design and implementation of closed loop control … · design and implementation of closed loop...

1 Advanced Engineering and Applied Sciences: An International Journal 2016; 6(1): 1-7

ISSN 2320–3927

Original Article

Design and Implementation of Closed Loop Control System for Buck

Converter Using Different Techniques

Magdy Saoudia, Ahmed El-Sayedb, Hamid Metwallya

aElectrical Power and Machines Dept., Faculty of Engineering, Zagazig university, 44519 Zagazig, Egypt b Engineering Management, Zagazig university, Zagazig, Egypt

Received 12 December 2015; accepted 28 January 2016

Abstract A DC-DC buck converter is employed to develop a regulated voltage or current, derived from an unregulated power supply, or a battery.

Instances of these applications include battery chargers, electronic air purifiers, emergency exit signs, distributed power systems, and

renewable energy solar cell. This paper presents different design procedures of different control techniques for voltage mode controlled

(VMC) DC–DC switching buck converter. Integral (I) controller, proportional plus integral (PI) controller, fuzzy logic controller (FLC)

and tuned fuzzy logic controller (TFLC) are used for the design and simulation of a buck converter using MATLAB/Simulink, Proteus

and micro programs. Comparative study results show that TFLC is superior compared with the other control strategies, because of the

fast transient response, and good disturbance rejection under various variations of the operating conditions. Hence, it accomplishes the

most tightly output voltage regulation. Observational results for integral and proportional plus integral controllers are shown and talked

about in this paper.

© 2016 Universal Research Publications. All rights reserved

Key words: MATLAB, Simulink, Proteus, Mikroc, VMC, I, PI, FLC, TFLC, Buck converter.

I. INTRODUCTION

Comparing between different techniques for the design and

implementation of closed loop control systems for buck

converters is carried away. Controllers used for this

comparison are integral, PI controllers and artificial

intelligence are represented in fuzzy logic controller and

tuned fuzzy logic controller. Design and implementation of

a control system demand the role of effective techniques

that offer simple and pragmatic solutions in society to meet

the performance requirements despite the system

disturbances and uncertainties [1]. The occurrence of

nonlinear phenomena in buck converters makes their

analysis and control difficult [2]. Classical linear

techniques have stability limitations around the operating

points [1] – [3]. Hence digital and nonlinear stabilizing

control methods must be applied to ensure large-signal

stability [3]. Fuzzy control has also been employed to

control buck converters because of its simplicity, simplicity

of design and simplicity of implementation [4], [5] – [10].

Fuzzy controllers are easily suited to nonlinear time-variant

systems and do not require an accurate mathematical model

for the system being controlled. They are usually designed

based on expert knowledge of the converters [5]. In this

survey, the design procedures of integral, proportional plus

integral, fuzzy logic and tuned fuzzy logic controller are

presented. The buck converter topologies with parameters

are given in Table 1. These parameters have been obtained

TABLE 1: THE PROPOSED BUCK CONVERTER PARAMETERS

Variable Parameter Value

Vg(V) Source input voltage 15

Fs(KHz) Switching frequency 2

L(𝑚H) Magnetizing inductance 10

C(𝜇F) Output filter capacitance 100

RC(𝑚Ω) Equivalent series resistance

(ESR) of capacitor 5

R (Ω) Load resistance 1

through trial and error that verify equation vout/vg=o. 5

when the value of duty Cycle is 50% to illustrate the result

of each controller type on this converter performance. The

proposed controller design procedures can be generally

applied to any buck converter topology for stability

enhancement, and output voltage regulation over a wide

range of operating conditions. The effect of the on-line

changes of reference voltage on the output voltage

regulation is discussed. In case of integral and proportional

plus integral controllers, values of integral gain (Ki) for

integral controller and proportional and integral gains (Kp

& Ki) for PI controller are determined from MATLAB.

Available online at http://www.urpjournals.com

Advanced Engineering and Applied Sciences: An International Journal

Universal Research Publications. All rights reserved

http://www.urpjournals.com/


Then use these gains in mikroc and Proteus programs for

buck converter design. In case of fuzzy logic controller

determines the operating condition from the measured

values and takes the appropriate control actions using the

rule base created from the expert knowledge. In case of

tunes fuzzy logic controller uses a PID controller for tuning

the output of FLC to improve output voltage configuration.

