Speed Sensor Less Control Of Im By Current Error Compensation

Speed Sensorless Control of Induction Motor by Current Error Compensation Young Ahn Kwon, Sung Hwan IGm, and Sang Ho Oh Department of Electrical Engineering Pusan National University, Pusan 609-735, Korea email : [email protected]

Abstract - Various control algorithms have been recently proposed for the speed . ~ n s o r l e s scontrol of induction motor. Those algorithms are generally based on the speed feedback through the flux and speed estimations. The present paper proposes a new scheme for speed1 sensorless control. The proposed scheme is based on the current error compensation without the flux and speed estimations, in which the controlled stator voltage is applied to the induction motor so that the difference between stator currents of the mathematical model and motor may be forced to decay to zero. The performance of the proposed scheme is verified through the simulation and experiment.

I . INTRODUCTION The vector control of induction motor is usually attained by the application of a speed sensor. However, a speed sensor requires a mounting space on the shaft of motor, reduces the reliability, and increases the cost of drive. Various control algorithms have been proposed for the elimination of speed sensor. Those algorithms are generally based on the speed and flux estimations which is obtained from the terminal electrical quantities. However, those algorithms are compliacted, and have difficulties in the speed estimation in the range of low speeds.[ll-[31 This paper proposes a new scheme for speed sensorless control of induction motor. The proposed scheme is based on the current error compensation without the speed and flux estimations, in which the controlled stator voltage is applied to the induction motor so that the difference between stator currents of the mathematical model and the motor may be forced to decay to zero. The good performances of the proposed scheme are shown in the simulation and experimental results.

II. INDIRECT METHOD OF VECTOR CONTROL Equations related to the indirect method of vector control of induction motor are described in

the below.[41 In the reference frame with the synchronously rotating speed of w e , d- and q-axis voltage equations are

ds - w6,

(1)

+ * dAdt' + wJds

(2)

uds = Rsid,+

v, O=

= Rsi,

i

~

dt

+-.ai.1dr

Y dY

dt

(@e-

w7')AqY

(3)

a2*Y +(we0 = RYiqy+dt where w y is the rotor speed, and the stator and rotor fluxes are

iqY)= Lsi,+ L,i,,

(6)

A q y = Llyiqy+ L,(iqs+ iqy) = Lyiq,.+L,i,

(8)

Aqs= LSi,+

L,(i,+

where Lk, Lir and L , are the stator leakage inductance, rotor leakage inductance, and mutual inductance. Voltage equations written in the matrix form are

where P(=d/dt) is the differential operator, and wXi (= w e - 0,) is the slip frequency. The electromagnetic torque is in terms of d- and

(20)

Ad,= LmiA

q-axis components

(10)

(21)

where P is the number of poles.

(22)

From (7) and (81, d- and g-axis rotor currents are

III. PROPOSED CONTROL SCHEME

(11)

(12) Substituting (11) and (12) into (3) and (4) yields

& R + -.LL , Aq, - LLr R , i, dt

+ wSl/Idr = 0

The proposed sensorless control scheme does not require the speed and flux estimations, but use directly the stator currents. An induction motor may be considered as a multi-variable input/output system shown in Fig. 1, in which the input variables are the stator voltages, and the output variables are the stator currents and rotor speed.

vos Vos-j

(14)

If the vector control is fulfilled such that q-axis rotor flux can be zero, and d-axis rotor flux can be constant, the electromagnetic torque is controlled only by q-axis stator current from (lo), and we have

I

-0

INDUCTION MOTOR

p-1

r 1.5

Fig. 1 Input and output variables of induction motor

The voltages and currents in Fig. 1 are the quantities in the stationary reference frame fixed to the stator. The voltage equations in the stationary reference frame are

(15) Substituting (15)into 113) and 14) yields (16)

(17) Fig. 2 Input and output variables of model

where T,(=L./R,.) is the time contant of rotor.

In case of the constant flux control, that is &d,-/dt'o, from ( 3 ) , (121, and (15) idr=

0

(18)

If (18) and (19) are substituted into (lo), (16) and (17), the flux, slip frequency and electromagnetic torque are

Fig. 2 shows a model where the input and output variables are newly established. The subscript

m

denotes the variable of the model. w r m is the the rotor speed of the model, and becomes the speed command. From the induction motor of Fig. 1 and the model of Fig. 2, the following inference is possible. If both the stator currents of the motor and model are forced to be same in case that both the stator voltages are same, the motor speed becomes same as the model speed, that is, the and speed command. In other words, if ias= ,i iB= im in case of vas= U, and vgs= vm , then

9 67

u y = u r m The . above things can be expressed in terms of the (quantities of the synchronously rotating reference frame. If i, = i,, and ids = id, in case of uqs= U*, and = zidm , then w,= w rm . These relations can be also obtained from the equations described in the section II. The q-axis stator voltage equations of the motor and model are

stator voltage) is obtained as the output of PI controller, and the difference between the torque producing currents of the model and motor is used as the input of PI controller. The d-axis stator voltage for the constant flux vector control is obtained from the output of another PI controller, and the difference between the reference current and the flux producing current of the model is used as the input of the PI controller.

