An Improved Two-stage Control Scheme For An Im

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IEEE 1999 International Conference on Power Electronics and Drive Systems, PEDS’99, July 1999, Hong Kong.

An Improved Two-stage Control Scheme for an Induction Motor K. L. Shi, T. F. Chan, Y. K. Wong, and S . L. Ho Department of Electrical Engineering, Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong Abstract - In this paper, an improved two-stage control scheme (previously developed by the authors) is presented. A slip-frequency controller operates together with a currentmagnitude controller to yield the desired values of current and frequency during the acceleration/deceleration stage and the steady-state stage. Simulation studies on a 7.5kW induction motor are performed using Matlab/Simulink. The simulation results indicate that the performance of the two-stage control scheme is comparable with that obtained using field-oriented control. Besides, the improved control scheme is much simpler to implement and the performance is less sensitive to machine parameter changes.

Stator phase current magnitude I i,$I can be expressed by:

Substituting Eqs.(2) and (3) into Eq.(4),

I. INTRODUCTION In order to control accurately the magnitude and phase of the stator current, field-oriented control has to depend on the motor parameters and the complicated calculations involved [I]. In practice, accurate current-phase control is impossible, due to uncertainty in motor parameters and controller’s time delay. Two features of field-oriented control, however, deserve attention. Firstly, although the field-oriented controller does not control the frequency directly, its slip frequency is constant during the acceleration1 deceleration period. Secondly, when the torque command is constant, the supply current magnitude will remain constant. The first feature may be explained using the slip frequency formulation of field orientation [2]:

When the torque command T* and flux command Xdr* are both constant, Eq.(5) becomes: .‘_ I i.,I= 2 &5$ = const.

The above two features of field-oriented control have been employed by the authors to design a two-stage controller [3] for an induction motor. In this paper, the two-stage controller is improved with a simpler slip frequency control.

11. TWO-STAGE CONTROL STRATEGY FOR AN INDUCTION MOTOR

where w, is slip frequency, R, is the rotor resistance, P is the number of poles, T* denotes the torque command, and Xdr* denotes rotor flux command. If r* and AF1,,* are maintained constant during acceleration, w,is also constant.

The current-input induction motor model [4]-[5] shown in Fig. 1 has three inputs, namely the stator current magnitude Zs,supply frequency w, and load torque TL.It has an output, namely the rotor speed U,,. The relationship between the output and inputs may be expressed as:

The second feature may be proved using the field orientation conditions. The fl,,s may be expressed as:

Current

where k,,=PLM/3Lr, LM is mutual inductance, and L, is rotor inductance.

-

speed Induction ~... motor

The equation of the stator flux vector in the excitation reference frame can be written as [2]:

Fig. 1 An induction motor model with current input

0-7803-5769-8/99/$10.000 1999IEEE

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The speed response of the motor may be divided into two stages, an initial acceleration/ deceleration stage (the speed response to rise from about 3% to about 97% of speed command), and a final steady-state stage (the speed response error is during about 3%), as shown in Fig.2.

the supply frequency rises too fast, the torque will produce oscillations so that the acceleratioddeceleration period is longer, but if the supply frequency rises too slowly, the torque will be so small that the acceleration/deceleration period is again prolonged. To tackle this problem, a frequency saturation controller is designed using the equations of field-oriented control. 111. CONTROL OF SLIP FREQUENCY

1.5

2

2.5

During the acceleratioddeceleration stage, the torque command has a larger value denoted as rod, whereas during the steady-state stage, the torque command has a smaller value, Ts,eo+

3.5

3

k Acceleration period

Final steady state period

Fig2 Typical speed response of an induction motor

From Eq.( I), the slip frequency of field-oriented control is

The basic principle of the two-stage controller may be described as follows. 1)During the accelerationldeceleration stage, the stator is maintained constant and the input current magnitude frequency depends on the slip frequency orand the rotor speed. 2)During the final steady-state stage, the input frequency U is held constant and the speed of rotor U ,is maintained constant by controlling the stator current magnitude IZJ. In the two-stage speed control scheme, the relationship between inputs and outputs is described by Table 1.

