The robust control of a servomechanism problem for linear time-invariant multivariable systems

TLDR

The problem permits arbitrary plant parameter perturbations as long as the closed‑loop system remains stable, and introduces a sorvocompensator—a compensator distinct from an observer that generalizes the classical integral controller. The study aims to design a stabilizing compensator that, when combined with a servocompensator, stabilizes the system after the servocompensator is applied to the plant. The servocompensator is a feedback compensator whose error input consists of multiple identical unstable subsystems—one per regulated output—whose dynamics depend on disturbances and reference inputs. The authors establish necessary and sufficient conditions for a robust controller that achieves asymptotic tracking/regulation independent of disturbances and plant perturbations; they show that any such controller must comprise a servocompensator and a stabilizing compensator, fully characterize all robust controllers, and prove that a.

Abstract

Necessary and sufficient conditions are found for there to exist a robust controller for a linear, time-invariant, multivariable system (plant) so that asymptotic tracking/regulation occurs independent of input disturbances and arbitrary perturbations in the plant parameters of the system. In this problem, the class of plant parameter perturbations allowed is quite large; in particular, any perturbations in the plant data are allowed as long as the resultant closed-loop system remains stable. A complete characterization of all such robust controllers is made. It is shown that any robust controller must consist of two devices 1) a servocompensator and 2) a stabilizing compensator. The servocompensator is a feedback compensator with error input consisting of a number of unstable subsystems (equal to the number of outputs to be regulated) with identical dynamics which depend on the disturbances and reference inputs to the system. The sorvocompensator is a compensator in its own right, quite distinct from an observer and corresponds to a generalization of the integral controller of classical control theory. The sole purpose of the stabilizing compensator is to stabilize the resultant system obtained by applying the servocompensator to the plant. It is shown that there exists a robust controller for "almost all" systems provided that the number of independent plant inputs is not less than the number of independent plant outputs to be regulated, and that the outputs to be regulated are contained in the measurable outputs of the system; if either of these two conditions is not satisfied, there exists no robust controller for the system.