Passivity-based Trajectory Tracking Control in Frictional Oscillators with Set-valued Friction

Overview & Synopsis

This article is largely concerned with the trajectory tracking control of frictional oscillators, which are nonsmooth nonlinear dynamical systems. The trajectory tracking problem, which is studied under a passivity-based controller addresses three main cases: the nominal case with known friction coefficient, uncertain friction coefficient, and when the Coulomb friction model is enhanced by including Stribeck effects. Monotonicity (or hypomonotonicity) of the friction model is crucial for the stability analysis of the tracking error. It can be relaxed to hypomonotonicity to handle Stribeck model. The framework of linear complementarity systems is used for the analysis. The case of a twomass system is tackled as an extension of the standard one-mass oscillator. Theoretical results are supported by numerical simulations.