Online Tuning Chattering Free Sliding Mode Fuzzy Control Design: Lyapunov Approach

This paper expands a sliding mode fuzzy controller which sliding surface gain is on-line tuned by minimum fuzzy inference algorithm. The main goal is to guarantee acceptable trajectories tracking between the second order nonlinear system (robot manipulator) actual and the desired trajectory. The fuzzy controller in proposed sliding mode fuzzy controller is based on Mamdani ’s fuzzy inference system (FIS) and it has one input and one output. The input represents the function between sliding function, error and the rate of error. The outputs represent torque, respectively. The fuzzy inference system methodology is on-line tune the sliding surface gain based on error-based fuzzy tuning methodology. Pure sliding mode fuzzy controller has difficulty in handling unstructured model uncertainties. To solve this problem applied fuzzy-based tuning method to sliding mode fuzzy controller for adjusting the sliding surface gain ( λ ). Since the sliding surface gain ( λ) is adjusted by fuzzy-based tuning method, it is nonlinear and continuous. Fuzzybased tuning sliding mode fuzzy controller is stable model-free controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in fuzzy-based tuning sliding mode fuzzy controller based on switching (sign) function.

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