Adaptive high order sliding mode controller/observer based terminal sliding mode for MIMO uncertain nonlinear system

In this paper, an adaptive super twisting high order sliding mode controller observer is investigated for multi input-multi output uncertain system, with application to robotic manipulator based only on position measurement. First, a type-2 Takagi-Sugeno fuzzy system is used to model the original system. Next, by combining thefuzzy model with third order sliding mode observer, a novel fuzzy observer is designed to estimate both the joint velocities and uncertainties. Moreover, based on super twisting algorithm the proposed controller generates a smooth control signal and guarantees the finite time stabilisation of second order sliding mode. The controller gains are generated based on adaptive estimation scheme, in which the gains overestimation problem and the prior knowledge of the upper boundaries of uncertainties can be avoided. The stability of proposed controller/ observer scheme is discussed using Lyapunov approach. Finally, the obtained simulation results for two link robot manipulator demonstrate the effectiveness of the proposed controller.