A Friction Model Describing Limit Cycles in Positioning Servos

Abstract

In this paper we describe a novel model for servo positioning systems. Non-linear representations of friction, backlash, controllers, and process dynamics are integrated into a model having a closed-loop configuration where unwanted oscillations, such as hunting (stick-slip) and resonant frequencies, are reproduced. This continuous model contains the different types of friction (Coulomb, Stribeck, and viscous) and the dynamics of a digital controller with a standard configuration. A case study consisting of a gun mount driven by hydraulic actuators is analyzed. Real data is used for the identification and validation of the mathematical representation. Empirically obtained static friction values are used for tuning the model at low speeds. An excellent matching is accomplished between the model and the real response. The model also reproduces the dependence of the resonant frequencies to the rotating velocity that is generally observed in this type of feedback system. The model can be a powerful tool for testing new control strategies. It looks for reductions in oscillation, predicts limit cycles, and detects faults.

Keywords

friction servo positioning systems limit cycles Coulomb Stribeck viscous friction backlash stick-slip

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