II. DISCUSSION

A. Mathematical Model of Buck Converter

The buck converter has an output voltage that is lower than

the input voltage. Fig. 1 shows the buck converter with

voltage controller and here it is assumed that all

components are ideal and the load consists of a resistor

with resistance R. The converter has an output low-pass

filter consisting of an inductor with inductance L and

capacitor with capacitance C. While the transistor is on, the

inductor current, iL (t), increases since the input voltage is

higher than the output voltage when the transistor is turned

off, the diode must start to conduct since the inductor

current cannot stop instantly. The voltage across the diode

is zero when it is conducting and the inductor current will

decrease. Fig. 2 shows the waveform of the control signal.

The converter is usually designed with low magnitude of

ripples in the output voltage. For RL circuit, the current

increases and decreases exponentially as shown in Fig. 3.

The voltage across the diode is equal to the input voltage or

equal to zero. The output filter of the converter filters this

voltage waveform and the magnitude of the ripple in the

output voltage depends on the filter design. If the inductor

current becomes zero before the transistor is turned on, it

will stay at zero until the transistor is turned on since the

diode only can convey in one way. If the converter is

controlled so that the inductor current is zero during some

portion of the switching period, it is supposed to be

operating in discontinuous conduction mode. Otherwise, it

operates in continuous conduction mode.

The switching period, Ts of the converter is determined by

figure, the switching period is held constant. The average

output voltage is controlled by changing the width of the

pulses. In Fig. 2, the falling edge is controlled, i.e. when the

transistor should turn off. The duty cycle, d(t) is a real

value in the interval 0 to 1 and it is equal to the ratio of the

width of a pulse ton to the switching period Ts. The duty

cycle is actually a discrete-time signal.

Fig. 1. The buck converter with a voltage controller

Fig. 2. The waveform of the control signal

Fig. 3. The waveform of the inductor current

Fig. 4. The circuit of the buck converter during ton

Fig. 5. The circuit of the buck converter during toff

In this section, a linear time-invariant model of the buck

converter is derived by means of state-space averaging

during mosfet on as in Fig. 4 and during mosfet off as in

Fig. 5. The converter can be described as switching

between different time-invariant systems and the state-

space description of each one of these systems is first

derived. These state-space descriptions are used as a

starting point in the method of state-space averaging. This

method is applied to the buck converter and the result is a

linear time-invariant model in state-space description.

Eventually, several transfer functions are drawn out from

this model until reaching to the control-to-output transfer

function is held by:

𝐺(𝑠) =�̂�𝑜(𝑠)

�̂�(𝑠)=

RVg(1+sRcC)

R+s(L+RRcC)+s2(R+Rc)LC (1)

B. Design of Buck Converter Using Integral (I) Controller

Integral (I) Controller is a special case of PID controller,

but with no use of proportional (P) and derivative (D) parts

of the error. So control signal U for integral controller is

presented below:

U = Ki ∫ ∆ dt (2)


Where Ki is integral gain, Δ is the error or deviation of

actual measured value (PV) from the set point (SP).

Δ=SP-PV (3)

The integral (I) controller transfer function C(s) is given

below

C(s) =Ki/S (4)

Fortunately, the basic approaches for optimal feedback

compensator design could be accomplished quickly and

easily in the MATLAB environment. The “Siso tool (‘bode

and root locus’)” command in the control system toolbox

provides a graphical user interface (GUI) so that the closed-

loop frequency response can be interactively changed by

online modifying of the pole-zero pattern of the feedback

controller as shown in Fig. 6. When the desired frequency

is obtained, users are also presented the corresponding

transfer function of the feedback controller in the same

interface

Fig. 6. Root locus and open loop bode plots of buck

converter

Fig. 7. Step response of buck converter

To determine integral gain constants, position of root locus

for buck converter is modified online as shown in Fig. 6 to

get Ki=36 at minimum settling time=0. 0852 Sec and rise

time=0. 0352 Sec as shown in Fig. 7.

Then mikroC software is used for programming the

microcontroller that controls the mosfet of the buck

converter based on previous Ki value. And so the

programmed microcontroller controls constructed buck

converter in Proteus software as indicated in Fig. 8.

