A HIGH PERFORMANCE FIELMFUENTED CONTROL FOR A SWITCHED RELUCTANCE MOTOR DRIVE

Tian-Hua Liu, Yung-Ju Chen, and Ming-Tzan Lin

Department of Electrical Engineering National Taiwan Institute of Technology

Taipei, Taiwan 106, R. 0. C.

ABSTRACT This paper presents a new controller design for a

switched reluctance motor drive system. The design, simulation, and implementation of a three phase, 10 HP, switched reluctance motor under field-oriented control is described. An optimal controller design based on field-oriented control is discussed. By using this control method, the performance of the switched reluctance motor drive system is improved. Experimental results validate theoretical analysis and computer simulation results.

INTRODUCTION A number of studies [1]-[3] have been published

recently on switched reluctance motors (SRMs), as they are simple in construction, and economical in comparison with synchronous and induction motors. This research has studied the analysis and design of the drive circuit. For example, R. Krishnan and P. N . Materu proposed a lowxost converter and a single-switch-per-phase converter for SRMs, [1]-[2]. C. Pollock and B. W. Williams presented a unipolar converter for a SRM, [3]. R. S. Wallace and D. G. Taylor presented a new method to reduce torque ripple, [4]. In addition, many papers have discussed the drive systems of SRMs. For instance, B. K. Bose, T. J. E. Miller, P. M. Szczesny, and W. H. Bicknell used a microprocessor to control a SRM, 151. J. T. Bass, M. Ehsani, T . J . E . Miller proposed a robust torque control of SRMs without a shaft position sensor, [6]. M. Ehsani, I. Husain, and A. B. Kulkarni, presented a SRM drive system without using position and current

This project is supported by National Science Council under grant NSC43-0404-E011-032.

sensors, (71. However, some disadvantages exist with these previous papers. For example, a huge torque pulsation is produced during the period of phase current switching. As a result of this pulsation, the speed range is not wide enough. Recently, N. Matsui, N. Akao, and T. Wakino presented a high-precision torque control of SRMs by using field-oriented control 181; However, the modelling of the drive system and the speed-loop controller design were not discussed in this paper. Unlike papers [5]-[8], this paper presents a systematic controller design for a switched reluctance drive. First, a simplified model of the motor based on field-oriented control is proposed. Based on the control method, the input currents can thus be decoupled as flux and torque currents, and the speed-loop controller design easily achieved. Next, an optimal controller of the speed-loop is derived. This controller can perform with both a fast response and a good load disturbance rejection capability. The proposed block diagram of vector control for a switched reluctance motor is shown in Fig. 1. The system consists of four major elements: a switched reluctance motor, a current regulated inverter, a digital controller implemented by a microcomputer, and some sensors. A 32-bit 16.7-MHz Motorola MC68020 monoboard microprocessor serves as the speed-loop controller. The microprocessor-based controller is connected to various peripheral devices such as D/A and A/D conversion modules, and a parallel 1/0 module via the VME bus. The controller determines the reference stator current magnitude command I , and current phase angle 6. Then, * ,* * It computes and provides three-phase currents ia, I,,, i c

to the current regulated inverter. The three-phase motor line currents are measured by Hall-effect current sensors. These measured currents are fed back to the current

IEEE Catalogue No. 95TH8025 0-7803-2423-41951$4.aoOl995 IEEE

180

controller to execute the current regulated algorithm. The other feedback quantity is the absolute rotor position, measured by the absolute encoder mounted on the motor shaft.

ncropmcessov

T Absdut.

Encoder I '

Fig. 1 Block diagram of proposed system.

CONTROL ALGORITHM The traditional control of a switched reluctance

motor is shown in Fig. 2. Both the stator and rotor have salient poles, but only the stator offers windings. Take the a-phase as an example. When the inductance of the a-phase is increasing, the current of the a-phase is injected with a constant amplitude. After the inductance of the a-phase reaches a maximum value, the a-phase current is blocked. So, the current is switched according to the position of the rotor in order to obtain a smooth torque.

(4 er Fig. 2 Traditional control of a switched reluctance motor.

(a) structure (b) inductances (c) phase currents

In this paper, the basic principle of controlling a SRM is proposed, Fig. 1. The motor is driven by a current-regulated voltage-source inverter. The inverter generates three-phase variable-frequency stator currents. The amplitudes and frequencies of the stator currents are determined by the speed-loop controller and the encoder. The simplified model and controller design are discussed in the following section.

A. Simplified Mathematical Model In this paper, a simplified model of the switched

reluctance motor is used. Based on vector control, with a d&q synchronous reference frame, the torque equation of the simplified model can be described as

T = ( L d - L q ) i q d i (1)

and the speed of the motor is

(2) 1

pur = J I T e - T ~ -Bm ur 1. m

where Te is the electromagnetic torque, Ld and L are

the d- and q- axes inductances, id and i are the d- and

q- axes currents, p is the differential operator d/dt , ur is

the rotor shaft speed, Jm is the inertia constant, T1 is the

load torque, and Bm is the coefficient of viscosity of the

motor.

