<scp>PID</scp> Stabilization of Retarded‐Type Time‐Delay System

Zhao, Xiu-wei; Ren, Jin

doi:10.1002/asjc.764

Cited by 3 publications

(2 citation statements)

References 21 publications

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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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Section: Introductionmentioning

confidence: 99%

Design of discrete PID controllers for maximizing stability margins

Guo

Hwang

2022

Asian Journal of Control

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“…This work was supported also by the development project of key laboratory of Liaoning Province. systems, the problem is relatively simple and general and effective techniques have been proposed mainly based on the Routh-Hurwitz criterion, such as, the Ziegler-Nichols method in [3], generalization of the Hermite-Biehler Theorem in [4], the Astrom-Hagglund method in [5], and also some new summary results in [6][7][8][9][10][11]. However, as inherent phenomena, time delays are encountered in a variety of interconnected real systems or processes, which makes the problem much more complex.…”

Section: Introductionmentioning

confidence: 99%

The τ Decomposition Method for PID Controllers of First Order Delayed Unstable Processes

Cai¹,

Zhang²,

Yang³

et al. 2014

Asian Journal of Control

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The stabilization of first‐order delayed (FOD) unstable processes with proportional–integral–derivative (PID) controllers is considered, and all the feasible PID controllers are determined. Different from the existing results which are based on the D‐partition technique and partitioning complex's real and imaginary parts, a novel procedure enlightened by the τ decomposition method is proposed to characterize the space of controller parameters. Generally speaking, the parameter space is mainly divided into four regions: delay independent stable region, delay independent unstable region, delay interval dependent stable region, and delay interval dependent unstable region. The depiction of the space partition boundaries and the determination of stable intervals become the main problems. In our work, these boundaries are related to the existence of the purely imaginary roots (PIRs) of the systems' characteristic equation, and the determination of stable intervals refers to the number and value of the PIRs. Thus, the key points are the number and calculation of PIRs. According to our discussion, analytical results on both topics are obtained in explicit form. Finally, vivid numerical simulations are given to illustrate the results.

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A Survey of Fractional Order Calculus Applications of Multiple-Input, Multiple-Output (MIMO) Process Control

Almeida

Lenzi

2020

Fractal Fract

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Multiple-input multiple-output (MIMO) systems are usually present in process systems engineering. Due to the interaction among the variables and loops in the MIMO system, designing efficient control systems for both servo and regulatory scenarios remains a challenging task. The literature reports the use of several techniques mainly based on classical approaches, such as the proportional-integral-derivative (PID) controller, for single-input single-output (SISO) systems control. Furthermore, control system design approaches based on derivatives and integrals of non-integer order, also known as fractional control or fractional order (FO) control, are frequently used for SISO systems control. A natural consequence, already reported in the literature, is the application of these techniques to MIMO systems to address some inherent issues. Therefore, this work discusses the state-of-the-art of fractional control applied to MIMO systems. It outlines different types of applications, fractional controllers, controller tuning rules, experimental validation, software, and appropriate loop decoupling techniques, leading to literature gaps and research opportunities. The span of publications explored in this survey ranged from the years 1997 to 2019.

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PID Stabilization of Retarded‐Type Time‐Delay System

Cited by 3 publications

References 21 publications

Design of discrete PID controllers for maximizing stability margins

Design of discrete PID controllers for maximizing stability margins

The τ Decomposition Method for PID Controllers of First Order Delayed Unstable Processes

A Survey of Fractional Order Calculus Applications of Multiple-Input, Multiple-Output (MIMO) Process Control

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