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1

Research on creep-fatigue model of anchored jointed rock mass

Song Yang, Fan Bo, Li Yong-Qi, Wang He-Ping

Journal of Theoretical and Applied Mechanics

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2023

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Vol. 61 nr 1

163--173

EN

To explore the mechanical response of anchored rock mass with an interaction of fatigue and creep, this paper selects the fatigue amplitude and fatigue frequency as influencing factors to carry out a fatigue-creep experiment of the anchored rock mass. Based on fractional order theory and binary perturbation theory, a new fractional order creep model is constructed. The results show that compared with the Burgers model, the newly proposed creep model can better describe the whole process of creep deformation of the anchored jointed rock mass under fatigue loading.

2

Design of a Fractional Order Low-pass Filter Using a Diﬀerential Voltage Current Conveyor

Krishna Battula Tirumala, Janarthanan Midhunchakkaravathy

Journal of Telecommunications and Information Technology

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2023

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nr 2

17--21

EN

In this paper, an active implementation of a diﬀerential voltage current conveyor (DVCC) based on a low-pass ﬁlter operating in the fractional order domain is presented. The transfer function for a fractional order system is dependent on the rational approximation of sα. Diﬀerent methods used for calculating the rational approximation, including Carlson, Elkhazalil, and curve ﬁtting, are evaluated here. Finally, to validate the theoretical results, a fractional order Butterworth ﬁlter is simulated in the Pspice environment using the 0.5 micrometer CMOS technology with an R-C network-based fractional order capacitor. Additionally, using the Monte Carlo analysis, the impact of current and voltage faults on DVCC response is investigated. It has been inferred that realization with a wider bandwidth is possible.

3

Generalized thermoelastic heat conduction model involving three different fractional operators

Saidi Anouar, Yahya Ahmed M. H, Abouelregal Ahmed E., Dargail Husam E., Ahmed Ibrahim-Elkhalil, Ali Elsiddeg, Mohammed F. A.

Advances in Materials Science

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2023

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Vol. 23, nr 2(76)

25--44

EN

The purpose of this paper is to introduce a new time-fractional heat conduction model with three-phase-lags and three distinct fractional-order derivatives. We investigate the introduced model in the situation of an isotropic and homogeneous solid sphere. The exterior of the sphere is exposed to a thermal shock and a decaying heat generation rate. We recuperate some earlier thermoelasticity models as particular cases from the proposed model. Moreover, the effects of different fractional thermoelastic models and the effect of instant time on the physical variables of the medium are studied. We obtain the numerical solutions for the various physical fields using a numerical Laplace inversion technique. We represent the obtained results graphically and discuss them. Physical views presented in this article may be useful for the design of new materials, bio-heat transfer mechanisms between tissues and other scientific domains.

4

An adaptive FLC-GAFOPI controller for WRSG based wind turbine

Bouziane Abdelkader Hafid, Debbat Mohamed, Tahour Ahmed

Przegląd Elektrotechniczny

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2022

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R. 98, nr 7

81--87

EN

This paper deals with design of an adaptive fuzzy logic control-genetic algorithm fractional order-proportional and integral (AFLC-GAFOPI) for a wound rotor synchronous generator (WRSG), based on a variable speed wind energy conversion system (WECS), for improving its power output quality . The AFLC-GAFOPI represents a hybridization of two GAFOPI and AFLC controllers respectively. The first one is designed to upgrade the performance of the system . The second one is chosen to overcome the nonlinearity of the system. To demonstrate the efficiency of the AFLC-GAFOPI controller, a comparison with the GAFOPI controller was performed for different wind regimes. The outcomes clearly demonstrate that the designed controller outperforms the compared controller in terms of response, robustness and overshoot.

PL

W artykule zajęto się projektowaniem adaptacyjnego algorytmu sterowania rozmytego, opartego na systemie konwersji energii wiatru o zmiennej prędkości (WECS). jego jakość wyjściowa mocy. AFLC-GAFOPI reprezentuje hybrydyzację odpowiednio dwóch sterowników GAFOPI i AFLC. Pierwsza ma na celu podniesienie wydajności systemu. Drugi wybierany jest w celu przezwyciężenia nieliniowości systemu. Aby zademonstrować wydajność sterownika AFLC-GAFOPI, przeprowadzono porównanie ze sterownikiem GAFOPI dla różnych warunków wiatrowych. Wyniki jasno pokazują, że zaprojektowany sterownik przewyższa porównywany sterownik pod względem odpowiedzi, niezawodności i przeregulowania.

