Designing Stable MIMO Fuzzy Controllers

This paper presents a systematic procedure for constructing a multi-input multi-output fuzzy controller that guarantees identical performance to an existing stabilizing linear controller. An algorithm is devised that generates a fuzzy controller which is functionally identical to a given time-invariant or time-varying finite-dimensional linear controller. The benefit of this transformation is that it provides an automated technique for the initial fuzzy controller setup while vital knowledge-based attributes are integrated afterwards. An important result of this work is that once a linguistic mapping into the fuzzy domain has been performed, one can see in linguistic terms how the linear controller operates. The effectiveness of this approach is demonstrated with a model for a flexible robot that exhibits nonminimum phase characteristics. An extension is outlined to use this deterministic approach for the case of a general dynamic control-law, and several applications to nonlinear control problems are discussed.