Adaptive Decoupling Control of MIMO System

Abstract

This paper describes a new adaptive controller for MIMO systems. The resulting closed loop system will be stable and decoupled. The system to be controlled can be non-minimum phase, and/or unstable linear systems. The interactor matrix of the system is not required. Instead of employing the certainty equivalent principle to design the adaptive controller, a new controller design procedure is proposed. By using this new scheme, the computation time required for controller design will be drastically reduced. Moreover, the boundedness of the controller parameters is automatically ensured. This is a desired property which is useful in stability analysis. The steady state performance of the controller designed by the proposed method will be the same as that of controllers designed using the certainty equivalent principle. Approximate decoupling can be achieved by underestimating the degree of the decoupling matrix without affecting the stability of the system. To achieve decoupling, we need to specify the denominator of the closed loop transfer function matrix of the system which is assumed to be in the form T(q -1)=t(q -1)I. Global stability of the adaptive system is obtained. A simulation example is presented at the end of this paper.