CONTROL-THEORY AND ADVANCED TECHNOLOGY Vol. 6, No.4, pp.57:J-594, December, 1990 C90019R @MITA PRESS LOOP TRANSFER RECOVERY FOR NON-STRICTLY PROPER PLANTS* B. M. CHEN,! A. SABERI,! S. BINGULAC"AND P. SANNUTI3 Abstract. Observer based controllers for loop transfer recovery of non-strictly proper systems which are left invertible and of minimum phase are considered. A complete analysis of loop transfer recovery problem using either full or reduced order observer based controller is provided. Key Words-Robust control, loop transfer recovery. 1. Introduction and Problem Statement In multi-input and multi-output feedback control system design, performance specifications such as command following, disturbance rejection, closed-loop band-width, stability robustness with respect to unstructured dynamic uncer- tainties etc., are naturally posed in frequency domain in terms of sensitivity and complementary sensitivity functions (Doyle and Stein, 1981). These sensitivity and complementary sensitivity functions are related to the loop transfer matrices evaluated by breaking the control loop at critical points, commonly either the input or output point of the given plant. Thus typically, one is interested in designing a closed-loop control system to arrive at a specified loop transfer function. In this paper, we concentrate on a case when the uncertainties are modeled at the input point of a nominal plant model and hence the required loop transfer function is specified at the plant input point. However, our results can be dualized for the case when the required loop transfer function is specified at the output point. In recent years, a design procedure called LQG/LTR, originally proposed by Doyle and Stein (1979) has gained some prominences. Essentially, LQG/LTR is a two step design procedure. In the first step of design, a standard state feedback design is done so that the resulting loop transfer function at the plant input point, here after called as a target loop transfer function, meets the given specifications. In the second step of design, one first assumes a closed-loop configuration as in Fig. 1 where C(s) and P(s) are respectively the transfer functions of a controller and the given plant. Given P(s) and the target loop transfer function L(s), one seeks to design a C(s) such * Received by the editors February 13, 1990 and in revised form July 16, 1990. The work of B.M. Chen and A. Saberi is supported in part by National Science Foundation under grant No. ECS 8618953 and in part by Boeing Commercial Airplane Group. ! Department of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164-2752, U.S.A. " Bradley Department of Electrical Engineering, Virginia Polytechnic Institute and State Universi- ty, Blacksburg, VA 24061, U.S.A. :J Department of Electrical and Computer Engineering, P. O. Box 909, Rutgers University, Piscataway, NJ 08855-0909, U.S.A. 573