First Order Plus Frequency Dependent Delay Modeling: New Perspective or Mathematical Curiosity?

Juchem, Jasper; Dekemele, Kevin; Chevalier, Amélie; Loccufier, Mia; Ionescu, Clara-Mihaela

doi:10.1109/smc.2019.8914386

Cited by 3 publications

(12 citation statements)

References 20 publications

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“…To find the FOPFDD model of a system, a methodology is provided to find the parameters as proposed in [20]. Also, a methodology to obtain a time domain analysis is presented in this paper.…”

Section: Methodsmentioning

confidence: 99%

“…Then, the normalized error for both objectives is minimized, such that the optimal fit is found. This methodology is earlier described in [20]. The minimization problem leads to the model parameters {K, τ, L, α}.…”

Section: Model Fitting: An Optimization Approachmentioning

confidence: 99%

“…In Figure 5a the Pareto front of the optimization problem for H 3 (s) is presented to show the trade-off between minimizing the error for the magnitude plot and the phase plot respectively. The Pareto front indicates for which weight q 1 the trade-off between both objectives is optimal [20]. This leads to an optimal Bode plot for each model such that the error between the model and the real system's Bode plot is minimal for the combined objectives.…”

Section: Modeling Of Higher-order Processesmentioning

confidence: 99%

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First Order Plus Fractional Diffusive Delay Modeling: interconnected discrete systems

Juchem,

Chevalier,

Dekemele

et al. 2021

Preprint

Self Cite

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This paper presents a novel First Order Plus Fractional Diffusive Delay (FOPFDD) model, capable of modeling delay dominant systems with high accuracy. The novelty of the FOPFDD is the Fractional Diffusive Delay (FDD) term, an exponential delay of non-integer order α, i.e. e −(Ls) α in Laplace domain. The special cases of α = 0.5 and α = 1 have already been investigated thoroughly. In this work α is generalized to any real number in the interval ]0, 1[. For α = 0.5, this term appears in the solution of distributed diffusion systems, which will serve as a source of inspiration for this work. Both frequency and time domain are investigated. However, regarding the latter, no closed-form expression of the inverse Laplace transform of the FDD can be found for all α, so numerical tools are used to obtain an impulse response of the FDD. To establish the algorithm, several properties of the FDD term have been proven: firstly, existence of the term, secondly, invariance of the time integral of the impulse response, and thirdly, dependency of the impulse response's energy on α. To conclude, the FOPFDD model is fitted to several delay-dominant, diffusive-like resistors-capacitors (RC) circuits to show the increased modeling accuracy compared to other state-of-the-art models found in literature. The FOPFDD model outperforms the other approximation models in accuratly tracking frequency response functions as well as in mimicing the peculiar delay/diffusive-like time responses, coming from the interconnection of a large number of discrete subsystems. The fractional First Order Plus Fractional Diffusive Delay Modeling: interconnected discrete systems A PREPRINT character of the FOPFDD makes it an ideal candidate for an approximate model to these large and complex systems with only a few parameters.

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Section: Methodsmentioning

confidence: 99%

Section: Model Fitting: An Optimization Approachmentioning

confidence: 99%

Section: Modeling Of Higher-order Processesmentioning

confidence: 99%

See 1 more Smart Citation

First Order Plus Fractional Diffusive Delay Modeling: interconnected discrete systems

Juchem,

Chevalier,

Dekemele

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…This new FDD term opens the door to a new fractional approximation model: the First Order Plus Fractional Diffusive Delay (FOPFDD) model. An exploratory research [7] first investigated the combination of FDD and a first-order model in frequency domain. The findings of Juchem et al (2019) were later used in [15] to examine stability margins related to closed-loop behavior.…”

Section: Introductionmentioning

confidence: 99%

“…An exploratory research [7] first investigated the combination of FDD and a first-order model in frequency domain. The findings of Juchem et al (2019) were later used in [15] to examine stability margins related to closed-loop behavior. The time domain aspect and the relation to time delay and diffusion are not explored in these preliminary works.…”

Section: Introductionmentioning

confidence: 99%

First order Plus Fractional Diffusive Delay Modeling: Interconnected Discrete Systems

Juchem¹,

Chevalier²,

Dekemele³

et al. 2021

Fract Calc Appl Anal

Self Cite

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This paper presents a novel First Order Plus Fractional Diffusive Delay (FOPFDD) model, capable of modeling delay dominant systems with high accuracy. The novelty of the FOPFDD is the Fractional Diffusive Delay (FDD) term, an exponential delay of non-integer order α, i.e. e −(Ls) α in Laplace domain. The special cases of α = 0.5 and α = 1 have already been investigated thoroughly. In this work α is generalized to any real number in the interval ]0, 1[. For α = 0.5, this term appears in the solution of distributed diffusion systems, which will serve as a source of inspiration for this work. Both frequency and time domain are investigated. However, regarding the latter, no closed-form expression of the inverse Laplace transform of the FDD can be found for all α, so numerical tools are used to obtain an impulse response of the FDD. To establish the algorithm, several properties of the FDD term have been proven: firstly, existence of the term, secondly, invariance of the time integral of the impulse response, and thirdly, dependency of the impulse response’s energy on α. To conclude, the FOPFDD model is fitted to several delay-dominant, diffusive-like resistors-capacitors (RC) circuits to show the increased modeling accuracy compared to other state-of-the-art models found in literature. The FOPFDD model outperforms the other approximation models in accurately tracking frequency response functions as well as in mimicking the peculiar delay/diffusive-like time responses, coming from the interconnection of a large number of discrete subsystems. The fractional character of the FOPFDD makes it an ideal candidate for an approximate model to these large and complex systems with only a few parameters.

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Generalization of the FOPDT Model for Identification and Control Purposes

Muresan

Ionescu

2020

Processes

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This paper proposes a theoretical framework for generalization of the well established first order plus dead time (FOPDT) model for linear systems. The FOPDT model has been broadly used in practice to capture essential dynamic response of real life processes for the purpose of control design systems. Recently, the model has been revisited towards a generalization of its orders, i.e., non-integer Laplace order and fractional order delay. This paper investigates the stability margins as they vary with each generalization step. The relevance of this generalization has great implications in both the identification of dynamic processes as well as in the controller parameter design of dynamic feedback closed loops. The discussion section addresses in detail each of this aspect and points the reader towards the potential unlocked by this contribution.

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First Order Plus Frequency Dependent Delay Modeling: New Perspective or Mathematical Curiosity?

Cited by 3 publications

References 20 publications

First Order Plus Fractional Diffusive Delay Modeling: interconnected discrete systems

First Order Plus Fractional Diffusive Delay Modeling: interconnected discrete systems

First order Plus Fractional Diffusive Delay Modeling: Interconnected Discrete Systems

Generalization of the FOPDT Model for Identification and Control Purposes

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