Coulomb Friction Limit Cycles in Elastic Positioning Systems

The state space control of a positioning system affected by torsional elasticity at the gearbox is considered, using a motor position transducer only. An output feedback, pole placement controller is used, with an additional integral action on the tracking error to cancel it at steady state. Both experiments and simulations point out that large oscillations may appear for some sets of closed-loop poles which yields, in contrast to stick-slip cycles, instantaneous motor velocity reversals. It is shown that such oscillations are induced by “pure” Coulomb friction. The period of the oscillations is predicted precisely following the Tsypkin’s relay control theory and also by the approximate describing function method. The latter also allows understanding of how oscillations depend on observer and feedback control design and on plant parameters; thus we are able to derive guidelines for the design of an oscillation free closed-loop system.