Output feedback system design via inverse systems

Abstract

Application of polynomial matrices to the representation of multivariable closed-loop control systems has found highly successful results. Many design methodologies have formulated the open-loop and desired closed-loop systems in terms of transfer function matrices, and choice of the proper compensation required for desired objectives result in a synthesis problem. A difficulty in direct application of synthesis methodologies to the feedback problem is in calculation of matrix inverses. This problem may be alleviated by working with the inverse open-loop and desired closed-loop system formulation. This paper presents some results on the inverse systems approach when applied to the output feedback system configuration. Conditions for the existence of compensators necessary to obtain desired overall system objectives are developed and applied to decoupling, model matching and pole placement problems. Examples are provided to illustrate application of the conditions to various design cases.