Abstract
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.
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Bonfè, M., Castaldi, P., Preda, N., Simani, S. (2014). Non-linear Geometric Approach to Friction Estimation and Compensation. In: Dalpiaz, G., et al. Advances in Condition Monitoring of Machinery in Non-Stationary Operations. Lecture Notes in Mechanical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39348-8_30
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DOI: https://doi.org/10.1007/978-3-642-39348-8_30
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