Quantitative Feedback Design of Decentralized Control Systems

Abstract

In the spirit of practical applicability, design transparency and quantitative specifications, this paper presents a new robust decentralized control design framework—model reference quantitative feedback design (MRQFD)—for multivariable control systems with large plant uncertainty and strong cross-coupling. The MRQFD method provides a connection between Rosenbrock’s Nyquist array and Horowitz’s quantitative feedback theory. There are two main stages in the MRQFD method. First, an internal model reference loop, based on non-negative matrix theory, is used to obtain robust generalized diagonal dominance and hence the reduction of uncertainty in the resultant compensated internal loop system. Then a single-loop quantitative feedback design scheme is applied to solve the resulting series of individual loops to guarantee the satisfaction of predefined MIMO quantitative specifications. The design procedure can be carried out either in the direct or in the inverse plant domains, as in Rosenbrock’s Nyquist array. The conditions of robust diagonal stabilization are also given for the MRQFD framework. The effectiveness of the MRQFD method and its ease of application are demonstrated by a 3 × 3 uncertain multivariable example.