Higher order sliding fuzzy type-2 interval control for SISO uncertain nonlinear systems

A higher order sliding fuzzy type-2 controller scheme for nonlinear uncertain perturbed systems is proposed in the paper. To overcome the constraint on the knowledge of the system model, local models related to some operating points were used to synthesize a nominal fuzzy type-2 global model. The controller uses integral sliding mode concept and contains two parts. The first one leads to achieve finite time stabilization of the higher order input output dynamics without uncertainties. The second part has the object to reject bounded uncertainties throughout the entire response of the system. Two adaptive fuzzy type-2 systems have been introduced to generate the two Super Twisting signals to avoid both the chattering and the constraint on the knowledge of upper bounds of both disturbances and uncertainties. These fuzzy type-2 systems are adjusted on-line by adaptation laws deduced from the stability analysis in Lyapunov sens. The advantages of the method are that its implementation is easy, the convergence time is chosen in advance and the robustness is ensured. A robot arm actuated by a DC motor is used as illustrative example. The obtained results show the good tracking performances and the applicability of the method.