Adaptive Boundary Control of an Axially Moving String System

[+] Author and Article Information
Rong-Fong Fung

Department of Mechanical and Automation Engineering, National Kaohsiung First University of Science and Technology, University Road, Yuanchau, Kaohsiung, Taiwan 824, ROC

Jinn-Wen Wu

Department of Mathematics

Pai-Yat Lu

Department of Mechanical Engineering, Chung Yuan Christian University, Chung-Li, Taiwan 320, ROC

J. Vib. Acoust 124(3), 435-440 (Jun 12, 2002) (6 pages) doi:10.1115/1.1476381 History: Received May 01, 2000; Revised February 01, 2002; Online June 12, 2002
Copyright © 2002 by ASME
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Ulsoy,  A. G., 1984, “Vibration Control in Rotating or Translating Elastic Systems,” ASME J. Dyn. Syst., Meas., Control, 106(1), pp. 6–14.
Mote,  C. D., 1972, “Dynamic Stability of Axially Moving Materials,” Shock Vib. Dig., 4, pp. 2–11.
Wickert,  J. A., and Mote,  C. D., 1989, “On the Energetics of Axially Moving Continua,” J. Acoust. Soc. Am., 85, pp. 1365–1368.
Wickert,  J. A., and Mote,  C. D., 1990, “Classical Vibration Analysis of Axially Moving Continua,” ASME J. Appl. Mech., 57, pp. 738–744.
Lee,  S. Y., and Mote,  C. D., 1997, “A Generalized Treatment of the Energetics of Translating Continua, Part I: Strings and Second Order Tensioned Pipes,” J. Sound Vib., 204(5), pp. 717–734.
Yang,  B., and Mote,  C. D., 1991, “Active Vibration Control of the Axially Moving String in the S Domain,” ASME J. Appl. Mech., 58, pp. 189–196.
Lee,  S. Y., and Mote,  C. D., 1996, “Vibration Control of an Axially Moving String by Boundary Control,” ASME J. Dyn. Syst., Meas., Control, 118, pp. 66–74.
Fung,  F. R., Wu,  J. W., and Wu,  S. L., 1999, “Stabilization of an Axially Moving String by Nonlinear Boundary Feedback,” ASME J. Dyn. Syst., Meas., Control, 121, pp. 117–121.
Fung,  F. R., and Tseng,  C. C., 1999, “Boundary Control of an Axially Moving String Via Lyapunov Method,” ASME J. Dyn. Syst., Meas., Control, 121, pp. 105–110.
Middleton,  R. H., and Goodwin,  G. C., 1988, “Adaptive Computed Torque Control for Rigid Link Manipulator,” Syst. Control Lett., 10, pp. 9–16.
Spong,  M. W., and Ortega,  R., 1990, “On Adaptive Inverse Dynamics Control of Rigid Robots,” IEEE Trans. Autom. Control, 35, pp. 92–95.
Lammerts,  I. M. M., Veldpaus,  F. E., Van de Molengraft,  M. J. G., and Kok,  J. J., 1995, “Adaptive Computed Reference Computed Torque Control of Flexible Robots,” ASME J. Dyn. Syst., Meas., Control, 117, pp. 31–36.
Wen, J., 1986, “Robust Model Reference Control for Distributed Parameter Systems,” IFAC Control of Distributed Parameter Systems, Los Angeles, California.
Kobayashi,  T., 1988, “Finite-dimensional Adaptive Control for Infinite-Dimensional Systems,” Int. J. Control, 48(1), pp. 289–302.
Balas,  M. J., 1995, “Finite-Dimensional Direct Adaptive Control for Discrete-Time Infinite-Dimensional Linear Systems,” J. Math. Anal. Appl., 196, pp. 153–171.
Böhm,  M., Demetriou,  M. A., Reich,  S., and Rosen,  I. G., 1998, “Model Reference Adaptive Control of Distributed Parameter Systems,” SIAM J. Control Optim., 36, No. 1, pp. 33–81.
Hong,  K. S., 1994, “Direct Adaptive Control of Parabolic System: Algorithm Synthesis and Convergence and Stability Analysis,” IEEE Trans. Autom. Control, 39(10), pp. 2018–2033.
Aihara,  S. I., 1997, “On Adaptive Boundary Control for Stochastic Parabolic Systems with Unknown Potential Coefficient,” IEEE Trans. Autom. Control, 42(3), pp. 350–363.
De Queiroz,  M. S., Dawson,  D. M., Rahn,  C. D., and Zhang,  F., 1999, “Adaptive Vibration Control of an Axially Moving String,” ASME J. Vibr. Acoust., 121, pp. 41–49.
Craig, J., 1985, Adaptive Control of Mechanical Manipulators, Addison-Wesley, Reading, MA.
Vidyasagar, M., 1978, Nonlinear Systems Analysis, Englewood Cliffs, Prentice-Hall, NJ.
Horn, R. A., and Johnson, C. R., 1985, Matrix Analysis, Cambridge University Press.
Popov, V. M., 1973, Hyperstability of Control Systems, Springer-Verlag, New York.
Hong, K. S., 1991, “Vibrational and Adaptive Control of a Class of Distributed Parameter Systems Described by Parabolic Partial Differential Equations,” Ph.D. thesis, University of Illinois, Urbana-Champaign.


Grahic Jump Location
An axially moving string system with the MDS controller
Grahic Jump Location
Comparison for the controlled and uncontrolled systems. (a) Transverse amplitudes at x=l. (“–”: controlled trajectory; “[[dashed_line]]”: uncontrolled trajectory, “-.-”: desired trajectory.) (b) Control input Fc. (c) Total mechanical energy H. (d) String mass per unit length ρ⁁. (e) Tension force T⁁o. (f ) Lumped mass m⁁. (g) Viscous damper coefficient d⁁m. (h) Stiffness coefficient k⁁m.




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