy October 2016

[9] C Kiree D Kumpanya S Tunyasrirut and D PuangdownreongldquoPSO-based optimal PI(D) controller design for brushless DCmotor speed control with back EMF detectionrdquo Journal ofElectrical Engineering and Technology vol 11 no 3 pp 715ndash7232016

[10] S Banerjee A Ghosh and N Rana ldquoAn improved interleavedboost converter with PSO-based optimal type-III[ controllerrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 1 pp 323ndash337 2017

[11] M Calvini M Carpita A Formentini and M MarchesonildquoPSO-based self-commissioning of electrical motor drivesrdquoIEEE Transactions on Industrial Electronics vol 62 no 2pp 768ndash776 2015

[12] S W Shneen A Z Salman Q A Jawad and H ShareefldquoAdvanced optimal by PSO-PI for DC motorrdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 165ndash175 2019

[13] M Rasheed R Omar M Sulaiman and W Abd Halim ldquoAmodified cascaded h-bridge multilevel inverter based onparticle swarm optimisation (PSO) techniquerdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 41ndash45 October 2019

[14] M Rasheed R Omar M Sulaiman and W A HalimldquoParticle swarm optimisation (PSO) algorithm with reducednumberof switches in multilevel inverter (MLI)rdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 14 no 3 pp 1114ndash1124 2019

[15] M Arun Devi K Valarmathi and R Mahendran ldquoRipplecurrent reduction in interleaved boost converter by usingadvanced PWM techniquesrdquo in Proceedings of the IEEE In-ternational Conference on Advanced Communication Controland Computing Technologies (lCACCCT) pp 115ndash119Ramanathapuram India May 2014

[16] S Kascak M Prazenica M Jarabicova and R KonarikldquoAnalysis of four-phase interleaved boost converterrdquo Trans-actions on Electrical Engineering vol 6 no 4 pp 110ndash1132017

[17] S Kascak M Prazenica M Jarabicova and R KonarikldquoFour-phase interleaved boost converter theory and appli-cationsrdquo WSEAS Transactions on Power Systems vol 13pp 272ndash282 2018

[18] S Kascak M Jarabicova and R Konarik ldquoFour phase in-terleaved boost converter-analysis and verificationrdquo ActaElectrotechnica et Informatica vol 18 no 1 pp 35ndash40 2018

[19] C W Reynolds ldquoFlocks herds and schools a distributedbehavioral modelrdquo ACM SIGGRAPH Computer Graphicsvol 21 no 4 pp 25ndash34 1987

[20] J Kennedy and R Eberhart Swarm Intelligence MorganKaufman Burlington MA USA 2001

12 Journal of Control Science and Engineering

[21] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceeding of IEEE International Conference Neural Networksvol IV pp 1942ndash1948 Perth Australia 1995

[22] K S Kumar K K Aggarwal and J Singh ldquoDesign of fuzzymodels through partical swarm optimizationrdquo in IntegratedIntelligent Systems for Engineering Design pp 43ndash62 IOSpress Amsterdam Netherlands 2006

[23] R Eberhart and Y Shi ldquoComparing inertial weights andconstriction factor in particle swarm optimizationrdquo in Pro-ceeding of Internationnal Congress on Evolutioning Compu-tation pp 84ndash88 La Jolla CA USA 2000

[24] Texas Instruments TMS320F28335 Digital Signal ControllerTexas Instruments Dallas TX USA 2007

[25] +e Math Works Inc MATLABSimulink Userrsquos Guide +eMath Works Inc Natick MA USA 1998

[26] V Viswanatha ldquoA complete mathematical modeling simu-lation and computational implementation of boost convertervia MATLABSimulinkrdquo International Journal of Pure andApplied Mathematics vol 114 no 10 pp 407ndash419 2017

[27] D E Goldberg Genetic Algorithm in Search Optimizationand Machine Learning Addison-Wesley Publishing BostonMA USA 1989

