Feedback representation of precompensators†

Abstract

An algebraic theory is developed for the design of internally stable control configurations, which consist of dynamic output feedback, inside-loop precompensation, and outside-loop precompensation. The underlying quantity is an equivalent pro-compensator which relates the given system to the desired system, and which may induce unstable pole-zero cancellations. From this equivalent precompensator, the controllers of the final internally stable control configuration are constructed. The main step in this construction involves a partial-fraction decomposition of matrices. The problem of minimizing the outside-loop precompensator (without affecting the transfer matrix of the final system) is considered. For infective systems, the outside-loop precompensator can be eliminated in almost all cases.