The role of single-loop subsystems in multivariable control by individual channel design of 2-input and 2-output systems

Abstract

Individual channel design is an applications-oriented framework for the analysis and design of multivariable control systems (O'Reilly and Leithead 1991). Whilst most previous work focuses on the analysis of multivariable systems using individual channel design, this present paper concentrates on some design aspects for 2-input 2-output systems. Two basic issues are examined: first, the role of single-loop subsystems (as opposed to channels) in multivariable control by individual channel design; second, how single-loop subsystems facilitate an attractively simple sequential design procedure for channels of any bandwidth. This sequential individual channel design procedure is based on two interesting results. First, there exists a dynamic performance relationship between the individual channels and their associated single-loop subsystems in that the deviation of the single-loop subsystem sensitivity function from the associated channel sensitivity function is the same for both channels. Second, provided that the required plot of the multivariable structure function γh_i (s) does not go near the (1,0) point, the phase and gain margins of one single-loop subsystem and the other channel constitute measures of closed-loop stability robustness for 2-input 2-output systems.