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

Almodaresi, Elham; Bozorg, Mohammad; Taghirad, Hamid D.

doi:10.1080/00207179.2015.1099166

Cited by 15 publications

(4 citation statements)

References 22 publications

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“…[12]. Finding the stability regions in the 2D controller parameter space for PI/PD [13,14], or PID controllers [14][15][16][17] are the fundamental components of stability analysis for time-delayed systems. In order to obtain the stabilizable regions, several methods like the Hermite-Biehler theorem applicable to quasi-polynomials [16,18], D-partitioning approach [19], Bode or Nyquist domain frequency response analysis [20], graphical methods [21,22], stability boundary locus [14] etc.…”

Section: Previous Work On Stability Analysis Of Time Delay Systemsmentioning

confidence: 99%

Stabilizing regions of dominant pole placement for second order lead processes with time delay using filtered PID controllers

Halder,

Das

2024

PLoS ONE

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In order to handle second order lead processes with time delay, this paper provides a unique dominant pole placement based filtered PID controller design approach. This method does not require any finite term approximation like Pade to obtain the quasi-polynomial characteristic polynomial, arising due to the presence of the time delay term. The continuous time second order plus time delay systems with zero (SOPTDZ) are discretized using a pole-zero matching method with specified sampling time, where the transcendental exponential delay terms are converted into a finite number of poles. The pole-zero matching discretization approach with a predetermined sampling period is also used to discretize the continuous time filtered PID controller. As a result, it is not necessary to use any approximate discretization technique, such as Euler or Tustin, to derive the corresponding discrete time PID controller from its continuous time counterpart. The analytical expressions for discrete time dominant pole placement based filtered PID controllers are obtained using the coefficient matching approach, while two distinct kinds of non-dominant poles, namely all real and all complex conjugate, have been taken into consideration. The stabilizable region in the controller and design parameter space for the chosen class of linear second order time delay systems with lead is numerically approximated using the particle swarm optimization (PSO) based random search technique. The efficacy of the proposed method has been validated on a class of SOPTDZ systems including stable, integrating, unstable processes with minimum as well as non-minimum phase zeros.

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Section: Previous Work On Stability Analysis Of Time Delay Systemsmentioning

confidence: 99%

Stabilizing regions of dominant pole placement for second order lead processes with time delay using filtered PID controllers

Halder,

Das

2024

PLoS ONE

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“…On the other hand, substituting s = ∞ in (19) gives no solution for k p and k i for any value of k d and therefore IRB line does not exist in (k p , k i )-plane. Expressions for CRB curve are obtained by equating (21) and (22) to zero and solving for k p and k i yields…”

Section: All Stability Region In (K P K I )-Plane For a Fixed Value Of K Dmentioning

confidence: 99%

“…Since closed‐loop stability is the primary requirement, it is desirable to obtain all stabilizing PID gains set before controller tuning. Various methods have been reported in the literature to compute the all stabilizing PI, PD and PID controllers such as Nyquist plot approach [18], D‐decomposition method [19], stability boundary locus approach [20], singular frequency method [21], kronecker summation method [22], Hermite–Biehler theorem [23], signature method [24]. Gain and phase margins are the two commonly used relative stability measures.…”

Section: Introductionmentioning

confidence: 99%

A graphical approach for controller design with desired stability margins for a DC–DC boost converter

Kalim

Ali

2021

IET Power Electronics

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A novel graphical tuning method of PID controller for output voltage regulation of a DC-DC boost converter is proposed. The advantage of the presented method is that the desired robustness level in terms of gain and phase margins can be pre-specified. A technique to limit the noise level in the control signal to a pre-specified value by selecting the derivative gain (k d ), is also discussed. Simplicity of the technique is an added advantage. Concept of root crossing boundaries along with the gain phase margin tester is applied to compute constant gain and phase margin boundaries in the controller parameters plane. The overlapping area of constant gain and phase margin boundaries within the all stability region is the desired gain and phase margin region (DGPMR). Controller parameters are obtained by computing the centroid of the triangular convex region of the DGPMR. Effectiveness of the proposed tuning strategy is illustrated by simulation and hardware experimental results. Furthermore, the proposed method yields improved closed-loop performance compared to a recently reported tuning strategy in nominal as well as perturbed scenarios.

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“…Several decades ago, the determination of stabilizing controller parameter sets relied on graphical methods [14][15][16][17][18][19]. In the recent two decades, there have been remarkable advances [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] in finding the entire stable domain in the gain parameter space of PID controllers. The main features of the stabilizing PID set for a given plant include the following: (A) The proportional gain k p is decoupled from the integral and derivative gains k i , k d ð Þ in the defining parametric equations of the set boundaries.…”

Section: Introductionmentioning

confidence: 99%

Design of discrete PID controllers for maximizing stability margins

Guo

Hwang

2022

Asian Journal of Control

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The objective of this paper is to provide a discrete PID controller design procedure for maximizing stability margins. First, a new and complete characterization of the entire set of stabilizing discrete PID controllers for a given plant is presented. Then, based on this characterization, an efficient algorithm is developed for testing if, for a given plant, there exists a digital PID controller gain parameter space corresponding to closed-loop poles being inside the circle of radius ρ centered at the origin. The developed algorithm is finally applied along with a bisection strategy to determine, for a specified small positive number ε, a minimum value ρ Ã ε and the corresponding ρ Ã ε À stabilizing discrete PID controller set for achieving at least 1 À ρ Ã ε of stability margin. To illustrate the features of our new characterization of stabilizing digital PID controller sets and the effectiveness of the presented algorithms to the maximum stability-margin discrete PID controller design, two numerical examples are provided.

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

Cited by 15 publications

References 22 publications

Stabilizing regions of dominant pole placement for second order lead processes with time delay using filtered PID controllers

Stabilizing regions of dominant pole placement for second order lead processes with time delay using filtered PID controllers

A graphical approach for controller design with desired stability margins for a DC–DC boost converter

Design of discrete PID controllers for maximizing stability margins

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