Discrete-Time Fractional-Order Systems: Modeling and Stability Issues

Guermah, Said; Djennoune, Saïd; Bettayeb, Maâmar

doi:10.5772/51983

Cited by 17 publications

(21 citation statements)

References 44 publications

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“…In some cases the ls aren't sufficiently accurate or n takes place in the description of na such as heat conduction, nomena etc. [1,2,3,4]. Recently conducted on the fractional-order stined mainly for control purposes these works the calculation tools are [1,5] that facilitate practical the intricate description connected us.…”

Section: Fractional-order Dynamic Modelsmentioning

confidence: 99%

“…In some cases, the integer order models are not sufficiently accurate or effective, which often takes place in the description of physical phenomena, such as heat conduction, electrochemical phenomena, etc. [1][2][3][4]. Recently, some works were conducted on the fractional-order dynamics models destined mainly for control purposes [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4]. Recently, some works were conducted on the fractional-order dynamics models destined mainly for control purposes [1,2]. As a result of these works, such calculation tools are generally available [1,5] that facilitate practical calculations without the intricate description connected with fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

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Fractional-order models: The case study of the supercapacitor capacitance measurement

Lewandowski¹,

Orzyłowski²

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. At the beginning of the paper, the fractional calculus is briefly presented. Then, the models of dielectric relaxation in supercapacitors are described. On the basis of the Cole-Cole model, a fractional-order model of supercapacitor impedance is formulated. The frequency characteristics of selected supercapacitors and their voltage response to a current step are assumed as a basis for the analysis of their dynamics. An example of the fractional dynamic model application was used for the critical assessment of the IEC standard recommendation on the conditions of supercapacitor capacitance measurements. The presented study shows some imperfections of the IEC standard recommendations, which probably result from the use of an inaccurate dynamics model. At the end of the paper, the authors propose a solution to this problem by changing the measurement conditions and introducing a concept of dynamic capacitance. The conclusions of the paper indicate that the models of fractional-order dynamics may be useful not only for the control purposes but also in other domains. At the beginning, after some information about fractional calculus, the models of dielectric relaxation in supercapacitors are described. On this basis, a fractional-order model of supercapacitor impedance is formulated. In accordance with the recommendation of the IEC standard concerning the requirements for supercapacitor capacitance measurement [21], the analyses of frequency characteristics of selected supercapacitor samples and their voltage responses to current steps were made. The study shows the imperfection of the IEC standard recommendations, which probably results from the use of an inaccurate dynamics model. At the end of the paper, the authors propose a solution to this problem by changing the measurement conditions and by introducing a concept of dynamic capacitance. Fractional-order dynamic modelsAs mentioned, most dynamic systems are described by the integer order models. The dynamics is described in many ways. One of the widely used methods is to employ the differential equation of general form: Abstract. At the beginning of the paper the fractional calculus is briefly presented. Then the models of dielectric relaxation in supercapacitors are described. On the basis of the Cole-Cole model a fractional-order model of supercapacitor impedance is formulated. The frequency characteristics of selected supercapacitors and their voltage response to a current step are assumed as basis to the analysis of their dynamics. An example of the fractional dynamic model application was used for a critical assessment of the IEC standard recommendation on the conditions of supercapacitor capacitance measurements. The presented study shows some imperfections of the IEC standard recommendations , which probably result from the use of inaccurate dynamics model. At the end of the paper the authors propose a solution to this problem by changing the measurement conditions and introducing a concept of dynamic capacitance. The conclusions of the paper ind...

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Section: Fractional-order Dynamic Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fractional-order models: The case study of the supercapacitor capacitance measurement

Lewandowski¹,

Orzyłowski²

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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“…The first one considers the stability of a finite-dimensional linear time-invariant system, known as practical stability, but fails to provide conditions for the actual fractional-order system to be (asymptotically) stable [17], [18]. This approach is tacitly pursued in many applied papers [12], [19].…”

Section: A Background and Motivationmentioning

confidence: 99%

Robust model predictive control for discrete-time fractional-order systems

Sopasakisy

Ntouskas²,

Sarimveis³

2015

2015 23rd Mediterranean Conference on Control and Automation (MED)

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In this paper we propose a tube-based robust model predictive control scheme for fractional-order discretetime systems of the Grünwald-Letnikov type with state and input constraints. We first approximate the infinitedimensional fractional-order system by a finite-dimensional linear system and we show that the actual dynamics can be approximated arbitrarily tight. We use the approximate dynamics to design a tube-based model predictive controller which endows to the controlled closed-loop system robust stability properties.

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“…Consider a thermal system subject to control of the temperature profile of an aluminium rod with constant thermal conductivity and diffusivity [17]. The model of such a system in a form of discrete-time commensurate fractional-order state space system (1) of order = 0.5 with and the sampling period h = 1 was proposed in [54].…”

mentioning

confidence: 99%

Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems

Rydel

Stanisławski

2019

Asian Journal of Control

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This paper presents a new algorithm for computation of controllability and observability Gramians for an expanded state space form of integer-order approximator to linear time-invariant discrete-time noncommensurate fractional-order systems. The introduced methodology can significantly reduce the time complexity of the Gramians' calculation, being the main computational burden in modeling of discrete-time fractional-order systems by means of a high integer-order expanded state space approximator and the balanced truncation reduction method. Simulation experiments illustrate an efficiency of the introduced methodology, in particular for low-dimension fractional-order systems and high implementation lengths.

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Discrete-Time Fractional-Order Systems: Modeling and Stability Issues

Cited by 17 publications

References 44 publications

Fractional-order models: The case study of the supercapacitor capacitance measurement

Fractional-order models: The case study of the supercapacitor capacitance measurement

Robust model predictive control for discrete-time fractional-order systems

Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems

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