Analysis and design of control systems by means of time domain matrices

Abstract

The aim of this dissertation is to present a new method of engineering analysis and design for complex control systems. This method is the time domain infinite matrix method. The formulation of the infinite matrix follows from the convolution summation of sampled data systems The mathematical basis of the time domain matrix formulation is presented in a discussion of the applicable concepts of infinite matrices and sequence spaces. This method of analysis and design is applicable to both continuous data and sampled data systems For continuous systems it is necessary to introduce a fictitious sam- pler and hold of sufficient sampling rate to effect an accurate ap- proximation. The time domain matrix method is presented and illustrated as a method of analysis and design of linear, nonlinear, and time varying systems of the continuous or sampled data class Sampled data time varying systems may not be conveniently investigated by any other existing method. Furthermore the investigation of nonlinear systems is greatly simplified by the time domain approach. Multiloop systems may be treated with ease and the signals at intermediate points throughout the loops are readily available Also 9 systems with multiple nonlinearities may be investigated, for which there is not a presently available method of analysis and design. Two methods of design of a discrete compensator for a sampled data system are presented. These methods are accomplished directly in the time domain and allow for a compromise of specifications in the time domain. Also the response between sampling instants is accted for in one of the two design procedures The time domain matrix method may be readily programmed on a digital computer and therefore provides a rapid analysis and design technique.