Global Asymptotic Stability of a PID Control System With Coulomb Friction

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...

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Published inIEEE 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
LanguageEnglish
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
Online AccessGet full text
ISSN0018-9286
1558-2523
DOI10.1109/TAC.2017.2774443

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Abstract 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 global asymptotic stability using a discontinuous Lyapunov-like function, and a suitable LaSalle's invariance principle. The well-posedness of the proposed model allows to establish useful robustness results, including an ISS property from a suitable input in a perturbed context. Simulation results are also given to illustrate our statements.
AbstractList 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 global asymptotic stability using a discontinuous Lyapunov-like function, and a suitable LaSalle's invariance principle. The well-posedness of the proposed model allows to establish useful robustness results, including an ISS property from a suitable input in a perturbed context. Simulation results are also given to illustrate our statements.
Author Bisoffi, Andrea
Teel, Andrew R.
Zaccarian, Luca
Da Lio, Mauro
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  organization: CNRS, LAAS, Toulouse, France
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Snippet 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...
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SubjectTerms 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
Title Global Asymptotic Stability of a PID Control System With Coulomb Friction
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https://laas.hal.science/hal-01700168
Volume 63
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