Robust Controller Design for Inverted Pendulum Using Sliding Mode Control Technique

Abstract

The physical structures of the systems are suffering from uncertainty because of parameter variations, external interferences, and persistence disturbances. These persistent disturbances create stability problem to system in the field of control engineering, therefore, the implementation of controllers for such systems has to be a difficult thing. The robust control of linear uncertain systems remained a subject of interest for researchers in the past. However, one vital design anxiety is handling the uncertainty, high control input is required to pay out by the controller, leading to the saturation of the actuator which is highly undesirable. Nowadays, design of controllers with the least control energy consumption is gaining high importance. The optimal control methodology is used to minimize certain performance index. In this paper, the linear uncertain system is tracked by presenting the work on optimal second-order sliding mode controller (OSOSMC). The proposed controller was developed using the linear quadratic regulator method (LQR) for the stable system response. For the simulation and analysis, the inverted pendulum which is highly nonlinear, under-actuated, and unstable is used. A meticulous combination of integral sliding mode controller (ISMC) and the optimal controller is done to obtain the robustness of the uncertain system which is influenced by external interferences, disturbances, and uncertainties. Adding an integral sliding surface with a non-singular terminal sliding surface gives a second-order sliding mode controller to obtain finite time convergence of the controller. The required control input is significantly less is the major benefit of the discussed OSOSMC to make it chattering-free.