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.
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e-mail: soojeon@newton.berkeley.edu
e-mail: tomizuka@me.berkeley.edu
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January 2008
Research Papers
Stability of Controlled Mechanical Systems With Ideal Coulomb Friction
Soo Jeon,
Soo Jeon
Graduate Student
Department of Mechanical Engineering,
e-mail: soojeon@newton.berkeley.edu
University of California at Berkeley
, Berkeley, CA 94720
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Masayoshi Tomizuka
Masayoshi Tomizuka
Professor
Department of Mechanical Engineering,
e-mail: tomizuka@me.berkeley.edu
University of California at Berkeley
, Berkeley, CA 94720
Search for other works by this author on:
Soo Jeon
Graduate Student
Department of Mechanical Engineering,
University of California at Berkeley
, Berkeley, CA 94720e-mail: soojeon@newton.berkeley.edu
Masayoshi Tomizuka
Professor
Department of Mechanical Engineering,
University of California at Berkeley
, Berkeley, CA 94720e-mail: tomizuka@me.berkeley.edu
J. Dyn. Sys., Meas., Control. Jan 2008, 130(1): 011013 (9 pages)
Published Online: January 14, 2008
Article history
Received:
May 12, 2006
Revised:
April 25, 2007
Published:
January 14, 2008
Citation
Jeon, S., and Tomizuka, M. (January 14, 2008). "Stability of Controlled Mechanical Systems With Ideal Coulomb Friction." ASME. J. Dyn. Sys., Meas., Control. January 2008; 130(1): 011013. https://doi.org/10.1115/1.2807069
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