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