Stability of Controlled Mechanical Systems With Ideal Coulomb Friction

Abstract

When a mechanical system with Coulomb friction is under feedback control, the closed-loop system may asymptotically converge to a point in the equilibrium set or generate nonlinear oscillations such as limit cycles depending on the control algorithm. Thus, it is important to know how to guarantee the stability in the presence of Coulomb friction. This paper presents the stability analysis of controlled mechanical systems with multiple ideal Coulomb friction sources. Common properties of controlled mechanical systems with multiple ideal Coulomb friction sources have been explored and generalized into the state space formulation leading to a class of ideal relay feedback systems. Various stability criteria are considered and a new sufficient condition for the pointwise global stability is suggested. Simulation results for a single mass system and experimental results for a single link flexible joint mechanism are presented to confirm the analysis and to illustrate various aspects of stability conditions for controlled mechanical systems with ideal Coulomb friction. The results given in this paper can be useful for the design of mechanical systems free from the limit cycle.