Approximate error regulation - The robust servomechanism problem for unknown input signals

This paper considers the problem of finding a robust servomechanism controller which achieves exact asymptotic tracking and regulation for a given class of reference and disturbance signals, and arbitrarily good approximate asymptotic regulation for other classes of reference and disturbance input signals. Necessary and sufficient conditions for the existence of such a controller, and a characterization of controllers which accomplish this are given. An explicit algorithm for such controllers is also given; in particular, it is shown that the design of such a controller can always be accomplished by using the cheap control design method as used in [1] for the multivariable robust servomechanism problem. A degenerate type of robust servomechanism controller (called a high gain servomechanism controller) consisting of only static feedback gains, is also given, which has the property that it produces arbitrarily good approximate regulation for all tracking/disturbance signals; thus this controller shows that dynamics in the feedback controller are not essential for achieving good approximate error regulation. Some numerical examples are included to illustrate the results.