In this paper, a fuzzy sliding mode controller (FSMC), which is synthesized by a collection of linguistic control rules whose membership functions of THEN-part is adapted, is proposed. Both the membership functions of IF-part and THEN-part are arranged symmetrically and distributed equally in the individual universe of discourse. In particular, the membership functions of the THEN-part can be adapted via one parameter adaptation to meet the required system specification. The proposed direct adaptive FSMC can be synthesized through the following stages. First, the control rules are constructed according to the concepts of SMC, and the fuzzy sets whose membership functions are symmetrically covered in state space. Then, the derived adaptive law is used to adjust the membership functions of the THEN-part. The FSMC is employed to approximate the equivalent control of SMC without knowing the mathematical model of the controlled system. Third, a hitting control is developed to guarantee the stability of the control system. Finally, we apply this FSMC to control a nonlinear inverted pendulum system for confirming the validity of the proposed approach.
EZ rules: Automatic Selection of Statistical Control Rules for Laboratory Tests. Westgard QC, Inc. Madison, WI: Westgard QC, Inc., 2000, 154 pp., $295.00. ISBN 1-886958-14-9.
