Servo Controller Design Using Polynomial Differential Operator Method and Its Applications

Abstract

A conventional PID controller has been used in most industrial fields so far. However, although the conventional PID controller can track a step type of reference without steady state error, it can have steady state error on disturbance, ramp, hyperbola, and higher order of references. Therefore, it is impossible to use the conventional PID controller in this cases. Moreover, a servo controller design problem for a given multi-input and multi-output system with disturbance and references which are polynomials attracting concern in control engineering field is one of most interested problems. To solve this problem, a new servo control design method is needed deeply. This dissertation proposes a new servo controller design method using polynomial differential operator method based on the internal model principle. To do this task, the followings are done. Firstly, modelings for an induction motor and an 4 wheel steering vehicle are proposed and are linearized. Secondly, a linearized system with disturbance is described. The disturbance and reference are expressed as the form of differential polynomial equations. Thirdly, it is shown that a closed loop system of the given system has zero steady errors by the final theorem when the controller includes the least common multiple of the denominators of reference and disturbance in its denominator using internal model principle. Fourthly, by operating the polynomial differential operator to the given system under the given conditions of reference and disturbance and an output error, an extended system is obtained. Fifthly, it is proven that the extended system is controllable. Sixthly, a full order observer of the extended system is designed to estimate its unknown states. To implement the proposed servo controller design method, a control system is developed to control speed of 1.5 Kw AC induction motor. Hardware for the proposed system is introduced. Hardware is designed to control 1.5 Kw AC induction motor. The TMS320F28335 DSP is selected as the digital controller for the system. Necessary peripheral and interface circuits are built for signal measurement, the three-phase inverter control and the system protection. Seventhly, the simulation and experimental results for an 1.5 Kw AC induction motor as a single-input and single-output system(SISO) and an 4wheel steering vehicle as a multi-input and multi-output system(MIMO) under a step type of disturbance and 3types of references such as step, ramp and parabola are shown to verify the effectiveness and the applicability of the proposed servo controller design method compared to PI controller. Finally, conclusions are presented and the future works are described.