5

A robust voltage H∞ controller in dg-connected inverter based on auto-calibration of adjustable fractional weights

Amieur Oualid, Zidani Fatiha

Przegląd Elektrotechniczny

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2022

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R. 98, nr 2

21--27

EN

In this paper a H∞ control technique addresses the voltage regulation in distributed generation (DG) system connected to power converter under harmonic disturbances. The DG control technique combines a discrete sliding mode control (DSMC) in the current control and a Robust Servomechanism Problem (RSP) in the voltage control. Besides, a fractional Order Proportional-Integral-Derivative (FOPID) controller synthesized with an automatic calibration of adjustable fractional weights is formulated in this work. For performance and high robustness requirements, the parameters of FOPID are optimized through solving a multiobjective optimization problematic based on the automatic calibration of the weighted-mixed sensitivity problem. Furthermore, for ensuring an adequate calibration of parameters, the Integral of Time Weighted Absolute Error (ITAE) criterion with Genetic Algorithm (GA) are used to achieve better voltage regulation. The simulation results show that it can achieve trade-off between nominal performance (NP) and robust stability (RS) margins for the constrained uncertain plants in the large range frequencies. Also, the results validate the effectiveness of the proposed control at which both low total harmonic distortion (THD) and low tracking error.

PL

W niniejszym artykule technika sterowania H∞ dotyczy regulacji napięcia w systemie generacji rozproszonej (DG) podłączonym do przekształtnika mocy w warunkach zakłóceń harmonicznych. Technika sterowania łączy dyskretne sterowanie w trybie ślizgowym (DSMC) w sterowaniu prądem i solidny problem z serwomechanizmem (RSP) w sterowaniu napięciem. Poza tym, w niniejszej pracy sformułowano regulator ułamkowo całkująco-różniczkujący (FOPID) zsyntetyzowany z automatyczną kalibracją regulowanych mas ułamkowych. Parametry FOPID są optymalizowane poprzez rozwiązanie problemu optymalizacji wielokryterialnej opartej na autokalibracji problemu wraźliwości mieszanej ważonej dla wymagań dotyczących odporności między nominalną wydajnością (NP), solidną stabilnością (RS) marżami i kompromisem między nimi w dużych zakres częstotliwości. Wyniki symulacji potwierdzają skuteczność proponowanego sterowania, przy którym zarówno wysoka odporność, jak i niskie całkowite zniekształcenia harmoniczne (THD).

6

Stability analysis of a fractional order prey-predator model with disease in prey

Sharmila N. B., Gunasundari Chandrasekar

Mathematica Applicanda

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2022

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Vol. 50, no. 2

287--302

EN

This paper discusses the formulation and study of a fractional-order ecoepidemiological model in the context of infectious diseases in the prey population. The purpose of fractional order analysis is to investigate the effect of time memory on the growth rate of the three populations. The fractional-order prey-predator model’s local and global stability are then discussed. The fractional order appears to have a stabilizing effect, which could aid in the control of coexistence between susceptible prey, infected prey, and predator populations.

PL

W artykule omówiono formułowanie i badanie modelu eko–epidemiologicznego ułamkowego rzędu z chorobami zakaźnymi w populacji ofiar. Celem analizy tego modelu jest zbadanie wpływu pamięci czasu na tempo wzrostu trzech populacji. W pracy są kluczowe ustalenia, takie jak istnienie, niepowtarzalność, nieujemność i ograniczoność rozwiązań układów dynamicznych ułamkowego rzędu. Następnie omówiono lokalną i globalną stabilność modelu ofiara-drapieżnik w ułamkowego rzędu. Wydaje się, że model ułamkowego rzędu ma działanie stabilizujące, które może pomóc w sterowaniu współistnienia podatnej ofiary, zakażonej ofiary i populacji drapieżników.

7

Performance analysis of the fractional-order vehicle mechatronic ISD suspension with parameter perturbation

Shen Yujie, Hua Jie, Xia Xiaohua, Liu Yanling, Yang Xiaofeng

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 1

141--152

EN

This paper concerns the performance analysis of a fractional-order vehicle mechatronic ISD suspension with parameter perturbation. A dynamic model of the vehicle mechatronic ISD suspension based on a fractional-order electrical network is constructed. The superiority of the vibration isolation performance of the fractional-order ISD suspension is demonstrated, and the dynamic performance of the suspension is analyzed considering perturbation of parameters. Results show that the inertance has an important role when the frequency is above 103 Hz, and the fractional inductance order and fractional capacitance order have significant impact in the frequency range of 10−2 Hz to 102 Hz.

