Dynamic Analysis of Decentralized 2 x 2 Control Systems in Relation to Loop Interaction and Local Stability

Abstract

A decentralized 2 x 2 control system is systematically analyzed from a novel perspective. On the basis of individual effective SISO loops obtained from a loop decomposition, classical concepts, such as open-loop stability, nonminimum phase behavior, and phase and gain margins, are extended to multivariable control systems within a strictly classical paradigm. Also, the closed-loop system is expressed as a function of various components such as loop interaction and local subsystem. Consequently, open- and closed-loop properties, such as open-loop stability, right-half-plane (RHP) zeros, closed-loop stability, and integrity, can be related to loop interaction, controller tuning, variable pairing, and local stability. Nyquist plots as well as characteristic equation approach, upon extending to multivariable control systems, are used to explore these properties. It is found that different loops in a multivariable control system can exhibit different properties. Several examples from literature are used to demonstrate the principles developed.