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dc.contributor.authorOstalczyk, Piotr
dc.date.accessioned2018-08-21T07:51:25Z
dc.date.available2018-08-21T07:51:25Z
dc.date.issued2008
dc.identifier.citationOstalczyk P., Zarys rachunku różniczkowo-całkowego ułamkowych rzędów : teoria i zastosowania w automatyce., Wydawnictwo Politechniki Łódzkiej, Łódź 2008, ISBN 978-83-7283-245-0.
dc.identifier.isbn978-83-7283-245-0
dc.identifier.otherid skryba-crisppl_PL
dc.identifier.urihttp://hdl.handle.net/11652/1843
dc.descriptionSeria : Monografie t. 12 / Komitet Automatyki i Robotyki Polskiej Akademii Nauk 1640-8969pl_PL
dc.description.abstractThis book is inspired by almost forty years' development in the Fractional Calculus and its applications in diff erent areas of science. The main task of this book is to acquaint Polish readers with a variety of applications of this mathematical tool including commonly known notions like derivatives and integrals. The book gives a comprehensive introduction to the Fractional Calculus. Chapter 1 contains Griinwald-Letnikov, Riemann-Liouville, Caputo and Nishimoto definitions of a non-integer order differ-integral. Some fundamental properties are presented. In Chapter 3, a one-sided Laplace transform of a fractional-order derivative and integral is discussed. Special attention is paid to an inverse Laplace transform. Series expansion -, Fourier series -, and Valsa methods of inverse Laplace transform of a strictly proper rational function of non-integer orders are presented. In Chapters 6 and 7 some applications of the Fractional Calculus in automatics are given. Fractional order dynamical system descriptions by a transfer function and state-space equations are introduced. Fundamental properties of a fractional-order integrator are discussed. Its transient and frequency characteristics are plotted. Oustaloup, series expansion, Roy, Charef and least square approximation methods of fractional-order integrator are compared. A relation between a state-space and a transfer function description is given. One state-space realisation of a fractional-order transfer function is also given. Michailov and Nyquist stability tests are applied to fractional-order dynamical systems. In Section 5 a closed-loop system with CRONE controller is introduced. One method of CRONE controller synthesis is given. Section 6 presents the properties of PID controller with fractional differentiation and integration orders. Transient and frequency characteristics of such a controller are presented. As one possible application of a fractional-order backward difference, a closed-loop system synthesis with an electromagnetic servo and a <lead-beat controller is presented. A synthesis based on a fractional-order transfer function poles configuration is the subject of Section 8. The content of the book does not cover all problems and applications of the Fractional Calculus in automatics and robotics.en_EN
dc.language.isoplpl_PL
dc.publisherWydawnictwo Politechnika Łódzkapl_PL
dc.subjectrachunek różniczkowypl_PL
dc.subjectrachunek całkowypl_PL
dc.subjectautomatyka - matematykapl_PL
dc.subjectregulatory PIDpl_PL
dc.subjectcałki ułamkowepl_PL
dc.subjectdifferential calculusen_EN
dc.subjectintegral calculusen_EN
dc.subjectautomation - mathematicsen_EN
dc.subjectregulators PIDen_EN
dc.subjectfractional integralen_EN
dc.titleZarys rachunku różniczkowo-całkowego ułamkowych rzędów : teoria i zastosowania w automatycepl_PL
dc.title.alternativeEpitome of the Fractional Calculus. Theory and its Applications in Automaticen_EN
dc.typeKsiążkapl_PL
dc.typebooken_EN
dc.contributor.reviewerKaczorek, Tadeuszpl_PL
dc.contributor.reviewerKlamka, Jerzypl_PL


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