Biunivocal Relation Between TSK Fuzzy Controller and PID Controller and, Guarantee and Manipulation of the Stability for the Proposed Fuzzy Controller

This paper presents firstly an approach between the PID control and the fuzzy control to get a stable generic fuzzy Tagaki-Sugeno-Kang controller type. Then we use this relation and the PID control theory to find out the conditions of the fuzzy controller stability. We define a Lyapunov surface to always guarantee the fuzzy controller stability, based on classical stability specifications. We use the previous results to do a more generic relation between the fuzzy controller and PID controller and derive a tuning procedure to meet required specifications. Simulation example is given to illustrate the design procedures and performance of the proposed method