Rotor Speed Estimation in Vector Controlled Induction Machine Using Neural Network

Abstract

The paper analyzes one of the structures of vector control of an induction motor (AM) without a speed measuring term. This vector control system of an induction motor is based on a reference model with an adaptive system (Model Reference Adaptive System, MRAS). The rotor magnetic flux vector is the physical quantity that is estimated by the voltage (stator winding equation) and current model (rotor winding equation). The current model was chosen to be reference, and the voltage model was adaptive. The difference in the estimation of the rotor magnetic flux vector obtained from these two models is used to estimate the rotational speed and identify the stator ohmic resistance. The computer algorithm that, in the described way, in calculations and in real operation, estimates the rotational speed and identifies the stator ohmic resistance is called the observer. This observer is based on the theory of adaptive control. The inter-inductance of the analyzed motor changes due to saturation in the iron, especially at lower frequencies of the supply voltage. Therefore, in the vector control system based on the MRAS theory, the influence of the error in the estimation of the motor’s mutual inductance, which is a parameter in the observer, was investigated, and it directly affects the indicators of the quality of the speed regulation and the stability of the vector control system. A simulation computer program for the AM vector control system was created, taking into account the saturation of the main magnetic circuit. Step changes in the speed reference and load torque were simulated. The mathematical model of the vector control system was created in a synchronously rotating d, q coordinate system related to the rotor magnetic flux. For the purposes of experimental research, a laboratory model of the AM vector control system was created. The vector control system is implemented using the digital signal processor TMS320F240, which is built into the control card DS1104, manufactured by dSpace. The frequency converter is self-made with IGBT transistors (100 [A]) and with a constant DC intermediate circuit voltage. In this work, it was chosen that the control of IGBT transistors is performed according to the algorithm of vector PWM modulation (eng. Space Vector Pulse Width Modulation, SVPWM). Spectral analysis of the calculated and measured AM stator current vector showed that the amplitudes of the higher harmonic components are negligible compared to the amplitude of the fundamental harmonic. For this reason, the inverter with vector PWM modulation, from the point of view of speed regulation, can be idealized in such a way that instead of the stator voltage vector, the reference voltage vector of the inverter is considered. In this dissertation, the estimation of the rotation speed of the AM was analyzed using a simple two-layer neural network and multi-layer static neural networks of different structures. Elements of the theory of neural networks are presented in this paper. The speed estimated by the neural network is sensitive to the accuracy of the estimation of the mutual inductance, which is given as a parameter in the vector control system. Errors in the estimation of the mutual inductance of the motor lead to distortion of the speed estimated by the neural network. This distortion is manifested in the fact that the speed estimated by the neural network differs from reference speed and that in addition to the DC component, higher harmonic components also appear in the speed. These higher harmonic components are more pronounced the greater the error in the estimation of the mutual inductance Lm. The frequency of the first higher harmonic in the estimated speed fN1 is equal to the frequency of the first harmonic of the supply voltage vector-controlled induction motor. As a quality criterion for estimating the rotational speed by a neural network in the steady state of an AM, an analysis based on the calculation of the mean value and standard deviation of the rotational speed estimated by the neural network has been proposed. It is shown that the ohmic resistance of the stator of a vector-controlled AM can be identified by the analyzed observer only in stationary operating modes, while in dynamic operating modes this identification is unsatisfactory. For the purposes of stability analysis, a linearized model of the AM and a linearized model of the control system were created. This The two models are combined and the transfer function of the vector control system at the reference speed is obtained. By observing the motion of the zeros and poles of this transfer function in the complex plane, one can conclude about the stability of the vector control system. It is shown that the best indicators of the quality of speed regulation are achieved if motor inductance estimated without error. If the inductance is estimated at a value smaller than the actual ( ), the motor speed first becomes oscillatory, and then the control system becomes unstable. If the intermediate inductance is estimated to be greater than the actual ( ) then there is a static deviation of the reference speed from the actual speed, and the settling time of the speed response to a sudden change in the speed reference is approximately twice as long as when there is no error in the estimation of the AM intermediate inductance.

Dinko Vukadinović

Full Professor | Department of Power Electronics and Control

Full professor at the Faculty of Electrical Engineering, Mechanical Engineering, and Naval Architecture in Split, specialized in modern control systems for power electronic converters, electric motors, and generators. At the Power Electronics Research Laboratory, he leads experimental projects and develops advanced methods for regulating electrical machines and converters, while supervising doctoral research in these areas.