A CAD PACKAGE FOR MULTIVARIABLE CONTROL SYSTEMS PRESENTED BY POLYNOMIAL MATRICES

Abstract

The basic theory for analysis and synthesis of differential systems using polynomial matrix representation is considered. Concepts like controllability, observability, stability etc. are defined and methods based on elementary row operations for checking them are given. As an example of synthesis methods an algorithm for synthesis of observers is given. A similar algorithm for synthesis of feedback compensators has been presented elsewhere. Computer aided design of multivariable control systems is performed interactively using a program which enables manipulation of polynomial matrices, and a simulation program that uses polynomial matrices as models of differential systems. The program for manipulation of polynomial matrices performs row operations and other transformations, calculates determinants and their roots etc. Synthesis problems can also be considered by studying different regulator compositions, constructing estimators and feedback compensators. The simulation program communicates with the manipulation program by means of polynomial matrices stored in files. Simulation results are presented by graphic displays or by separate plotter and design decisions can be based on these results. The use of the CAD package is demonstrated by considering an observer synthesis problem.