Fig. 8. Closed loop control of buck converter using

integral (I) controller

The simulation result of the system of Fig. 8 is recorded in

Fig. 9.

Fig. 9. Output voltage (vout) & Reference voltage (vref)

As clearly shown on Fig. 9, the following results are

obtained for the buck converter controlled by the integral

controller:

The output voltage follows the reference voltage.

Rise time equals 0.05 Sec.

Steady state error equals (+⁄- 0.1) v.

100

105

1010

-360

-180

0

P.M.: 68.1 deg

Freq: 40.1 rad/sec

Frequency (rad/sec)

-500

0

500

G.M.: 47.3 dB

Freq: 1e+003 rad/sec

Stable loop

Open-Loop Bode Editor

-10000 -5000 0

-60

-40

-20

0

20

40

Root Locus Editor

Real Axis

Step Response

Time (sec)

Am

plit

ude

0 0.02 0.04 0.06 0.08 0.1 0.120

0.5

1

1.5

2

2.5

3

D1DIODE

L1

10m

C1100u

R25m

R31

vout

vg

vin

Q2(D)

RA

0/A

N0

2

RA

1/A

N1

3

RA

2/A

N2

/VR

EF

-/C

VR

EF

4

RA

4/T

0C

KI/C

1O

UT

6

RA

5/A

N4

/SS

/C2

OU

T7

RE

0/A

N5

/RD

8

RE

1/A

N6/W

R9

RE

2/A

N7

/CS

10

OS

C1

/CL

KIN

13

OS

C2

/CL

KO

UT

14

RC

1/T

1O

SI/C

CP

216

RC

2/C

CP

117

RC

3/S

CK

/SC

L18

RD

0/P

SP

019

RD

1/P

SP

120

RB

7/P

GD

40

RB

6/P

GC

39

RB

538

RB

437

RB

3/P

GM

36

RB

235

RB

134

RB

0/IN

T33

RD

7/P

SP

730

RD

6/P

SP

629

RD

5/P

SP

528

RD

4/P

SP

427

RD

3/P

SP

322

RD

2/P

SP

221

RC

7/R

X/D

T26

RC

6/T

X/C

K25

RC

5/S

DO

24

RC

4/S

DI/S

DA

23

RA

3/A

N3

/VR

EF

+5

RC

0/T

1O

SO

/T1

CK

I15

MC

LR

/Vp

p/T

HV

1

MICROPIC16F877A

MICRO(I CONTROL)(MCLR/Vpp/THV)

R43k

R52k

ou

t o

f m

icro

feed back (vout* 2/(2+3))

reference value

source of micro

feedback

MICRO(I CONTROL)(RA0/AN0)

K

K1OP : GAIN

vref

Q2

IRF540

K

K2

OP : GAIN

D2DIODE

0 1 2 3 4 5 6

x 104

6

7

8

9

10

11

Time (sec)

vou

t&v

ref

(v)

Rise time= 𝟑𝟓 𝒎𝒔𝒆𝒄

Settling time= 𝟖𝟓 𝒎𝒔𝒆𝒄


C. Design of Buck Converter Using Proportional And

Integral (PI) Controller

PI Controller is a special case of PID controller, but with no

use of derivative (D) part of the error. So control signal U

for PI controller is given below:

U = Kp + Ki ∫ ∆ dt (5)

Where Kp, Ki is proportional, integral gain, Δ is the error or

deviation of actual measured value (PV) from the set point

(SP)

Δ=SP-PV (6)

The PI controller transfer function C(s) is given below

C (s) =Kp+Ki/S (7)

As carried out with integral controller, the MATLAP is

used to calculate Kp and Ki of the PI controller.

General approach to PI tuning:

1. Firstly set Ki = zero.

2. Increase KP until desired response has been obtained

3. Add integral gain and modify Ki until the removed

steady state error.

Fig. 10. Root locus and open loop bode plots of buck

converter

To determine PI gain constants, position of root locus for

buck converter is modified online as shown in Fig. 10 to

get Kp & Ki equal to 4&415 at minimum settling time=0.

