Swing-up controller design for inverted pendulum by using energy control method based on Lyapunov function

The purpose of this paper is swing-up control of a cart-type single inverted pendulum by using energy control method based on Lyapunov function. Energy control method is one of the effective control methods for under-actuated system, and some examples of applying energy control method based on Lyapunov function to swing-up control of inverted pendulum systems have been reported. This paper focuses on Lyapunov function used in energy control method. In conventional researches, the possibility that the value of Lyapunov function becomes zero excluding the upright position has not been considered. In order to design the controller with considering this possibility, three new Lyapunov functions are created, and controllers are designed for each function. Swing-up control of the pendulum is done by switching these three controllers. In addition, numerical simulation is conducted to verify the effectiveness of the proposed method.