For the induction motor to be studied, R,=O.ISIR, and P=6. If the acceleration/deceleration torque is k180 N.m, X,Ir*=0.6Wb, and substituting the motor parameters into Eq.(8), then

* 37.8

accelerationI deceleration stage

0.2 l ~ , c , 4 v

steady - state stage

(9)

In the simulation studies of a FOC controller and the twostage controller, the following variable load [6] is assumed Steady-state

Constant

change

:onstant

I

I

I

eliminate oscillations

where coefficient p = 0.43 N.m/(radsec). In this paper, the control strategy between the two stages is designed as follows. When (wl,*-ml, (13,control is from a steady-state stage to

an acceleration stage. When 2.5
-0, l<3,

When the load characteristic of Eq.(lO) is assumed, Eq.(9) becomes f 37.8

acceleratbnldeceleratwn stage

0.090,,

stea&

- state stage

(1 1)

control stage is unchanged.

When Jw,*-w,,l9.5,control is from an acceleration stage to a steady-state stage.

In this paper, a constant load is also used to investigate a closed-loop V/Hz controller and the two-stage controller. When a constant load is assumed, Eq.(9) becomes

A problem arises as how to vary the supply frequency from zero to the final frequency of the command speed. If

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o,=

{

accelerationldeceleratbt?, stage

k 37.8 0.2 1

q.

400

(12)

~

steady - state stage

The slip-frequency control scheme to implement Eq.(l1) can be constructed by a simple controller whose output is limited to k37.8 by an output saturation [7]. For the variable load of Eq.(lO), simulation program of the slip-frequency controller consists of the blocks Suml, Sum2, Gain, and Saturationl, as illustrated in Fig.3.

c

m

r

Speed

SumZ

command

Saturation1

Slip

frequency

04rc

Rotor

Suml

Fig5 Speed is controlled by stator current amplitude.

speed

Fig. 3. Simulation blocks of slip-frequency control for the varied load

The following proportional-and-integral(PI) control with output saturation is used in the nonlinear control.

Similarly, for a constant load, simulation program of the slip-frequency controller expressed by Eq.( 12) can be constructed as shown in Fig.4.

Saturation1

command

Rdcr

Slip frequency

In this paper, coordination of the current magnitude control for the two stages is achieved using the following strategy:

Sum1

speed

1) When l0,*-w,~123, the current magnitude control changes from a steady-state stage to an acceleration stage.

Fig. 4. Simulation blocks of slip-frequency control for a constant load

2) When 2.5
3) When lw,,*-wf,l,112.5, the current magnitude control changes from an acceleration stage to a steady-state stage. During the steady-state stage, stator current 1,has a small value. When I w,,*-wl,/13, the current magnitude control changes from the steady-state stage to an acceleration stage. If we let Kp(w,,*-w,,)>lOO, i.e., Kp>33, then [,of Eq.(13) is larger than lOOA, hence the proportional coefficient K p may be chosen as 35.

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Fig. 7. Sirnulink blocks of the two-stage controller for the variable load

The maximum value of the integral part of Eq.( 13) can be estimated from an acceleration process with U,,*= IZO, w,,(t=Os)=O, assuming that the rotor speed rises at uniform acceleration and w,(t=O.Zs)=IZO, i.e.,

For a constant load, the model of two-stage speed controller for the induction motor can be constructed using Simulink as shown in Fig.8.

0.2

j(o,, * -w,,)d.r = 12

r=O r L

When the current magnitude control changes from an acceleration stage to a steady-state stage, substituting (U,, *w,,)=2.5, Kf,=35, and Eq.(15) into Eq.(13), and let Z,
,

command

A current-magnitude controller is designed as shown in Fig.6. It consists of a sum block to calculate speed error, a PI block to implement Eq.(13), and a saturation block to implement Eq.( 14).