00746 Sec and rise time=0. 00425 Sec as shown in Fig. 11.

Fig. 11. Step response of buck converter

Then mikroC software is used for programming the

microcontroller to control the mosfet of the buck converter

based on previous Kp & Ki values. And so the programmed

microcontroller controls constructed buck converter circuit

in Proteus software as indicated in Fig. 12.

Fig. 12. Closed loop control of buck converter using PI

controller

The simulation results of the circuit shown in Fig. 12 are

shown in Fig. 13.

Fig. 13. Output voltage (vout) & reference voltage (vref)

100

105

-180

-135

-90

-45

P.M.: 87.5 deg

Freq: 522 rad/sec

Frequency (rad/sec)

-150

-100

-50

0

50

G.M.: Inf

Freq: NaN

Stable loop

Open-Loop Bode Editor

-10000 -5000 0

-8

-6

-4

-2

0

2

4

6

8

Real Axis

Root Locus Editor

Step Response

Time (sec)

Am

plit

ude

0 0.002 0.004 0.006 0.008 0.01 0.0120

0.5

1

1.5

2

2.5

RA

0/A

N0

2

RA

1/A

N1

3

RA

2/A

N2

/VR

EF

-/C

VR

EF

4

RA

4/T

0C

KI/C

1O

UT

6

RA

5/A

N4

/SS

/C2

OU

T7

RE

0/A

N5

/RD

8

RE

1/A

N6/

WR

9

RE

2/A

N7

/CS

10

OS

C1

/CL

KIN

13

OS

C2

/CL

KO

UT

14

RC

1/T

1O

SI/C

CP

216

RC

2/C

CP

117

RC

3/S

CK

/SC

L18

RD

0/P

SP

019

RD

1/P

SP

120

RB

7/P

GD

40R

B6

/PG

C39

RB

538

RB

437

RB

3/P

GM

36R

B2

35R

B1

34R

B0

/INT

33

RD

7/P

SP

730

RD

6/P

SP

629

RD

5/P

SP

528

RD

4/P

SP

427

RD

3/P

SP

322

RD

2/P

SP

221

RC

7/R

X/D

T26

RC

6/T

X/C

K25

RC

5/S

DO

24R

C4

/SD

I/SD

A23

RA

3/A

N3

/VR

EF

+5

RC

0/T

1O

SO

/T1

CK

I15

MC

LR

/Vp

p/T

HV

1

U1PIC16F877A

R1

10k

R1

(2)

Q2(15v)

R21

C1100u

R35m

L110m

D1DIODE

vo

U1(RA1/AN1)

R52k

R63k

ADC1(VIN)

K

K1

OP : GAIN

vref

VIN

VR

EF

+

VR

EF

-

CL

K

HO

LD

OE

D0

D1

D2

D3

D4

D5

D6

D7

ADC1ADC_8

ADC1(VREF+)

ou

tpu

t p

wm

fro

m m

icro

to

igp

t

feed

ba

ck fro

m b

uck(2

/(2+

3))=

0.4

refe

ren

ce v

alu

e

switch for reset micro to initial valus

Q2IRF540

K

K2

OP : GAIN

R2

(2)

D2 DIODE

0 0.5 1 1.5 2 2.5 3 3.5 44

x 104

4

5

6

7

8

Time (sec)

Vout&

Vre

f

Error= + −⁄ 0.05

V 𝐯𝐫𝐞𝐟

𝐯𝐨𝐮𝐭


As shown on Fig. 13, the PI controlled buck converter

exhibits the following results:

The output voltage follows the reference voltage.



D. Design of Buck Converter Using Fuzzy Logic Controller

(FLC)

Fuzzy logic, proposed by Lofty Zadeh in 1965, emerged as

a tool to deal with uncertain, imprecise, or qualitative

decision making control problems. Controllers that

combine intelligent and conventional techniques are

commonly used in the intelligent control of complex

dynamic systems. Therefore, embedded fuzzy controllers

automate what has traditionally been a human control

activity.

So Fuzzy logic control is a control algorithm based on a

linguistic control strategy, which is derived from expert

knowledge into an automatic control strategy. Fuzzy logic

control doesn’t need any difficult mathematical calculation

like the other control system. So it is one of the available

answers today for a broad class of challenging controls.

FLC controller has three principal components:

1) Fuzzifier: A fuzzyfication interface which converts input

data into suitable linguistic values.

