LMI-based multiobjective integral sliding mode control for rotary inverted pendulum system under load variations

Abstract

This paper presents a multiobjective integral sliding mode controller (ISMC) for a rotary inverted pendulum system under the influence of varying load. Firstly, the nonlinear system is approximated to facilitate the desired control design via extended linearization and deterministic approach. By using both of these techniques, the nonlinear system is formulated into a nonlinear state-space representation where the uncertainties are retained in the model. Next, the design objectives are formulated into linear matrix inequalities (LMI) which are then solved efficiently through convex optimization algorithms. With proper selection variables, numbers of the decision variables for LMIs are reduced. Hence, it will reduce the numerical burden and believes the calculated values more viable in practice. Finally, simulation works are conducted and comparison is made between the proposed controller, such as normal ISMC and LQR. The simulation results illustrate the effectiveness of the proposed controller and the performance is evaluated through integral of absolute-value error (IAE) performance index.