Modeling and control of hula-hoop system

Hula-hoop is not only one of familiar toys but also interesting system as a nonlinear control system. While humans play hula-hoop, hoop does not slide on the body but rotates around it. Though it is controlled only by the motion of the body, humans can realize enduring rotary motion without dropping hoop. The purpose of this paper is modeling and control of hula-hoop system as a nonlinear control systems. For modeling, hula-hoop system is regarded as the motion of the hoop and the pole in contact constraints. Note that there exist two types of models depending on constraints. For control, hula-hoop system can be divided to two subsystems. One is derived from dynamic equation, and the other is derived from contact constraints. The former subsystem has the motion of the pole and the angle of rotation as input and output, respectively. The latter subsystem has the angle of rotation and the altitude of contact point as input and output, respectively. For the latter subsystem, the angle of rotation to stabilize the altitude of contact point is derived. From the former subsystem, the motion of the pole to realize the angle of rotation is derived by output zeroing control. Finally, the validity of the proposed controller is verified by numerical simulations.