Controlofmechanicalmotionsystemswithnon-collocationofactuationand friction:APopovcriterionapproachforinput-to-statestabilityandset-valued

a b s t r a c t The presence of friction in mechanical motion systems is a performance limiting factor as it induces stickslip vibrations. To appropriately describe the stiction effect of friction, we adopt set-valued force laws. Then, the complete motion control system can be described by a Lur’e system with set-valued nonlinearities.Inordertoeliminatestickslipvibrat ionsformechanicalmotionsystems,astate-feedback control design is presented to stabilize the equilibrium. The proposed control design is based on an extension of a Popov-like criterion to systems with set-valued nonlinearities that guarantees input-tostate stability (ISS). The advantages of the presented controller is that it is robust to uncertainties in thefrictionanditisapplicabletosystemswithnon-collocationofactuationandfrictionwherecommon controlstrategiessuchasdirectfrictioncompensationfail.Moreover,anobserver-basedoutput-feedback design is proposed for the case that not all the state variables are measured. The effectiveness of the proposed output-feedback control design is shown both in simulations and experiments for a typical motioncontrolsystem. ’2008ElsevierLtd.Allrightsreserved.