Speed Sensor Less Field Orientation Control Of The Induction Machine

Speed Sensorless Field Orientation Control of the Induction Machine Hirokazu T-4JIMA and k'oichi HORI Department of Electrical Engineering The University of Tokyo 7-3-1 Hongo, Bunkyo-ku, 113 Tokyo, Japan TEL +81-3-3812-2111. FAX +81-3-5684-3986 E-mail tajiniaG kaya. t .U-t okyo.ac. j p

Abstract

is instantaneously used for the Flux Observer based Field Orientation (FOFO) controller which we proposed some years ago [3]. Through the implementation using DSP (Digital Signal Processor), and some laboratory experiments. we will show that the speed sensorless FOFO operates with enough stability and has strong robustness to changes in machine parameters such as the rotor resistance.

We propose a speed estimation method for an induction machine and its application to the Flux Observer based Field Orientation (FOFO) control system, which we proposed previously. The motor speed is estimated based on the difference between two flux estimators. We analyze its convergence performance and propose the novel pole assignment method. Next, we apply this speed estimator to the FOFO controller. We implement the system centered about the DSP and through some laboratory experiments we will show that the speed sensorless FOFO operates with enough stability and has a strong robustness to rotor resistance variation.

1

2

The state equation of the induction machines are given by

Introduction

We know two major techniques for high performance control of induction machines:

.

x=

1. Slip frequency controlled type vector control, and 2 . Field orientation control.

[

A1z A21

A22

] [ ] 5+

U,

where

Recently the elimination of speed sensor has been one of the important requirenients in vector control systems, because the speed sensor spoils the ruggedliess and simplicity of ac motors. We can see some excellent speed sensorless approaches (for example in [2] ). but they are applicable only to slip frequency controlled type systems. In this paper, we mill propose the speed sensorless control method applicable to the field orientation COIItrol. It is well known that the field orientation control is inherently more insensitive to rotor resistance variation than the slip frequency coiltrolled system [3]. Howevei, since the field orientation controller has no concept of frequency. we should estimate the rotor speed from the instantaneous values of stator voltages and currents. First, we refer the speed cstiniatioii nicthod proposed by Schander [l]based on the idea of 52RAS (Model Reference Adaptive System) and propose its novel pol^ allocation method. The estimated speed

@'/803-0453-S/91$1 .WO1991IEEE

Model of Induction Machine

5

=

[is. A,]"

Thr state vaiiables are the ststor current z, = i 6 b ) T and the rotor flux A, = (Ar,. A,+)?'. The ziSt,)'. input variable is the stator voltage w, = (?isar Note that all variables are haidled on the stator COordillate system. ,z(

385

I

y;

Voltage Model

~

I

1

Fig. 2: Speed Estimator Dynamics

h-p= (2(iuc - 1 / ~ , ./1A,I2 ) h-I = W',2/IA,12 I

From (7) the transfer function from Aw, to A;,.

Fig. 1: Configuration of the Speed Estimator

l/T,.)S + d; + P(ld,s + w,"

A& (2
Speed Estimator

3

Configuration of Speed Estimator

3.1

=

L, (vs - R,i, - uLSas)

=

(2)

Current model: (3) The voltage model of (2) does not involve rotor speed W , while the current model of (3) does. We can then estimate the speed based on the output difference between these two models.

2,

=

(4)

where ~~

A

zero: s, = -

A

AriaArvb - ArvaArib (5) Fig. 1 illustrates this idea of speed estimation. Through the linearization with respect to a certain operating point, we can obtain the transfer function to A€ as follows from the estimation error Aw, -A;, 111.

(8)

4

l/rr poles: sp = -(wc f jwJ1-T"

4

2<W, -

(9)

Flux Observer

We designed another flux observer to be used for the field orientation control by using Gopinath's reduced order observer theory, which we proposed previously [3]. The observer equation takes the form of

+ Ail is +G(H, - A12Ar - Ailis - B i v , )

A,. = A22 A,. =

(KP+?)€

is

We can see that the speed estimation dynamics are characterized by one zero and two poles given by

From (l),we can obtain two well known flux simulators. One is called the voltage model and the other the current model. Voltage model: A,,

s2

(7)

+

-HA, (A21 - GAll)i, - G B l v , + GZ,

(10)

In this equation, the eigenvalues of

- H = A22

- GA12

(11)

are the observer poles which can be specified freely by the observer gain G. Fig. 3 depicts configuration of Flux Observer. We specified the observer poles -a j,B as

-N = -CkI+$J =

Ji/.p2

3 =

-4,

a

+r*(i/rp2++:).

Fig. 2 depicts the whole block diagram for the proposed speed estimation.

3.2 Pole Assignment of the Speed Est imat or Assuming that cu', = 0 for simplicity, we can specify the damping factor ( and natural angular frequency dc by using h-p and KI in (4) as follows.

