Abstract
This chapter describes several linear feedback control techniques that can be used to robustly control flexible dynamic systems. As with any dynamic system, it is often difficult to accurately model the system with enough fidelity that open loop control performs as intended. Because modeling errors are often unavoidable, linear feedback is often used to compensate for these modeling uncertainty. Even though many of the flexible dynamic systems are nonlinear, their models can be adequately linearized about operating points and standard linear feedback control techniques can be applied with satisfactory results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. F. Jones, B. J. Petterson, and J. C. Werner, “Swing damped movement of suspended objects,” Sandia Report 87-2189, Reprinted February 1993.
B. C. Kuo, Automatic Control Systems, 4th Ed., Prentice-Hall, 1982.
B. J. Petterson, R. D. Robinett, and J. C. Werner, “Lag-stabilized force feedback damping,” SAND91-0194, May 1991.
J. Roskam, Airplane Flight Dynamics and Automatic Flight Controls: Part II, Roskam Aviation and Engineering Corporations, Lawrence, Kansas, 1979.
W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing, Univ. Press, Cambridge, 1988.
R. D. Robinett, B. J. Petterson, and J. C. Fahrenholtz, “Lag-stabilized force feedback damping,” Journal of Intelligent and Robotic Systems, 21: 277–285, 1998.
C. Abdallah, P. Dorato, J. Benitez-Read, and R. Byrne, “Delayed positive feedback can stabilize oscillatory systems,” Proceeding of the American Control Conference, San Francisco, CA, pp. 3106–7, 1993.
R. H., Jr. Cannon, and Schmitz, E., “Initial experiments on the end-point control of a flexible one-link robot,” International Journal of Robotics Research, 3(3):62–75, 1984.
C. M. Oakley, and R. H. Cannon, “Anatomy of an experimental two-link flexible manipulator under end-point control,” In proceedings of the IEEE Conference on Decision and Control, Honolulu, HI, Dec. 1990.
C. M. Oakley, and C. H. Barratt, “End-point controller design for an experimental two-link flexible manipulator using convex optimization,” In proceedings of the American Control Conference, pages 1752–1759, San Diego, CA, May 1990.
P. A. Chodovarapu, and M. W. Spong, “On non-collocated control of a single flexible link,” Proceedings of the 1996 IEEE International Conference on Robotics and Automation, Minneapolis, Minnesota, April 1996, pp. 1101–1106.
M. Karkoub, and K. Tamma, “Modelling and µ-synthesis control of flexible manipulators,” Computers and Structures 79 (2001), pp. 543–551.
J. T. Feddema, G. R. Eisler, and D. J. Segalman, “Integration of Model-Based and Sensor-Based Control of a Two-link Flexible Robot Arm,” Proceedings of the 1990 IEEE Conference on Systems Engineering, Pittsburgh, PA, August 9–11, 1990.
R. F. Stengel, Stochastic Optimal Control: Theory and Application, John Wiley & Sons, Inc., 1986.
P. S. Maybeck, Stochastic Models, Estimation, and Control, Volume 1, Academic Press, New York, 1979.
A. E. Bryson, and Y. Ho, Applied Optimal Control, Hemisphere Publishing Corporation, Washington, D.C., 1975.
B. D. O. Anderson, and J. B. Moore, Optimal Control: Linear Quadratic Methods, Prentice-Hall, New Jersey, 1990.
E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, Springer-Verlag, New York, 1990.
F. L. Lewis, Optimal Estimation: With an Introduction to Stochastic Control Theory, John Wiley & Sons, Inc., New York, 1986.
K. J. Astrom, Introduction to Stochastic Control Theory, Academic Press, New York, 1970.
B. D. O. Anderson, and J. B. Moore, Optimal Filtering, Prentice-Hall Information and System Sciences Series, 1979.
J. L. Junkins, An Introduction to Optimal Estimation of Dynamic Systems, Sijhhof & Noordhoff International Publishers, The Netherlands, 1978.
R. E. Kalman, and R. S. Bucy, “New results in linear filtering and prediction theory,” Transactions of ASME, Journal of Basic Engineering, Vol. 83, pp. 95–107, 1961.
P. A. Ruymgaart, and T. T. Soong, Mathematics of Kalman-Bucy Filtering, Springer-Verlag, New York, 1988.
D. A. Schoenwald, J. T. Feddema, G. R. Eisler, and D. J. Segalman, “Minimum-Time Trajectory Control of Two-Link Flexible Robotic Manipulator,” Proceedings of the 1991 IEEE International Conference on Robotics and Automation, Sacramento, CA, April 1991, pp. 2114–2120.
D. J. Segalman, “A mathematical formulation for the rapid simulation of a flexible multilink manipulator,” SAND89-2308, Sandia National Laboratories, Albuquerque, NM.
T. J. Tarn, A. K. Bejczy, and X. Ding, “On the modelling of flexible robot arms,” Department of Systems Science and Mathematics, Washington University, St. Louis, MO, Robotics Laboratory Report SSM-RL-88-11, September 1988.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Robinett, R.D. et al. (2002). Linear Feedback Control. In: Flexible Robot Dynamics and Controls. International Federation for Systems Research International Series on Systems Science and Engineering, vol 19. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0539-6_6
Download citation
DOI: https://doi.org/10.1007/978-1-4615-0539-6_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5122-1
Online ISBN: 978-1-4615-0539-6
eBook Packages: Springer Book Archive