Perfect control of the robust servomechanism problem

The problem of finding a robust servomechanism controller which achieves exact asymptotic tracking/regulation for a modeled class of reference and disturbance signals, arbitrarily good approximate error regulation (AGAER) for reference/disturbance signals which lie outside of this design class, and arbitrarily good transient response is considered. It is shown that a necessary condition that must be satisfied to accomplish this requirement is that the initial conditions of the servocompensator should be zero. An explicit algorithm for designing such controllers is then given. A simple controller, called the high gain servomechanism controller is also presented, which has the property that it gives AGAER and arbitrarily good transient response, when the robust exact asymptotic tracking/regulation requirement is relaxed. This controller shows that dynamics in a controller is not essential for achieving good error regulation in the presence of unknown unmeasurable disturbances. It is also shown that using the controllers proposed, exact error regulation occurs, for a larger class of design signals, called the extended disturbance/reference input signals, even if the conditions for perfect control are not satisfied. Some examples are included to illustrate the type of results obtained.