DIGITAL CONTROL OF LINEAR DYNAMIC SYSTEMS

Abstract

The advent of inexpensive and easily available mini computers and microprocessors has led to renewed interest in the field of digital control systems and in particular controller design methods. The objective of this thesis is to develop new methods for digital controller design in the frequency-domain. The main emphasis has been to develop design techniques that are mathematically simple, computationally elegant and its translation from theory to hardware is easy and their performance is comparable, if not superior, to those of the existing techniques. - - The design philosophy of the methods developed in this work is based on a frequency-domain approximate model-matching concept. The desired time and frequency-domain specifications are converted into a rational model. The unknown controller parameters are determined such that the augmented system approximates the desired model in the Pade sense. Thus, in effect, the initial few time-moments of the respective systems are matched. This leads to a set of linear algeb raic equations in the unknown parameters. This design method has been successfully extended to suboptimal control and controller syn thesis for systems with a transport lag. Often in practice, identification procedures lead to a high order plant model. A new model order reduction method is developed that minimizes frequency response deviations between the original and the reduced systems. Gradient techniques like Fletcher-Powell method •are found to quickly converge to the optimal values irrespective of the initial guess vector. The same technique is extended to the design of controllers in the z-plano.

The thesis is organised as under. The introductory chapter gives a brief review of present day available frequency-domain digital controller design methods. In the second chapter the new method for controller design using the Fade approximation technique is described. Discretization of an existing analog controller using time-moment matching is inclu ded in the third chapter. Gradient optimization technique (Flet cher-Powell) has been effectively used for controller design and for reduced order modelling. These are described in chapters four and five respectively. The concluding chapter highlights the cont ributions made in this thesis.