The presence of friction in mechanical motion systems is a performance limiting factor as it induces stick–slip 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. In order to eliminate stick–slip vibrations for mechanical motion systems, a state-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-to-state stability (ISS). The advantages of the presented controller is that it is robust to uncertainties in the friction and it is applicable to systems with non-collocation of actuation and friction where common control strategies such as direct friction compensation fail. Moreover, an observer-based output-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 motion control system.
Bruin, de, J. C. A., Doris, A., Wouw, van de, N., Heemels, W. P. M. H., & Nijmeijer, H. (2009). Control of mechanical motion systems with non-collocation of actuation and friction: a Popov criterion approach for input-to-state stability and set-valued nonlinearities. Automatica, 45(2), 405-415. https://doi.org/10.1016/j.automatica.2008.09.008