Fig. 3: Configuration of Flux Observer

(12)

-

Fig. 7: Voltage Model

vs

L -

Volt age Model

iS

Fig. 4: Pole Allocation of the Flux Observer

s

1’1

-

& (estimated speed) 1

(stator current)

-+

+ 1/T

s

Xr., 1/T

Current,

I

I

Fig. 9: Speed Estimator (Experiment)

Fig. 5: Setup of the Experimental System centered about DSP

Fig. 6 shows the block diagram of the speedsensorless field orientation control system. The speed estimator calculates the speed L, from the stator voltage and current components, and this estimated speed is immediately used for the flux observer and the speed controller. The DSP performs the calculations required for the speed estimator and the flux observer (inside the dashed line box in Fig. 6). The program size is about 900 steps and Its control period is about 135 [ps].

This pole allocation keeps a kind of sensitivity norm to be constant regardless of the motor speed. This was the key of our success [3]. Fig. 4 shows that the observer poles move according t o the motor speed U,. r is the parameter in our pole allocation. In the following experiments, we used r = 1.0.

5 5.1

Experimental Result

Some Modification Speed Estimator

5.2

Experimental setup

Actual

In practice the original voltage model of (2) is difficult to implement because it requires a pure integrator, which has the initial value and drift problems. To avoid these problems, we replaced the pure integrator by the low pass filter. This modified voltage model has the form of

Fig. 5 shows the DSP based implementation of the speed sensorless FOFO controller. The DSP used was pPD77230 made by NEC, which can perform 32bit floating point mult,iplication. Its clock frequency is 13.333 [MHz] and machine cycle for every calculation is 150 [ns]. The tested machine is a 4-pole 2.2 [kW] induction machine which has the following parameters.

R, = 0.8770 L , = 165.142mH M = 160.8mH

in

. I

1-1

= ---ATu

T

L +2 (w. M

- R,i, - aL,;,) . (13)

The voltage model and the modified voltage model are illustrated in Fig. 7 and Fig. 8, respectively. Since the output of the modified voltage model of (13) is different from the rotaor flux. we have to

R, = 1.47R L , = 165.142mH a = 0.0519

387

I

I

DSP

U,;"

I

I

21ib

J

VR : Vector Rotator

I

IM : Induction Machine

Fig. 6: Speed-Sensorless Field Orientation Control Systeiii modify the current model simultaneously. The modified voltage model in Fig. 8 is equivalent to one that consists of a voltage model and a high-pass filter (HPF). Hence the modification of the current model is achieved by inserting H P F (see Fig. 9). T is a time constant of HPF. In experiment we use T = 0.05, then its cut off frequency is about 3.2 Hz.

5.3

150 Speed [r .p. m.]

0

Experimental Result of Speed Estimation

I

200ms

I

( a ) Experiinental Result

Fig. 10 (a) and (b) show the speed estimation performances. (a) is a experimental result of Fig. 9, and (b) is calculation result by linear model of (8). In case of = 1.0, wc = 100, PI parameters are then K p = 399, h-1 = 20408. However when we use these PI parameters, the estimated speed became very noisy. Finally we used K p = 100. It is equivalent to the case of = 0.29 and w, = 100. The agreement of Fig. 10 (a) and (b) is not so good, because the linear model (8) ignores H P F and the existence of slip. We can say that the speed can be estimated effectively with the specified convergence characteristics by and U,.

speedlr.p.m.1

I

0.00 0.00

I 200.00

1

time[msl

400.00

( b ) Calculation Result Fig. 10: Dynamic Response of Speed Estimator (< = 0.29. ~3~ = 100)

388

..

Experimental Results of Flux Estimation

5.4

0.5Wrb/d

T h e estimated speed is used in the Hux observer as an important paranieter of matrices in (10). Figs. l l ( a ) and ( b ) show the flux estimation performances of thp Hux observers using the measured speed w', and the estimated speed 2,. respectively.

Robustness of Torque Control to the Machine Parameter Variation

5.5

'div

Figure 13 shows the stationary torque errors caused by the variation of rotor resistance R , . The tested induction machine is connected t o a de generator and the induction machine commands the generation of constant torque. The rotation is maintained a t a constant speed by the load dc machine (see Fig. 12). We can see that the proposed field-orientation coiltroller using thc estimated speed (it is noted "Speedsensorless field orientation type ") is completely insensitive t o R, variation. This can be f>xplained as follows. The flux observer (10) has & skew-synirnetric structure, so we can interpret its diagonal parts as the real paits and the skew symmetric. parts as imaginary parts of the coniplex nuniber as follows

0.5\." b/d

.5Wb/div (b) Using Estimated Speed 2, Fig. 11: Flux Observation Torque Control Reference

Ay

is thc observed flux where A , is tlic real flux and in steady state. respectively. The steady state error of the estimated flux can be calculated using ( l o ) , (14). When the rotor resistance varies and we use the estimated speed for the Hux observer. it takes the form of

A , - A,- -_ A 1'

-I

a - JW,. CI

+

jujs

(l/T,

- jw,)

( ,; us-

-

Speed Control Reference

or*

IT*

Extemal Resistors Torque Control

Speed Control

Fig. 12: Setup of the hIeasuring Systeni of the Stationary Torque Errors t o Changes in the Rotor Resistance

A+

Torque current(A) 50

where

40

R: is the actual rotor resistance. Aw,.the estimation

20

error of the speed can be calculated using (3). It is given by

10 0

50

100

150

Rotor resistance variation

200

250

@)

Fig. 13: Stationary Torqur Errors Caused by R, Variation ( u j , = 7 5 r.p.ni.)

