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CHAPTER 6

CURRENT REGULATED PWM SCHEME BASED FOUR-

SWITCH THREE-PHASE BRUSHLESS DC MOTOR DRIVE

6.1 INTRODUCTION

Permanent magnet motors with trapezoidal back EMF and

sinusoidal back EMF have several advantages over other motor types

(Hanselman et al 1994). Most notably, (compared to dc motors) they are

lower maintenance due to the elimination of the mechanical commutator and

they have a high-power density which makes them ideal for high-torque-to

weight ratio applications (Miller 1989). The permanent magnet brushless dc

(PMBLDC) motor is gaining popularity being used in computer, aerospace,

military, automotive, industrial and household products because of its high

torque, compactness, and high efficiency (Pillay et al 1989).

A conventional BLDC motor drive is generally implemented via a

six-switch, three-phase inverter and three Hall-effect position sensors that

provide six commutation points for each electrical cycle (Krishnan 1985).

Cost minimization is the key factor in an especially fractional horse-power

BLDC motor drive for home applications. Cost reduction of BLDC motor

drive is accomplished by two approaches: the topological approach and the

control approach. In topology approach, minimum number of switches and

eliminating the mechanical sensors are the options while the control approach

has choices in terms of complexity in control (Dhaouadi et al 1991), nature of

the control, implementation platform etc. In the control approach, using high

performance processors, algorithms are designed and implemented in

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conjunction with a reduced component inverter to produce the desired torque

characteristics (Krishnan et al 2001). Therefore, effective algorithms should

be designed for the desired performance.

Recently, a four-switch, three-phase inverter (FSTPI) topology has

been developed and used for a three-phase BLDC motor drive (De Rossiter

Correa et al 2006). Reduction in the number of power switches, dc power

supplies, switching driver circuits, losses and total price are the main features

of this topology (Lee et al 2003). It results in the possibility of the four-switch

configuration instead of the six switches. Compared with the four-switch

converter for the induction motor, it is identical for the topology point of

view. However, in the four-switch converter, the generation conducting

current profiles is inherently difficult due of 120 to its limited voltage

vectors. This problem is well known as “asymmetric voltage PWM.” It means

that conventional PWM schemes for the four-switch induction motor drive

cannot be directly used for the BLDC motor drive. Therefore, in order to use

the four-switch converter topology for the three-phase BLDC motor drive, a

modified control scheme should be developed. A complete model of the

PMBLDC motor drive with its performance in closed loop has been presented

(Varatharaju et al 2011). The discussions have been a readable text on the

operation, modeling, and control of BLDC motor for graduate students

studying electric drives and control as well as practicing engineers in

industries.

The solutions can be obtained from a modification of the

conventional voltage controlled PWM strategies, such as the space vector

PWM. However, it naturally requires lots of equations for the transformation

of voltage and current vectors, and a–b–c frames. As a result, the current

control such as block becomes much more complicated. Moreover, in order to

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handle the complicated calculations in one sampling period, a high-speed

digital processor is also necessary, which increases the manufacturing cost.

Therefore, for the low cost BLDC motor applications, voltage vector PWM

schemes cannot be regarded as a good solution for cost effective purpose.

Modeling and simulation of electromechanical systems with BLDC drives are

essential steps at the design stage of such systems.

The fundamental operation of FSTP inverter fed BLDC motor drive

has been analyzed by simulation. The developed the nonlinear simulation

model of the BLDC motors drive system is used for proportional-integral (PI)

control. The simulated results in terms of electromagnetic torque and rotor

speed are given.

6.2 DESCRIPTION OF PMBLDCM DRIVE

Figure 6.1 describes the basic building blocks of the PMBLDC

motor drive. The drive consists of speed controller, reference current

generator, pulse width modulation (PWM) current controller, position sensor,

the motor and a IGBT based voltage source inverter (VSI). The speed of the

motor is compared with its reference value and the speed error is processed in

PI speed controller. The output of this controller is considered as the reference

torque. A limit is put on the speed controller output depending on permissible

maximum winding currents. The reference current generator block generates

the three phase reference currents (ia , ib , ic ) using the limited peak current

(Qiang Han et al 2007).

