Single State Elasto-Plastic Models for Friction Compensation

For control applications involving small displacements and velocities, friction modeling and compensation can be very important. In particular, the phenomena of stiction and presliding displacement (motion during sticking) can play pivotal roles. In this paper, it is shown that existing single-state-variable friction models possess either stiction or presliding displacement. Next, those models with continuous states are interpreted as examples of Prandlt’s elasto-plastic material model. A class of general one-state models is derived that is stable, dissipative and exhibits both stiction and presliding displacement. For this class of models, a discrete observer for friction force compensation is derived. The observer uses only position and velocity (not force) measurements and integrates over space rather than time. State convergence relies on the occurrence of fully-developed slip of the friction contact. Moreover, the formulation yields a computationally parsimonious discrete observer.