Swing-up control of a serial double inverted pendulum

A swing-up control scheme for a serial double inverted pendulum is proposed. 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 next step are given. The rule bases on the states of the system. For the controller of step 1, the energy control method is applied to swing up the first pendulum. For the controller of step 2, a new method is given. The method combines a stabilization control method of the first pendulum using sliding mode control method and a swing-up control method of the second pendulum using energy control method. And for a controller in step 3, the sliding mode controller stabilizing both of the pendulums is used. A numerical simulation is given to show the effectiveness of the proposed scheme.