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PM

BLDC

Motor

Four switch

Three Phase

VSI

PWM

Current

Controller

Reference

Current

Generator

Speed

controller

Limiter

Actual

Speed

r

dcV

aI

bI

*

aI

*

bI

*T

Sensors

Position

ref e

r

Figure 6.1 PI-Speed Controller

The PI controller is widely used in industry due to its ease in design

and simple structure. The rotor speed r(n) is compared with the reference

speed r(n) and the resulting error is estimated at the nth sampling instant as:

e r r(n) (n) * (n) (6.1)

The new value of torque reference is given by

P e e 1 eT(n) T(n 1) K (n) (n 1) K (n) (6.2)

Where, ‘ e(n 1)’ is the speed error of previous interval, and ‘ e(n)’ is the

speed error of the working interval. KP and KI are the gains of proportional

and integral controllers respectively. By using Ziegler Nichols method the KP

and KI values are determined.

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6.2.1 Reference Current Generator

Unlike a brushed DC motor, the commutation of a BLDC motor is

controlled electronically (Sebastian 1989). To rotate the BLDC motor, the

stator windings should be energized in a sequence. Most of BLDC motors

have three Hall sensors embedded into the stator on the non-driving end of the

motor. Rotor position is sensed by Hall Effect sensors embedded into the

stator which gives the sequence of phases. Whenever the rotor magnetic poles

pass near the Hall sensors, they give a high/low signal, indicating the N or S

pole is passing near the sensors. Based on the combination of these three Hall

sensor signals, the exact sequence of commutation can be determined (Rubai

et al 1992). The magnitude of the reference current (I ) is determined by

using reference torque (T ) and the back emf constant (Kb);*

*

b

TI

K.

Depending on the rotor position, the reference current generator block

generates three-phase reference currents (ia , ib , ic ) considering the value of

reference current magnitude as I , I and zero. The reference current

generation is shown in Figure 6.2 and Table 6.1 (Luk et al 1994).

Table 6.1.Rotor position signal Vs reference current

Rotor Position Signal r

Reference Currents

(ia , ib , ic )

330°-0° to 0°-30° 0 I I

30° - 90° I I 0

90° -150° I 0 I

150° - 210° 0 I I

210° - 270° I I 0

270° - 330° I 0 I

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Figure 6.2 Back EMF, current profile, modes, conducting switches in the

four-switch converter for three-phase BLDC motor drives

Figure 6.3 shows the FSTP BLDC drive with current regulation.

The PMBLDC motor is modeled in the 3-phase abc frame. The general volt-

ampere equation for the circuit is shown in the Figure.6.4. Terminal voltages

of a BLDC motor in the four-switch inverter with respect to the mid-point of

the dc bus are as follows:

aao a a no

diV Ri L e V

dt (6.3)

bbo b b no

diV Ri L e V

dt (6.4)

cco c c no

diV Ri L e V

dt (6.5)

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a

b

c

ae

be

ce

1S

2S

3S

4S

c1V

c2V

ai

bi

ci

ai bi

1S 2S 3S4S

a Refib Ref

i

R

R

R

sL M

sL M

sL M

Current Reference GeneratorRefI

aH

bH

cH

Current

Regulators

Figure 6.3 Four-switch converter topology for three-phase BLDC motor

Figure 6.4 Inverter circuit with PMBLDCM drive

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6.3 DIRECT CURRENT CONTROLLED PWM

From the motor point of view, even though the BLDC motor is

supplied by the four-switch converter, ideal back-EMF of three-phase BLDC

motor and the desired current profiles can be described as shown in Figure

6.2. From the detailed investigation of the four-switch configuration and

back-EMF and current profiles, it could be concluded that the existing PWM

method for B6 inverter can not perform with FSTP inverter. Under a balanced

condition, the three-phase currents always satisfy the following condition:

a b cI I I 0 (6.6)

Then, (6.6) can be modified as

c a bI (I I ) (6.7)

In the case of the ac induction motor drive, at any instant there are always

three phase currents flowing through the load, such as

aI 0 ; bI 0 ; cI 0 (6.8)

However, in the case of the BLDC motor drive, (6.8) is not valid anymore.

Note that in Figure 6.2 phase A and B currents are only controllable and

phase C is uncontrollable. The modes of operation FSTP inverter is depicted

in Figure 6.5. Table 6.2 implies that due to the characteristics of the BLDC

motor, such as two-phase, only two phases (four switches) needed to be

controlled, not three phases. Therefore, based on Table 6.2, one can develop

a switching sequence using four switches.

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1S

2S

3S

4S

a

b

c

1S

2S

3S

4S

a

b

c

(a) (b)

1S

2S

3S

4S

a

b

c

1S

2S

3S

4S

a

b

c

(c) (d)

1S

2S

3S

4S

a

b

c

1S

2S

3S

4S

a

b

c

(e) (f)

Figure 6.5 Switching modes of FSTP Inverter with direct controlled

PWM

(a) Mode I (S4). (b) Mode II (S1 and S4). (c) Mode III (S1).

