Adaptive Fuzzy Sliding Mode Controller Design

Adaptive Fuzzy Sliding Mode Controller represents an advanced control strategy that integrates fuzzy logic with sliding mode variable structure control, effectively handling system uncertainties and suppressing chattering phenomena. The core concept involves online adjustment of sliding mode gains through fuzzy rules, preserving the strong robustness of traditional sliding mode control while reducing dependence on system parameters via adaptive mechanisms.

The design process typically comprises three critical stages: First, establish the system state equations and design the sliding surface to ensure sliding mode stability. Second, utilize fuzzy inference systems to dynamically adjust control law parameters, commonly selecting input variables such as the distance between system states and the sliding surface. Finally, demonstrate closed-loop system stability through Lyapunov functions to guarantee error convergence.

In MATLAB implementation, developers can employ the Fuzzy Logic Toolbox to construct membership functions and rule bases, combined with S-functions for real-time parameter adjustment. A typical implementation approach involves defining fuzzy input variables (e.g., error and error derivative) and output variables (sliding mode gain) using fuzzy function, then designing rule bases with linguistic variables. The controller can be implemented through smc.fis file configuration or programmatic rule definition using addrule method. Common application scenarios include robotic trajectory tracking and motor speed control in nonlinear systems with modeling errors or external disturbances. The method's advantage lies in not requiring precise mathematical models while maintaining strong robustness against parameter variations and external disturbances.