A SMALL NEURAL NETWORK STRUCTURE APPLICATION IN SPEED ESTIMATION OF AN INDUCTION MOTOR USING DIRECT TORQUE

CONTROL Pedro Ponce Cruz. Jaime J. Rodriguez Rivas.

Section of Graduate Studies and Research College of Electrical and Mechanical Engineering

National Polytechnic Institute. Pho./fax:+(S2)S7296000.ext.S42 18. E-MAIL: peterpon@hotmail.com

jairod66@hotmail.com

Abstract- This paper shows a small structured neural network speed estimator for induction motors using direct torque control (DTC) method. The backpropagation technique was used to train the neural network. The small structure leads to short off line training and processing times. The overall algorithm based on a conventional DTC close loop is simple and the results are validated through simulation and implementation. -

I. INTRODUCTION For over fifty years, dc motors have been widely used in variable speed drives applications principally due to their dynamic response and the possibility to use these motors in whichever mode of operation. However, the characteristics of the induction motor: high efficiency, robust, low costs, volume and maintenance, and the capacity to work in practically all environments in a safe and reliable way, makes the induction motor attractive in variable speed drives applications. With the introduction of new techniques in vector control as proposed F. Blaschke and K. Hasse, a new stage was set in which the control of induction motors started replacing the control of dc motor. Vector contiol methods based in the orientation of the machine’s magnetic field along one of the rotating reference axis makes it possible to uncouple the rotor magnetic field from the electromagnetic torque. The equations obtained within the reference framework selected permit the implementation of a control scheme for the induction motor, thus achieving dynamic response similar to that given by a separately excited dc motor. In vector control methods, it is necessary to determine correctly the orientation of the rotor flux vector, lack of which leads to degradation in the speed control of the motor [ 121. The complexity of vector control and its sensitivity to parameters makes the DTC a good solution in high performance drives [lo].

11. DIRECT TORQUE CONTROL DTC has demonstrated its potential in optimizing the operating characteristics of the induction motor drive fed by a PWM inverter [14]. It can achieve a response as quick as in a dc motor. Although the motor is not controlled by a conventional field oriented method, PWM waveforms have been obtained owing to the on - off control of both the stator flux and the torque by using an optimum switching table (six non zero voltage vectors have phase displacement of 60 degrees from each other, and two zero voltage vectors are selected to stop the stator flux). For the case, which must be performed with less sensitivity to the motor parameters [14], the stator flux and torque are either measured or estimated and used as feedback signals for control. The inputs of the selection table used are the torque error, the error in the magnitude of the stator flux space vector, and the angle of the stator flu space vector. The magnitude error signal of the stator flux is discretized into two levels by means of a hysteresis comparator. The torque error signal is discretized into three levels by means of three stage hysteresis comparator. The output of the selection table is the setting for the power switching device of the inverter [ 131.

Fig. 1. Conventional DTC

0-7803-7067-8/01/$10.00 02001 IEEE 823

V_k+l VJ+2 The basic equations for the DTC are shown below

[14]: The phase output vector is given by

+2-1-1 A

[;]=;v+;-][;]

where v,, - is the DC supplying voltage.

[A B is the switching vector (fig. 2). The stator voltage space vector is given by

'"I .2n

VA+VBe"+VCe

Equation (2) can be implemented using an inverter where the eight conduction modes can be achieves using an appropiate combination of the switches A, B and C whose value can be I or 0

The stator flux linked space vector is given by the integral of the voltage vector

(fig. 2).

vl,=J(T-CR,)dt (3) And the developed torque is given by

(4)

where 6,, - Angle between the stator and the rotor flux space vector. The angle of stator flux space vector is given by

The change of the stator flux and torque is defined by the selection of six non zero voltage vectors and the zero voltage vectors (fig. 3). A selection table can be obtained to control the stator flux and torque of an induction motor in optimal way.

V-h-2 V-k-1

Fig. 3. Space vector voltage.

Table 1 . Space vector voltage influence on torque and stator flux space vector.

