In this paper, a solution to the regulation problem of mechanical systems in presence of Coulomb friction is proposed. The control objective is attained by means of continuous control signals designed according to a second-order sliding mode algorithm. The proposed solution avoids the main drawback presented by the standard first-order sliding mode control, that is the chattering phenomenon which is due to the unavoidable presence of non idealities and to the discontinuous nature of the control signals. The proposed algorithm is proved to be efficient in counteracting discontinuous disturbances such as friction. [S0022-0434(00)00704-8]
Issue Section:
Technical Papers
1.
Bartolini
, G.
, and Pydynowski
, P.
, 1996
, “An improved, chattering free, V.S.C. scheme for uncertain dynamical systems
,” IEEE Trans. Autom. Control
, 41
, No. 8
, pp. 1220
–1226
.2.
Sira-Ramirez
, H.
, 1992
, “Asymptotic output stabilization for nonlinear systems via dynamical variable structure
,” Dynam. Control
, 12
, No. 1
, pp. 45
–58
.3.
Zinober
, A. S. I.
, El-Ghezawi
, O. M. E.
, and Billings
, S. A.
, 1982
, “Multivariable variable structure adaptive model following control systems
,” Proc. Inst. Electr. Eng.
, 5
, pp. 6
–12
.4.
Sira-Ramı`rez
, H.
, 1993
, “On the dynamical sliding mode control strategies in the regulation of nonlinear systems
,” Int. J. Control
, 57
, No. 5
, pp. 1039
–1061
.5.
Lu
, X.-Y.
, and Spurgeon
, S. K.
, 1998
, “Output feedback stabilization of siso nonlinear systems via dynamic sliding modes
,” Int. J. Control
, 70
, No. 5
, pp. 735
–759
.6.
Wu
, Y.
, Yu
, X.
, and Man
, Z.
, 1998
, “Terminal sliding mode control design for uncertain dynamic systems
,” Syst. Control Lett.
, 34
, pp. 281
–287
.7.
Bartolini
, G.
, Ferrara
, A.
, and Usai
, E.
, 1998
, “Chattering avoidance by second order sliding modes control
,” IEEE Trans. Autom. Control
, 43
, No. 2
, pp. 241
–247
.8.
Bartolini
, G.
, Ferrara
, A.
, and Usai
, E.
, 1997
, “Output tracking control of uncertain nonlinear second-order systems
,” Automatica
, 33
, No. 12
, pp. 2203
–2212
.9.
Levant
, A.
, 1993
, “Sliding order and sliding accuracy in sliding mode control
,” Int. J. Control
, 58
, No. 6
, pp. 1247
–1263
.10.
Levant, A., and Fridmann, L., 1996, “Higher order sliding modes as a natural phenomenon in control theory,” Robust Control Via Variable Structure and Lyapunov Techniques, F. Garofalo and L. Glielmo, eds., Vol. 217 of Lecture Notes in Control and Information Sciences, pp. 107–133. Springer-Verlag, London.
11.
Kwatny, H. G., Teolis, C., and Mattice, M., 1999, “Variable structure control of systems with nonlinear friction,” Proc. of the 38th IEEE Conf. on Decision and Control, Phoenix, Arizona, pp. 5164–5169.
12.
Canudas de Wit
, C.
, Noe¨l
, P.
, Aubin
, A.
, and Brogliato
, B.
, 1991
, “Adaptive friction compensation in robot manipulators: Low velocities
,” Int. J. Robot. Res.
, 10
, No. 3
No. 3
.13.
Armstrong-He´louvry
, B.
, Dupont
, P.
, and Canudas de Wit
, C.
, 1994
, “A survey of models, analysis tools and compensation methods for the control of machines with friction
,” Automatica
, 30
, No. 7
, pp. 1083
–1138
.14.
Canudas de Wit
, C.
, 1998
, “Comments on ‘A new model for control of systems with friction,’
” IEEE Trans. Autom. Control
, 43
, No. 8
, pp. 1189
–1190
.15.
Armstrong-He´louvry
, B.
, and Amin
, B.
, 1996
, “PID Control in presence of static friction: a comparison of algebraic and describing function analysis
,” Automatica
, 32
, No. 5
, pp. 679
–692
.16.
Kim
, S.-J.
, and Ha
, I.-J.
, 1999
, “On the existence of Carathe`odory solutions in mechanical systems with friction
,” IEEE Trans. Autom. Control
, 44
, No. 11
, pp. 2086
–2089
.17.
Utkin, V. I., 1992, Sliding Modes in Control and Optimization, Springer-Verlag, Berlin.
18.
Filippov, A. F., 1988, Differential Equations with Discontinuous Right-Hand Side, Kluwer, Dordrecht, The Netherlands.
19.
Canudas de Wit
, C.
, Olsson
, H.
, A˚stro¨m
, K. J.
, and Lischinsky
, P.
, 1995
, “A new model for control of systems with friction
,” IEEE Trans. Autom. Control
, 40
, No. 3
, pp. 419
–425
.Copyright © 2000
by ASME
You do not currently have access to this content.