关键词: 3D rigid pendulum, quaternion, chaotic motion, Poincar´e section, open-plus-closed-loop (OPCL) control

Abstract: An open-plus-closed-loop (OPCL) control problem for the chaotic motion of a 3D rigid pendulum subjected to a constant gravitational force is studied. The 3D rigid pendulum is assumed to be consist of a rigid body supported by a fixed and frictionless pivot with three rotational degrees. In order to avoid the singular phenomenon of Euler’s angular velocity equation, the quaternion kinematic equation is used to describe the motion of the 3D rigid pendulum. An OPCL controller for chaotic motion of a 3D rigid pendulum at equilibrium position is designed. This OPCL controller contains two parts: the open-loop part to construct an ideal trajectory and the closed-loop part to stabilize the 3D rigid pendulum. Simulation results show that the controller is effective and efficient.

Key words: 3D rigid pendulum, quaternion, chaotic motion, Poincar´e section, open-plus-closed-loop (OPCL) control