Observer-based integral sliding mode control of nonlinear systems with application to single-link flexible joint robotics

This paper proposes the topics of sliding mode control for nonlinear Takagi-Sugeno systems based on a state observer with application to single-link flexible joint robotic. Firstly, a state observer relying on estimated premise variables is constructed, based on which we define an integral-type switching surface function on the estimation space. Secondly, by the equivalent control method, a sliding mode dynamics with an error system is obtained. Then, an adaptive variable structure controller is constructed to make sure that the predefined switching surface will be arrived in finite-time. Furthermore, stability analysis with an 𝐻 1 performance is analyzed for the whole closed-loop system by linear matrix inequality condition. Finally, simulation study based on the robotics is conducted to confirm the validity of the proposed observer-based fuzzy controller.