New hybrid model and switched PI observer for dry friction systems

In this paper, a polytopic approach is used to derive a new hybrid model of systems submitted to dry friction. The principal characteristics of the proposed approach are that it is easily comprehensible, has few parameters, allows the adjustment of the model complexity to the treated case, models the stick-slip phenomena, and has low simulation time. The proposed new dry friction model is applied to the modeling of a real experimental mechanical system. The model parameters are obtained using an adequate position control which is based on a controller with very low bandwidth. To estimate the states of such system, a polytopic PI observer is proposed using a H∞ formulation. Its performance and robustness against model uncertainty are shown in simulation.