Finite-Dimensional Robust Controller Designs for Distributed Parameter Systems: ASurvey

摘要

Although there has been much research on the stabilization of distributedparameter systems, the theory usually produces infinite dimensional controllers. For example, the theory of linear quadratic control produces a state feedback law in which both the state and the gain operator are infinite dimensional. To produce an implementable finite dimensional controller entails approximating both this gain operator and the state, which is a complicated numerical procedure and sometimes (in the case of unbounded inputs) difficult to justify theoretically. The continuing popularity of this approach is somewhat surprising, since there exist several direct methods of designing finite dimensional controllers for infinite dimensional systems. The first finite dimensional compensator design was a state space approach in 1981 and since then there have been many others. In particular, there exist various frequency domain theories for designing finite dimensional controllers which are robust to certain types of uncertainties or which satisfy other additional performance objectives. A survey and comparison of ways of designing finite dimensional controllers for infinite dimensional systems with the emphasis on robust controllers is presented.