III. ARTIFICIAL, NEURAL NETWORKS The artificial neural networks (ANNs) are based on the model of the human brain and contain artificial neurons. The ANNs are capable of learning the desired mapping between the inputs and outputs signals of the system without knowing the exact mathematical model of the system. Since the ANNs do not use the mathematical model of the system, the same ANNs arquitecture can solve many problems. The ANNs are excellent estimators in non linear systems [5], [9]. The basic elements of ANNs are the neuron. A neuron has four main parts:

Input (s) Weighted summer and bias Activation Function output (s)

xo*-/

Fig. 4. Artificial Neuron Fig. 2. Diagram of PWM Inverter.

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Multi layer ANNs are built with neuron blocks, There are four neurons in the input layer, six neurons in the neurons are arranged in several parallel layers, the hidden layer, and one neuron in the output layer. this layers fall into the classifications input layer, The backpropagation training algorithm used adapted hidden layer and output layer. weights and biases taking as a reference the output from The arquitecture of the ANNs is not predefined, the induction motor speed model. The weights and some times one hidden layer is sufficient to biases were then set ready for simulation and perform any non linear input- output mapping implementation. system. The training is the part of the process, which adjusts the weights and biases. The training algorithms can be supervised or non supervised. Backpropagation algorithm is used in supervised training for multi-layer feedfonvard ANNs which was used in this work.

IV. CONTROL SCHEME PROPOSED DTC is known to give quick and robust responses in open loop speed control in ac drives. However, in order to achieve higher precision, it is necessary to use a closed loop control scheme [ 1, 2 and 31. Controllers based on direct torque control do not require complex coordinate transformations. The uncoupling of a non linear induction motor results in a simple model, and the small neural network structure suggested here is also simple, hence the overall closed loop structure obtained is not complex. The resulting closed loop scheme is shown in fig.5. In this work we used a conventional DTC scheme [1,2] and propose a small structured neural network speed estimator to make a closed loop speed controller. Neural networks approximate complicated functions using several layers of neurons, structured in the same way as the human brain. Artificial Neural Networks (ANN'S) have learning and generalization capabilities, thus are referred to as universal approximators. [4,5,6 and 71. The generalization property makes it possible to train neural networks with a limited training data set. In this case, the currents (Isd and Isq) and the voltages (Vsd and Vsq) form the data set used (see fig. 6 and fig. 7). Each neuron has a Sigmoid

. function as an output.

INPUT HIDDEN LAYER LAYER

Fig. 6. Neural network structure.

I o;.: ' 1 L "

I

Fig. 7. Set up to teach the neural network

V. SIMULATION RESULTS. The simulation result obtained are shown below:

Fig. 5. Closed loop speed control in an induction motor using a neural networks speed

Fig. 8. Open loop response of a conventional DTC scheme (flux in webbers, torque in Nm, time in

estimator. seconds).

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Fig. 9. Closed loop speed response of an induction motor using neural network speed estimation with a conventional DTC scheme (speed in rads, time

in seconds).

From fig. 8, the conventional DTC response is satisfactory, the response (flux and torque) tends towards the reference values used. From fig. 9, the motor speed response is seen to tend towards the reference value, confirming than the network has been correctly trained. The induction motor and drive system parameters used in the simulation and implementation are given in the appendix

VI. IMPLEMENTATION. Fig. 5 shows the closed loop scheme implemented using an MCK-240 TECHNOSOFT motion control kit [SI. This kit includes a DSP324F240 digital signal processor (see fig. 10). The estimated speed obtained from the kit (ANN) is shown in fig. 1 1, together with motor speed values read using an encoder, and the absolute error is shown in fig. 12.

Fig. 10. General kit MCK240 scheme [8].

I I;$ 11, ill m4 322 :*e z$'* re#? *!a

l x r a i a x w . a n . l t r 2 ,

Fig. 1 1. Estimated speed and actual motor speed (read using an encoder) against time

(speed in rads).

0.06 0 ' 0 7 7

0.04 O . O 5 l h O ' O 4

-0 " O ' ~ 02

50 I00 150 200 250 300 350 400 450 51

Fig. 12. Absolute error (root-mean-square error between the desired speed and the estimated speed).

n=* - 1 9 1 me $3.- if

Fig. 13. Motor speed against time with increasing load torque (speed in rads).