8

Exponential decay of transient values in discrete-time positive nonlinear systems

Kaczorek Tadeusz, Ruszewski Andrzej

Archives of Control Sciences

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2022

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Vol. 32, No. 3

577--588

EN

The exponential decay of transient values in discrete-time nonlinear standard and fractional orders systems with linear positive linear part and positive feedbacks is investigated. Sufficient conditions for the exponential decay of transient values in this class of positive nonlinear systems are established. A procedure for computation of gains characterizing the class of nonlinear elements are given and illustrated on simple example.

9

Design of a fuzzy fractional order adaptive impedance controller with integer order approximation for stable robotic contact force tracking in uncertain environment

Cao Hongli

Acta Mechanica et Automatica

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2022

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Vol. 16, no. 1

16--26

EN

Current research in robot compliance control is unable to take both transient contact force overshoots and steady-state force tracking problems into account. To address this problem, we propose a fuzzy fractional order (FO) adaptive impedance controller to avoid the force overshoots in the contact stage while keeping force error in the dynamic tracking stage, where traditional control algorithms are not competent. A percentage gain is adopted to map FO parameters to integer order (IO) parameters by their natural properties, and a fuzzy logical controller is introduced to improve the system stability. The simulation results indicate that the proposed controller can be made more stable than and superior to the general impedance controller, and the force tracking results also have been compared with the previous control methods.

10

Stability analysis of fractional order SEIR model for malaria disease in Khyber Pakhtunkhwa

Badshah Noor, Akbar Haji

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

326--334

EN

We discussed stability analysis of susceptible-exposed-infectious-removed (SEIR) model for malaria disease through fractional order and check that malaria is epidemic or endemic in Khyber Pakhtunkhwa (Pakistan). We show that the model has two types of equilibrium points and check their stability through Routh-Hurwitz criterion. We find basic reproductive number using next-generation method. Finally, numerical simulations are also presented.

11

Analysis of time-fractional heat transfer and its thermal deflection in a circular plate by a moving heat source

Thakare S., Warbhe M.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 3

158--168

EN

Mathematical modeling of a thin circular plate has been made by considering a nonlocal Caputo type time fractional heat conduction equation of order […], by the action of a moving heat source. Physically convective heat exchange boundary conditions are applied at lower, upper and outer curved surface of the plate. Temperature distribution and thermal deflection has been investigated by a quasi-static approach in the context of fractional order heat conduction. The integral transformation technique is used to analyze the analytical solution to the problem. Numerical computation including the effect of the fractional order parameter has been done for temperature and deflection and illustrated graphically for an aluminum material.

12

A study on fractional order thermoelastic half space

Roy Sourov, Lahiri Abhijit

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 4

191--202

EN

In this paper, we consider a one dimensional problem on a fractional order generalized thermoelasticity in half space subjected to an instantaneous heat source. The Laplace transform as well as eigen value approach techniques are applied to solve the governing equations of motion and heat conduction. Closed form solutions for displacement, temperature and stress are obtained and presented graphically.

13

Global stability of positive standard and fractional nonlinear feedback systems

Kaczorek T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2020

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Vol. 68, nr 2

285--288

EN

The global stability of positive continuous-time standard and fractional order nonlinear feedback systems is investigated. New sufficient conditions for the global stability of these classes of of positive nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple examples of positive nonlinear systems.

14

On LQ optimization problem subject to fractional order irregular singular systems

Muhafzan, Nazra Admi, Yulianti Lyra, Zulakmal, Revina Refi

Archives of Control Sciences

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2020

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Vol. 30, No. 4

745--756

EN

In this paper we discuss the linear quadratic (LQ) optimization problem subject to fractional order irregular singular systems. The aim of this paper is to find the control-state pairs satisfying the dynamic constraint of the form a fractional order irregular singular systems such that the LQ objective functional is minimized. The method of solving is to convert such LQ optimization into the standard fractional LQ optimization problem. Under some particularly conditions we find the solution of the problem under consideration.

