A nonlinear compensation force for stick-slip friction is developed to supplement a proportional + derivative control law applied to a one-degree-of-freedom mechanical system. Inertial control objects acted on by stick-slip friction are common mechanical components in mechanical servo systems and the conceptual model chosen for this investigation is a mass sliding on a rough surface. The choice of a discontinuous compensation force is motivated by the requirement that the desired reference be a unique equilibrium point of the system. The stick-slip friction force, modelled with a sticking force term and a slipping force term, generates discontinuous state derivatives. A Lyapunov function is introduced to prove global asymptotic stability of the desired reference using a modification of the direct method for discontinuous systems. Stability is verified numerically as well as experimentally. The nonlinear compensation force is robust with respect to the character of the slipping force which is assumed to lie within a piecewise linear band. Exact knowledge of the static friction force levels is not required, only upper bounds for these levels. Stability and control effectiveness is verified analytically, numerically and experimentally on a laboratory test stand.
Robust Nonlinear Stick-Slip Friction Compensation
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Southward, S. C., Radcliffe, C. J., and MacCluer, C. R. (December 1, 1991). "Robust Nonlinear Stick-Slip Friction Compensation." ASME. J. Dyn. Sys., Meas., Control. December 1991; 113(4): 639–645. https://doi.org/10.1115/1.2896469
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