Estimation of discontinuous friction using continuous-discrete unscented Kalman filter for adaptive compensation

In this paper, we consider joint state and parameter for a system with Stribeck friction, where coefficients of Stribeck curve and viscous coefficient are considered as state variables together with velocity. As friction model is discontinuous, for its estimation we use continuous-discrete unscented Kalman filter for which the propagation of prediction and correction can be done via unscented transform. The estimate friction is then used for compensation in position control system with PID controller. On the estimation we discuss the observability of the joint state and parameter model. We find that the model is unobservable at zero velocity by using Filippov´s convex method. To avoid divergence of parameter estimation we propose temporary break of parameter update at velocity around zero, which is defined by a threshold. At the same time, we use Filippov approach joined with attraction manifold to avoid chattering and have velocity approach to zero. The judgement of performance for our proposed method is made from simulation results.