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PID Stabilization of Linear Neutral Time-Delay Systems in a Numerical Approach
Faculty of Electrical & Computer Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran
Faculty of Electrical & Computer Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran
Faculty of Electrical & Computer Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran
- 1 Faculty of Electrical & Computer Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran
- 2 Faculty of Electrical & Computer Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran
- 3 Faculty of Electrical & Computer Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran
Intelligent Control and Automation·Volume 03 (2012)·Pages 313–318·Published 28 November 2012·DOI10.4236/ica.2012.34036
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Abstract
In this paper, the stabilization of neutral time-delay systems is investigated. An efficient numerical approach is presented in an algorithm to establish results so that stability of such systems is achieved and stabilizing PID parameters are determined directly. It is based on determining the rightmost characteristic roots and Nyquist plot. The Newton-Raphson’s iterative method based on Lambert W function is used for the calculation of these stabilizing roots directly from the closed-loop characteristic equation of the neutral time-delay system and then stability is checked by Nyquist plot and step response of closed-loop system. Two numerical examples are included to illustrate the effectiveness of the proposed approach.
KeywordsNeutral Time-Delay SystemsPID ControllerStabilityIterative MethodRightmost Characteristic RootNyquist Plot
- J. P. Richard, “Time-Delay Systems: An Overview of Some Recent Advances and Open Problems,” Automatica, Vol. 39, No. 10, 2003, pp. 1667-1694. doi:10.1016/S0005-1098(03)00167-5
- J. E. Normey-Rico and E. F. Camacho, “Control of Dead-Time Processes,” Springer-Verlag, London, 2007.
- V. B. Kolmanovskii and J. P. Richard, “Stability of Some Linear Systems with Delays,” IEEE Transactions on Automatic Control, Vol. 44, No. 5, 1999, pp. 984-989. doi:10.1109/9.763213
- J. K. Hale and S. M. V. Lunel, “Introduction to Functional Differential Equations,” Springer-Verlag, New York, 1993.
- L. Dugard and E. E. Verriest, “Stability and Control of Time-Delay Systems,” Springer, New York, 1998. doi:10.1007/BFb0027478
- S. I. Niculescu and R. Lozano, “On the Passivity of Linear Delay Systems,” IEEE Transactions on Automatic Control, Vol. 46, No. 3, 2001, pp. 460-464. doi:10.1109/9.911424
- K. Gu, V. L. Kharitonov and J. Chen, “Stability of Time-Delay Systems,” Birkhauser, Boston, 2003. doi:10.1007/978-1-4612-0039-0
- J. R. Partingtona and C. Bonnet, “H∞ and BIBO Stabilization of Delay Systems of Neutral Type,” Systems & Control Letters, Vol. 52, No. 3, 2004, pp. 283-288. doi:10.1016/j.sysconle.2003.09.014
- S. I. Niculescu, “Delay Effects on Stability: A Robust Control Approach,” Springer, New York, 2001.
- V. B. Kolmanovskii and A. D. Myshkis, “Applied Theory of Functional Differential Equations,” Kluwer, Dordrecht, 1992.
- V. B. Kolmanovskii and V. R. Nosov, “Stability of Functional Differential Equations,” Academic Press, New York, 1986.
- J. H. Park and O. Kwon, “On New Stability Criterion for Delay-Differential Systems of Neutral Type,” Applied Mathematics and Computation, Vol. 162, No. 2, 2005, pp. 627-637. doi:10.1016/j.amc.2004.01.001
- V. Chellaboina, A. Kamath and W. M. Haddad, “TimeDomain Sufficient Conditions for Stability Analysis of Linear Neutral Time-Delay Systems,” Proceedings of the 2007 American Control Conference, New York, 9-13 July 2007, pp. 4917-4918.
- Z. H. Wang, “Numerical Stability Test of Neutral Delay Differential Equations,” Hindawi Publishing Corporation, Cairo, 2008, pp. 1-10.
- J. G. Ziegler and N. B. Nichols, “Optimum Settings for Automatic Controllers,” Transactions on ASME, Vol. 64, 1942, pp. 759-768.