Swinging-Up and Balancing Control of Double Furuta Pendulum by Using State-Dependent Riccati Equation

Abstract

In this paper, we present a control system design where the swinging-up of a double Furuta pendulum from the pendant position to the upright position and the balancing of the pendulum at the upright position are achieved by only one controller. The double Furuta pendulum is one of simple under-actuated mechanical systems, but it also has chaotic properties, and high nonlinearity, so that it is often used as examples to show the effectiveness of the control system. The control objective is a kind of global stabilization of such pendulum system, and it is known to be difficult in general. To overcome this problem, the controller is designed utilizing the state-dependent Riccati equation. Recently, the nonlinear optimal control using the state-dependent Riccati equation is highlighted again by Cloutier et al. to stabilize nonlinear systems. This method allows designers to use any matrix function of the state as the weight matrices in the quadratic cost function. This advantage is effectively used to design the controller for the swinging-up of the double pendulums. A numerical examples illustrates that the swinging-up and balancing of the double Furuta pendulum can be achieved effectively by the presented method.