Second-Order Nonsingular Terminal Sliding Mode Control for Tracking and Stabilization of Cart–Inverted Pendulum

A second-order nonsingular terminal sliding mode control (SONTSMC) is proposed to solve the stabilization and tracking problems of an inverted pendulum. Although, a first-order sliding mode controller with the integral of the cart position can eliminate the offset in the cart position caused by incorrect calibration of the pendulum angle while balancing the pendulum at the upright equilibrium position, its control precision and chattering reduction can be improved by using a higher-order sliding mode controller. Therefore, the SONTSMC is designed by combining nonsingular sliding mode control and first-order sliding mode control to construct a second-order sliding mode controller that enhances tracking accuracy and reduces the chattering problems associated with sliding mode control. The performance of the proposed control is compared with that of the linear quadratic regulator sliding mode control (LQRSMC) and the integral linear quadratic regulator sliding mode control (ILQRSMC) for CIP’s stabilization and tracking. The results indicate that SONTSMC significantly increases the control performance of CIP while efficiently utilizing control energy.