Piotr Ostalczyk

Lodz University of Technology

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Dominik Sankowski

Lodz University of Technology

Piotr Duch

Lodz University of Technology

Dariusz W. Brzeziński

Lodz University of Technology

Marcin Bąkała

Lodz University of Technology

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Maciej Łaski

Lodz University of Technology

Jacek Nowakowski

STMicroelectronics (France)

Sylwester Błaszczyk

Lodz University of Technology

Dorota Mozyrska

Bialystok University of Technology

Rafał Jachowicz

Lodz University of Technology

Adam Wulkiewicz

Lodz University of Technology

Cooperative Institutions

Lodz University of Technology

Cairo University

Nile University

University of Łódź

Institute of Computer Science

Brno University of Technology

University of Patras

King Abdullah University of Science and Technology

King Abdulaziz University

Benha University

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An application of forward difference of higher fractional-order in dynamic system modelling

Dorota Mozyrska Piotr Ostalczyk

In the paper linear time-invariant difference equations are applied to model dynamic systems. The forward difference with higher fractional-order is used. Admitting fractional-orders of systems, we gather a better modelling of the inductive and capacitive couplings in the electrical circuit. The investigations are illustrated by numerical examples with real simple electrical circuit and electrical circuit with DC micromotor and supercapacitors modelling.

Electrical network

LTI system theory

10.1109/tsp.2017.8076082

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Citations (1)

State Delays Extraction in the Fractional-Order State-Space Model

Lecture notes in electrical engineering (2018)

Piotr Ostalczyk Marcin Bąkała Jacek Nowakowski

State-space representation

Fractional-order system

10.1007/978-3-319-78458-8_18

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Variable-, fractional-order discrete PID controllers

Piotr Ostalczyk

The fractional calculus is the area of mathematics that handles derivatives and integrals of any arbitrary order (fractional or integer, real or complex order) [1,2,3,4]. Nowadays it is applied in almost all areas of science and engineering. Here one can mention its numerous and successful applications in dynamical systems modeling and control with increasing number of studies related to the theory and application of fractional-order controllers, specially ones. In such controllers μ _k <;0 and v _k >; 0 denote the integration and differentiation order, respectively. Now research activities are focused on developing new analysis and closed-loop system synthesis methods for fractional-order controllers being an extension of classical control theory. In the fractional-order controller tuning there are two additional parameters μ _k <; 0 and v _k >; 0. This impedes the controller tuning procedure but leads to new (unattainable in classical PID control [5]) closed-loop system transient responses. The closed-loop system with fractional controller must satisfy typical requirements among which one can mention the system robustness due to the plant model uncertainties.

Robustness

10.1109/mmar.2012.6347829

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Citations (30)

Variable-, fractional-order Grünwald-Letnikov backward difference selected properties

Dorota Mozyrska Piotr Ostalczyk

There were investigated some particular properties of variable-, fractional-order backward differences (VFOBD). The most of proved properties are connected with coefficients of VFOBD. There are presented examples of the numerical results of VFOBD.

10.1109/tsp.2016.7760959

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Fractional-order Mathematical Model of Pneumatic Muscle Drive for Robotic Applications

Lecture notes in control and information sciences (2009)

Edward Jezierski Piotr Ostalczyk

10.1007/978-1-84882-985-5_11

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Citations (10)

ADVANCED VISION SYSTEMS IN DETECTION AND ANALYSIS OF CHARACTERISTIC FEATURES OF OBJECTS

Series in computer vision (2014)

Adam Wulkiewicz Rafał Jachowicz Sylwester Błaszczyk Piotr Duch Maciej Łaski

10.1142/9789814583725_0005

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Contributors

Elsevier eBooks (2018)

H.L. Abdel-Malek Amr M. AbdelAty M.M. Abdelwahab Magdy A.S. Aboelela S.M. Al-Mekhlafi

10.1016/b978-0-12-816152-4.09988-x

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Variable-, Fractional-Order Inertial Element

Lecture notes in electrical engineering (2016)

Piotr Ostalczyk Dorota Mozyrska

10.1007/978-3-319-45474-0_8

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Citations (4)

Partial fractional-order backward difference and its properties

Zeszyty Naukowe. Elektryka / Politechnika Łódzka (2008)

Piotr Ostalczyk J. Kacerka

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High-accuracy numerical integration methods for fractional order derivatives and integrals computations

Bulletin of the Polish Academy of Sciences Technical Sciences (2014)

Dariusz W. Brzeziński Piotr Ostalczyk

Abstract In this paper the authors present highly accurate and remarkably efficient computational methods for fractional order derivatives and integrals applying Riemann-Liouville and Caputo formulae: the Gauss-Jacobi Quadrature with adopted weight function, the Double Exponential Formula, applying two arbitrary precision and exact rounding mathematical libraries (GNU GMP and GNU MPFR). Example fractional order derivatives and integrals of some elementary functions are calculated. Resulting accuracy is compared with accuracy achieved by applying widely known methods of numerical integration. Finally, presented methods are applied to solve Abel’s Integral equation (in Appendix).

Quadrature (astronomy)

Rounding

10.2478/bpasts-2014-0078

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Citations (16)