A robust nonlinear control approach is presented for parametric uncertain systems with unknown friction. First- and second-order systems are considered, respectively. A model reference controller is developed such that the tracking error is bounded and converges to zero in the presence of the parameter uncertainty and the unknown friction. Then, the controller is extended to general case with any order. To design the controller, exact friction force is not required, only the upper bound for the level. Lyapunov’s direct method is used to prove robust global convergence of the tracking error. Finally, experimental results are given by applying the proposed controller to a pneumatic control valve. [S0022-0434(00)01802-5]

Issue Section:
Technical Papers
Keywords:
valves, pneumatic control equipment, robust control, nonlinear control systems, uncertain systems, model reference adaptive control systems, convergence, control system synthesis, Lyapunov methods
Topics:
Control equipment, Errors, Friction, Pneumatic control valves, Uncertain systems, Theorems (Mathematics)
1.
Armstrong-Helouvry
,
B.
,
Dupont
,
P.
, and
Canuadas de Wit
,
C.
,
1994
, “
A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines With Friction
,”
Automatica
,
30
, pp.
1083
–
1138
.
2.
Karnopp
,
D.
,
1985
, “
Computer Simulation of Stick-Slip Friction in Mechanical Dynamic Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
107
, pp.
100
–
103
.
3.
Haessig
, Jr.,
D. A.
, and
Fredland
,
B.
,
1991
, “
On the Modeling and Simulation of Friction
,”
ASME J. Dyn. Syst., Meas., Control
,
113
, pp.
354
-
362
.
4.
Canuadas de Wit
,
C.
,
Olsson
,
H.
,
Astrom
,
K. J.
, and
Lischinsky
,
P.
,
1995
, “
A New Model for Control of Systems with Friction
,”
IEEE Trans. Autom. Control.
,
40
, pp.
419
–
425
.
5.
Canuadas de Wit, C., and Seront, V., 1990, “Robust Adaptive Friction Compensation,” Proc. Int. Conf. on Robotics and Automation, Cincinnati, OH, pp. 1383–1388.
6.
Bai
,
E. W.
,
1997
, “
Parameterization and Adaptive Compensation of Friction Forces
,”
Int. J. Control Signal Proc.
,
11
, pp.
21
–
31
.
7.
Southward
,
S. C.
,
Radcliffe
,
C. J.
, and
MacCluer
,
C. R.
,
1991
, “
Robust Nonlinear Stick-Slip Friction Compensation
,”
ASME J. Dyn. Syst., Meas., Control
,
113
, pp.
639
–
645
.
8.
LaSalle, L., 1961, Stability by Lyapunov’s Direct Method With Application, Academic Press, San Diego.
Copyright © 2000
 by ASME
You do not currently have access to this content.