%0 Journal Article
%T External Periodic Force Control of a Single-Degree-of-Freedom Vibroimpact System
%A Jingyue Wang
%A Haotian Wang
%A Tie Wang
%J Journal of Control Science and Engineering
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/570137
%X A single-degree-of-freedom mechanical model of vibro-impact system is established. Bifurcation and chaos in the system are revealed with the time history diagram, phase trajectory map, and Poincar¨¦ map. According to the bifurcation and chaos of the actual vibro-impact system, the paper puts forward external periodic force control strategy. The method of controlling chaos by external periodic force feedback controller is developed to guide chaotic motions towards regular motions. The stability of the control system is also analyzed especially by theory. By selecting appropriate feedback coefficients, the unstable periodic orbits of the original chaotic orbit can be stabilized to the stable periodic orbits. The effectiveness of this control method is verified by numerical simulation. 1. Introduction In the field of nonlinear, along with people understanding the nature of chaos, how to control chaos and chaos synchronization has been a hot topic studied by researchers. In the 1990s, Ott et al. proposed the OGY chaos control method [1]. Scholars put forward a lot of modified control methods [2, 3] based on the OGY method. Although small perturbation of the system parameters for the control of chaos has been confirmed, the method requires detailed information about the target trajectory and brings a lot of inconvenience to the practical application. Therefore the domestic and foreign researchers put the traditional control theory and chaotic motion characteristics used in chaos control and present a lot of chaos control method, such as delayed feedback control [4, 5], periodic parameter perturbation control [6], continuous feedback control [7], pulse feedback control [8], and adaptive control [9], and so forth. There are also examples of control on the vibroimpact system [10, 11]. Vibroimpact system as a typical nonsmooth dynamical system generally exists in practical engineering. Because of the frequent collision, the system has strong nonlinearity and discontinuities compared with a smooth nonlinear system, presents more complex nonlinear phenomena, and causes hazards on the safe operation of the system. Because of the collision interface differential discontinuities, the original method applied to continuous system can not be used for such system. This paper puts forward a sine periodic force feedback controller based on the periodic external force feedback control strategy and analyzes the stability of control theory. When selecting the appropriate feedback coefficients, the chaotic orbits can be controlled onto the stable periodic orbits. A
%U http://www.hindawi.com/journals/jcse/2013/570137/