Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System

Rihem Farkh Kaouther Laabidi Mekki Ksouri

Rihem Farkh, Kaouther Laabidi, Mekki Ksouri. Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System[J]. 国际自动化与计算杂志(英)/International Journal of Automation and Computing, 2014, 11(2): 210-222. doi: 10.1007/s11633-014-0783-8
引用本文: Rihem Farkh, Kaouther Laabidi, Mekki Ksouri. Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System[J]. 国际自动化与计算杂志(英)/International Journal of Automation and Computing, 2014, 11(2): 210-222. doi: 10.1007/s11633-014-0783-8
Rihem Farkh, Kaouther Laabidi and Mekki Ksouri. Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System. International Journal of Automation and Computing, vol. 11, no. 2, pp. 210-222, 2014 doi:  10.1007/s11633-014-0783-8
Citation: Rihem Farkh, Kaouther Laabidi and Mekki Ksouri. Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System. International Journal of Automation and Computing, vol. 11, no. 2, pp. 210-222, 2014 doi:  10.1007/s11633-014-0783-8

Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System

doi: 10.1007/s11633-014-0783-8
详细信息
    作者简介:

    Kaouther Laabidi received her master degree from the Higher School of Sciences and Technologies of Tunis in 1995, her Ph.D. degree and the post-doctoral degree allowing to supervise Ph.D. in electrical engineering from the National Engineering School of Tunis, Tunis El-Manar University in 2005 and 2011, respectively. She is currently an associate professor at Tunis University, Tunisia. Her research interests include identification and control of complex systems. E-mail: Kaouther.Laabidi@enit.rnu.tn

Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System

  • 摘要: In this paper, the problem of stabilizing an unstable second order delay system using classical proportional-integral-derivative (PID) controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasi-polynomials, is used to seek the set of complete stabilizing proportional-integral/proportional-integral-derivative (PI/PID) parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizing set in the space of the integral and derivative gains is shown to be a triangle.
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Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System

doi: 10.1007/s11633-014-0783-8
    作者简介:

    Kaouther Laabidi received her master degree from the Higher School of Sciences and Technologies of Tunis in 1995, her Ph.D. degree and the post-doctoral degree allowing to supervise Ph.D. in electrical engineering from the National Engineering School of Tunis, Tunis El-Manar University in 2005 and 2011, respectively. She is currently an associate professor at Tunis University, Tunisia. Her research interests include identification and control of complex systems. E-mail: Kaouther.Laabidi@enit.rnu.tn

摘要: In this paper, the problem of stabilizing an unstable second order delay system using classical proportional-integral-derivative (PID) controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasi-polynomials, is used to seek the set of complete stabilizing proportional-integral/proportional-integral-derivative (PI/PID) parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizing set in the space of the integral and derivative gains is shown to be a triangle.

English Abstract

Rihem Farkh, Kaouther Laabidi, Mekki Ksouri. Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System[J]. 国际自动化与计算杂志(英)/International Journal of Automation and Computing, 2014, 11(2): 210-222. doi: 10.1007/s11633-014-0783-8
引用本文: Rihem Farkh, Kaouther Laabidi, Mekki Ksouri. Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System[J]. 国际自动化与计算杂志(英)/International Journal of Automation and Computing, 2014, 11(2): 210-222. doi: 10.1007/s11633-014-0783-8
Rihem Farkh, Kaouther Laabidi and Mekki Ksouri. Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System. International Journal of Automation and Computing, vol. 11, no. 2, pp. 210-222, 2014 doi:  10.1007/s11633-014-0783-8
Citation: Rihem Farkh, Kaouther Laabidi and Mekki Ksouri. Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System. International Journal of Automation and Computing, vol. 11, no. 2, pp. 210-222, 2014 doi:  10.1007/s11633-014-0783-8
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