Control System Design to Minimize Maximum Errors

Abstract

The standard approach to classical control system design is to shape the loop gain function in order to meet specifications [1]. Generally the idea is to keep errors small and this involves high loop gain in the low frequency ranges where command inputs and plant disturbances are expected to lie and low loop gain where high frequency sensor noise is a problem. It is clear that the intuitive approach described above is motivated by trying to keep integral-square errors small. The H ^∞-optimization theory introduced into control system design recently by Zames [2] furnishes a systematic way to minimize the error-signal energy where the system inputs are bounded energy signals. This is very closely related to the techniques used in classical design, but is constrained by the requirement of bounded energy signals.

In many control systems, a desirable objective is to limit the magnitudes of certain signals in the system. Using H ^∞-theory, an indirect and not too effective way to do this is to include the integral square values of these signals in the performance index, and thus limit the maximum energy that these signals can have. Although classical design is a firmly entrenched tool that has been successfully used for many years, it is clearly not applicable to problems in which maximum error magnitudes must be limited or when inputs are not finite energy signals. Although these problems have been recognized as important for years, no substantial progress has been made toward their solution until recently when Vidyasagar [3] posed the problem of minimizing the maximum error magnitude when the system inputs are bounded in magnitude. This represented the first serious attempt to carefully formulate the problem and obtain solutions. This paper will report on research in progress on the discrete-time version of this problem.

This research was supported by NSF Grant ECS 85-05645.