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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

By: Brian Cogan and  Annraoi de Paor  
Open Access
|Dec 2011

References

  1. CORLESS, R. M.—GONNET,—HARE, G. H.—JEFFREY, D. J.—KNUTH, D. E.: On the Lambert W Function, Advances in Computational Mathematics 5 (1996), 329-359.10.1007/BF02124750
  2. ANDERSEN, K.: The Geometry of Art - The History of the Mathematical Theory of Perspective from Alberti to Monge, Springer, 2007.
  3. SENGUPTA, P.: The Lambert W Function and Solutions to Kepler's Equation, Celestial Mechanics and Dynamical Astronomy 99 (2007), 13-22.10.1007/s10569-007-9085-6
  4. FURSE, C.: Applications of the Lambert W Function in Electromagnetics, IEEE Antennas and Propagation Magazine 44 (2002), 139-142.10.1109/MAP.2002.1039394
  5. WARBURTON, R. D. H.: An Analytical Investigation of the Bullwhip Effect, Production and Operations Management 13 (2004), 150-160.10.1111/j.1937-5956.2004.tb00151.x
  6. VALLURI, S. R.—GIL, M.—JEFFREY, D. J.—BASU, S.: The Lambert W Function and Quantum statistics, Journal of Mathematical Physics 50 (2009), 102-111.10.1063/1.3230482
  7. WILLIAMS, B. W.: Exact Solutions to a Schrodinger Equation Based on the Lambert Function, Physics Letters A 334 (2005), 117-222.10.1016/j.physleta.2004.11.012
  8. CRANMER, S. R.: New Views of the Solar Wind with the Lambert W Function, American Journal of Physics 72 (2004), 1397-1403.10.1119/1.1775242
  9. Maplesoft, Maple, 615 Kumpf Drive, Waterloo, Ontario, Canada.
  10. MathWorks, MatLab, The Math Works, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098, USA.
  11. WolframReseach, Mathematica, Wolfram Research Inc., 100 Trade Canter Drive, Champaign, IL 61820, USA.
  12. POWER, H. M.—SIMPSON, R. J.: Introduction to Dynamics and Control, McGraw-Hill, 1978.
  13. D'AZZO, J. J.—HOUPIS, C. H.: Linear Control System Analysis and Design Conventional and Modern, Mc Graw Hill, New York, 1988.
  14. OGATA, K.: Modern Control Engineering, Prentice Hall, 2002.
  15. PALM, W. J. III: Control System Engineering, John Wiley & Sons, 1986.
  16. BENDRIKOV, G. A.—TEODORCHIK, K. F.—: The Analytic Theory of Constructing Root Loci, Automation and Remote Control 20 (1959), 340-344.
  17. COGAN, B.: Use of the Analytic Method and Computer Alge- bra to Plot Root Loci, International Journal of Electrical Engineering Education 35 (1998), 350-356.10.1177/002072099803500406
  18. KING-SMITH, E. A.: Stability Analysis of Linear Continuous Time-Delay Feedback Systems, International Journal of Control 13 (1971), 633-655.10.1080/00207177108931973
  19. COGAN, B.: Optimum Stability in Control System Design, PhD thesis, Department of Electronic and Electrical Engineering, Trinity College, Dublin, 2006.
  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 31 (2009), 365-379.10.1177/0142331208095019
  21. SHINOZAKI, H.—MORI, T.: Robust Stability Analysis of Linear Time-Delay Systems by Lambert W Function: Some Extreme Point Results, Automatica 42 (2006), 1791-1799.10.1016/j.automatica.2006.05.008
  22. WANG, Z. H.—HU, H. Y.: Calculation of the Rightmost Characteristic Root of Retarded Time-Delay Systems via Lambert W Function, Journal of Sound and Vibration 318 (2008), 757-767.10.1016/j.jsv.2008.04.052
  23. HWANG, C.—CHENG, Y.-C.: A Note on the Use of the Lambert W Function in the Stability Analysis of Time-Delay Systems, Automatica 41 (2005), 1979-1985.10.1016/j.automatica.2005.05.020
  24. CHEN, Y.—MOORE, K. L.: Analytic Stability Bound for Delayed Second-Order Systems with Repeating Poles Using Lambert Function W, Automatica 38 (2002), 891-895.10.1016/S0005-1098(01)00264-3
  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 49 (1989), 1273-1284.10.1080/00207178908559705
  26. STEFANI, R. S.—SHAHIAN, B.—SAVANT, C. J.—HOSTETTER, G. H.: Design of Feedback Control Systems, Oxford University Press, 2002.
  27. de PAOR, A. M.: Concepts of Optimum Stability for Linear Feedback Systems, International Journal of Electrical Engineering Education 36 (1999), 46-64.10.7227/IJEEE.36.1.6
DOI: https://doi.org/10.2478/v10187-011-0052-9 | Journal eISSN: 1339-309X | Journal ISSN: 1335-3632
Language: English
Page range: 327 - 334
Published on: Dec 21, 2011
In partnership with: Paradigm Publishing Services
Publication frequency: 6 issues per year

© 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)