Sensor Less Control Of Im Using A Neural Network For Speed Estimation

Sensorless Control of Induction Motor Using a Neural Network for Speed Estimation

M. P. Kazmierkowski, D. L. Sobczuk

P. Z. Filipek

Warsaw University of Technology, Institute of Control & Industrial Electronics ul. Koszyltowa 75, 00-662 Warszawa, Poland Fax: +48/22/6256633 E-mail: mi)lt(a~nov.isei~.l)w.edu.pl

Lublin Technical University Chair of Electrical Drive Systems ul. Nadbystrzycka 3Sa 20-618 Lublin, Poland phone: +48/81/5251051 ext. 311 E-mail: [email protected]

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Abstract In the paper the application of an on-line trained neural network working as speed estimator is presented. Three different speed estimation algorithms: back propagation, conjugate gradient as well as least square are investigated and compared. Some oscillograms which illustrate properties and sensitivity to parameter changes of the speed estimation techniques are presented.

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1. INTRODUCTION In recent years a lot of methods have been developed whtch allows to eliminate speed sensors, because in many industrial applications it is neither possible nor desirable to use a mechanical sensors. These methods can be generally divided in two groups: closed loop sensorless speed control where the motor speed is estimated from other measurable quantities as stat.or voltage and currents, and, open loop speed conrrol with slip compensnfion where the motor synchronous speed is controlled and the effect of load torque changes 011 motor sha€t speed is only compensated, For speed estimation very often advanced observer technique or iieural networks are applied [ 1,2,4,12]. Slip compensation methods. in contrast. are usually much simpler but cannot guarantee good dynamic perforinances [2,4,5-9,121. A very good review of different techniques for speed sensorless operation has been prescuted in the recently published IEEE Press book with selected papers reprints [ 111. Among published papers only one is based on Neural Networks (NN) approach [l]. Therefore. this work is devoted to study and compare different speed estimation algorithms implemented in the NN based system configuration proposed in [ 11. The general block diagram of sensorless control of induction motor based on NN speed estimation is shown in Fig. 1. The speed cominaitd signal u , ~ is , ~compared with estimated value U,,, and the error is delivered to the speed controller. As input signals to the NN speed estimator are stator voltage and current vectors. The actual speed om is measured by tacho for testing only.

IEEE Catalog Number: 97TH8280

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Fig. I . Sensorless control of PWM inverter-fed induction motor based on NN speed estimation

11. PRINCIPLE OF THE METHOD The concept proposed in [l] is based on two independent rotor flux simulators described in per unit system [SI: - voltage model

- current model

where:

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=

[U,,

uSB] - stator voltage vector,

stator current vector, flux vector estimated froin (l), Xr, = [ v,,, - rotor flux vector estimated from (Z), r,. , rr - rotor and stator resistance, x, , x,- rotor and stator reactance, T,= (TNx,/r,)- rotor time constant, TN= (1/2nFSN)= ( I / 2 ~ 5 Hz) 0 - nominal time constant, CT = 1- (xMxM/x,xs ) - leakage factor is = [is@

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[ 'yruna. ~y,,~~] - rotor

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C. Least square method ( L q

The third method of speed estimation is not based on neural network structure. The idea is to apply to (3) least square optimization method. Therefore, one can obtain the following equation: Fig 2. Block diagram ofthe NN based speed estiiiiator

The block diagram of the NN speed estimator is shown in Fig. 2.

111. SPEED ESTIMATION ALGORITHMS

Note, that this method carries out optimization in one step, and the learning process does not exist.

The discrete current iiiodel of 1-otor flux one can calculate from (2).

IV. HARDWARE CONFIGURATION

where T, is tlie sampling tune The model based on (3) 1s similar to neural network One weight is mechanical speed, and the output is & ! [I] The error output IS given by

Therefore, to calculate estimated mechanical speed can use training algorithm to above systeni.

U),,,

one

A. Back propagation algonthrr (BP1

The experimental system configuration is shown in Fig. 3. The inverter power circuit feeding induction motor is coinposed of IGBT power modulus rated 75 A, 1200 V. IGBT power switches are controlled using fibber optic transmitters. Induction motor and inverter parameters are given in the Appendix. The inaiii processor TMS320C31 DSP is used in the laboratory set up. The system operates at 40 MHz clock frequency and is capable of 32-bit floating point operation. The actual two phase currents and voltages as well as DC link voltage are detected by LEM sensors and processed by 12-bit A/D converters. All internal data of DSP can be displayed trough a 4-channel 12-bit D/A converter.

The most popular learning algoritlini is based on gradient descent method and IS called back propagation algorithm [IO]. Using this learning method one can get following formula:

Hidden Signals

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Isolating Cowerters (Sigma Delta) Light transmiters (LED) and detector

.where q is called learning rate a i d a - momcntum factor

E. Conjugate gradient algorithin(C '(i) There exists some methods that make the learning algorithm faster One of them IS based on conjugate algorithm technic [ 131 This iuetliod implies. that the momentum factor U is changed during learning time according to the following foriiirila

DSP Board DS1102 with TMS320C31

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Host Computer

Fig. 3. Experiineiital system based on TMS320C3 1

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V. RESULTS

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Back propagation- .Conjugate gradient Least square -

