Global position regulation of friction manipulators via switched chattering control

Switched position control algorithms are developed to globally stabilize friction mechanical manipulators around a desired position. Both static and dynamic position feedback designs are presented. The controllers constructed, referred to as chattering controllers, do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts. Stability analysis is given within the Lyapunov vector functions framework extended to discontinuous dynamic systems. Performance issues of the chattering controllers are evaluated in an experimental study of a three degrees-of-freedom robot manipulator.

[1]  Arie Levant,et al.  Higher order sliding modes as a natural phenomenon in control theory , 1996 .

[2]  A. Michel,et al.  Qualitative Theory of Dynamical Systems: The Role of Stability Preserving Mappings , 1997, Proceedings of the IEEE.

[3]  F.R. Rubio,et al.  Gain-scheduling control of systems with dynamic friction , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[4]  S. Schael,et al.  Measurement of at , 1989 .

[5]  Vladimir Borisov,et al.  Theory of Chattering Control , 1994 .

[6]  G. Bartolini,et al.  Chattering avoidance by second-order sliding mode control , 1998, IEEE Trans. Autom. Control..

[7]  Integral Characterizations of Set UGAS of Differential Inclusions and Applications , 2001 .

[8]  Vasile Mihai Popov,et al.  Hyperstability of Control Systems , 1973 .

[9]  M. I. Zelikin,et al.  Theory of Chattering Control: with applications to Astronautics, Robotics, Economics, and Engineering , 1994 .

[10]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[11]  A. T. Fuller,et al.  Relay control systems optimized for various performance criteria , 1960 .

[12]  A. Levant Sliding order and sliding accuracy in sliding mode control , 1993 .

[13]  S. Ghosh Introduction to robotics: Mechanics and control (second edition): by J.J. Craig, Addison-Wesley, Wokingham, 1989. ISBN 0-201-09528-9, xiii + 450 pages, hardcover, £18.95 , 1991 .

[14]  Tsuneo Yoshikawa,et al.  Lyapunov Stability Theory , 2003 .

[15]  Rafael Kelly,et al.  A measurement procedure for viscous and coulomb friction , 2000, IEEE Trans. Instrum. Meas..

[16]  G. Bartolini Chattering phenomena in discontinuous control systems , 1989 .

[17]  Henk Nijmeijer,et al.  Global regulation of robots using only position measurements , 1993 .

[18]  B. Paden,et al.  Lyapunov stability theory of nonsmooth systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[19]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[20]  J. Alvarez,et al.  An Invariance Principle for Discontinuous Dynamic Systems With Application to a Coulomb Friction Oscillator , 2000 .