Fractional Calculus and its Applications

Petráš, Ivo

doi:10.1002/9781118462706.ch15

Cited by 10 publications

(16 citation statements)

References 28 publications

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“…Choosing active elements with electronically controlled characteristics, such as OTAs, the resulting controller topology is fully adjustable and versatile because the characteristics of the controller are tuned through appropriate DC bias currents. On the other hand, in the case in which a controller with predefined characteristics must be designed, the employment of op-amp-based RC filter topologies is a cheaper solution [9,22]. Another attractive solution that combines an easy design procedure with programmability and versatility is the utilization of field-programmable analog arrays (FPAAs), which are based on configurable analog blocks (CABs) connected through programmable interconnects [37,38].…”

Section: Discussionmentioning

confidence: 99%

“…Studies over the past few decades have provided important information on the way in which variations of the FO-PID controller contribute to the development of the industry of motion-control systems [18][19][20][21][22][23]. On the basis of values of λ, µ, the main subcategories of FO-PID controllers, employed towards this purpose, are summarized in Table 1.…”

Section: Introductionmentioning

confidence: 99%

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Design of Low-Voltage FO-[PD] Controller for Motion Systems

Malatesta

Kapoulea

Psychalinos

et al. 2021

JLPEA

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Fractional-order controllers have gained significant research interest in various practical applications due to the additional degrees of freedom offered in their tuning process. The main contribution of this work is the analog implementation, for the first time in the literature, of a fractional-order controller with a transfer function that is not directly constructed from terms of the fractional-order Laplacian operator. This is achieved using Padé approximation, and the resulting integer-order transfer function is implemented using operational transconductance amplifiers as active elements. Post-layout simulation results verify the validity of the introduced procedure.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design of Low-Voltage FO-[PD] Controller for Motion Systems

Malatesta

Kapoulea

Psychalinos

et al. 2021

JLPEA

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“…In particular, a stability condition that implies the inspection of the hodograph (a Nyquist-like diagram) of a polynomial with complex coefficients has been derived. This procedure and the resulting stability criterion are briefly reviewed in the next section because they will be used in the subsequent Section IV to determine the root distribution of the characteristic equation of a feedback system with respect to the boundary of sector (6).…”

Section: Essentials Of Fractional System Stabilitymentioning

confidence: 99%

“…The location of the poles of (15) characterises the system dynamics very well. The problem considered here is that of determining how many of these poles are inside sector (6).…”

Section: Extended Nyquist Theorem and Criteriamentioning

confidence: 99%

Elementary Derivation of the Nyquist Criterion for Fractional-Order Feedback Systems

Casagrande

Krajewski

Viaro

2021

IEEE Open J. Circuits Syst.

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It is shown that the classic Nyquist criterion can be extended in a straightforward way to feedback systems of fractional order. The proof of this extension merely requires basic notions of vector analysis and of closed-loop system transfer functions. The criterion can be used not only to ascertain the stability of a fractional-order system but also to detect the presence of closed-loop poles inside any given sector of the complex plane. The test is finally applied to three examples of didactic value.

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“…Applying Theorem 2 to system (19) indicates that (qa−qad) is locally stabile around 0 for every positive definite matrix λ. Thus, tracking qa to qad is achieved.…”

Section: Controller Designmentioning

confidence: 99%

Fractional-Order Sliding Mode Control of Overhead Cranes

2020

JST: SsaD

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We constitute a control system for overhead crane with simultaneous motion of trolley and payload hoist to destinations and suppression of payload swing. Controller core made by sliding mode control (SMC) assures the robustness. This control structure is inflexible since using fixed gains. For overcoming this weakness, we integrate variable fractional-order derivative into SMC that leads to an adaptive system with adjustable parameters. We use Mittag–Leffler stability, an enhanced version of Lyapunov theory, to analyze the convergence of closed-loop system. Applying the controller to a practical crane shows the efficiency of proposed control approach. The controller works well and keeps the output responses consistent despite the large variation of crane parameters.

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Fractional Calculus and its Applications

Cited by 10 publications

References 28 publications

Design of Low-Voltage FO-[PD] Controller for Motion Systems

Design of Low-Voltage FO-[PD] Controller for Motion Systems

Elementary Derivation of the Nyquist Criterion for Fractional-Order Feedback Systems

Fractional-Order Sliding Mode Control of Overhead Cranes

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