CONTROL OF INDUCTION MOTOR BASED ON NEURAL ESTIMATOR

The paper deals with a sensorless control of induction motor based on neural network estimators. In the paper are presented simulation and results of designing neural estimators for observing the rotor magnetic current and the motor angular speed. The neural estimators of rotor magnetic current and angular speed for induction motor field oriented control were designed in MATLABSimulink. Controllers for simulation of shaft sensorless field oriented control have been designed by state space method.


INTRODUCTION
Motors play important roles in industrial producing and in many other applications.In their early days, d.c.motors had the advantage of precise speed control when utilized for the purpose of accurate driving.However, d.c.motors have the disadvantage of brush erosion, maintenance requirements, environmental effects, complex structures and power limits.On the other hand, induction motors are robust, small in size, low in cost, almost maintenance-free.
Hasse [9] and Blaschke [10] developed a field oriented control theory to simplify the structure of IM speed control used to drive the d.c.motor.In recent years, the field oriented control theory has become more feasible due to progress in the development of electronics techniques and high-speed microprocessors.Nonlinear control problems can often be solved if full state information is available; in the IM case the rotor states are immeasurable and often the angular speed of the rotor is too costly to be monitored.
In most applications, speed sensors are necessary in the speed control loop.On the other hand, there are applications where lower performance is required, cost reduction and high reliability are necessary, or hostile environment does not allow using speed sensors.In these fields, speed sensorless IM control can be usefully applied.Many different solutions for the estimation of states variables or model parameters have been proposed currently, for example estimators utilizing the motor construction properties, estimators based on the drive dynamic model or estimators based on artificial intelligence [7,8,13,15,16].
At present, requirements on the dynamic precision are not too strict and virtual or soft sensors are alternatively successfully utilized.Estimators based on artificial intelligence are divided into the following groups:  systems based on the fuzzy logic,  systems based on neural networks,  systems based on hybrid systems,  systems based on evolutionary algorithms (genetic algorithms).

DESIGN OF NEURAL ESTIMATOR FOR CONTROL OF INDUCTION MOTOR
The neural modelling can perform estimation of the induction motor angular speed or of other non-measurable variables on the neural networks base.
Nowadays, commonly used in the industry there are field oriented controlled drives based on different solutions and performances.With field-oriented techniques, the decoupling of flux and torque control commands of the IM is guaranteed, and the induction motor can be controlled linearly like a separately excited DC motor.The DC motor like performance can be obtained by preserving a fixed and orthogonal orientation between the field and armature fields in the induction motor by orientation of the stator current with respect to the rotor flux in order to attain independently controlled flux and torque.Block diagram of the control scheme is presented in figure 1.Using the field oriented control principle, the stator current component i d1 is aligned in the direction of the rotor flux vector and the stator current component i q1 is aligned in the direction perpendicular to it.The rotor flux orientation in the squirrel-cage rotor IM cannot be directly measured, but it can be obtained from terminal variables.
After using transformation of coordinates d, q to the rotating system x-y, the electric torque is proportional to the i 1y component and the relation between the rotor flux and i 1x component is given by the first order linear transfer function with T 2 = L 2 /R 2 time constant.
From this fact and for the considered flux control, the stator current and voltage components were chosen as input signals for reconstruction of the induction motor speed.The developed estimators were trained according to selected training patterns from the direct field oriented control of the induction motor.

Induction motor FOC simulation design
In the design of state control by method of the poles determine for two input variables and one output based on the following equations: Define the state variables: i 2m =x 1 ; i 1x =x 2 ; ω=x 3 ; i 1y =x 4 ; m z =z; u 1 =u 1x /K T ; u 2 =u 1y /K T .
Then, written can be the state equation for induction motor: The constants and functions used in the state equation ( 6): Nonlinear function f 2 (x), f 4 (x) in the control scheme shown in Fig. 2 compensating for introduction of control u, so as to simplify the state equation: From the characteristic polynomial of all controller circuits were calculated constants for field oriented control scheme.

Magnetising current neural estimator
If for vector control the x-th component of the stator current vector is considered as a basis of current-creating component then the magnetising current i 2m estimator will process current-creating component of the stator current.
As mentioned above, the magnetising current i 2m neural estimator bases its estimation of the currentcreating component of stator current i 1x .Dependence between currents i 2m and i 1x is linear, and hence the estimator can be made up of a feed-forward neural network without any hidden layer.For the activating function the purelin linear function can be used.The input data vector consists of values of the stator current i 1x in step (k) and step (k-1), respectively, and also the preceding value of magnetising current i 2m in step (k-1).Basic equation of such neural estimator we can describe as: Here, O stands for output values vector here, I is the input data vector and w i presents weights of individual connections of neurons.Substituting the input matrix to equation ( 7), we will obtain the equation for the magnetising current neural estimator in the following form: where current i 2m (k) is the output variable and the input variables are i 1x (k), i 1x (k-1) and i 2m (k-1).

Magnetising current neural estimator
If for the basis of torque-creating component we establish the y-th component of the vector then the speed estimator will estimate this torque creating component from the stator voltage and current.
As it was already mentioned above, the angular speed ω neural estimator bases its estimation on the torque component of stator voltage u 1y and current i 1y .The relation between the input and output quantities is not represented by a simple linear dependency, and this is the reason why for the estimation a cascade neural network with one hidden layer consisted of eight neurons will be used.As an activating function for the hidden layer used there was the tansig nonlinear function and for the output layer used was a purelin linear function.The input data vector is represented by values of stator voltage u 1y and stator current i 1y in steps (k) and (k-1), as well as by value of magnetising current i 2m in steps (k) and (k-1).Simply we can describe this neural estimator as: Here, O is the output values vector, I present a vector of input variables and w i , w j , w k are weights of individual connections of neurons.Post substituting the input matrix to equation ( 9) the neural speed estimator can be described by the following equation: where the output quantity is ω(k) angular speed value and where the input are values u 1y (k), u 1y (k-1), i 1y (k), i 1y (k-1), i 2m (k) and i 2m (k-1).

RESULTS
In the following, shown there are simulation results of sensorless vector control of an induction motor when applying neural estimators of the speed and magnetising current, respectively.
The principal diagram of the vector control with connected neural estimators of the magnetising current and speed is shown in figure 2. Figure 3 and figure 4 shows a comparison of real and observed values of the magnetizing current and the angular speed, whilst shown by a dashed line there is the required angular speed value during starting, reversing and loading transients.In time of 2s the motor was loaded by the rated load torque.The waveforms shown in figure 3 and figure 4 are valid for case of no feedback to control from the neural observers but led directly from the motor mathematical model.

Fig. 1
Fig. 1 Basic field oriented control scheme

Fig. 2
Fig. 2 Basic diagram of vector control with neural estimators

Fig. 3
Fig. 3 Comparison of the estimated versus actual magnetising current

Fig. 4 Fig. 5
Fig. 4 Comparison of the estimated versus actual speed of the IM