Swing-Up Control of a Serial Cart-Type Double Inverted Pendulum System

In this paper, a swing up control scheme for a serial double inverted pendulum system is proposed. The pendulum system is cart-type and the swing upcontrol includes a position control of the cart. The control scheme is to swing up the pendulum in three steps, Step 1 : to swing up the first pendulum. Step 2 : to swing up the second pendulum while stabilizing the first pendulum at the upright position, and Step 3 : to stabilize the two pendulums around the unstable equilibrium state. In each step a control scheme and a switching rule from a step to the next step are given. And the position control of the cart by using feedback stabilization control is included in the controller of each step. For the controller of Step 1, the energy control method based on Lyapunov method is applied to swing up the first pendulum and the feedback stabilization controller of a cart position is added so as to satisfy the condition of Lyapunov method of the first pendulum. For the controller of Step 2, the proposed method combines a stabilization control method of the first pendulum and the cart position using sliding mode control method, and a swing-up control method of the second pendulum using energy control method. And for the controller in Step 3, the sliding mode controller stabilizing both of the pendulums and the cart position is used. A numerical simulation and an experimental result are given to show the effectiveness of the proposed scheme