Discrete-Time Elasto-Plastic Friction Estimation

For control applications involving small displacements and velocities, friction modeling and compensation can be very important, especially around velocity reversal. We previously described single-state friction models that are based on elasto-plastic presliding, something that reduces drift while preserving the favorable properties of existing models (e.g., dissipativity) and that provide a comparable match to experimental data. In this paper, for this class of models, discrete estimation for friction force compensation is derived. The estimator uses only position and velocity (not force) measurements and integrates over space rather than time, yielding a discrete-time implementation that is robust to issues of sample size and sensor noise, reliably renders static friction and is computationally efficient for real-time implementation. Boundedness with respect to all inputs, convergence during steady sliding and dissipativity are established for the discrete-time formulation.