Nonlinear control of inverted pendulum based on potential function

摘要

As is well-known, an inverted pendulum is one of the typical examples of nonlinear control systems, and, for the stabilization, many controller design methods have been studied. A nonlinear controller was designed by using an approximated model which consists of a series connection of a pendulum and a cart. In the first place, the desired signal of acceleration of the cart is determined for stabilizing the pendulum. Then the control input to cart is determined so that actual acceleration of cart may follow the desired signal. The controller thus designed was shown to expand the range of initial angle from which the system can be stabilized. In this paper, the generalization of the previous method was investigated based on Potential function. With the proposed method, the range of initial angle from which stabilization is possible is made larger, and, at the same time, the required input amplitude may be made smaller. These points were confirmed by comparative simulations.