Practical Swing-up controller design for a cart-type single inverted pendulum having a serial second pendulum as parasitic dynamics

This paper proposes a swing-up control scheme for a cart-type single pendulum having a serial second pendulum as a parasitic part. The proposed control scheme swings up the first pendulum with controlling the motion of a cart and being robust to the parasitic part. In the swing-up, the second pendulum is swinging at the top of the first pendulum and the motion of the second pendulum works as strong disturbance to the control of the first pendulum. Hence the control scheme is required to be strongly robust to the disturbance, and this paper uses sliding mode control law as the controller, which is strongly robust to disturbance. After the swing-up, the controller also stabilizes both angles of the pendulums and cart position. A numerical simulation is given to show the effectiveness of the proposed scheme.