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1
Content available Results on the controllability of Caputo’s fractional descriptor systems with constant delays
Beata Sikora
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2023
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Vol. 71, nr 4
art. no. e146287
EN
The paper investigates the controllability of fractional descriptor linear systems with constant delays in control. The Caputo fractional derivative is considered. Using the Drazin inverse and the Laplace transform, a formula for solving of the matrix state equation is obtained. New criteria of relative controllability for Caputo’s fractional descriptor systems are formulated and proved. Both constrained and unconstrained controls are considered. To emphasize the importance of the theoretical studies, an application to electrical circuits is presented as a practical example.
2
Content available Review, design, stabilization and synchronization of fractional-order energy resources demand-supply hyperchaotic systems using fractional-order PD-based feedback control scheme
Soukkou Ammar, Soukkou Yassine, Haddad Sofiane, Benghanem Mohamed, Rabhi Abdelhamid
Archives of Control Sciences
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2023
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Vol. 33, No. 3
539--563
EN
This paper introduces a fractional-order PD approach (F-oPD) designed to control a large class of dynamical systems known as fractional-order chaotic systems (F-oCSs). The design process involves formulating an optimization problem to determine the parameters of the developed controller while satisfying the desired performance criteria. The stability of the control loop is initially assessed using the Lyapunov’s direct method and the latest stability assumptions for fractional-order systems. Additionally, an optimization algorithm inspired by the flight skills and foraging behavior of hummingbirds, known as the Artificial Hummingbird Algorithm (AHA), is employed as a tool for optimization. To evaluate the effectiveness of the proposed design approach, the fractional-order energy resources demand-supply (Fo-ERDS) hyperchaotic system is utilized as an illustrative example.
3
Content available Practical Mittag-Leffler stability of quasi-one-sided Lipschitz fractional order systems
Basdouri Imed, Kasmi Souad, Lerbet Jean
Archives of Control Sciences
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2023
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Vol. 33, No. 1
55--70
EN
This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones. Based on the quasi-one-sided Lipschitz condition, firstly, we provide sufficient conditions for the practical observer design. Then, we exhibit that practical Mittag-Leffler stability of the closed loop system with a linear, state feedback is attained. Finally, a separation principle is established and we prove that the closed loop system is practical Mittag-Leffler stable.
4
Content available The Lepschy stability test and its application to fractional-order systems
Casagrande Daniele, Krajewski Wiesław, Viaro Umberto
Archives of Control Sciences
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2021
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Vol. 31, No. 1
145--163
EN
It is shown how a stability test, alternative to the classical Routh test, can profitably be applied to check the presence of polynomial roots inside half-planes or even sectors of the complex plane. This result is obtained by exploiting the peculiar symmetries of the root locus in which the basic recursion of the test can be embedded. As is expected, the suggested approach proves useful for testing the stability of fractional-order systems. A pair of examples show how the method operates. It is believed that the suggested geometric approach can also be of some didactic value in introducing basic control-system tools to engineering students.
5
Content available The Microcontroller Implementation of the Basic Fractional-Order Element
Oprzędkiewicz Krzysztof, Rosół Maciej, Żegleń-Włodarczyk Jakub
Pomiary Automatyka Robotyka
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2020
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R. 24, nr 4
19--26
EN
The paper presents the implementation of the basic fractional order element sγ, γ ∈ R on the STM32 microcontroller platform. The implementation employs the typical CFE and FOBD approximations, the accuracy of approximation as well as duration of calculations are experimentally tested. Microcontroller implementation of fractional order elements is known; however, real-time tests of such implementations have been not presented yet. Results of experiments show that both methods can be implemented at the considered platform. The FOBD approximation is more accurate, but the CFE one is faster. The presented experimental results prove that the STM32F7 family processor could be used to develop the embedded fractional-order control systems for a broad class of linear and nonlinear dynamic systems. This is crucial during the implementation of the fractional-order control in the hard real-time or embedded systems.
PL
W pracy przedstawiono implementację podstawowego układu ułamkowego rzędu sγ, γ ∈ R na platformie mikrokontrolera STM32. Implementacja wykorzystuje typowe aproksymacje CFE oraz FOBD. Dokładność aproksymacji oraz czas trwania obliczeń testowane są eksperymentalnie. Implementacja układów ułamkowych na mikrokontroler jest znana, jednak ich testy w czasie rzeczywistym nie były jak dotąd omawiane w literaturze. Wyniki wskazują, że obie metody można wdrożyć na rozważanej platformie. Aproksymacja FOBD jest dokładniejsza, z kolei CFE jest szybsza. Przedstawione rezultaty eksperymentów dowodzą, że procesor z rodziny STM32F7 może zostać wykorzystany do opracowania wbudowanych ułamkowych układów sterowania dla szerokiej klasy liniowych i nieliniowych układów dynamicznych. Zaprezentowane wyniki są istotne z punktu widzenia implementacji algorytmów ułamkowych w twardych systemach czasu rzeczywistego lub w systemach wbudowanych.
6
Content available Cluster consensus of general fractional-order nonlinear multi agent systems via adaptive sliding mode controller
Yaghoubi Zahra, Talebi Heidar Ali
Archives of Control Sciences
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2019
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Vol. 29, No. 4
643--665
EN
In this paper cluster consensus is investigated for general fractional-order multi agent systems with nonlinear dynamics via adaptive sliding mode controller. First, cluster consensus for fractional-order nonlinear multi agent systems with general form is investigated. Then, cluster consensus for the fractional-order nonlinear multi agent systems with first-order and general form dynamics is investigated by using adaptive sliding mode controller. Sufficient conditions for achieving cluster consensus for general fractional-order nonlinear multi agent systems are proved based on algebraic graph theory, Lyapunov stability theorem and Mittag-Leffler function. Finally, simulation examples are presented for first-order and general form multi agent systems, i.e. a single-link flexible joint manipulator which demonstrates the efficiency of the proposed adaptive controller.
7
Content available remote Is the generalized Padé approximation of the dead time applicable to stability margins analysis?
Horla D.
Studia z Automatyki i Informatyki
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2017
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T. 42
19--27
EN
The paper discusses the applicability of the generalized Padé approximation to stability analysis of systems with time delays, which proves to be inapplicable. As the result of the approximation, the stability margin of the resulting fractional-order closed-loop system is strongly dependent on the order of the fractional-order approximation, leading to inaccuracies.
PL
W artykule przedstawiono dyskusję możliwości zastosowania uogólnionej aproksymacji Padégo w analizie stabilności układów regulacji zawierających opóźnienia transportowe, w wyniku czego stwierdzono niecelowość stosowalności metody. Na skutek aproksymacji, zapas stabilności otrzymanego zamkniętego układu ułamkowego rzędu silnie zależy od ułamkowego rzędu transmitancji aproksymującej opóźnienie, co prowadzi do niedokładności.
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