Delay Margin of Low-Order Systems Achievable by PID Controllers

Ma, Dan; Chen, Jie

doi:10.1109/tac.2018.2853567

Cited by 103 publications

(73 citation statements)

References 34 publications

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“…This work focuses on the effect of multiplicity of spectral values on the exponential stability of the generic second-order retarded differential equation. The investigation of conditions on the equation parameters that guarantee the exponential stability of solutions is a question of ongoing interest, see for instance [19,28]. An efficient way to study a solution's stability is the frequency domain approach since in the Laplace domain, where a number of effective methods have been proposed, the stability analysis amounts to studying the distribution of the characteristic quasipolynomial function's roots, see for instance [3,4,17,18,20,23,34,42,53,54,58,59].…”

Section: Introductionmentioning

confidence: 99%

Multiplicity-induced-dominancy in parametric second-order delay differential equations: Analysis and application in control design

et al. 2020

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This work revisits recent results on maximal multiplicity induced-dominancy for spectral values in reduced-order time-delay Systems and extends it to the general class of second-order retarded differential equa- tions. A parametric multiplicity-induced-dominancy property is characterized, allowing to a delayed stabilizing design with reduced complexity. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates’ delays and gains result from the manifold defining the maximal multiplicity of a real spectral value, then, the dominancy is shown using the argument principle. Sensitivity of the control design with respect to the pa- rameters uncertainties/variation is discussed. Various reduced order examples illustrate the applicative perspectives of the approach.

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Section: Introductionmentioning

confidence: 99%

Multiplicity-induced-dominancy in parametric second-order delay differential equations: Analysis and application in control design

et al. 2020

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“…Based on the multiple linear copositive storage technique, passivity and feedback passification deserve to be considered as a research direction in the future. In addition, PID passivity‐based control is also an interesting topic …”

Section: Discussionmentioning

confidence: 99%

Dissipativity and dissipative control for positive switched systems: A multiple linear copositive storage function method

Wang

Zhao

2019

Intl J Robust & Nonlinear

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Summary In this article, the problems of dissipativity analysis and dissipative control are investigated for positive switched linear systems in both continuous and discrete‐time domains. We aim at solving the problems via employing a multiple linear copositive storage function scheme. The solvability of the problems for individual subsystem is only on their active regions. Switching laws and a set of feedback controllers are jointly devised such that the associated closed‐loop switched systems are not only positive but also dissipative, which is from the exogenous input to the output. Asymptotic stability is derived if all subsystems are zero‐state detectable. Moreover, sufficient conditions guaranteeing dissipativity with positivity constraint are presented, which can be easily examined on the grounds of linear programming approach. Finally, an example is offered, illustrating that the proposed control strategy is successful.

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“…We consider proportional feedback and PD controllers respectively. It is known that the addition of the integral control will perform no better, if not worse, than PD controllers for feedback stabilization ( [171]); as such, it suffices to consider PD control only.…”

Section: Delay Margin With Pid Controllersmentioning

confidence: 99%

Distributed Consensus of Linear Multiagent Systems: Laplacian Spectra-Based Method

Chen

Shi

2020

IEEE Trans. Syst. Man Cybern, Syst.

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With the help of rapidly advancing communication technology, control systems are increasingly integrated via communication networks. Networked control systems (NCSs) bring significant advantages such as flexible and scalable structures, easy implementation and maintenance, and efficient resources distribution and allocation. NCSs empowers to finish some complicated tasks using some relatively simple systems in a collaborated manner. However, there are also some challenges and constraints subject to the imperfection of communication channels. In this thesis, the stabilization problems and the performance limitation problems of control systems subject to networked-induced constraints are studied. Overall, the thesis mainly includes two parts: 1) Consensus and consensusability of multi-agent systems (MASs); 2) Delay margins of NCSs. Chapter 2 and Chapter 3 deal with the consensus problems of MASs, which aim to properly design the control protocols to ensure the state convergence of all the agents. Chapter 4 and Chapter 5 focus on the consensusability analysis, exploring how the dynamics of the agents and the networked induced constraints impact the overall systems for achieving consensus. Chapter 6 pays attention to the delay margins of discrete-time linear time-invariant (LTI) systems, studying how the dynamics of the plants limit the time delays that can be tolerated by LTI controllers. on the discrete-time delay margin led to negative results, the bounds developed in this chapter provide instead a guaranteed range of delays within which the delayed plants can be robustly stabilized, and in turn solve the special class of simultaneous stabilization problems in question. Finally, in Chapter 7, the thesis is summarized and some future research topics are also presented.

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Delay Margin of Low-Order Systems Achievable by PID Controllers

Cited by 103 publications

References 34 publications

Multiplicity-induced-dominancy in parametric second-order delay differential equations: Analysis and application in control design

Multiplicity-induced-dominancy in parametric second-order delay differential equations: Analysis and application in control design

Dissipativity and dissipative control for positive switched systems: A multiple linear copositive storage function method

Distributed Consensus of Linear Multiagent Systems: Laplacian Spectra-Based Method

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