Controlling chaotic impacts of an impact-forming machine by adjusting the driving force

An impact-forming machine is considered. Based on the analysis of oscillatory and impacting motions of the machine, we introduce an impact Poincaré map with dynamical variables defined at the impact instants. The stability and bifurcations of single-impact periodic motion of the machine are analyzed. The simulative results show that dynamic behavior of this system is very complex under parameter variation, varying from different types of periodic motions to chaos. A controlling method is proposed to suppress chaotic impacts by applying an external periodical force to the machine. The periodical force is adjusted according to some real-time algorism related to an error between real-time state and the desired periodical state. With the numerical simulation, the effectiveness of the method is demonstrated.