2) Rule Base and Data Base: Both are known as knowledge

base which consists of a data base with the necessary

linguistic definition and control rule set

3) Decision Making: A decision making logic, which is

simulating a human.

To design fuzzy controller, fuzzy inputs shape and fuzzy

output shape must be constructed, then rules that control

the relation between these input and output of fuzzy

controller must be determined to make the surface of fuzzy

controller change as shown in Fig. 14. In this figure, input1

reflects the negative error, which represents the higher

value of the required output and input2 represents the

positive error, which represents less than the desired output,

while the output1 represents the value of duty Cycle that

control in the firing of the mosfet.

Fig. 14. Change surface of fuzzy controller

Then a closed loop buck converter using a fuzzy logic

controller is constructed in MATLAP/Simulink as shown in

Fig. 15.

Fig. 15. Closed loop control for buck converter using an

FLC

Finally, a simulation program for the circuit in Fig. 15 is

run to get the shape of output voltage w.r.t reference

voltage as shown in Fig. 16.


As shown on Fig. 16, the fuzzy controlled buck converter

exhibits the following answers:

The Output voltage follows the reference voltage.



v+

-

vout

vg=15 v

1/0.4reference gain

Discrete,

Ts = 1e-006 s.

powergui

l=10 mH

fuzzy inputs

0.4feedback gain

error value

carrier

ts=500 micro sec

Vref

Vout curve

Rload=1 ohm

>=Relational

OperatorRc=5m ohm

g

D

S

Mosfet

Fuzzy Logic

Controller

Diode

C=100 uF

0 0.05 0.1 0.15 0.26

7

8

9

10

11

Vout&

Vre

f

Time (sec)

Error= + −⁄ 0.

05 V

𝐯𝐫𝐞𝐟

𝐯𝐨𝐮𝐭

Referen

ce Outpu

t


E. Design of Buck Converter Using Tuned Fuzzy Logic

Controller (FLC)

A PID controller is used to tune the previously

mentioned FLC for eliminating the output steady state error

and improving the output voltage configuration.

The proportional, integral, and derivative controller

gains are estimated by trail & error procedure, based on the

mentioned design concepts in Control tutorials for Matlab,

PID tutorial. For this proposed buck controller, the

recommended proportional gain constant; KP = 10, and the

integral gain constant; Ki =5, and the derivative gain

constant; KD =5. So this PID controller could be

represented as in Fig. 17.

Fig. 17. Closed loop control for buck converter using a

TFLC

The simulation results of the circuit shown in Fig. 17 are

presented in Fig. 18.


From Fig. 18, the fuzzy controlled buck converter

exhibits the following results:

The Output voltage follows the reference voltage.



III. EXPERIMENTAL VERIFICATION

To verify the concept, the buck converter with the

parameters given in table 1 has been constructed as

pictured in Fig. 19.

Fig. 19. designed buck converter circuit

The connection diagram of the test rig is shown in Fig.

20.Results in the case of integral and PI controllers are

obtained using oscilloscope as shown in Fig. 20 based on

switching frequency equals 2 kHz as shown in Fig. 21.

Fig.20. Buck converter circuit connected to an

oscilloscope

Fig. 21. 2kHz switching frequency

A. Results of Buck Converter Using Integral (I) Controller

After programming of microcontroller as integral (I)

controller, we get the following results:

v+-

vout

vg=15 v

-K-

reference gain

Discrete,Ts = 1e-006 s.

powergui

l=10 mH

fuzzy inputs

0.4

feedback gain

error value

carrier

ts=500 micro sec

Vref (3:4)

Vout curve

Vout & Vref

>=Relational

Operator

Rc=5m ohm

R=1 ohm

PID

PID FOR TUNNING FUZZY

g

DS

Mosfet

Fuzzy Logic

Controller

Diode

C=100 uF

0 0.05 0.1 0.15 0.26

7

8

9

10

11

Vo

ut&

Vref

(v)

time (sec)

𝐯𝐫𝐞𝐟

𝐯𝐨𝐮𝐭

Error= + −⁄ 0.01

V Reference

Output

Fs = 2 KHz


Fig. 22. Output voltage & Reference voltage

Fig. 23. Output voltage rise time

Fig. 22 shows that output voltage follows the reference

and Fig. 23 shows that rise time equals 0.024 Sec.