389

I

current to increase. Thus in turn causes a proportional increase in slip frequency and also source frequency causing flux simulator output to improve.

Im

6

Fig. 14: Vector diagram of Flux and Current Fig. 14 depicts the vector diagram of flux and current. Under the field orientation control, the stationary torque error is given by

where T* is torque reference, T is actual torque, respectively. Eqs.(l5) and (17) tell us that the flux estimation error is zero. This means that the angle 4 in Fig. 14 is zero. Then from (18) we can notice that the stationary torque is insensitive t o R, variation.

5.6

Speed Control Response

Fig. 15 and Fig. 16 show the speed control responses. (a) is of the slip frequency controller using the measured speed w,, and (b) is of the speed sensorless FOFO controller using the estimated speed G,. The waveforms are speed reference (U;), actual speed (w,),estimated speed (G,.) and flux simulator outputs (A,,,, A r i a ) , respectively. Speed reference was 0.5Hz rectangular waveform of 0 150 [r.p.m.] (Fig. 15)and -150 150 [r.p.m.](Fig. 16). The estimated speed in Fig. 15 (a) and Fig. 16 (a) are calculated but not used for speed control. The estimated speed is in good agreement with the actual speed in the higher speeds, but in the lower speed region the estimated speed has a considerable transient error. It is caused by H P F used in the speed estimator (see Fig. 9). Due to the presence of HPF, the flux simulator output signal a t low frequency is highly attenuated and so speed estimation performance is poor. In contrast, in Fig. 15 (b) and Fig. 16 (b), the estimated speed is immediately used for speed controller feedback signal and the flux observer. The estimated speed corresponds with the actual speed even a t lower speed range and the speed itself can be controlled fairly well. Estimated speed feedback causes torque

-

N

Conclusion

We proposed the speed sensorless FOFO (Flux Observer based Field Orientation) controller for the induction machine. The motor speed is estimated based on the difference between the outputs of two flux simulators. The torque generated by this system is extremely robust to rotor resistance variations. We implemented the system using a DSP and showed its efficacy through laboratory experiments.

Acknowledgment I would like to express my best acknowledgment to Professor Yoichi Kaya for his guidance, all kinds of wise advice.

References C. Schauder : Adaptive Speed Identification For Vector Control Of Induction Motors Without Rotational Transducers, IAS '89, pp 493-499

T. Ohtani, N. Takada ,K.Tanaka : Vector Control of Induction Motor Without Shaft Encoder, IAS '89, pp 500-507 Y. Hori, T. Umeno : Implementation of Robust Flux Observer Based Field Orientation Controller for Induction Machines, IAS '89, pp 523528 I. Miyashita, Y. Ohmori : Speed Sensorless Highspeed Torque and Speed Control Based on Instantaneous Spatial Vector Theory, IPEC- Tokyo '90, pp 1144-1151

X. Xu, D. Mi. Xovotny

: Implementation of Direct Stator Flux Orientation Control on a Versatile DSP Based System, IAS'90, pp 404-409

M. Vklez-Reyes, E;. Minami, G. C. Verghese : Recursive Speed and Parameter Estimation For Induction Machines, IEEE IAS '89, pp 607-611

U. Baader, M. Depenbrock, G. Gierse: Direct Self Control of Inverter-Fed Induction Machine, A Basis For Speed Control Without SpeedMeasurement, IEEE IAS '89, pp 486-492

Speed Reference 1r.p.m.l

1 11 w:

T-L

O

Estimated 150 Speed 1r.p.m.1 O 15 Torque Current [AI

0 -15

(a) Using Measured Speed

( b ) Using Estimated Speed

Fig. 15: Speed Control Response (0

Reference Ir.p.m.1

Actual Speed Ir.p.m.1

15:

150 [r.p.m.])

---I i ,/I 1

0 -150

t-1

w;

1 ,/-kr

[r.p.m.l

Actual

[r.p.m.l

-150

-150 I

Estimated 150 Speed [r.p.m.l Torque Current [AI

0

-15

Estimated

] x z

[r.p.m.l -150 Torque Current

IT

__

~

0

Speed

Gr

--

l5 0

-15

(a) Using Measured Speed

(11) Using Estimated Speed

Fig. 16: Speed Control Response (-150

391

-

150 [r.p.m.])