Global Asymptotic Stability of a PID Control System With Coulomb Friction

被引：27
|
作者：
Bisoffi, Andrea [1 ]
Da Lio, Mauro [1 ]
Teel, Andrew R. [2 ]
Zaccarian, Luca [1 ,3 ,4 ]
机构：
[1] Univ Trento, Dipartimento Ingn Ind, I-38122 Trento, Italy
[2] Univ Calif Santa Barbara, Dept Elect & Comp Engn, Santa Barbara, CA 93106 USA
[3] CNRS, LAAS, F-31400 Toulouse, France
[4] Univ Toulouse, F-31077 Toulouse 4, France
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2018年 / 63卷 / 08期
关键词：
asymptotic stability; robust asymptotic stability; Lyapunov methods; discontinuous Lyapunov function; friction; position control; PID control; mechanical systems; nonlinear dynamical systems; MODEL; COMPENSATION;
D O I：
10.1109/TAC.2017.2774443
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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.
引用
收藏
页码：2654 / 2661
页数：8
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