Approximating the Fractional-Order Element for the Robust Control Framework

Mihaly, Vlad; Şuşcă, Mircea; Dulf, Éva-Henrietta; Dobra, Petru

doi:10.23919/acc53348.2022.9867658

Cited by 8 publications

(9 citation statements)

References 24 publications

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“…As stated in [11], the most common method to choose the approximation order is by the number of frequency range decades Ω = [ω, ω] where this approximation is valid. The purpose of this paper is to find a reduced-order approximation of the fractional-order controller initially designed using the methodology described in the previous section by keeping similar performance.…”

Section: Proposed Methodsmentioning

confidence: 99%

“…However, fixed-structure controller synthesis can be performed if the controller can be described using only arithmetical expressions in terms of tunable parameters, which is a limitation for a large number of available approximations, including ORA. In order to benefit from this method, the authors proposed a solution based on Taylor approximations in [9], which was further developed in [10] and improved in [11], where the fractional-order element approximated using ORA has been successfully integrated into the RCF using an isomorphic expression of the tunable fractional-order.…”

Section: A Literature Reviewmentioning

confidence: 99%

“…To integrate the FO element into the integer-order Robust Control Framework, some adjustments should be made. Because the fixed-structure H ∞ control problem can be formulated only involving arithmetical operations in terms of the controller's parameters [7], in [11] the IIR approximation given by Oustaloup has been successfully integrated in RCF by considering the isomorphic representation for case k = 1:…”

Section: B Fractional-order Elementmentioning

confidence: 99%

“…with the steps detailed in the algorithm of [11]. Additionally, the fractional-order interval plants have been also integrated into the integer-order RCF in [22] using a similar idea.…”

Section: B Fractional-order Elementmentioning

confidence: 99%

See 3 more Smart Citations

Reduced-Order Approximation of Fractional-Order Controllers by keeping Robust Stability and Robust Performance

Mihaly

Şuşcă

Birs

et al. 2023

2023 American Control Conference (ACC)

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Recently, the fractional-order element has been integrated into the Robust Control Framework considering the Oustaloup method. As such, the resulting infinite impulse response approximation manages to satisfy the robust stability and the robust performance criteria according to a given uncertainty block. However, the recommended approximation order for each fractional-order element is the number of decades of the frequency range where the approximation is valid, which can lead to a high-order controller. The current paper describes an optimization-based technique to find a loworder approximation of a fractional-order controller such that the resulting controller maintains the robust stability and robust performance as well. A set of numerical experiments have also been performed in order to illustrate the proposed method.

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Section: Proposed Methodsmentioning

confidence: 99%

Section: A Literature Reviewmentioning

confidence: 99%

Section: B Fractional-order Elementmentioning

confidence: 99%

“…with the steps detailed in the algorithm of [11]. Additionally, the fractional-order interval plants have been also integrated into the integer-order RCF in [22] using a similar idea.…”

Section: B Fractional-order Elementmentioning

confidence: 99%

See 2 more Smart Citations

Reduced-Order Approximation of Fractional-Order Controllers by keeping Robust Stability and Robust Performance

Mihaly

Şuşcă

Birs

et al. 2023

2023 American Control Conference (ACC)

Self Cite

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“…This subsection concerns with two classical closed-loop structures: single-loop control structure and cascade control structure. There are multiple control design approaches available in the literature for linear and time-invariant systems, starting from classical PID, linear quadratic regulator (LQR), and leading to the robust fractional-order PID (FO-PID) [33,34]. Robust synthesis methods allows the design of both structured or unstructured regulators alike [35,36].…”

Section: Control Design Summarymentioning

confidence: 99%

Sampling rate selection for multi‐loop cascade control systems in an optimal manner

Şuşcă

Mihaly

Dobra

2023

IET Control Theory & Appl

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This article proposes an optimization‐based approach to selecting the sampling periods for classes of linear time‐invariant (LTI) regulators in a cascaded multi‐rate control structure, to account for practical implementation on numeric systems. Starting from the Shannon‐Nyquist sampling theorem, which proposes the minimum required sampling frequency for completely recovering the original analog signal from its discrete samples, the scope of the sampling process, viewed from a control perspective, is to ensure asymptotic stability of the closed‐loop system, with the smallest possible degradation of the initially‐proposed performance indices as possible according to a set of well‐picked criteria. As such, a configurable optimization‐based approach is proposed, solved with the mixed‐integer artificial bee colony (MI‐ABC) algorithm, for selecting the sampling periods by specifying the emphasis between closed‐loop fidelity and ease of implementation, with an intuitive visualization method. The proposed solution is illustrated on two case studies, with emphasis on the construction of the proposed functionals and their practical implications.

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