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 system is 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.


Criticality of Hopf Bifurcation in Precision Motion Stage With PID and Time-Delayed Feedback Controls

Division / Sponsors: 
Design Engineering Division and Computers & Information In Engineering Division


Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2020/volume/83907

IDETC2020 - Virtual Conference

Supporting the need among researchers worldwide for additional online and multimedia content, ASME now offers the ASME Conference Video Collection. This platform will collect and provide long-term access to conference presentation videos, encompassing all technology areas within ASME's technical conference and events program. About 30,000-40,000 engineers across all mechanical engineering and related disciplines participate in ASME conferences each year. This includes authors of approximately 6,000 to 8,000 technical papers published by ASME, the majority of whom also submit video presentations for our virtual conferences. The video collection will be available as an add-on to existing product packages or as a separate subscription.