Fuzzy sliding mode control approach for two time scale system: Stability issues

This paper addresses design of optimal fuzzy sliding mode control technique for minimization of reaching time along with robust stabilization of nonlinear singularly perturbed systems (NSPS). In singular perturbation method, the original system is decomposed into two reduced order subsystems such as slow and fast models, in which nonlinear uncertain terms are involved with two-times scale representation. The proposed control technique has single input singe output (SISO) Sugeno type fuzzy inference engine applied to slow subsystem so as to achieve minimum settling time for slow state variables but this scheme does not consider for fast dynamic model. Each subsystem has a separate control target expressed in terms of slow and fast control command. The composite control action based on slow and fast control signal is applied for asymptotic stabilization of two-times scale model which minimizes the effect of chattering by considering boundary layer width for full order system. Further, we investigated parameter estimation of fuzzy sliding mode control such as sliding surface coefficient, hitting gain and boundary layer width with simplified control framework based on minimum number of rule base, utilized in the control design. Finally closed loop stability can be proved by direct method and Composite Lyapunov function for the two-time scale model.