Hierarchical sliding mode control and disturbance observer for the double inverted pendulum on a cart

This paper presents a control approach for the double inverted pendulum on a cart (DIPC) by combining Hierarchical Sliding Mode Control (HSMC) and Disturbance Observer (DOB). The proposed method utilizes HSMC to ensure balance in both the pendulum angles and a cart position, while the DOB accurately estimates the system's disturbance. Through the simulations, the integrated HSMC and DOB approach demonstrates remarkable efficacy in achieving stable equilibrium control of the double inverted pendulum. Comparative analysis against the commonly used Linear Quadratic Regulator (LQR) controller highlights the superior performance and efficiency of our proposed method.