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The algorithms for induction motor speed estiinatioii presented in the Section I11 were investigated in term of learning abilities and sensitivity to the rotor resistance changes. It can be seen from siinulated oscillograms of Fig. 4, that the longest learning time is needed for the back propagation algorithm, whereas least square is an on h e algorithm which do not need any teaching time. In Figures 5 , 6 and 7 the behaviour of vector controlled PWM inverter-fed induction motor with closed loop (measured by taclio) speed regulation are presented. In each case starting (0 -+ 0.2 pu), speed reversal (0.2 -+ 0.2 pu) and braking (- 0.2 pu 4 0) characteristics are shown. As can be seen froin Fig. 5 , all three algorithm can give satisfied speed estimate (b) when the rotor resistance is set correctly. The speed estimation error, however, increase multitimes when rotor resistance change (Fig. 6 and 7). This is especially observed in the case when the rotor resistance used in estimation algorithm is 5 0 %I higher rr* = rr (Fig. 7). In all cases the ininirnal estiinatioii error (c) can be observed for least square algorithm. Selected parameters of three types of speed estimation algorithms are compared in Table 1. The results show clearly superiority of Least square over Back propagation and Conjugate gradient algorithms. However, all three algorithms are very sensitive to rotor resistance changes. TABLE I Comparison of tlvee speed estimation algontlmis

BP 6 171.5 12

CRITERION Learning time Algorithm complexity (multplrcatrorzs) Stability

Sensitivity to parameter changes RMS error * rr = rr constant load variable load rr*= 0.5 r,. ini = 0.5 m, = 2 or -2 rr*=1.5 rr mi,= 0.5 ml = 2 or -2

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Fig. 4. Learning process using three methods (BP, CG, LS): a) leaming error, b) ims of leaming error.

VI. CONCLUSIONS Application of artificial NN speed estimators for PWM inverter-fed induction motors creates many new schemes. One of the simplest scheme is based on combination of the voltage (1) and current (2) rotor flux estimation proposed in [ 11. This paper outlines two new algorithms (Conjugate gradient and Least square) for speed estimation implemented in the scheme of Fig. 2, and gwes a comparison. The presented results show that - from the point of view of complexity, stability, calculation time and sensitivity to parameter changes - the Least square algorillim is the best. This is quite understandable, because for the particular linear NN is possible to calculate minimum of flux error in one step.

References [ 11 L. Ben-Rrahim and R. Kurosawa, "Identification of induction motor speed using neural networks," in PCC-Yokohama, pp. 689-694. 1993. [2] B.K. Bose (Ed),"PowerElectronics and Variable Frequency Drives, " EEE Press, 1996 [3] T. Fukuda, and T. Shibata, "Theory and application of neural networks for industrial control," IEEE Trans. on Ind. Electronics, vol. 39, no. 6, pp. 472-489, 1992. [4] J. Holtz, "Speed Estimation and Sensorless Control of AC Drives", IEEE/IEUIN'93, Con$ Rec., pp. 649-654, 1993. 151 A. B.Kasprowicz, M. P. Kazmierkowski, S. Kanoza, "Speed Sensorless Direct Torque Control of DC Link Resonant Inverter-Fed Induction Motor Drive," in Proc. IEEE Intern. S-vmposiunr on lndustrial Electronics ISIE'96, Warsaw, POlaIld, pp. 186-189, 1996. 161 M.P. Kazmierkowski, H.-J. Koepcke, "A simple control system for current source inverter-fed induction motor drives," IEEE Trans. on Ind. Application, MaylJune, N o . 3, pp. 617-623, 1985. [7]M E'. Kazinierkowski, H.-3. Koepcke, "Current source

inverter-fed induction motor drive system controlled without speed sensor," in European Conference on Power Electronics EPE,Brussels, Belgium, Con$ Rec., pp. 3.345-

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where: inL - load torque

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Kazinierkowski, H. Tunia, Automatic Control of llrives. Warsaw - Amsterdam - New York -

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Tokyo: PWN - ELSEVIER 1994.

IEEE Catalog Number: 97TH8280

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Fig. 5 . Simulated oscillograms of spced dynamic usiiig t h e e methods (M', CG, LS): a) mechanical speed and r e

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IEEE Catalog Number: 97TH8280

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Fig. 7 . Siniulated oscillograms of speed dyiianiic using thee Inethods (RP, CG; LS) with

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a) mechanical speed and reference s p d . b) estimated speed. c) speed estiiiiatioii m o r . d) filtered speed estimation error, e) m of speed estimation error.

191 M. P. Kazmierkowski. M. A lL)zicuial;owski, A. B. Kasprowicz, S. Karioza, "Speed Seiisorless Control of DC Link Resonant Inverter-Fed hiduction Motor Drives," in Yroc. PEMC'96, Budapest, l-Iuiigary pp. 1 10-1 14 , 1996. [ I O ] K.P. Lippinaim, " A n introduction 10 computing with iieural nets," IEEE ASSPA4agozirre, April, pp. 4-22, 1987. [l 11 T. S. Low, T H. Lee, and 1-1 K. Lim. "A methodology for iieural network trniiiiiig for control of drives with nonlinearitites," IEEE Truirs. OYI I JE~vctiwJies, ~. vol. 39, no. 2, pp. 243-249, 1993. [ 121 K. Rajashekara et. al.: ':Cwsoi,les.r ~ 7 ( 1 i 1 ~ 7qfd ACI Motor Drives. Speed and f'o.cilioir .Seiisrii~lcs.v Opeintion, IEEE Press, 1996. [ 13 I Zhou G~~ozhong, Sui1 Yaiiiiiip: 'L4 ( 'on/hirrcd Lear-rizng A~gOi~z~h?7? *for*n/iullz-la.vrr.crl N e u ~ iV
APPENDIX

Motor Data (per unit): r, = 0.0464 rr = 0.0311x, = 2.237 x, = 2.194 x,%t 2.133 T M = 0.4 s

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IEEE Catalog Number: 97TH8280

Inverter Data: DC link voltage = 1.5 pu Sampling h i e = 10 KS

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