[28] D E Goldberg ldquoGenetic and evolutionary algorithms come ofagerdquo Communications of the ACM vol 37 no 3 pp 113ndash1191994

[29] F Glover ldquoTabu search-Part Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[30] F Glover ldquoTabu search-Part IIrdquoORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[31] F Glover ldquoParametric tabu-search for mixed integer pro-gramsrdquo Computers amp Operations Research vol 33 no 9pp 2449ndash2494 2006

[32] A Ghosh and S Banerjee ldquoControl of switched-mode boostconverter by using classical and optimized type controllersrdquoCEAI vol 17 no 4 pp 114ndash125 2015

[33] A Ghosh S Banerjee M K Sarkar and P Dutta ldquoDesign andimplementation of type-II and type-III controller for DC-DCswitched-mode boost converter by using K-factor approachand optimisation techniquesrdquo IET Power Electronics vol 9no 5 pp 938ndash950 2016

Journal of Control Science and Engineering 13

applied for the four-phase interleaved boost converterHowever there are no overshoot and time to steady statereaches faster than their study

8 Conclusion

In this paper the four-phase interleaved boost convertercircuit is controlled by the PI controller In order to tune thegains of the PI controller the PSO GA and TS and met-aheuristic optimizations are applied In testing the controlsystem the response of the four-phase interleaved boostconverter obtained by PSO has the rise time and setting timefaster than the GA and TS methods Additionally it is foundthat the tracing and controlling response result of outputvoltage is extremely satisfactory when load condition isconstant and while changing the load It can be concludedthat the four-phase interleaved boost converter circuit usingthe PI controller tuned gains by PSO is greatly effective forregulating the voltage in a real system

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors would like to acknowledge Department ofElectrical Engineering and Faculty of EngineeringPathumwan Institute of Technology for the financial sup-port and facilities +ey would also like to show theirgratitude to Assoc Prof Dr Decha Pungdaorueng and AsstProf Dr Wachirapond Permpoonsinsup who gave veryuseful advices and suggestions for completing this research

References

[1] C Jain and B Singh ldquoAn adjustable DC link voltage-basedcontrol of multifunctional grid interfaced solar PV systemrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 2 pp 651ndash660 2017

[2] Y A Zuniga-Ventura D Langarica-Cordoba J Leyva-Ramos L H Diaz-Saldierna and V M Ramirez-RiveraldquoAdaptive backstepping control for a fuel cellboost convertersystemrdquo IEEE Journal of Emerging and Selected Topics inPower Electronics vol 6 no 2 pp 686ndash695 2018

[3] P Mungporn P +ounthong S Sikkabut et al ldquoDifferentialflatness-based control of currentvoltage stabilization for asingle-phase PFC with multiphase interleaved boost con-verterrdquo in Proceedings of the European Conference on Elec-trical Engineering and Computer Science pp 124ndash130 AthensGreece November 2017

[4] A Marcos-Pastor E Vidal-Idiarte A Cid-Pastor andL Martinez-Salamero ldquoInterleaved digital power factorcorrection based on the sliding-mode approachrdquo IEEETransactions on Power Electronics vol 31 no 6 pp 4641ndash4653 2016

[5] D Apablaza and J Munoz ldquoLaboratory implementation of aboost interleaved converter for PV applicationsrdquo IEEE LatinAmerica Transactions vol 14 no 6 pp 2738ndash2743 2016

[6] F H Aghdam and M Abapour ldquoReliability and cost analysisof multistage boost converters connected to PV panelsrdquo IEEEJournal of Photovoltaics vol 6 no 4 pp 981ndash989 2016

[7] R Seyezhai and B L Mathur ldquoA comparison of three-phaseuncoupled and directly coupled interleaved boost converterfor fuel cell applicationsrdquo International Journal on ElectricalEngineering and Informatics vol 3 no 3 pp 394ndash407 2011

