Analysis of Friction Compensation Effects in Controlled Mechanical Systems

In this paper, the effects of friction compensation, including exact compensation, undercompensation and overcompensation, in PD controlled 1DOF mechanical systems are investigated. 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. In order to capture the sticking phenomenon at zero velocity, the friction model is expressed as a multi-valued map. Lyapunov’s stability theorem, LaSalle’s invariance principle and the properties of the ω-limit set of trajectories of a 2-dimensional differential inclusion are employed to show that firstly, exact compensation leads to global exponential stability of the setpoint, secondly, undercompensation leads to steady state errors, and thirdly, overcompensation conditionally induces limit cycling.