15

Synchronization of fractional-order discrete-time chaotic systems by an exact delayed state reconstructor: Application to secure communication

Djennoune Said, Bettayeb Maamar, Al-Saggaf Ubaid Muhsen

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 1

179--194

EN

This paper deals with the synchronization of fractional-order chaotic discrete-time systems. First, some new concepts regarding the output-memory observability of non-linear fractional-order discrete-time systems are developed. A rank criterion for output-memory observability is derived. Second, a dead-beat observer which recovers exactly the true state system from the knowledge of a finite number of delayed inputs and delayed outputs is proposed. The case of the presence of an unknown input is also studied. Third, secure data communication based on a generalized fractional-order Hénon map is proposed. Numerical simulations and application to secure speech communication are presented to show the efficiency of the proposed approach.

16

Fractional-order feedback control of a pneumatic servo-drive

Laski P. A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2019

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Vol. 67, nr 1

53--59

EN

A fractional-order control strategy for a pneumatic position servo-system is presented in this paper. The idea of the fractional calculus application to control theory was introduced in many works, and its advantages were proved. This paper deals with the design of fractional order PIλDμ controllers, in which the orders of the integral and derivative parts, λ and μ, respectively, are fractional. Experiments with fractionalorder controller are performed under various conditions, which include position signal with different frequencies and amplitudes or a step position signal. The results show the effectiveness of the proposed schemes and verify their fine control performance for a pneumatic position servo-system.

17

Punktowa zupełność oraz punktowa degeneracja wybranej klasy układów dyskretnych singularnych niecałkowitego rzędu

Kociszewski R.

Pomiary Automatyka Robotyka

|

2016

|

R. 20, nr 4

5--8

PL

W pracy podano kryteria punktowej zupełności i punktowej degeneracji układów liniowych dyskretnych singularnych niecałkowitego rzędu. Pokazano, że przy zastosowaniu pewnych przekształceń, można oceny punktowej zupełności lub degeneracji dokonywać stosując kryteria jak dla układów standardowych niecałkowitego rzędu. Rozważania zilustrowano przykładem liczbowym.

EN

The paper presents a problem of pointwise completeness and pointwise degeneracy of selected class of singular linear discrete-time systems. It has been shown that after decomposition of considered system into two independent systems: regular (standard) fractional system and closely singular system (with a nilpotent matrix N) pointwise completeness and pointwise degeneracy conditions can be formulated in reference to standard fractional discrete-time system. Proposed approach is possible if the matrix N = 0. The considerations are illustrated by a numerical example.

18

D-decomposition technique for stabilization of Furuta pendulum: fractional approach

Mandić P. D., Lazarević M. P., Šekara T. B.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

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Vol. 64, nr 1

189--196

EN

In this paper, the stability problem of Furuta pendulum controlled by the fractional order PD controller is presented. A mathematical model of rotational inverted pendulum is derived and the fractional order PD controller is introduced in order to stabilize the same. The problem of asymptotic stability of a closed loop system is solved using the D-decomposition approach. On the basis of this method, analytical forms expressing the boundaries of stability regions in the parameters space have been determined. The D-decomposition method is investigated for linear fractional order systems and for the case of linear parameter dependence. In addition, some results for the case of nonlinear parameter dependence are presented. An example is given and tests are made in order to confirm that stability domains have been well calculated. When the stability regions have been determined, tuning of the fractional order PD controller can be carried out.

19

Practical and asymptotic stability of fractional discrete-time scalar systems described by a new model

Ruszewski A.

Archives of Control Sciences

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2016

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Vol. 26, no. 4

441--452

EN

The stability problems of fractional discrete-time linear scalar systems described by the new model are considered. Using the classical D-partition method, the necessary and sufficient conditions for practical stability and asymptotic stability are given. The considerations are il-lustrated by numerical examples.

20

Fractional Order Dynamic Positioning Controller

Witkowska A.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

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2015

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Vol. 9, no. 3

399--404

EN

Improving the performance of Dynamic Positioning System in such applications as station keeping, position mooring and slow speed references tracking requires improving the position and heading control precision. These goals can be achieved through the improvement of the ship control system. Fractional-order calculus is a very useful tool which extends classical, integer-order calculus and is used in contemporary modeling and control applications. Fractional-order PI?D? controller, based on the added flexibility of fractional-order operators, are capable of superior performance compared to their integer-order counterparts. This paper presents the fractional order PI?D? controller designed to maintain the ship position and heading and the results were compared with classical integer order PID controller.