Controlling Chaos In A One-Degree-of-freedom Vibro-Impact System By The Ogy Method

The phenomenon of vibro-impact is widely encountered in engineering. The study of the periodic motion and bifurcation of a single degree of freedom vibro-impact system has important theoretical and practical significance. Chaotic control is a new research field of the nonlinear science. A one-degree-of-freedom vibro-impact system with a single stop is considered in this article. The Poincare map of the system is established. The theory of bifurcation of fixed points is applied to such model. The periodic motion of the system corresponds to fixed points of the Poincare map. During the process that varying the frequence of the external exciting force, we observe the process of the system changing from the simple periodic motion to the period doubling bifurcation, then the transition route of bifurcation to chaos. When the Jacobian matrix of the Poincare map has a eigenvalue passing through the unit circle at (-1,0), stable periodic orbits become unstable, and chaos occurs via period-doubling bifurcation. Chaos control of several classical mathematical model is introduced in this article, we elaborate the main idea of the OGY method.The chaos of the vibro-impact system is controlled by the OGY method. Due to sensitivity to tiny perturbations, chaos can be stabilized to desired orbits by tiny perturbations of system parameters. Based on a large number of numerical Simulation Analysis, We compared the difference of control efficiency and control results under different control parameter conditions, and i get some regular pattern and applicable conditions about OGY method.