Swing-up and Stabilization Control of a Flexible Rotational Inverted Pendulum by Nonlinear Frequency Optimal Control

Abstract

Flexible rotational inverted pendulum is an extension of Furuta inverted pendulum in which pendulum is no longer a rigid body and vibrates due to the elasticity of the flexible beam. In this paper, we design a nonlinear controller based on nonlinear frequency optimal control for swinging up and stabilization of the flexible beam by a single feedback control. This controller is solved via the stable manifold approach which is recently proposed for solving the Hamilton-Jacobi equation.