INTEGRAL SLIDING MODE CONTROL DESIGN FOR INVERTED PENDULUM

Abstract

Beginning in the late 1970s and continuing till today, the sliding mode control has received plenty of attention due to its insensitivity to disturbances and parameter variations. In case of sliding mode control, the system states are made to confine to a selected sub-set of the state space so as to achieve some desirable dynamics. An inverted pendulum is multivariable, higher order, non linear and extremely unstable system. The sliding mode control is designed for controlling pendulum angle and cart position independently. These controllers have been tested for robustness property in the presence of sinusoidal disturbance independently. Inverted pendulum is a single input multi output system. To combine the control laws to make it a single control input various techniques are available like switched mode, decoupled mode etc. In this report, sliding mode control has been tested for the robustness property in the presence of sinusoidal disturbance considering single control input using decoupled mode suggested by J. Chung. Coupling of the two control laws leads to non robust nature of the system against sinusoidal disturbance. Due to deterioration in the robust performance, Integral Sliding Mode (ISM) control theory has been applied to achieve robustness property for the system considering the pendulum angle and cart position both. Linearized model of inverted pendulum has been used for ISM control design. An LQR control is used as a nominal control and discontinuous term is introduced using ISM control. The designed ISM controller is tested under the sinusoidal disturbance having amplitude of 1 unit. The simulation results provided to show effectiveness of the ISM control scheme for inverted pendulum. MATLAB has been used as simulation tool to provide simulation results at each stage.