Analysis of undercompensation and overcompensation of friction in 1DOF mechanical systems

This paper investigates the effects of undercompensation and overcompensation of friction in PD controlled 1DOF mechanical systems. The friction force that is acting on the mechanical system and the friction compensation term in the feedback loop are described by a class of discontinuous friction models consisting of static, Coulomb and viscous friction, and including the Stribeck effect. Lyapunov's stability theorem and LaSalle's invariance principle are applied to prove that undercompensation of friction leads to steady-state errors and the properties of the ω-limit set of trajectories of a two-dimensional autonomous differential inclusion are used to show that overcompensation of friction may induce limit cycling. Furthermore, the analysis also indicates that the limit cycling effect can be eliminated by tuning the PD controller gains.