Skip to main content
SpringerLink
Log in

Optimal control of a single-link flexible manipulator

  • Published:
Journal of Intelligent and Robotic Systems Aims and scope Submit manuscript

Abstract

This paper deals with an exact state space dynamic model for manipulators with flexible links. We use the Bernoulli-Euler beam equations to derive a frequency domain matrix transfer function. This transfer function is then used to compute the Laplace transform of the state vector as a function of the lateral position along a single link manipulator. The problem of optimal end point control of the beam is then addressed. A sixth-order state space model is derived for the manipulator and the controller is based on this model. Several control laws are studied for this model. Next, the manipulator is modeled as eighth order but the control law based on the sixth-order model is retained. We then estimate the six states from the output of the eighth-order model and feed these states back to the controller to derive the control torque used to drive the manipulator. A filter is introduced to compensate for spillover. The results are very satisfactory, and are illustrated by simulated case studies.

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. Mirro, J., Automatic feedback control of a vibrating flexible beam, MS Thesis, Dept. of Mech. Engineering, MIT (1972).

  2. BookW.J., Analysis of massless elastic chains with servo controlled joints, J. Dynamic Sys., Meas. and Cont., Trans. ASME 101, 148–153 (1979).

    Google Scholar 

  3. Book, W.J., Maizza-Neto, O., and Whitney, D. E., Feedback control of two joint systems with distributed flexibility, J. Dynamic Sys., Meas. and Control, Trans. ASME, (1975), pp. 424–431.

  4. CannonR.H. and SchmitzE., Initial experiments on the end point control of a flexible one link robot, Int. J. Robotics Res. 3, 841–865 (1984).

    Google Scholar 

  5. Balas, M.J., Feedback control of flexible systems, IEEE Trans. Auto. Cont. AC-23, No. 4 (1978).

    Google Scholar 

  6. Rakhasha, F. and Goldenberg, A.A., Dynamics modelling of a single-link flexible robot, IEEE Int. Conf. Robotics and Automation (1985), pp. 984–989.

  7. SchwarzR.J. and FriedlandB., Linear Systems, McGraw-Hill, New York (1965).

    Google Scholar 

  8. Pal, S., Stephanou, H.E., and Cook, G., State space modeling and control of flexible manipulators, Proc. IEEE Int. Symp. Intelligent Cont., Philadelphia, PA (1987).

  9. Pal, S., Cook, G., and Stephanou, H.E., Near optimal control of flexible robots, IECON '87, Boston, MA (1987).

Download references

Author information

Authors and Affiliations

  1. Center for Robotics and Control, George Mason University, 22030, Fairfax, VA, USA

    S. Pal, H. E. Stephanou & G. Cook

Authors
  1. S. Pal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. E. Stephanou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Cook
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pal, S., Stephanou, H.E. & Cook, G. Optimal control of a single-link flexible manipulator. J Intell Robot Syst 2, 187–199 (1989). https://doi.org/10.1007/BF00238688

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00238688

Key words

Search

Navigation