Skip to main content
SpringerLink
Log in

Control Parametrization Enhancing Technique and Simulation on the Design of a Flexible Rotating Beam

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

In this paper, a computational approach is adopted to solve the optimal control and optimal parameter selection problems of a rotating flexible beam fully covered with active constrained layer damping (ACLD) treatment. The beam rotates in a vertical plane under gravity with variable angular velocity and carries an end mass. The problem is posed as a continuous-time optimal control problem and solved via MISER3. Using the control parametrization enhancing technique (CPET), the results show that substantial improvements are obtained with ACLD as compared to the passive constrained layer damping (PCLD) treatment. In addition, accurate switching times of the system are determined. A parametric analysis is also included through simulation results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bainum, P.M., Xu, J.K.: Calibration of tip position during maneuvers of space-robotic systems. J. Astronaut. Sci. 43, 1–23 (1995)

    Google Scholar 

  2. Xu, J.K., Bainum, P.M.: Dynamics of flexible multilink robot arms with mass center offset. Acta Astronaut. 36, 99–111 (1995)

    Article  Google Scholar 

  3. Gouliaev, V.I., Zavrazhina, T.V.: Dynamics of a flexible multi-link cosmic robot manipulator. J. Sound Vib. 243, 641–657 (2001)

    Article  Google Scholar 

  4. Yang, T.W., Xu, W.L., Tso, S.K.: Dynamic modeling based on real-time deflection measurement and compensation control for flexible multi-link manipulators. Dyn. Control 11, 5–24 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Baz, A., Ro, J.: Optimum design and control of active constrained layer damping. J. Mech. Des., Trans. ASME 117 Supplement, 135–144 (1995)

    Google Scholar 

  6. Lesieutre, G.A., Lee, U.: A finite element for beams having segmented active constrained layers with frequency-dependent viscoelastics. Smart Mater. Struct. 615–627 (1996)

  7. Baz, A., Ro, J.: Vibration control of rotating beams with active constrained layer damping. Smart Mater. Struct. 10, 112–120 (2001)

    Article  Google Scholar 

  8. Lam, M.J., Inman, D.J., Saunders, W.R.: Hybrid damping models using the Golla-Hughes-McTavish method with internally balanced model reduction and output feedback. Smart Mater. Struct. 9, 362–371 (2000)

    Article  Google Scholar 

  9. Fasana, A., Marchesiello, S.: Rayleigh-Ritz analysis of sandwich beams. J. Sound Vib. 241, 643–652 (2001)

    Article  Google Scholar 

  10. Zou, J.Q., Fung, E.H.K., Lee, H.W.J.: Dynamic analysis of a flexible manipulator with passive constrained layer damping. In: IMECE2003-41246. ASME International Mechanical Engineering Congress and Exposition, Washington (2003)

  11. Fung, E.H.K., Zou, J.Q., Lee, H.W.J.: Lagrangian formulation of rotating beam with active constrained layer damping in time domain analysis. J. Mech. Des. 126, 359–364 (2004)

    Article  Google Scholar 

  12. Fung, E.H.K., Yau, D.T.W.: Vibration characteristics of a rotating flexible arm with ACLD treatment. J. Sound Vib. 269, 165–182 (2004)

    Article  Google Scholar 

  13. Hau, L.C., Fung, E.H.K.: Effect of ACLD treatment configuration on damping performance of a flexible beam. J. Sound Vib. 269, 549–567 (2004)

    Article  Google Scholar 

  14. Miele, A., Pritchard, R.E., Damoulakis, J.N.: Sequential gradient-restoration algorithm for optimal control problems. J. Optim. Theory Appl. 5, 235–282 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  15. Gonzalez, S., Miele, A.: Sequential gradient-restoration algorithm for optimal control problems with general boundary conditions. J. Optim. Theory Appl. 26, 395–425 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  16. Miele, A., Mohanty, B.P., Venkataraman, P., Kuo, Y.M.: Numerical solution of minimax problems of optimal control, Parts 1, 2. J. Optim. Theory Appl. 38, 97–135 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  17. Jennings, L.S., Fisher, M.E., Teo, K.L., Goh, C.J.: MISER3 optimal control software, version 3: Theory and user manual. http://www.maths.uwa.edu.au/~les/miser3.3.html

  18. Teo, K.L., Goh, C.L., Wong, K.H.: A Unified Computational Approach to Optimal Control Problems. Longman Scientific and Technical, London (1991)

    MATH  Google Scholar 

  19. Lee, H.W.J., Teo, K.L., Rehbock, V., Jennings, L.S.: Control parametrization enhancing technique for time optimal control problems. Dyn. Syst. Appl. 6, 243–262 (1997)

    MATH  MathSciNet  Google Scholar 

  20. Lee, H.W.J., Teo, K.L., Rehbock, V., Jennings, L.S.: Control parametrization enhancing technique for optimal discrete-valued control problems. Automatica 35, 1401–1407 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  21. Lee, H.W.J., Teo, K.L., Lim, A.E.B.: Sensor scheduling in continuous time. Automatica 37, 2017–2023 (2001)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Y. C. E. Lee & H. W. J. Lee

  2. Department of Mechanical Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    E. H. K. Fung

Authors
  1. Y. C. E. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. H. K. Fung
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. W. J. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. C. E. Lee.

Additional information

Communicated by T.L. Vincent.

We thank Chief Editor A. Miele and Associate Editor T.L. Vincent for handling the manuscript and two anonymous reviewers for valuable comments which contributed a significant improvement in the paper.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, Y.C.E., Fung, E.H.K. & Lee, H.W.J. Control Parametrization Enhancing Technique and Simulation on the Design of a Flexible Rotating Beam. J Optim Theory Appl 136, 247–259 (2008). https://doi.org/10.1007/s10957-007-9303-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-007-9303-0

Keywords

Search

Navigation