<i>k<sub>p</sub></i>-stable regions in the space of time delay and PI controller coefficients

Almodaresi, Elham; Bozorg, Mohammad

doi:10.1080/00207179.2014.971433

Cited by 6 publications

(6 citation statements)

References 15 publications

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“…2 is replaced by G(s) and consequently rewritten to (7). Following the analogous procedure as outlined in Section 2, the stability boundary locus (or rather performance boundary locus in this case) for PI controllers (1) can be computed by solving the parametric equations (8) simultaneously, but now a set of relations (9) is modified to [9]: The performance boundary locus for a selected gain margin M can be obtained by equaling θ to zero in (11), whereas assuming that 0 M  results in the performance boundary locus for a chosen phase margin θ. The intersection of two relevant performance regions (the first one for guaranteed minimum gain margin, and the second one for guaranteed minimum phase margin) leads to the region that ensures the given minimum gain margin and phase margin at the same time.…”

Section: Figure 2 Feedback Control Loop With An Interval Plant and Gmentioning

confidence: 99%

“…Thus, the even and odd parts of the numerator and denominator of (7) are again in the form (20). Then, the parts (20) are used in the modified set of auxiliary variables (11), where M and θ are the chosen gain margin and phase margin, respectively, and subsequently, (11) is put into the parametric equations (8).…”

Section: Robust Performancementioning

confidence: 99%

“…The computation of all stabilizing PI(D) controllers by using the Kronecker summation method was presented in [10]. A Nyquist plotbased technique for calculation of KP-stable regions was developed in [11] (for time delay and PI controller parameters) and [12] (for PID controller parameters). A Lyapunov equation-based stability mapping approach can be found in [13], [14].…”

Section: Introductionmentioning

confidence: 99%

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Robust PI Control of Interval Plants With Gain and Phase Margin Specifications: Application to a Continuous Stirred Tank Reactor

2020

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The paper is focused on robust Proportional-Integral (PI) control of interval plants with gain and phase margin specifications and on the application of this approach to a Continuous Stirred Tank Reactor (CSTR). More specifically, the work aims at the determination of PI controller parameter regions, for which not only robust stability but also some level of robust performance of the closed-loop control system is guaranteed, and this robust performance is represented by the required gain and phase margin that has to be ensured for all potential members of the interval family of controlled plants, even for the worst case. The applied technique is based on the combination of the previously published generalization of stability boundary locus method (for specified gain and phase margin under the assumption of fixedparameter plants) with the sixteen plant theorem. This extension enables the direct application of the method to design the robustly performing PI controllers for interval plants. The effectiveness of the improved method is demonstrated on a CSTR, modeled as the interval plant, for which the robust stability and robust performance regions are obtained.

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Section: Figure 2 Feedback Control Loop With An Interval Plant and Gmentioning

confidence: 99%

Section: Robust Performancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust PI Control of Interval Plants With Gain and Phase Margin Specifications: Application to a Continuous Stirred Tank Reactor

2020

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“…Moreover, the parameter space method is used in [16] and Ddecomposition approach is employed in [17] to compute the stable regions of the controller coefficients for a time delay system with a known delay. For the case of uncertain delay, the stable regions are determined in the common space of the delay and the controller coefficients in [18,19]. The parameter space method is extended to linear time variant systems in [20] In this paper, a method is presented to compute the stabilising PID set without needing to sweep the proportional gain.…”

Section: Introductionmentioning

confidence: 99%

k _P ‐stable regions in the space of PID controller coefficients

Almodaresi

Bozorg

2017

IET Control Theory & Applications

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“…With suitable modifications of the results presented in and the descending magnitude property of all‐pole transfer functions, all stabilizing gains are computed for first‐ and second‐order time‐delay systems in , employing the Nyquist stability criterion. Then, using a similar strategy, all‐stabilizing PI controllers are computed in . It is worth noting that the last two methods work under either uncertain or fixed time delay, unlike the previous ones.…”

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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k_p-stable regions in the space of time delay and PI controller coefficients

Cited by 6 publications

References 15 publications

Robust PI Control of Interval Plants With Gain and Phase Margin Specifications: Application to a Continuous Stirred Tank Reactor

Robust PI Control of Interval Plants With Gain and Phase Margin Specifications: Application to a Continuous Stirred Tank Reactor

k _P ‐stable regions in the space of PID controller coefficients

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

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kp-stable regions in the space of time delay and PI controller coefficients

Cited by 6 publications

References 15 publications

Robust PI Control of Interval Plants With Gain and Phase Margin Specifications: Application to a Continuous Stirred Tank Reactor

Robust PI Control of Interval Plants With Gain and Phase Margin Specifications: Application to a Continuous Stirred Tank Reactor

k P ‐stable regions in the space of PID controller coefficients

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

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k_p-stable regions in the space of time delay and PI controller coefficients

k _P ‐stable regions in the space of PID controller coefficients