Global Asymptotic Stability of a PID Control System With Coulomb Friction

• Published in: IEEE transactions on automatic control Vol. 63; no. 8; pp. 2654 - 2661
• Main Authors: Bisoffi, Andrea, Da Lio, Mauro, Teel, Andrew R., Zaccarian, Luca
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Asymptotic properties; Asymptotic stability; Automatic; Computer simulation; Control stability; Control systems; Coulomb friction; discontinuous Lyapunov function; Engineering Sciences; Force; Friction; Integral equations; Lyapunov methods; mechanical systems; nonlinear dynamical systems; PD control; PI control; PID control; position control; Proportional integral derivative; robust asymptotic stability; Robustness; Static friction; Well posed problems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2017.2774443

For a point mass subject to Coulomb friction in feedback with a PID controller, we consider a model based on a differential inclusion comprising all the possible magnitudes of static friction during the stick phase and having unique solutions. We study the set of all equilibria and we establish its...