SumZ

Saturation1

Slip frequency

Fig. 8. Sirnulink blocks of the two-stage controller for a constant load

VI. SIMULATION RESULTS A computer simulation was performed on the two-stage controller with a current-input induction motor model [4]. The inputs of the motor are the current magnitude I.,, the frequency u=u,+(P/Z)U,, and the load TL. Four investigations were undertaken: 1) comparison with fieldoriented control, 2) comparison with a closed-loop V/Hz controller, 3) effects of parameter variations, and 4) effects of noise in the measured speed and input current. Following are the parameters of the induction motor chosen for the simulation studies:

command

Fig. 6. Current magnitude controller

Type: three-phase, 7.5kW, 220 V, 60Hz, 6-pole, wyeconnected, squirrel-cage, induction motor

V. TWO-STAGE CONTROLLER FOR AN INDUCTION MOTOR

Combining the slip-frequency controller and the currentmagnitude controller, a two-stage controller may be designed. During the acceleration or deceleration period, the current-magnitude controller outputs the maximum permissible current. During the steady-state period, the slipfrequency controller outputs the slip-frequency that corresponds to the speed command. For the variable load, the model of two-stage speed controller for the induction motor is constructed using Simulink as shown in Fig.7.

command S ! T * - F 2

:E

Saturation1

R.,=O .282Wph L,v=0.044Wph R i o . 15 1n/ph Lr=0.043Wph Ln,=0.042Wph J p 0 . 2 kg.m' J p 0 . 2 kg.m2 C,= 0.065

I) Comparison with field-oriented control: In this simulation study, the load is assumed to be variable and the two-stage controller model of Fig.7 is used. It is assumed that the induction motor is taken through the following control cycle:

w Gain

Stator resistance: Stator inductance: Rotor resistance referred to stator: Rotor inductance: Mutual inductance: Moment of inertia of the rotor: Moment of inertia of the load: Coefficient of friction:

Slip frequency

SPEED COMMAND

PERIOD

otl*= 120(rad/sec) U,,* = - 120(rad/sec) ofI*= 40(rad/sec)

osstas 2sIt<4s 4sIt<6s

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96. FOC controller

1

1

0

1

1

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SPEED COMMAND

30 20

120(rad/sec) 20(rad/sec) U(,* = 120(rad/sec) U(,* = 20(rad/sec) U(,* = 120(rad/sec)

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100

200

100

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-100

-100

-200

-200

Fig.IOu, IOc, IOe, and IOg show the simulation results of the two-stage controller. In order to compare the two-stage controller with a V/Hz controller, a closed-loop V/Hz controller [5] was investigated. Fig.IOb, I O 4 IOJ and IOh show the simulation results of a closed-loop V/Hz controller. The speed response of the two-stage controller is obviously faster than the closed-loop V/Hz controller. As shown in Fig.IO6, maximum value of the stator current magnitude of the V/Hz controller is not limited and is over lOOA during the starting period. Fig.IOf shows that the V/Hz controller produces oscillating torques during the steady-state stage. A comparison of the two controllers shows that the new controller has distinct advantages in the speed response, torque characteristic, and current characteristicthan the closed-loop V/Hz controller.

0

-300 0

2

4

6 1 Tim. (..
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Oslt<2s 2srt<4s 4slt<6s 6s
9d. FOC controller

9c. Two-stage controller

-300

PERIOD

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9a. Two-stage controller

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2) Comparison with closed-loop V/Hz control: In this simulation study, the load is assumed as constant at 20N.m and the two-stage controller model of Fig.8 is used. Because the voltage-frequency relationship of a general V/Hz controller has a dead area around zero frequency, it can not work well from a positive speed command to a negative speed command. From a consideration of the characteristic of the V/Hz controller, it is assumed that the induction motor is taken through the following control cycle of positive speed commands:

0

1 , m . (..=and)

9J FOC controller

9e. Two-stage controller

100

50

0 .50

2

4

6

lul.

