Non-linear Geometric Approach to Friction Estimation and Compensation

This contribution describes the application of differential geometry and nonlinear systems analysis to the estimation of friction effects in a class of mechanical systems. The proposed methodology, that has been developed for the more general problem of fault detection and diagnosis, relies on adaptive filters designed with a nonlinear geometric approach to obtain the disturbance de-coupling property. The classical model of an inverted pendulum on a cart is considered as an application example, in order to highlight the complete design procedure, including the mathematical aspects of the disturbance de-coupling method as well as the feasibility and the efficiency of the approach. Thanks to accurate estimation, friction effects can also be compensated by means of a controller designed to inject the on-line estimate of friction force to the control action calculated by classical linear state feedback. This strategy, which belongs to the class of so-called Active Fault-Tolerant Control Schemes, allows to maintain existing controllers and enhance their performance by introducing an adaptive estimator of unmodeled friction forces.