Pulse width control refers to the use of a control law to determine the duration of fixed-height force pulses for point-to-point position control of a plant that is subject to mechanical friction, including stiction. The use of constant-gain pulse width control laws for precise positioning of structurally flexible plants subject to stiction and Coulomb friction is analyzed. It is shown that when the plant is a simple two-mass system subject to stiction and Coulomb friction, a position error limit cycle can result. Sufficient conditions for stability and self-sustained oscillation of this closed-loop system are derived. The sufficient conditions for stability are used to determine conditions on the plant parameters and the control gain that guarantee closed-loop stability and thus limit-cycle-free operation and zero steady-state position error. The analysis methods that are introduced are demonstrated in applications to the control of the position of the end-effector of an industrial robot.

1.
Armstrong-Helouvry
,
B.
,
Dupont
,
P.
, and
De Witt
,
C. C.
,
1994
, “
A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines With Friction
,”
Automatica
,
30
, pp.
1083
1138
.
2.
Spector
,
V. A.
, and
Flashner
,
H.
,
1990
, “
Modeling and Design Implications of Noncollocated Control in Flexible Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
112
, pp.
186
193
.
3.
Yang
,
S.
, and
Tomizuka
,
M.
,
1988
, “
Adaptive Pulse Width Control for Precise Positioning Under the Influence of Stiction and Coulomb Friction
,”
ASME J. Dyn. Syst., Meas., Control
,
110
, pp.
221
227
.
4.
Yang, S., and Tomizuka, M., 1988, “Pulse Control for Vibration Attenuation in Nonlinear Mechanical Systems,” Symposium on Robotics, ASME WAM, DSC, 11, pp. 103–114.
5.
Rathbun, D. B., 2001, “Pulse Modulation Control for Precise Positioning of Structurally Flexible Systems Subject to Stiction and Coulomb Friction,” Ph.D. dissertation, Department of Electrical Engineering, University of Washington, Seattle.
6.
Kalman
,
R. E.
, and
Bertram
,
J. E.
,
1960
, “
Control System Analysis and Design via the Second Method of Lyapunov, Part II: Discrete-Time Systems
,”
ASME J. Basic Eng.
,
82
, pp.
394
400
.
7.
Thomson, W. T., 1981, Theory of Vibration with Applications, Prentice-Hall, Englewood Cliffs, New Jersey.
You do not currently have access to this content.