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VU. CONCLUSION , The simulation and implementation results

obtained show that speed estimation using a small . neural network structure was effective and gives

satisfactory results in a closed loop DTC scheme. On loading the motor, the neural network estimation successfully tracks down the changing speed as shown in fig. 13. The use of the proposed neural network scheme does not increase the complexity of the overall structure, making it a good alternative for closed loop speed control with a conventional DTC.

Electrical time constant

Magnetization current

REFERENCE [l]. James N. Nash., “Direct Torque Control,

Induction Motor Vector Control without an Encoder”. IEEE Transation on industry applications, vol. 33 No 2 March/ April 1997 pp.

[2]. Takahashi, I and Asakawa, S, “Ultra-Wide Speed Control of Induction Motor Covered 10A6 Range”. IEEE Transactions on Industrial Aplications, IA25,pp 227-232,1987. [3]. Boldea, I. and Nasar,S.A, “Vector Control of AC Drivers”. CRC Press Inc.,1992. [4]. K. Hornilk, “Multilayer Networks are

333-341. tau el = 1.8474 ms

Im = 0.657 A

[14] I. Tajahashi and T. Noguchi, “A New Quick Response and High Efficiency Strategy of an Induction Motor”. In conf. Rec. IEEE-IAS.

I Flux factor I 1.52 Nm I A I

APPENDIX

Flux factor Acceleration factor Total inertia Motor nole nairs

INDUCTION MOTOR PARAMETERS:

Rated current

Power factor 0.8 = 50 Hz.

1.52 Nm I A 4331.97 Nm I A I kg m2 3.5 e -4 kg mz

P = 1

Stator resistance Rotor resistance Rr =16.8Ohms

Lm =1.537H

Acceleration factor Total inertia Motor nole nairs

4331.97 Nm I A I kg mz 3.5 e -4 kg mz

P = 1

PEDRO PONCE CRUZ born in Universal Approximations”. Neural Networks,

Mexico, did his undergraduate degree in Control and Automation at [5]. K.Funashi, “On the Approximation of

National Polytechnic Institute, Continuos Mappings by Neural Networks”.

graduating in 1995. Did his masters Neural Networks, v01.2 pp 183-192,1989.

at the department of the Electrical [6]. B. Kosco, “Neural Networks and Fuzzy

Engineering, National Polytechnic Systems: A Dynamic Systems Approach to Machine Intelligence”. Englewood Cliffs, NY Prentice Hall 1992. Institute graduating in 1998. Currently, he is a doctorate 171. Lippmann, “And Introduction to Computing student at the same institute. His research interests with Neural Networks Nets,”. IEEE ASSP include artificial intelligence, control systems, electrical Mag.,Apr. 1987pp 4 -2 1. drives, electrical machines and power electronics.

vol. 2,pp 359-366,1989.

[8].-User Manual kit MCK 240 Technosoft (DSP Motion Solutions) 1997. [9]. Cybenko G, “Approximation by Superposition of Sigmoidal Function”. Marthematics of Control , Signal and Systems, 2,

[lo]. Pedro Ponce, Jaime Rodriguez, “Simulation of Direct Torque Control”. RVP’ 2000,pp 174- 179, Acapulco Mexico. [ 1 11. Peter Vas,”Artificial-Intelligence-Based- Electrical Machines and Drives“. Oxford Universyty Press, 1999. [ 121 Pedro Ponce, Jaime Rodriguez, “Induction Motor Space Vector Control Using Adaptive Reference Model Direct and Indirect Methods”. ISIE2000, vol 1,pp. 300-305, Puebla Mexico. [ 131.1 Ludtke, Dr mgjayne “Direct Torque Control of Induction Motor”.-

304-14-1989

JAIME J. RODRIGUEZ RIVAS born in Cienfuegos, Cuba in 1955. Graduated as an Electrical Engineer from the Central University of Las Villas in 1980. Worked as a lecturer in the Faculty of Electrical Engineering at UCLV from 1980

to 1994. In 1987 obtained his Ms and in 1991, obtained his doctorate both from The Moscow Energy Institute. Was the head of department at UCLV from 1992-1994. He currently works as a lecturer and research at the Graduate School, Department of Electrical Engineering, The National Polytechnic Institute.

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