Stabilization of second-order unstable delay processes by simple controllers

Chen, Xiang; Wang, Q.G.; Lu, Xiuzhen; Nguyen, Luong T. H.; Lee, T.H.

doi:10.1016/j.jprocont.2007.03.002

Cited by 57 publications

(44 citation statements)

References 11 publications

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“…The stabilizability analysis for quasi-polynomials remains as a difficult topic. Use of some tools such as the Hermite-Biehler Theorem, the Root-Locus technique, and Nyquist stability analysis are reported in stabilizability studies, on which exact stabilizability results are obtained for some cases only [5,6]. The explicit stabilizability results for many common unstable processes are still not available.…”

Section: Introductionmentioning

confidence: 99%

Stabilizing control for a class of delay unstable processes

2010

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Section: Introductionmentioning

confidence: 99%

Stabilizing control for a class of delay unstable processes

2010

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“…When designing such controllers, knowledge of the all-stabilizing controller set, in terms of controller parameters, may provide considerable advantages for the designer, such as flexibility and avoiding recurring stability checks when the controller parameters need to be changed. By employing the well-known Nyquist stability criterion, many graphical-based stabilizing controller results are available for time delay systems with different limitations [6][7][8][9][10][11]. As well as the graphical-based results, there are also many studies about the analytical characterization of all-stabilizing low-order controllers for time delay systems with different limitations [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

All‐Stabilizing Proportional Controllers for First‐Order Bi‐Proper Systems with Time Delay: An Analytical Derivation

Nesimioğlu

Söylemez

2016

Asian Journal of Control

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In this paper, a simple derivation for an all-stabilizing proportional controller set for first-order bi-proper systems with time delay is proposed. In contrast to proper systems, an extremely limited number of studies are available in the literature for such bi-proper systems. To fill this gap in the literature, broader aspects of the stabilizing set are taken into consideration. The effect of zero on the stabilizing set is clearly discussed and we also prove that, when their zeros are placed symmetrically to the origin, the stabilizing set of non-minimum phase plant is always smaller than that of the minimum phase one. Moreover, for an open-loop unstable plant, maximum allowable time delay (MATD) is explicitly expressed as a function of the locations of the pole and zero. From that function, it is shown that for a minimum phase plant, the supremum of the MATD is two times that of the time constant of the plant and the infimum of the MATD is the time constant of the plant. We also prove that the supremum is the time constant and the infimum is zero for a non-minimum phase plant.

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“…This theorem proves the interlacing property of roots of the real and imaginary parts of a stable polynomial. A couple of works have also employed the Nyquist plot properties to compute the delay A c c e p t e d M a n u s c r i p t 3 stability margins for the second-order and all-pole delay systems (Lee, Wang, & Xiang, 2010;Xiang, Wang, Lu, Nguyen, & Lee, 2007). The Lambert W function is used in (Yi, Nelson, & Ulsoy, 2007) to compute an analytical solution for delay differential equations.…”

Section: Introductionmentioning

confidence: 99%

Stability domains of the delay and PID coefficients for general time-delay systems

Almodaresi

Bozorg

Taghirad

2015

International Journal of Control

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Time delays are encountered in many physical systems, and they usually threaten the stability and performance of closed-loop systems. The problem of determining all stabilizing PID controllers for systems with perturbed delays is less investigated in the literature. In this study, the Rekasius substitution is employed to transform the system parameters to a new space. Then, the singular frequency (SF) method is revised for the Rekasius transformed system (RTS). A novel technique is presented to compute the ranges of time delay for which stable PID controller exists. This stability range cannot be readily computed from the previous methods. Finally, it is shown that similar to the original SF method, finite numbers of singular frequencies are sufficient to compute the stable regions in the space of time delay and controller coefficients.

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Stabilization of second-order unstable delay processes by simple controllers

Cited by 57 publications

References 11 publications

Stabilizing control for a class of delay unstable processes

Stabilizing control for a class of delay unstable processes

All‐Stabilizing Proportional Controllers for First‐Order Bi‐Proper Systems with Time Delay: An Analytical Derivation

Stability domains of the delay and PID coefficients for general time-delay systems

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