9

9

B. Field Oriented Control Method In this method, the d- axis current is fixed a t a

constant value to produce flux. The q- axis current, which is called "torque current", is determined by the

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speed-loop controller and the speed error. A fast response to the torque can thus be achieved. The torque of the motor can be expressed as

T = ( L - L ) i i e d q d q = K i (3) t q

where Kt is the constant coefficient of torque.

The current magnitude and phase are 2 2 112 I = ( i d + i q ) (4)

(5)

C. Controller Design Under field-oriented control, the transfer function

of the plant can be obtained from equations (1)-(3), and expressed as P(s)= wr(s)/ i (9) = Kt/ (J,s + Bm). In

9 the real system, however, exists the delay time due to the sampling interval of the microprocessor and the switching interval of the inverter. In addition, there are coulomb friction and transportation lag between the motor shaft and the mechanical load. So, the plant can be expressed as a more precisemodel as

t e-rds K

= Jms+Bm

where rd is the equivalent delay time between the

current i and the motor speed wr. In order to simplify

the design of the controller, we use l / ( l t r d s ) to

approach e-'ds. Then, the plant is shown in Fig. 3 and can be expressed as

9

: Fig. 3 Block diagram of the closed-loop control system.

In this paper, we set up a quadratic performance index which weights speed error Awr(t) relative to control

input i (t) as follows q

J = [ (q2 Aur(t)2 + i;(t)) dt

where J is the quadratic performance index, q is the weighted factor, Aur(t) is the speed error, i (t) is the

control input (q-axis current). The controller design is shown as follows.

First, By using spectral factorization, the denominator of the optimal closed-loop transfer function is obtained as (101

9

Dt(s) D t ( W = Dp(s) D p W + q2 Np(s) Np(-S)

(9) where Dt(s) is the denominator of the optimal

closed-loop system, D (s) is the denominator of the

transfer function of the plant, and N (5) is the nominator

of the transfer function of the plant. The weighted factor q is chosen according to the closed-loop performance of the system. If q is chosen as a larger value, the speed response is better but the control input i ( t ) becomes

larger, which requires a lot of energy. On the other hand, if q is selected as a small value, the control input i is

reduced; however, in this case the speed response performs poorly. The closed-loop transfer function of the system is chosen as [lo]

P

P

q

9

( Y S + P

T(s) = (10)

K 2 - - r d J m (11)

K2S2+X1 S +KO

From equations (7), (9), and (lo), we can obtain

nl =J2rciJmJni+K:q2 +Bm2r2+Jm2 (12)

If we allow the steady-state error of the ramp input t n ( t ) to become zero, we can easily obtain

ess = 1 i m SE( s) s-, 0

182

0 (("1--(y)S+(Ko-P)) = l i m

S-+o K 2 S 3 + K l S 2 + K o S

=O (14) According to the equation (14), we can conclude that the parameters of the nominator are nl = a, and K~ = P. From Fig. 2, the closed-loop transfer function can he

Substituting (10)-(14) into (15) and letting x1=", K ~ = P , the controller C(s) can be derived as

6 J 7 (KIBm+KOJm)Td+KIJm C(Sl = ~ m d s +

K t K 2 Kt n2

(16) + KOBmrd+KIBm+KOJm 1 + 'OB, 1

K t K 2 s -2 When the viscous coefficient is small and can he neglected, then the controller can be simplified as a PID controller

(17) Ki C(S) = K p + - + K ~ s

and K = 'OJm7d+"lJm

P K t K 2 'OJm

t K 2

K t "2

K. =-

Kd = "1 Jmrd

When Bm is neglected, the controller is reduced as a PID

controller; however, the result is different from traditional PID control. The parameters of the traditional PID control are determined by trial and error. In this paper, the parameters of PID are related to the parameters of the plant and the parameters of the optimal closed-loop transfer function.

IMPLEMENT ATION The implementation of the system is shown in Fig.

1, where the microprocessor system consists of a MC 68020 CPU, a MC 68881 coprocessor, and some peripheral devices such as a D/A converter, an A/D converter, and parallel I /O ports. The microprocessor system executes the field-oriented control algorithm. The

microprocessor computes the speed error, executes the optimal control algorithm and coordination transformation, and generates threephase sinusoidal waves to the current-regulated inverter. The sampling period of the microprocessor is 1 ms. The motor is three-phase, eight-pole, and 10HP, and is made by Allenwest Company. The parameters of the switched reluctance motor are shown in Table I.

