Research on Neural Network Based Inverse Model of Induction Motor Drives

—Since the realization of inverse model is very important for inverse decoupling control of induction motor (IM) drives, the purpose of this paper is to develop an efficient artificial neural network (ANN) based inverse model for IM drives. First, the existence of the inverse system for IM drives is proved by inverse system theory. However, the analytic inverse model is hardly applied in the engineering since it excessively depends on the parameters. Then a novel neural network based inverse model, which synthesizes non-analytic method and analytic method, is suggested in this paper. To accelerate the convergence speed of ANN and enhance its generalization ability, the nonlinear parts are realized by the analytic expressions and the corresponding results act as the inputs of network. A three-layered feed-forward ANN with 11-40-2 structure is introduced to approach the inverse mode of IM drives. This study shows that the procedure using ANN based inverse model is applicable to substitute the analytic inverse model of IM drives. Simulation results are given to verify the developed models.


INTRODUCTION
Induction motors are a theoretically interesting and practically important class of nonlinear systems which constitutes a benchmark example for nonlinear control [1]. The control task is further complicated by the fact that induction motor is a nonlinear, multivariable system, and there is coupling between the stator and the rotor circuit, in addition, the parameters are highly uncertain. In order to control electrical torque exactly, the electrical torque is decoupled from the flux in the course of transient and steady processes [1]. However, in the vector control (VC) method, the decoupled relationship is obtained by the stator current vector divided into torque part and flux part in the rotor flux-oriented coordinates under the hypothesis that the rotor flux is kept constant. So the electrical torque is only decoupled asymptotically from rotor flux during steady state. Recently, decoupling control methods based on inverse system theory have been used in the design of induction motor drives for high performance applications [2].
Artificial neural network (ANN) have been used in various control field with the characteristics of self-adaptive and learning, nonlinear mapping, strong robustness and faulttolerance. In the past few years, ANN technique has been also studied in electric drive [3][4][5]. In this paper, an ANN Inverse decoupling control of torque and stator flux is presented. First, the existence of the inverse system for IM drives is approved by inverse system theory. To accelerate the convergence speed of neural network and enhance its generalization ability, a novel method of synthesizing neural network and analytic function is suggested, in which the nonlinear parts are realized by the analytic expressions and the corresponding results act as the inputs of network. A three-layered feed-forward ANN with 11-40-2 structure is introduced to approach the inverse mode of IM drives. Simulation results shows the feasibility of the proposed scheme.

II. DYNAMIC MODEL OF INDUCTION MOTOR DRIVE SYSTEM
For an induction motor, if the stator current and stator flux are selected as the state variables, the state equation is described as Eq. (1) in the stationary reference frame: ( ) where s R and r R are stator and rotor resistances, sd u and The mathematical model of an induction motor can be expressed in the classical state-space representation as Eq.
It can be seen from Eq. (1) to Eq. (3) that the induction motor is a 2-input, 2-output, nonlinear, strong coupling system.

III. ANALYSIS OF INVERSE SYSTEM
According to Eq. (3), it can be concluded that there is indirect relations between output variables and input control variables. In order to get direct relations, the output equation is differentiated by time as In terms of invertible theorem in [3], the system is invertible. From Eq. (4), the control effort can be expressed as The inverse model and the original model constitute a generalized induction motor system, which is characterized by decoupling and linearization.
Dynamic model of the general system after decoupling control is described as Under the assumption of exact decoupling by using Eq. (6), the decoupling control system with classic PID can obtain perfect torque response performance. But due to state estimation errors and IM parameter variations, the decoupling precision gets worse and the control performance is destroyed in the realistic applications.

IV. NEURAL NETWORK BASED INVERSE MODEL
In order to overcome the defect that the analytic method excessively relies on IM model and its parameters, an ANN based inverse decoupling control is researched in this paper.

A. Neural Network Design
According to Eq. (5), there are static relations but not dynamic relations between states and control effort in the inverse system. So a static neural network can be chosen to approach the nonlinear static function. In order to simplify the neural network structure, the Eq. (5) can be modified as To accelerate the convergence speed of ANN, the nonlinear operations are realized by the analytic operation method and the corresponding results act as the inputs of network. Then the ANN is expressed linear structure as

B. Data Processing
The input I 1 and I 2 of ANN are very sensitive by highfrequency noise for using differential operates. Therefore, it is necessary to design digital low-pass filter for torque and stator flux. A linear phase FIR filter is designed in this paper, whose idea is that according to given performance index of filter, the length N and window function Wn of filter are chosen, then finite unit impulse response sequence is determined by adding window. Its performance index demands include: 1) passband cutoff frequency is 10Hz; 2) stopband cutoff frequency is 15Hz; 3) passband ripple is 0.0005; 4) stopband ripple is 0.001; 5) sample frequency is 1kHz.The FIR filter is easy to be designed by using the order function and filter function of MATLAB (a part code seen in Appendix A), and its magnitude and phase frequency characteristic is seen in Fig. 1., and its comparative results are seen in fig. 2-3, which shows the highfrequency noise is well restrained. , whose number is 1200, in which 2/3 of data sample is used to train ANN and the rest is applied to verify the ability of generalization. The goal of train-parameter is set 0.25. The training results is shown in Fig. 4, which shows the performance goal met after 4 epochs, i.e. good convergence performance.   VI. CONCLUSIONS ANN based inverse model of IM is deeply researched in this paper. The major contributions of this paper are organized as followings: 1)the well restraining high-frequency noise; 2) the successful application of ANN with analytic function; and 3) the successful training of the proposed ANN.