Web-winding systems, such as tape drives, are often modeled as linear and time-invariant, but at least two nonlinearities are common in these systems. First, the reel radii and moments of inertia change as web media spools from one reel to another. Second, friction can draw a thin layer of air between the layers of web media wrapped on the take-up reel, making the system’s spring and damping characteristics nonlinear by allowing a greater length of media to vibrate freely. In addition to these nonlinearities, there is often uncertainty in the motor parameters. In the first part of this paper, feedback linearization ideas motivate state feedback and changes of variables that transform the system into decoupled and intuitively meaningful tension and velocity loops. For the case where tension measurements are available, Lyapunov redesign techniques are then used to develop control laws that are robust with respect to these nonlinearities and uncertainties. The second part of this paper then develops an observer-based controller for the case where no tension measurements are available. Performance is established analytically for both the measurement-based and observer-based schemes. Simulations illustrate this performance.

1.
Franklin
,
G. F.
,
Powell
,
J. D.
, and
Workman
,
M. L.
, 1990,
Digital Control of Dynamic Systems
,
Addison-Wesley
,
Reading, MA
.
2.
Keshavan
,
M. B.
, and
Wickert
,
J. A.
, 1997, “
Air Entrainment During Steady-State Web Winding
,”
ASME J. Appl. Mech.
0021-8936,
64
, pp.
916
922
.
3.
Keshavan
,
M. B.
, and
Wickert
,
J. A.
, 1998, “
Transient Discharge of Entrained Air From a Wound Roll
,”
ASME J. Appl. Mech.
0021-8936,
65
, pp.
804
810
.
4.
Mathur
,
P. D.
, and
Messner
,
W. C.
, 1998, “
Frequency Domain Characterization of Take-Up Reel Air-Entrainment in Low Tension and High-Speed Tape Transport
,”
ASME J. Tribol.
0742-4787,
120
, pp.
554
558
.
5.
Baumgart
,
M. D.
, and
Pao
,
L. Y.
, 2005, “
Time-Optimal Control of Web-Winding Systems With Air Entrainment
,”
IEEE/ASME Trans. Mechatron.
1083-4435,
10
, pp.
257
262
.
6.
Mathur
,
P. D.
, and
Messner
,
W. C.
, 1998, “
Controller Development for a Prototype High-Speed Low-Tension Tape Transport
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
6
(
4
), pp.
534
542
.
7.
Lu
,
Y.
, and
Messner
,
W. C.
, 2001, “
Disturbance Observer Design for Tape Transport Control
,”
Proc. Amer. Ctrl. Conf.
,
Arlington, VA
,
IEEE
,
Piscataway, NJ
, pp.
2567
2571
.
8.
Lu
,
Y.
, and
Messner
,
W. C.
, 2001, “
Robust Servo Design for Tape Transport
,”
Proc. IEEE Intl. Conf. on Ctrl. App.
,
Mexico City
,
IEEE
,
New York
, pp.
1014
1019
.
9.
Panda
,
S. P.
, and
Engelmann
,
A. P.
, 2002, “
Modeling and Control System Design of Reel-to-Reel Tape Drives
,”
Proc. Amer. Ctrl. Conf.
,
Anchorage
,
IEEE
,
Piscataway, NJ
, pp.
927
932
.
10.
Khalil
,
H. K.
, 1996,
Nonlinear Systems
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
11.
Baumgart
,
M. D.
, and
Pao
,
L. Y.
, 2002, “
Transient Control of Web-Winding Systems With Air Entrainment
,”
Proc. IFAC Conf. Mechatronic Sys.
,
Berkeley, CA
,
IFAC
, pp.
17
22
.
You do not currently have access to this content.