Spectrum Analysis of LTI Continuous-Time Systems With Constant Delays: A Literature Overview of Some Recent Results

Pekař, Libor; Gao, Qingbin

doi:10.1109/access.2018.2851453

Cited by 74 publications

(41 citation statements)

References 218 publications

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“…where α > 0 (to compensate for a negative delay), s i stands for a right-half plane (RHP) pole of RP ij with the multiplicity of n i , and f (s) is an appropriate polynomial acting as the inverse of a low-pass filter to get a non-negative relative degree of RP ij . Note that the question of feasibility or stability of systems with delays in its dynamics [104] goes far beyond this work and it is to be solved within the future research. However, the use of (35) destroys the ideal decoupling.…”

Section: Elimination Of Disturbance Variables and Loop Interactionmentioning

confidence: 99%

Control of a Multivariable System Using Optimal Control Pairs: A Quadruple-Tank Process

2020

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This paper deals with one of the possible ways to control multivariable (MIMO) control loops. The suggested control design procedure uses the so-called primary controllers, auxiliary controllers, and also correction members. Parameters of the primary controllers are determined for the optimal control pairs using arbitrary single-variable synthesis methods; namely, the modulus optimum method, the balanced tuning method, and the desired model method. The optimal control pairs are determined using the so-called relative gain array tool or the relative normalized gain array tool combined with other tools, as the condition number or the Niederlinski index. The auxiliary feedback controllers serve for ensuring a control loop decoupling. Invariance to load disturbance of a control loop is realized by using the correction members. The novelty lies especially in the combination of the original inverted decoupling with disturbance rejection and provided tuning methods. The proposed control design for a MIMO loop is verified by simulation for the two-variable controlled plant of a quadruple-tank process and evaluated by using various criteria. Moreover, a numerical comparison to some other methods is given to the reader. INDEX TERMS Control loop decoupling and invariance, multivariable control, optimal control pairs, quadruple-tank process, simulation.

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Section: Elimination Of Disturbance Variables and Loop Interactionmentioning

confidence: 99%

Control of a Multivariable System Using Optimal Control Pairs: A Quadruple-Tank Process

2020

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“…where M, C, and K are known as the n × n mass, damping, and stiffness matrices, respectively; u is a control force vector and f is an external applied force vector; B is the n × p control input distribution matrix; G 2 and G 1 are the p × n velocity and displacement feedback gain matrices respectively, and p < n; τ 1 and τ 2 are the displacement and velocity feedback time-delays, respectively. Substituting (2) into (1) gives M…”

Section: System Description and Reduced Characteristic Functionmentioning

confidence: 99%

“…Its corresponding eigenvalues inside the contour are completely identical to those given by the contour integral method within the same contour (denoted by "o"), as shown in Figure 3. For the spectral method, the closed-loop time delayed control systems (i.e., (1) and (2)) with f(t) = 0 are analysed by the following first-order state space model, .…”

Section: Numerical Examplesmentioning

confidence: 99%

“…There are some ways to numerically determine a part of eigenvalues within a specified region in the complex plane for a retarded or neutral TDS with constant delays [1]. In addition to traditional methods for computing the zeros of analytic functions, e.g., the well-known Newton's method and recently proposed QPmR algorithm [2], two other groups of methods are usually found in the literature.…”

Section: Introductionmentioning

confidence: 99%

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Receptance-Based Dominant Eigenvalues Computation of Controlled Vibrating Systems with Multiple Time-Delays Using a Contour Integral Method

Yang¹,

Ouyang²,

Zhang³

et al. 2019

Applied Sciences

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The computation of dominant eigenvalues of second-order linear control systems with multiple time-delays is tackled by using a contour integral method. The proposed approach depends on a reduced characteristic function and the associated characteristic matrix comprised of measured open-loop receptances. This reduced characteristic function is derived from the original characteristic function of the second-order time delayed systems based on the reasonable assumption that eigenvalues of the closed-loop system are distinct from those of the open-loop system, and has the same eigenvalues as those of the original. Then, the eigenvalues computation is equivalent to solve a nonlinear eigenvalue problem of the associated characteristic matrix by using a contour integral method. The proposed approach also utilizes the spectrum distribution features of the retarded time-delay systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

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“…The investigation of the stability of (2) in the domain of the delays is a basic yet challenging problem among researchers in the control community [1]- [5]. The notorious delay terms in (1) bring about the exponential terms rendering (2) transcendental and thus extremely difficult to be tackled.…”

Section: Introductionmentioning

confidence: 99%

A Novel Frequency-Domain Approach for the Exact Range of Imaginary Spectra and the Stability Analysis of LTI Systems With Two Delays

et al. 2020

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This paper presents a novel frequency-domain approach to reveal the exact range of the imaginary spectra and the stability of linear time-invariant systems with two delays. First, an exact relation, i.e., the Rekasius substitution, is used to replace the exponential term caused by the delays in order to transform the transcendental characteristic equation to a quasi-polynomial. Second, this quasi-polynomial is uniquely tackled by our proposed Dixon resultant and discriminant theory, leading to the elimination of delay-related elements and the revelation of the exact range of the frequency spectra of the original system of interest. Then, by sweeping the frequency over this obtained range, the stability switching curves are declared exhaustively. Last, we deploy the cluster treatment of characteristic roots (CTCR) paradigm to reveal the exact and complete stability map. The proposed methodologies are tested and verified by a numerical method called Quasi-Polynomial mapping-based Root finder (QPmR) over an example case. INDEX TERMS Time-delay system, Dixon resultant, stability, frequency domain.

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Spectrum Analysis of LTI Continuous-Time Systems With Constant Delays: A Literature Overview of Some Recent Results

Cited by 74 publications

References 218 publications

Control of a Multivariable System Using Optimal Control Pairs: A Quadruple-Tank Process

Control of a Multivariable System Using Optimal Control Pairs: A Quadruple-Tank Process

Receptance-Based Dominant Eigenvalues Computation of Controlled Vibrating Systems with Multiple Time-Delays Using a Contour Integral Method

A Novel Frequency-Domain Approach for the Exact Range of Imaginary Spectra and the Stability Analysis of LTI Systems With Two Delays

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