Skip to main content
Have a personal or library account? Click to login
Analytic Root Locus and Lambert W Function in Control of a Process with Time Delay Cover

Analytic Root Locus and Lambert W Function in Control of a Process with Time Delay

Journal of Electrical Engineering
Volume 62 (2011): Issue 6 (November 2011)
By:  and    
Open Access
|Dec 2011
References

References

  1. CORLESS, R. M.—GONNET,—HARE, G. H.—JEFFREY, D. J.—KNUTH, D. E.: On the LambertFunction, Advances in Computational Mathematics(1996), 329-359.
    Open DOISearch in Google Scholar
  2. ANDERSEN, K.: The Geometry of Art - The History of the Mathematical Theory of Perspective from Alberti to Monge, Springer, 2007.
    Search in Google Scholar
  3. SENGUPTA, P.: The LambertFunction and Solutions to Kepler's Equation, Celestial Mechanics and Dynamical Astronomy(2007), 13-22.
    Open DOISearch in Google Scholar
  4. FURSE, C.: Applications of the LambertFunction in Electromagnetics, IEEE Antennas and Propagation Magazine(2002), 139-142.
    Open DOISearch in Google Scholar
  5. WARBURTON, R. D. H.: An Analytical Investigation of the Bullwhip Effect, Production and Operations Management(2004), 150-160.
    Open DOISearch in Google Scholar
  6. VALLURI, S. R.—GIL, M.—JEFFREY, D. J.—BASU, S.: The LambertFunction and Quantum statistics, Journal of Mathematical Physics(2009), 102-111.
    Open DOISearch in Google Scholar
  7. WILLIAMS, B. W.: Exact Solutions to a Schrodinger Equation Based on the Lambert Function, Physics Letters A(2005), 117-222.
    Open DOISearch in Google Scholar
  8. CRANMER, S. R.: New Views of the Solar Wind with the Lambert W Function, American Journal of Physics(2004), 1397-1403.
    Open DOISearch in Google Scholar
  9. Maplesoft, Maple, 615 Kumpf Drive, Waterloo, Ontario, Canada.
    Search in Google Scholar
  10. MathWorks, MatLab, The Math Works, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098, USA.
    Search in Google Scholar
  11. WolframReseach, Mathematica, Wolfram Research Inc., 100 Trade Canter Drive, Champaign, IL 61820, USA.
    Search in Google Scholar
  12. POWER, H. M.—SIMPSON, R. J.: Introduction to Dynamics and Control, McGraw-Hill, 1978.
    Search in Google Scholar
  13. D'AZZO, J. J.—HOUPIS, C. H.: Linear Control System Analysis and Design Conventional and Modern, Mc Graw Hill, New York, 1988.
    Search in Google Scholar
  14. OGATA, K.: Modern Control Engineering, Prentice Hall, 2002.
    Search in Google Scholar
  15. PALM, W. J. III: Control System Engineering, John Wiley & Sons, 1986.
    Search in Google Scholar
  16. BENDRIKOV, G. A.—TEODORCHIK, K. F.—: The Analytic Theory of Constructing Root Loci, Automation and Remote Control(1959), 340-344.
    Search in Google Scholar
  17. COGAN, B.: Use of the Analytic Method and Computer Alge- bra to Plot Root Loci, International Journal of Electrical Engineering Education(1998), 350-356.
    Open DOISearch in Google Scholar
  18. KING-SMITH, E. A.: Stability Analysis of Linear Continuous Time-Delay Feedback Systems, International Journal of Control(1971), 633-655.
    Open DOISearch in Google Scholar
  19. COGAN, B.: Optimum Stability in Control System Design, PhD thesis, Department of Electronic and Electrical Engineering, Trinity College, Dublin, 2006.
    Search in Google Scholar
  20. COGAN, B.—de PAOR, A. M.—QUINN, A.: PI Control of First-Order Lag Plus Time-Delay Plants, Transactions of the Institute of Measurement and Control(2009), 365-379.
    Open DOISearch in Google Scholar
  21. SHINOZAKI, H.—MORI, T.: Robust Stability Analysis of Linear Time-Delay Systems by Lambert W Function: Some Extreme Point Results, Automatica(2006), 1791-1799.
    Open DOISearch in Google Scholar
  22. WANG, Z. H.—HU, H. Y.: Calculation of the Rightmost Characteristic Root of Retarded Time-Delay Systems via LambertFunction, Journal of Sound and Vibration(2008), 757-767.
    Open DOISearch in Google Scholar
  23. HWANG, C.—CHENG, Y.-C.: A Note on the Use of the LambertFunction in the Stability Analysis of Time-Delay Systems, Automatica(2005), 1979-1985.
    Open DOISearch in Google Scholar
  24. CHEN, Y.—MOORE, K. L.: Analytic Stability Bound for Delayed Second-Order Systems with Repeating Poles Using Lambert Function, Automatica(2002), 891-895.
    Open DOISearch in Google Scholar
  25. de PAOR, A. M.—O'MALLEY, M. J.: Controllers of the Ziegler-Nichols Type for Unstable Process with Time Delay, International Journal of Control(1989), 1273-1284.
    Open DOISearch in Google Scholar
  26. STEFANI, R. S.—SHAHIAN, B.—SAVANT, C. J.—HOSTETTER, G. H.: Design of Feedback Control Systems, Oxford University Press, 2002.
    Search in Google Scholar
  27. de PAOR, A. M.: Concepts of Optimum Stability for Linear Feedback Systems, International Journal of Electrical Engineering Education(1999), 46-64.
    Open DOISearch in Google Scholar
DOI: https://doi.org/10.2478/v10187-011-0052-9 | Journal eISSN: 1339-309X (formerly 1335-3632) | Journal ISSN: 1335-3632
Journal RSS Feed
Language: English
Page range: 327 - 334
Published on: Dec 21, 2011
Published by: Slovak University of Technology in Bratislava
In partnership with: Paradigm Publishing Services
Keywords:
Lambert W function,
root locus,
time-delay system,
stability,
eigenvalues
Related subjects:
Engineering,
Introductions and overviews,
Engineering, other

© 2011 Brian Cogan, Annraoi de Paor, published by Slovak University of Technology in Bratislava
This work is licensed under the Creative Commons License.

Volume 62 (2011): Issue 6 (November 2011)
Previous article
Next article