On error systems and the servomechanism problem†

Abstract

This paper considers the problem of controlling a multi-input, multi-output, linear, time-invariant dynamic system subjected to disturbances belonging to a known class of signals. The objective is to find a feedback control law which makes the outputs of the system track command signals belonging to a known class with zero steady-state error and a satisfactory transient response. Necessary and sufficient conditions for the existence of a state feedback control law that achieves this objective are obtained. The problem of stabilizing the closed-loop system while tracking with zero steady-state error is solved, the problem of controlling the system using output feedback is discussed and sufficient conditions for its solution are obtained. In addition, it is shown that if certain of the above conditions are not satisfied for a given system and class of disturbance and command input signals, then they cannot be satisfied using dynamic (integrator) compensation.