A Smoothed GMS friction model for Moving Horizon friction state and parameter estimation

This paper presents a smoothed friction model that closely approximates the Generalized Maxwell-Slip (GMS) model, a multi-state friction model known to describe all essential friction characteristics in presliding and sliding motion. In contrast to the GMS model, which consists of a switching structure to accommodate for its hybrid nature, the Smoothed GMS (S-GMS) model consists of an analytic set of differential equations well suited for on-line state and parameter estimation, such as in Moving Horizon Estimation (MHE). Efficient on-line state and parameter estimation is essential for model-based friction compensation in order to track friction characteristics changes in time and space. Moreover, MHE is known to better handle model nonlinearities, disturbances and constraints than Extended Kalman Filter (EKF). This paper discusses the implementation of the EKF and MHE estimators for both the GMS and the S-GMS friction models. The benefit of the combination of MHE and S-GMS model is shown.