Anti-controlling quasi-periodic impact motion of an inertial impact shaker system

In this paper, anti-controlling quasi-periodic impact motion of an inertial impact shaker system is addressed. There exist two aspects of difficulty in the anti-control design: one is from the implicit Poincaré map of the system itself and the other from the limitation of the classical critical criterion of Hopf bifurcation described by the properties of eigenvalues. Through using linear feedback control method in the original differential system and applying an explicit criterion of Hopf bifurcation without using eigenvalues to the Poincaré map of the close-loop system, the two difficulties above can be overcome and the control design for creation of the quasi-periodic impact motion at a specified system parameter location is achieved. Numerical simulation shows that the stable quasi-periodic impact motion of the system is created at a desired parameter location by adjusting control parameter appropriately.