H∞ based integral sliding mode controller design for stabilization of cart pendulum system

H∞ based sliding mode control has several advantage viz. fast response, robustness to parameter variation and disturbance rejection ability. Inverted pendulum qualifies as a benchmark system to test the suitability of controller design for under-actuated, nonlinear unstable system. In this context, H∞ based integral sliding mode controller is designed for inverted pendulum for stabilizing the system. The H∞ state feedback gains are obtained by formulating the Riccati equation. These gains stabilize not only the closed loop transfer function, which maps the performance output to the disturbance input but also the system around its unstable equilibrium point. However this will not account for parameter variation and disturbance effect. Hence, a robust integral sliding surface is constructed such that during sliding motion the closed loop system will lead to disturbance rejection. Next, the switching control law is synthesized to maintain the states on the sliding surface from the initial time. The effectiveness of the controller design is verified by considering various uncertainties.