On harmonic disturbance rejection of an undamped Euler-Bernoulli beam with rigid tip body

Bao-Zhu Guo; Qiong Zhang

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 10, Issue: 4, page 615-623
  • ISSN: 1292-8119

Abstract

top
A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity.

How to cite

top

Guo, Bao-Zhu, and Zhang, Qiong. "On harmonic disturbance rejection of an undamped Euler-Bernoulli beam with rigid tip body." ESAIM: Control, Optimisation and Calculus of Variations 10.4 (2010): 615-623. <http://eudml.org/doc/90746>.

@article{Guo2010,
abstract = { A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity. },
author = {Guo, Bao-Zhu, Zhang, Qiong},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Beam equation; disturbance rejection; noncollocated control; strong stability.; noncollocated control; strong stability},
language = {eng},
month = {3},
number = {4},
pages = {615-623},
publisher = {EDP Sciences},
title = {On harmonic disturbance rejection of an undamped Euler-Bernoulli beam with rigid tip body},
url = {http://eudml.org/doc/90746},
volume = {10},
year = {2010},
}

TY - JOUR
AU - Guo, Bao-Zhu
AU - Zhang, Qiong
TI - On harmonic disturbance rejection of an undamped Euler-Bernoulli beam with rigid tip body
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 10
IS - 4
SP - 615
EP - 623
AB - A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity.
LA - eng
KW - Beam equation; disturbance rejection; noncollocated control; strong stability.; noncollocated control; strong stability
UR - http://eudml.org/doc/90746
ER -

References

top
  1. R.H. Cannon, Jr. and E. Schmitz, Inital experiments on the end-point control of a flexible one-link Robot. Inter. J. Robotics Res.3 (1984) 62-75.  
  2. G. Chen, M.C. Delfour, A.M. Krall and G. Payre, Modeling, stabilization and control of serially connected beam. SIAM J. Control Optim.25 (1987) 526-546.  Zbl0621.93053
  3. P.A. Chodavarapu and M.W. Spong, On noncolocted control of a single flexible link, in Proc. of the 1996 IEEE International Conference on Robotics and Automation, Minneapolis, Minnesota (April 1996) 1101-1106.  
  4. B.Z. Guo and Q. Song, Tracking control of a flexible beam by nonlinear boundary feedback. J. Appl. Math. Stochastic Anal.8 (1995) 47-58.  Zbl0822.93040
  5. B.Z. Guo, Riesz basis approach to the tracking control of a flexible beam with a tip rigid body without dissipativity. Optim. Methods Softw.17 (2002) 655-681.  Zbl1056.74044
  6. T. Hämäläinen and S. Pohjolainen, A finite dimensional robust controller for systems in the CD-algebra. IEEE Trans. Autom. Control45 (2000) 421-431.  Zbl0972.93014
  7. S. Lee and J.L. Junkins, Explicit generalization of Langrange's equations for hybrid coordinate dynamic systems, J. Guid. Control Dyn.15 (1992) 1443-1452.  Zbl0762.70011
  8. Z.H. Luo, B.Z. Guo and Ö. Morgül, Stability and Stabilization of Linear Dimensional Systems with Applications. Springer-Verlag, London (1999).  Zbl0922.93001
  9. J.C. Oostveen and R.F. Curtain, Robustly stabilizing controllers for dissipative infinite-dimensional systems with collocated actuators and sensors. Automatica36 (2000) 337-348.  Zbl0979.93101
  10. R. Rebarber and G. Weiss, Internal model based tracking and disturbance rejection for stable well-posed systems. Automatica, in press.  Zbl1028.93012
  11. Y. Sakawa, F. Matsuno and S. Fukushima, Modeling and feedback control of a flexible arm. J. Rob. Syst. 2 (1985) 453-472.  
  12. Y. Sakawa and Z.H. Luo, Modeling and control of coupled bending and torsional vibrations of flexible beam. IEEE Trans. Autom. Control34 (1989) 970-977.  Zbl0693.93041
  13. V.A. Spetor and H. Flashner, Modeling and design implification of noncollocated control in flexible systems. J. Dyn. Syst. Meas. Control112 (1990) 186-193.  
  14. G. Weiss and R. Rebarber, Optimizability and estimatability for infinite-dimensional linear systems. SIAM J. Control Optim.39 (2001) 1204-1232.  Zbl0981.93032
  15. K. Yuan and L. Liu, Achieving mininmum phase transfer function for a noncollocated single-link flexible manipulator. Asian J. Control2 (2000) 179-191.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.