9g. Two-stage controller

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9b. FOC controller

Fig.9. Simulation results of two-stage controller and FOC controller

/Ob. VMz controller

IOa. Two-stage controller

F i g . 9 ~9c, 9e, and 9g show the simulation results of the two-stage controller. Very fast speed response is obtained with the two-stage control method. Due to the current control in the steady-state stage, the oscillations of speed about the final operating point are completely eliminated. In order to compare the new controller with a field-oriented controller, an indirect rotor flux field-oriented controller [2] was investigated. Fig.96, 94 9f;and 9h show the simulation results of the indirect FOC controller.

1

100

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Tlrn. I..so"dI

IOc. Two-stage controller

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Tim. (*.condl

IOd. VMz controller

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variance of 10) demonstrates that the two-stage controller has good disturbance rejection.

VII. CONCLUSION The improved two-stage controller has almost the same frequency and current characteristics as the field-oriented controller. During the acceleratioddeceleration stage, the stator current magnitude is maintained at the maximum permissible value to give a large torque, and during the steady-state stage, the stator current magnitude is adjusted to control the rotor speed. Because the two features of fieldoriented control are exploited, the performance of the improved two-stage controller is obviously superior to a scalar controller [SI. Besides, the new controller has the advantages of simplicity and insensitivity to motor parameter changes. Very encouraging results are obtained from a computer simulation using Matlab/Simulink.

Tom. (..son41

1 Oe. Two-stage controller

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Tim. (%.and)

VIII. ACKNOWLEDGEMENT

1 Og. Two-stage controller

The work reported in this paper was funded by the Hong Kong Polytechnic University research grant V157.

Fig.10. Simulation results of two-stage controller and VWz controller

3) Efects ofparameter variations: The simulation of the two-stage controller for the variable load is repeated with the rotor resistance and mutual inductance changed to 2R, and 0.7LM respectively. A comparison between Fig. 11 and Fig.9g shows that the speed response of the two-stage controller is insensitive to parameter variations.

Fig.1 1. Speed response with motor parameter variation

Fig.12. Speed response with speed and current noises

4) Effects of noise in the measured speed and input current: In order to evaluate the effects of the noise of speed sensor and the noise of the input current, distributed random noises are added into the feedback speed and input current of the two-stage controller in Fig.7. The simulation is achieved using the random number blocks of Simulink, which generates a pseudo-random, normally distributed (Gaussian) number [6]. As shown in Fig.12, the speed response with the measured speed noise (mean of zero and variance of 3) and with the current noise (mean of zero and

IREFERENCES 1. K.S. Rajashekara, A. Kawamura, and K. Matsuse, “Speed sensorless control of induction motors,” Sensorless Control of AC Motor Drives, IEEE Press, pp. 1-19, 1996. 2. A.M. Trzynadlowski, The Field Orientation Principle in Control of Induction Motors, Kluwer Academic Publishen, 1994. 9 3 . K.L. Shi, T.F. Chan, and Y.K. Wong, “A Novel Two-Stage Speed Controller for an Induction Motor,” Record of The 1997 I€€€ International Electric Machines and Drives Conference, USA, May 1997, pp.MD2-4. 4. K.L. Shi, T.F. Chan, and Y.K. Wong, “Modelling of the Three-phase Induction Motor Using SIMULMK,” Record of The 1997 I€€€ International Electric Machines and Drives Conference, USA, May 1997, pp.WB3-6. 5. M. Chee, Dynamic Simulation of Electric Machinev Using Matlab/ Simulink Prentice-Hall, Inc., 1998 6. Using SIMULINK, mnamic System Simulation for MATLAB, The Mathworks Inc. 1997. 7. S . Wade, M. W. Dunnigan, and B. W. Williams, “Modeling and Simulation of Induction Machine Vector Control with Rotor Resistance Identification” I€EE Transactions. Power Hecfronics, vol.12, No.3, pp.495-505, May 1997. 8. G O . Garcia, R.M. Stephan, and E.H. Watanabe, “Comparing the Indirect Field-Oriented Control with a Scalar Method,” IEEE Transactions on Industrial Electronics, vo1.41, No.2, pp.201-207, 1994.

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