A Hybrid Control Framework for Swing-Up and Stabilization of the Double Inverted Pendulum on a Cart

This paper presents a comprehensive study on the application of advanced control methods to the Double Inverted Pendulum on a Cart (DIPC) system. The focus is on the design and implementation of swing-up control laws, balancing strategies, and disturbance rejection techniques to achieve robust system stability. The control scheme integrates energy-based controllers (EC) with stabilizing controllers based on sliding mode control (SMC), including a variant incorporating the H-infinity norm, to address the challenges of swinging up and stabilizing the pendulums and the overall DIPC system. Simulation results demonstrate the effectiveness of these controllers in bringing the DIPC system from the Down-Down position to the Up-Up position. During the transition from Down-Down to Up-Down, the SMC controller combined with the H-infinity norm has shown superior performance in reducing disturbance effects compared to traditional SMC controllers. The proposed control framework is expected to contribute significantly to the control of nonlinear and complex systems like DIPC, with potential applications in various fields.