[8] S Banerjee A Ghosh and N Rana ldquoDesign and fabricationof closed loop two-phase interleaved boost converter withtype-III controllerrdquo in Proceedings of the IECON 2016mdash42ndAnnual Conference of the IEEE Industrial Electronics Societypp 3331ndash3336 Florence Italy October 2016

[9] C Kiree D Kumpanya S Tunyasrirut and D PuangdownreongldquoPSO-based optimal PI(D) controller design for brushless DCmotor speed control with back EMF detectionrdquo Journal ofElectrical Engineering and Technology vol 11 no 3 pp 715ndash7232016

[10] S Banerjee A Ghosh and N Rana ldquoAn improved interleavedboost converter with PSO-based optimal type-III[ controllerrdquoIEEE Journal of Emerging and Selected Topics in PowerElectronics vol 5 no 1 pp 323ndash337 2017

[11] M Calvini M Carpita A Formentini and M MarchesonildquoPSO-based self-commissioning of electrical motor drivesrdquoIEEE Transactions on Industrial Electronics vol 62 no 2pp 768ndash776 2015

[12] S W Shneen A Z Salman Q A Jawad and H ShareefldquoAdvanced optimal by PSO-PI for DC motorrdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 165ndash175 2019

[13] M Rasheed R Omar M Sulaiman and W Abd Halim ldquoAmodified cascaded h-bridge multilevel inverter based onparticle swarm optimisation (PSO) techniquerdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 16 no 1 pp 41ndash45 October 2019

[14] M Rasheed R Omar M Sulaiman and W A HalimldquoParticle swarm optimisation (PSO) algorithm with reducednumberof switches in multilevel inverter (MLI)rdquo IndonesianJournal of Electrical Engineering and Computer Sciencevol 14 no 3 pp 1114ndash1124 2019

[15] M Arun Devi K Valarmathi and R Mahendran ldquoRipplecurrent reduction in interleaved boost converter by usingadvanced PWM techniquesrdquo in Proceedings of the IEEE In-ternational Conference on Advanced Communication Controland Computing Technologies (lCACCCT) pp 115ndash119Ramanathapuram India May 2014

[16] S Kascak M Prazenica M Jarabicova and R KonarikldquoAnalysis of four-phase interleaved boost converterrdquo Trans-actions on Electrical Engineering vol 6 no 4 pp 110ndash1132017

[17] S Kascak M Prazenica M Jarabicova and R KonarikldquoFour-phase interleaved boost converter theory and appli-cationsrdquo WSEAS Transactions on Power Systems vol 13pp 272ndash282 2018

[18] S Kascak M Jarabicova and R Konarik ldquoFour phase in-terleaved boost converter-analysis and verificationrdquo ActaElectrotechnica et Informatica vol 18 no 1 pp 35ndash40 2018

[19] C W Reynolds ldquoFlocks herds and schools a distributedbehavioral modelrdquo ACM SIGGRAPH Computer Graphicsvol 21 no 4 pp 25ndash34 1987

[20] J Kennedy and R Eberhart Swarm Intelligence MorganKaufman Burlington MA USA 2001

12 Journal of Control Science and Engineering

[21] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceeding of IEEE International Conference Neural Networksvol IV pp 1942ndash1948 Perth Australia 1995

[22] K S Kumar K K Aggarwal and J Singh ldquoDesign of fuzzymodels through partical swarm optimizationrdquo in IntegratedIntelligent Systems for Engineering Design pp 43ndash62 IOSpress Amsterdam Netherlands 2006

[23] R Eberhart and Y Shi ldquoComparing inertial weights andconstriction factor in particle swarm optimizationrdquo in Pro-ceeding of Internationnal Congress on Evolutioning Compu-tation pp 84ndash88 La Jolla CA USA 2000

[24] Texas Instruments TMS320F28335 Digital Signal ControllerTexas Instruments Dallas TX USA 2007

