Adaptive MIMO Fuzzy Compensate Fuzzy Sliding Mode Algorithm: Applied to Second Order Nonlinear System

This research is focused on proposed adaptive fuzzy sliding mode algorithms with the adaptation lawsderived in the Lyapunov sense. The stability of the closed-loop system is proved mathematically based onthe Lyapunov method. Adaptive MIMO fuzzy compensate fuzzy sliding mode method design a MIMO fuzzysystem to compensate for the model uncertainties of the system, and chattering also solved by linearsaturation method. Since there is no tuning method to adjust the premise part of fuzzy rules so wepresented a scheme to online tune consequence part of fuzzy rules. Classical sliding mode control isrobust to control model uncertainties and external disturbances. A sliding mode method with a switchingcontrol low guarantees the stability of the certain and/or uncertain system, but the addition of the switchingcontrol low introduces chattering into the system. One way to reduce or eliminate chattering is to insert aboundary layer method inside of a boundary layer around the sliding surface. Classical sliding modecontrol method has difficulty in handling unstructured model uncertainties. One can overcome this problemby combining a sliding mode controller and artificial intelligence (e.g. fuzzy logic). To approximate a timevaryingnonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. This largenumber of fuzzy rules will cause a high computation load. The addition of an adaptive law to a fuzzy slidingmode controller to online tune the parameters of the fuzzy rules in use will ensure a moderatecomputational load. The adaptive laws in this algorithm are designed based on the Lyapunov stabilitytheorem. Asymptotic stability of the closed loop system is also proved in the sense of Lyapunov.