Abstract
The use of precision motion stages is very popular among advanced manufacturing and machining industries. However, the performance of these motion stages is usually undermined by friction-induced vibration. In this paper, we propose the use of time-delayed feedback control to minimize the undesirable effects of friction-induced vibrations. The use of time-delayed feedback control is well established in the literature; however, the use of time-delayed feedback control in PID controlled motion-stages has not been explored yet. Here, we consider a lumped parameter model of the PID controlled precision motion stage with a linear time-delayed state feedback control. The dynamical friction in the systemis modeled using the LuGre model. Stability and nonlinear analysis of the system are carried out using analytical methods. The stability analysis reveals the existence of multiple stability lobes and codimension-2 Hopf points for a given choice of system parameters. Also, the nature of Hopf bifurcation is determined by using the method of multiple scales. We observe the existence of both subcritical and supercritical Hopf bifurcations in the system, depending on the choice of control parameters. This observation implies that the nonlinearity in the system could both be stabilizing or destabilizing in nature.
Time-delayed feedback control of dynamical small-world networks at Hopf bifurcation
