Controlling chaos of a periodically forced nonsmooth mechanical system

This paper deals with the control of the chaotic motion of a periodically forced mechanical system having nonsmooth restoring force due to elastic stops or clearances, so as to regulate the chaotic motion to a desired periodic motion by means of small time-dependent perturbation of a control parameter. The study begins with a rigorous description of OGY scheme of controlling chaos, and then focuses on the validity of the control scheme through analyzing the smoothness of the Poincaré mapping in the scheme with respect to the system state and the control parameter. To simplify the control experiments, the selection of delay coordinates is subsequently discussed. Presented finally is an experiment of controlling chaotic motion of a harmonically forced mass-beam system with an elastic stop.