Discrete-in-time feedback control of near-grazing dynamics in the two-degree-of-freedom vibro-impact system with a clearance

Abstract

Grazing bifurcation might bring dramatic and abrupt qualitative changes of system responses in non-smooth systems. The control problem of near-grazing dynamics in a two-degree-of-freedom vibro-impact system with a clearance is addressed in this paper. The discontinuity mapping is built to derive a normal form map near the grazing point. Based on the stability criterion of grazing orbit formulated through the normal form map, a discrete-in-time feedback method is developed to control the stability of grazing orbit in the vibro-impact system. Numerical simulations reveal a discontinuous grazing bifurcation with a jump between the transitions of periodic motions and show the feasibility of the proposed control strategy.