B. Results of Buck Converter Using Proportional And

Integral (PI) Controller

After programming of microcontroller as PI controller,

we obtain the following effects:

Fig. 24. Output voltage & Reference voltage

Fig. 25. Output voltage rise time

Fig. 24 shows that output voltage follows the reference

and Fig. 25 shows that rise time equals 0.01 Sec. So, rise

time in case of PI controller is improved by comparison to

the integral controller case.

IV. CONCLUSION

In this paper, four control schemes have been proposed

for DC-DC buck converter output voltage control. Design

procedures of FLC, TFLC, I and PI controllers have been

discussed. A comparative survey of the output voltage

regulation and rise time are introduced as shown in Table 2.

TABLE 2: RISE TIME AND STEADY STATE ERROR OF

DIFFERENT CONTROLLERS

Controller

Type Rise time (Sec)

Steady state

error (v)

Integral (I) Controller

0.024 +⁄- 0.1

Proportional integral (PI)

controller 0.01 +⁄- 0.05

Fuzzy logic

Controller (FLC) 0.007 +⁄- 0.05

Tuned Fuzzy logic Controller (TFLC)

0.007 +⁄- 0.01

Simulation results show that the TLFC causes an output

steady state error equals (+⁄- 0.01 v) and rise time equals

0.007 Sec. Then TFLC has smallest output voltage rise

time and minimum output voltage oscillations. So TFLC

has the best performance compared to other controllers as

shown in Table 2.

ACKNOWLEDGEMENT

The author would like to thank Eng. Mostafa Hasneen

and Mohamed Fawzy, for the support. The author would

like to thank them for the help and knowledge that they

have given to him.

REFERENCE

1) Eker, I. and Torun, Y. (2006), “Fuzzy logic control

to be conventional method,” Energy Conversion and

Management, Vol. 47 (4), pp. 377-394.

2) Guesmi, K., Essounbouli, N. and Hamzaoui, A.

(2008) “Systematic design approach of fuzzy PID

stabilizer for DC–DC converters,” Energy

Conversion and Management, Vol. 49 (10), pp.

2880–2889.

3) Khaligh, A. and Emadi, A. (2007), “Suitability of

the pulse adjustment technique to control single

DC/DC choppers feeding vehicular constant power

loads in parallel with conventional loads,”

International journal Electric and Hybrid Vehicles,

Vol. 1, pp. 20-45.

4) Gao, D., Jin, Z. and Lu, Q. (2008) “Energy

management strategy based on fuzzy logic for a fuel

cell hybrid bus, Journal of Power Sources“.

5) Guo, L., Hung, J. Y. and Nelms, R. M. (2009),

“Evaluation of DSP-Based PID and Fuzzy

Controllers for DC–DC Converters,” IEEE Trans.

On Industrial Electronics, Vol. 185 (1), pp. 311-

317.

6) Samosir, A. S. and Yatim, A. M. (2010), “Dynamic

evolution control for synchronous buck DC–DC

converter: Theory, model and

simulation,”Simulation Modeling Practice and

Theory, Vol. 18 (5), pp. 663-676.

7) Bouchafaa, F., Hamzaoui, I. and Hadjammar, A.

(2011), “Fuzzy Logic Control for the tracking of

maximum power point of a PV system,”Energy

Procedia, Vol. 6, pp. 633-642.

8) Cheng, C. (2011) “Design of output filter for

inverters using fuzzy logic,” Expert Systems with

Applications, Vol. 38 (7), pp. 8639-8647.

9) Dereli, T., Bayasoglu, A., Altun, K., Durmusoglu,

A. and Türksen, I. B. (2011), “Industrial

applications of type-2 fuzzy sets and systems: A

concise review,” Computers in Industry, Vol. 62 (2),

pp. 125-137.

10) Messai, A., Mellit, A., Guessoum, A. and Kalogirou,

S. A. (2011), “Maximum power point tracking using

a GA optimized fuzzy logic controller and its FPGA

implementation,” Solar Energy, Vol. 85 (2), pp.

265-277.

Source of support: Nil; Conflict of interest: None declared

design and implementation of closed loop control … · design and implementation of closed loop...

Documents