(24) where Kit K j , KO and K, are the gains.

(25) where B,,is the angle of the d-axis synchronously rotating reference frame. where

0 (=

1- Lkl LJr 1 is the leakage factor.

of

the

Fig. 3 shows the overall block diagram of the proposed sensorless control scheme.

If the voltages applied to the motor and model are same, that is, uqs= uqsm,from (24)and (25)

From (26) and E r ) , it is recognized that if i,= i,, and ib=idm then w,=u,, and w y = u r m . Therefore the motor speed is forced to be same as the model speed if the difference between the torque producing currents(q-axis stator currents) and the difference between the flux producing currentdd-axis stator currents) of the motor and model are controlled to be zero in case that the same voltages are applied to the motor and model. Furthermore, if the same voltages are applied to the motor and model in the reference frame with the same synchronously-rotating speed (w,= U em), from (26) it is recognized that the difference between the

flux producing (-l.lrrents Shuld be zero if the difference between the torque producing currents is controlled to be zero. For the realization of the above mentioned, the control quantity(the T a x i s

Fig. 3 Block diagram of the control system

IV. SIMULATIONS The following simulations have been performed for the verification of the proposed control scheme. The nominal power and speed of induction motor are 3hp and 1735rpm. Fig. 4(a), (b) and (c) show

the

speed responses in

cases of the speed

commands 1500, 50 and 25”. ~ i 5 ~shows . the bidirectional operation of the speed command +200rpm. ~ i 6 ~shows . the speed response in that the load torque 10” is applied in the of the operation of the speed command 2OOIpm. Fig.

7 shows the speed response in case that the rotor resistance is decreased by 20% below the nominal value, and the load torque 10" is applied in the middle of the operation of the speed command 200rpm.

100

TIME[I seddiv]

Fig. 6 Speed response in the load variation (O-flONm) I

I

I

I

I

TIME[Sec]

(a)

Fig. 7 Speed response in the rotor resistance decreased by 20% with the load variation (O-tlONm)

V . EXPERIMENTS AND DISCUSSIONS

(c) . Fig. 4 Speed responses in the speed command (a)15orPm (b1501gm (c125mm

TIME[lseddiv]

Fig. 5 Speed response in the bidirectional operation (200rpm--200rpm)

The experiments have been performed for the verification of the proposed scheme. The 80586 microprocessor system is used for the digital processing of the proposed algorithm. Fig. 8(a), (b) and (c) show the speed responses in cases of the speed commands 1500, 50 and 25rpm. Fig. 9 shows the bidirectional operation of the speed command f200rpm. Fig. 10 shows the speed response in case that the load torque 10" is applied in the middle of the operation of the speed command 200rpm. Fig. 11 shows the speed response in case that the rotor resistance is decreased by 20% below the nominal value, and the load torque 10" is applied in the middle of the operation of the speed command 200rpm. The results of simulation and experiment indicate that the proposed scheme has a good performance. The proposed scheme has a comparable performance in the respects of the steady state error, the low speed performance and the parameter variation performance. Furthermore the proposed control scheme has a simple algorithm without the speed and flux estimations.

969

.... a

2i w v)

TIME[seo]

TIME[lseddivj

Fig. 10 Speed response in the load variation (0- 10")

-

ziE a

Fig. 11 Speed response in the rotor resistance decreased by 20% with the load variation (O@lO[Nml)

Fig. 8 Speed responses in the speed command (a) 1503rpm (b) 3 r p m (c) 25rpm

motor speed indirectly follows the model speed (command speed) by forcing the difference between stator currents of the mathematical model and motor to decay to zero. The simulation and experiment have been conducted for the verification of the proposed scheme. The proposed scheme has been easily implemented through the microprocessor system. The simulation and experimental results show the good speed responses. W. REFERENCES

[ll Edited by K. Rajashekara, A. Kawamura and K. TIME[lseddiv]

Fig. 9 Speed response in the bidirectional operation (200rpm-*-200rpm)

VI. CONCLUSIONS This paper proposed a sensorless control scheme without the speed and flux estimations in which the

Matsuse, Sensorless Control of A C Motor Drives, IEEE press, pp. 1-258, 19% [2] J. Holtz, "State of the art of controlled AC drives without speed sensors", Int. J. Electronics, vol. 80, no. 2, pp. 249-263, 1996 [31 C. Ilas, A. Bettini, L. Ferraris, and F. Profumo, "Comparison of different schemes without shaft sensors for field oriented control drives", IEEEAECON, pp. 1579-1588, 1994 [4] Peter Vas, Vector Control of A C Machine, Clarendon press, 1990

97 0