(d) Mode IV (S3). (e) Mode V (S3 and S2). (f) Mode VI (S2).

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Table 6.2 Switching Sequence of Four switch BLDC motor

Modes Active Phases Silent Phases Switching Devices

Mode 1 Phase B and C Phase A S4

Mode 2 Phase A and B Phase C S1 and S4

Mode 3 Phase A and C Phase B S1

Mode 4 Phase B and C Phase A S3

Mode 5 Phase A and B Phase C S2 and S3

Mode 6 Phase A and C Phase B S2

As shown in Table 6.2, the two-phase currents need to be directly

controlled using the hysteresis current control method by four switches

(Lajoie-Mazen et al 1985). Hence, it is called the direct current controlled

PWM scheme.

6.3.1 Current Regulation

Based on the switching sequences in Table 6.2, the current

regulation is actually performed by using hysteresis current control. The

purpose of regulation is to shape quasi-square waveform with acceptable

switching (ripple) band. The detailed waveforms and switching sequences are

described in Figure 6.6. The bold line is the current reference value, which is

obtained from the torque and speed control loop to achieve the reference

torque. The switching frequency and torque ripple are the main considerations

for setting the upper and lower limits. It means that a smaller band causes

higher switching frequency, but lower torque ripple.

Using mode II and mode III, the current regulation can be

explained as follows: In mode II, Ia and Ib currents (Ia>0, Ib<0) flow and Ic=0.

Therefore, mode II is divided into two cases, such as adi

0dt

, bdi

0dt

and

135

adi

0dt

, bdi

0dt

. In this mode, as shown in Figure 6.6(b), switches S1and S5

are used. Until Ia (Ib) reaches the upper (lower) limit, S1 and S4 are turned on

for supplying dc-link energy to increase the current. When the current reaches

to the upper limit, S1and S4 are turned off to decrease the current through the

anti-parallel diodes D2 and D3.

Upper Limit (UL)

Lower Limit (UL)

aI

bI

cI

Mode V Mode VI Mode IMode I Mode II Mode III Mode IV

1S 1S 1S1S4S 3D

2D 2D 2D 2D 3S4D 3S 4D

2S1D 2S 1D

2S 1D 2S1D 4S 3D

4S 3D 4S3D

3S4D 3S 4D

Reference

Figure 6.6 Current regulation and detailed switching sequences

At that time, the reverse bias (negative dc-link voltage) is applied to

the phases, resulting in decreasing the current. On the other hand, in mode III,

only one current (Ia) can be controllable. It means that only switch S1 can be

used as shown in Figure 6.5(c). However, the same principle as used for mode

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II is applied to mode III. When Ia increases, S1 is turned on and other case S1

is turned off.

Special attention should be paid to mode II and mode V. In these

modes, phases A and B are conducting the current and phase C is regarded as

being unexcited, so that it is expected that there is no current in the phase C.

However, the back EMF of phase C can cause an additional and unexpected

current, resulting in current distortion in the phases A and B. Therefore, in the

direct current controlled PWM, the back-EMF compensation problem should

be considered. This phenomenon can be explained with the aid of the

simplified equivalent circuit in Figure 6.7. As an example of mode II, in the

ideal case, only one current (phase A or phase B) needs to be sensed and

switching signals of S1 and S4 are identical. In the case of sensing phase A

current, the switching signal of S1 is determined independently and S4

depends on the S1 signal, so that phase A current can be regarded as a

constant current source. However, in this case, phase B current can be

distorted by the phase C current.

On the other hand, if phase B is controlled, phase B current can be

a constant current source, and then the phase A current can be distorted. The

same explanation can be applied to mode V. From the equivalent circuits of

Figure 6.8, one can come up with a solution. If phases A and B are regarded

as independent current sources, the influence of the back-EMF of phase C can

be blocked and cannot act as a current source, so that there is no current in

phase C. It means that in the direct current controlled PWM, phase A and

phase B currents should be sensed and controlled independently and the

switching signals of S1 (S3) and S4 (S2) should be created independently, as

shown in Figure 6.8.

