Friction Induced Limit Cycling: Hunting R.H.A.Hensen

In this paper friction induced limit cycles are predicted for a simple motion system of a single motor-driven inertia subjected to friction and a PID-controlled regulator task. The two friction models used, i.e., (i) the dynamic LuGre friction model and (ii) the static Switch friction model, are compared with respect to the so-called hunting phenomenon. Analysis tools originating from the field of nonlinear dynamics will be used to investigate the friction induced limit cycles. For a varying controller gain, stable and unstable periodic solutions are computed numerically which, together with the stability analysis of the closed-loop fixed points, result in a bifurcation diagram. For both friction models, the bifurcation analysis indicates the disappearance of the hunting behaviour for controller gains larger than the gain corresponding to the cyclic fold bifurcation point.