Swing up and Arm Trajectory Tracking of the Furuta Pendulum with Sliding Mode Control

In this paper, the swing-up problem of the Furuta pendulum has been solved by introducing a new combined method based on the frequency response, and the sliding mode method. Furthermore, a trajectory tracking controller has been introduced and applied to the Furuta pendulum; which the pendulum remained regulated at the upward position, while the arm tracks a desired time-varying trajectory. The hierarchical sliding mode control (HSMC) approach has been employed to achieve the mentioned goals. The Furuta system is made up of two subsystems. Based on this physical structure, the hierarchical structure of the sliding surfaces is designed as follows: first, the sliding surface of each subsystem is defined. Then the sliding surface of one subsystem is established as the first layer sliding surface. Eventually, this layer is used to construct the second layer sliding surface with the sliding surface of the other subsystem. According to the hierarchical structure, the total control law is deduced, and stability of the closed-loop system has been proved by the Lyapunov theorem. Simulation results have been shown the validity of the proposed method. Finally, the tracking performance of the mentioned method has been compared with the feedback linearization controller and superiority of the HSMC has been revealed.