PERFECT CONTROL OF THE ROBUST SERVOMECHANISM PROBLEM

A general servomechanism problem is considered which combines the usual objective of achieving exact robust asymptotic error regulation for a known class of design signals, with the added objective of obtaining perfect control in the system. In this case, existence conditions and a controller design procedure which produces perfect control are given using H//2 cheap control methods. 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 arbitrarily good approximate error regulation 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 unmeasureable disturbances. It is also shown that, using the controllers proposed, exact error regulation occurs for a larger class of design signals even if the conditions for perfect control are not satisfied.