Anti-Controlling Quasi-Periodic Oscillations of Vibro-Impact Systems.

Purpose: The bifurcating solution generated by Neimark-Sacker bifurcation of map exhibits a typical quasi-periodic oscillation behavior, which is beneficial for the active use of bifurcation in bifurcation control field. In this paper, an impulsive state feedback control method is proposed to create the quasi-periodic oscillation with certain desired characteristic in the vibro-impact system. Method: The linear control gains determined by using the explicit criteria of Neimark-Sacker bifurcation without directly using eigenvalues are designed to guarantee the existence of quasi-periodic oscillation. On the other hand, the non-linear control gains, which are determined by using center manifold reduction theory and normal form approach, ensure that the created quasi-periodic oscillation is stable. The amplitude of the trajectory section on the torus of quasi-periodic oscillation is analytically derived to achieve the control of the amplitude of invariant torus section by selecting appropriate non-linear control gains. Results and conclusions: Numerical experiments are provided to show the effectiveness of the proposed control method in a two-degree-of-freedom vibro-impact system. The results of quantitative analysis show that a stable quasi-periodic oscillation in the vibro-impact system can be created at a preassigned bifurcation point by desiging linear and nonlinear control gains, and the effect of the nonlinear control gains on the amplitude is either a positive relationship or a negative correlation to the amplitude. [ABSTRACT FROM AUTHOR]