In this paper, vibration control of a nonlinear string system is considered. The system consists of a nonlinear string, two boundary supporting mechanisms, and a moving transporter at the base. To suppress the vibration, boundary control designs are carried out. A new robust and adaptive boundary controller is designed using the Lyapunov direct method. The proposed control is implemented at the two ends supporting the string to compensate for vibration induced by the base motion. It is shown that the adaptive/robust boundary control can asymptotically stabilize the nonlinear string. Numerical simulation of the closed loop system demonstrates the effectiveness of the proposed control.

1.
Qu, Z., 2000, “Robust and Adaptive Boundary Control of a Stretched String,” Proceedings of American Control Conference, June, pp. 1478–1482.
2.
Zhang, F., Dawson, D. M., Nagarkatti, S. P., and Haste, D. V., 1998, “Boundary Control for a General Class of Nonlinear Actuator-String System,” Proceedings of IEEE Conference on Decision and Control, December, pp. 3484–3489.
3.
Canbolat
,
H.
,
Dawson
,
D. M.
,
Rahn
,
C.
, and
Nagarkatti
,
S.
,
1998
, “
Adaptive Control of Out-of-Plane Cable Vibration
,”
ASME J. Appl. Mech.
,
65
(
12
), pp.
963
969
.
4.
Canbolat, H., Dawson, D. M., Nagarkatti, S. P., and Costic, B., 1998, “Boundary Control for a General Class of String Models,” Proceedings of American Control Conference, July, pp. 3472–3476.
5.
Shahruz, S. M., 1997, “Suppression of Vibration in Stretched Strings by the Boundary Control,” Proceedings of IEEE Conference on Decision and Control, December, pp. 535–536.
6.
Shahruz, S. M., 1997, “Suppression of Vibration in Nonlinear Axially Moving String by the Boundary Control,” Proceedings of American Control Conference, June, pp. 3242–3243.
7.
Fung
,
R.
, and
Tseng
,
C.
,
1999
, “
Boundary Control of an Axially Moving String via Lyapunov Method
,”
ASME J. Dyn. Syst., Meas., Control
,
121
(
2
), pp.
105
110
.
8.
Meirovitch, L., 1967, Analytical Methods in Vibrations, The Macmillan Company, New York, NY.
9.
Jin, W., Qu, Z., and Serra, R., 2001, “Nonlinear Simulation of a String System Under Boundary Robust Control,” 2001 IEEE Conference on Control Applications and 2001 IEEE International Symposium on Intelligent Control, CCA-1071, Mexico City, Mexico, September.
10.
Qu, Z., 1998, Robust Control of Nonlinear Uncertain Systems, Wiley Interscience, New York, NY.
You do not currently have access to this content.