Table I Parameters of the Switched Reluctance Motor

0.13H

0.065H

2R

Ld

Lq

RS 2 Jm 0.0222 N-msec /rad

Bm 0.00028 N-m-sec/rad

EXPERIMENTAL RESULTS The concepts behind this paper have been

validated in the laboratory. The system has very low torque pulsation and can reduce the noise of motor operation. The implemented system can he operated at as low as 15 r/min. Fig. 4 shows the speed responses of the motor at 400 [/min. By adjusting the weighted factor, the rising time and overshoot can he changed. Fig. 5 shows the load disturbance rejection responses at 2 N. m. The measured responses match the simulation results. Fig. 6 shows the low speed response of 25 r/min. This system has a lower speed range than traditional control. Generally speaking, the lowest speed of the traditional control is 40 r/min. Fig. 7 shows the steady-state a-phase current at 2 N. m. Fig. 8 shows the line to line voltage Vab of the motor. Fig. 9 shows the torque to

current curves of the drive system. The maximum torque is operated when i is equal to id and 6 is 45'. Although

the maximum torque control can obtain a larger torque/current ratio, it is very difficult to design a speed-loop controller because the relationship between torque and q-axis current is nonlinear. Fig. 10 shows the responses of field-oriented control and maximum torque control.

q

183

(b) Fig. 4 Speed Responses (a) simulation (b) measured.

Im , , I I I I I , I T

I -

Y I -

:I, - LU--- - 0

'-2) - .YI

. is -

.,m " I " '

-- ..o.o>, ... W. - . . a m ,

1 I , I., I , 1 4 1, 1 0 $, I. I * 8

Tim @4

(a)

I O I.! 1.1 3J 3 , 1.1 3.6 1.7 1 . 1.1

(b) Fig. 5. Load disturbance response

(a) simulation (b)measured.

I 1

131 116 IJ7 IJI I 3 9 1 4 1 1 4 1 1 1 2 1 4 3 144 145

(b) Fig. 7 Steady-state current (a)simulation (b)measured.

-ml I ,.a, I,. I.,, I,. I.,. L . 4 ! . I 1.11

-8.". ,I.,

184

no, , , , , , , , , I

J

.,I

I I I I I I I I,, 126 1J1 121 I19 L.0 1.11 1.41

nm 1-1

(b) Fig. 8 Steady-state voltage (a)simulation (b)measured.

,. ..... - , I , 1 1 4 5 '

i I A ~ P )

Fig. 9 Torquecurrent curves.

I,"..

# @ m m Lm ,",

Fig. 10 Speed responses of field-aiented control and maximum torque control.

CONCLUSIONS In this paper, the design and implementation of a

switched reluctance motor system are proposed. Based on the field-oriented control formulation, a new optimal controller design algorithm is presented. Experimental results validate the theoretical analysis, and show the applicability of field-oriented control and optimal controller design in switched reluctance drive. In comparison with the conventional design method, this drive system has lower noise, lower harmonics, and better performance a t low speed. Moreover, from the simplified

model, a systematic controller design procedure can be easily derived. The results presented herein represent a first step toward the vector control and reliability improvement for a switched reluctance motor.

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REFERENCES R. Krishnan and P. N. Materu, "Design of a single-switch-per-phase converter for switched reluctance motor drives," IEEE Trans. Ind. Electron.,vol. 37, no.6, pp. 469-476, Dec. 1990.

R. Krishnan and P. N. Materu, "Analysis and design of a low-cost converter for switched reluctance motor drives," IEEE Trans. Ind. Appl., vol. 29, no. 2, pp. 320-327, March/Apr. 1993.

C. Pollock and B. W. Williams, "A unipolar converter for a switched reluctance motor," IEEE Trans. on Ind. Appl., vol. 26, no. 2, pp. 222-228, March/ Apr. 1990.

R. S. Wallace and D. G. Taylor, "A balanced commutator for switched reluctance motors to reduce torque ripple," IEEE Trans. Power Electron., vol. 7, no. 4, pp. 617-626, Oct. 1992.

B. K. Bose, T. J. E. Miller, P. M. Szczesny, and W. H. Bicknell, "Microcomputer control of switched reluctance motor," IEEE Trans. Ind. Appl., vol. 22, no. 4, pp. 708-715, July/ Aug. 1986.

J. T. Bass, M. Ehsani, T . J. E. Miller, "Robust torque control of switched-reluctance motors without a shaft-position sensor," IEEE Trans. Ind. Electron., vol. 33, no. 3, pp. 212-216, Aug. 1986.

M. Ehsani, I. Husain, and A. B. Kulkarni, "Elimination of discrete position sensor and current sensor in switched reluctance motor drives," IEEE Trans. Ind. Appl., vol. 28, no. 1, pp. 128-135, Jan./Feb. 1992.

N. Matsui, N. Akao, and T. Wakino, "High-precision torque control of reluctance motors," IEEE Trans. Ind. Appl., vol. 27, no. 5 , pp. 902-907, Sep./ Oct. 1991.

T. H. Liu, J . R. Fu, and T . A. Lipo, "A strategy for improving reliability of field-oriented controlled induction motor drives," IEEE Trans. Ind. Appl., vol. 29, no.5, pp. 910-918, Sep./Oct. 1993.

D. R. Towill, "Coefficient plane models for control system analysis and design," New York: Research Studies Press, 1981.

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