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a

b

c ncnV 0

dV

dV

Phase A

Winding

Phase B

Winding

a

b

c n

dV

dV

Phase A

Winding

Phase B

Winding

ec

(a) (b)

Figure 6.7 Simplified equivalent circuits of modes II and V

(a) Ideal case. (b) Actual case when the back EMF causes current in

phase C

a Re fI

bRefI

aI

bI

1S signal

4S signal

Current

Controller

Figure 6.8 PWM strategy for compensating the back-EMF problem

6.4 PROBLEM FORMULATION

Permanent magnet brushless dc motor (PMBLDCM) drives are

continually gaining popularity in motion control applications. This paper

investigates the performance of direct current controlled pulse width

modulation (DCC-PWM) based control of four-switch three-phase (FSTP)

inverter feeding permanent magnet brushless dc (PMBLDC) motor.

138

A MATLAB/Simulink model for the FSTP fed PMBLDC motor is

developed and tested with direct current controlled PWM method. The

triumph of the DCC-PWM in obtaining desired speed-torque characteristics is

validated with help of simulation results. The DCC-PWM is also

implemented with proportional-integral controller using TMS320LF2407

digital signal processor.

The fundamental operation of FSTP inverter fed BLDC motor drive

has been analyzed by simulation. The developed the nonlinear simulation

model of the BLDC motors drive system is used for proportional-integral (PI)

control. The simulated results in terms of electromagnetic torque and rotor

speed are given

6.5 SIMULATION RESULTS

In this work the drive model with PI speed controller is developed

and simulated in order to validate the FSTP inverter control of BLDC motor

model and the designed controller and the complete simulink diagram as

shown in figure appendix A-5. The set of equations representing the model of

the drive system is schematized. For conducting the studies and analysis, this

paper considers a typical industrial BLDC motor (Arrow Precision Motor Co.,

LTD) with importance specifications: Power =180, 300rpm, 8 poles.

Figure 6.9 represents the back EMF resulted in the simulation and

Figure 6.10 shows the sectors of FSTP inverter while feeding BLDC motor.

The phase currents are illustrated in Figure 6.11. Figure 6.12 shows the torque

and the speed variations in starting for the reference speed of 150RPS and

load on 6 N-m. The motor speed quickly converges to the reference during the

startup.

139

Figure 6.9 Back EMF

Figure 6.10 Sector Representation of FSTP inverter fed BLDC motor

140

Figure 6.11 Stator phase currents.

Figure 6.12 Torque and speed responses during startup transients

141

6.6 HARDWARE IMPLEMENTATION

Based on the statute presented in the previous sections it is possible

to derive an algorithm that can control the BLDC drive better. This algorithm

is adequate for compensating the back EMF and current distortions. The

direct control PWM is implemented in DSP processor TMS320LF2407A. The

Texas instruments TMS320LF2407 DSP [103] controller (referred to as

LF2407) is a programmable digital controller with a C2XX DSP central

processing unit (CPU) as the core processor. The LF2407 contains the DSP

core processor and useful peripherals integrated onto a single piece of silicon.

It combines the powerful CPU with an on-chip memory and peripherals

(Bhim singh et al 2002). The complete setup is shown in Figure.6.14.

Figure.6.15 shows the representative phase current waveform. The

effectiveness of the designed PI controller is validated for the step change in

dc link voltage and presented in Figure 6.16 and Figure 6.17.

Figure 6.13 Hardware setup

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Figure 6.14 Hardware schematic of the sensor-controlled, four-switch

BLDC Motor drive based on TMS320LF2407A DSP

Figure 6.15 Representative Phase Current

143

Figure 6.16 Speed response for step increase dc-link voltage

Figure 6.17 Speed response for step decrease in dc-link voltage

144

For Step change reference speed the drive takes negligible steady

state error and settling time of 0.01s without any overshoot. The hardware

results are very marginal to simulation result which is much lesser, and then

the difference occurred during multiple observations in digital storage

oscilloscope

6.7 SUMMARY

This chapter presents a method to generate PWM signals for control of four-

switch three-phase inverters. The simulation model of the BLDC motors drive

system with PI control based four switch three phase inverter on

MATLAB/Simulink platform is presented. The system is realized in

TMS320LF2407 DSP platform. The main advantages are increased system

reliability and cost reduction of the overall system. The performance of the

developed algorithm based speed controller of the drive has revealed that the

algorithm devises the behavior of the PMBLDC motor drive system work

satisfactorily. In comparison with the usual three-phase voltage-source

inverter with six switches, the main features of this converter are twofold: the

first is the reduction of switches and freewheeling diode count; the second is

the reduction of conduction losses. For a step change the reference speed the

drive takes negligible settling time of 0.01s without any overshoot.