[25] +e Math Works Inc MATLABSimulink Userrsquos Guide +eMath Works Inc Natick MA USA 1998

[26] V Viswanatha ldquoA complete mathematical modeling simu-lation and computational implementation of boost convertervia MATLABSimulinkrdquo International Journal of Pure andApplied Mathematics vol 114 no 10 pp 407ndash419 2017

[27] D E Goldberg Genetic Algorithm in Search Optimizationand Machine Learning Addison-Wesley Publishing BostonMA USA 1989

[28] D E Goldberg ldquoGenetic and evolutionary algorithms come ofagerdquo Communications of the ACM vol 37 no 3 pp 113ndash1191994

[29] F Glover ldquoTabu search-Part Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[30] F Glover ldquoTabu search-Part IIrdquoORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[31] F Glover ldquoParametric tabu-search for mixed integer pro-gramsrdquo Computers amp Operations Research vol 33 no 9pp 2449ndash2494 2006

[32] A Ghosh and S Banerjee ldquoControl of switched-mode boostconverter by using classical and optimized type controllersrdquoCEAI vol 17 no 4 pp 114ndash125 2015

[33] A Ghosh S Banerjee M K Sarkar and P Dutta ldquoDesign andimplementation of type-II and type-III controller for DC-DCswitched-mode boost converter by using K-factor approachand optimisation techniquesrdquo IET Power Electronics vol 9no 5 pp 938ndash950 2016

Journal of Control Science and Engineering 13

[21] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceeding of IEEE International Conference Neural Networksvol IV pp 1942ndash1948 Perth Australia 1995

[22] K S Kumar K K Aggarwal and J Singh ldquoDesign of fuzzymodels through partical swarm optimizationrdquo in IntegratedIntelligent Systems for Engineering Design pp 43ndash62 IOSpress Amsterdam Netherlands 2006

[23] R Eberhart and Y Shi ldquoComparing inertial weights andconstriction factor in particle swarm optimizationrdquo in Pro-ceeding of Internationnal Congress on Evolutioning Compu-tation pp 84ndash88 La Jolla CA USA 2000

[24] Texas Instruments TMS320F28335 Digital Signal ControllerTexas Instruments Dallas TX USA 2007

[25] +e Math Works Inc MATLABSimulink Userrsquos Guide +eMath Works Inc Natick MA USA 1998

[26] V Viswanatha ldquoA complete mathematical modeling simu-lation and computational implementation of boost convertervia MATLABSimulinkrdquo International Journal of Pure andApplied Mathematics vol 114 no 10 pp 407ndash419 2017

[27] D E Goldberg Genetic Algorithm in Search Optimizationand Machine Learning Addison-Wesley Publishing BostonMA USA 1989

[28] D E Goldberg ldquoGenetic and evolutionary algorithms come ofagerdquo Communications of the ACM vol 37 no 3 pp 113ndash1191994

[29] F Glover ldquoTabu search-Part Irdquo ORSA Journal on Computingvol 1 no 3 pp 190ndash206 1989

[30] F Glover ldquoTabu search-Part IIrdquoORSA Journal on Computingvol 2 no 1 pp 4ndash32 1990

[31] F Glover ldquoParametric tabu-search for mixed integer pro-gramsrdquo Computers amp Operations Research vol 33 no 9pp 2449ndash2494 2006

[32] A Ghosh and S Banerjee ldquoControl of switched-mode boostconverter by using classical and optimized type controllersrdquoCEAI vol 17 no 4 pp 114ndash125 2015

[33] A Ghosh S Banerjee M K Sarkar and P Dutta ldquoDesign andimplementation of type-II and type-III controller for DC-DCswitched-mode boost converter by using K-factor approachand optimisation techniquesrdquo IET Power Electronics vol 9no 5 pp 938ndash950 2016

Journal of Control Science and Engineering 13