Variable-, fractional-order simple model of the robot arm

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dc.contributor.authorBąkała, Marcin
dc.contributor.authorDuch, Piotr
dc.contributor.authorSankowski, Dominik
dc.contributor.authorOstalczyk, Piotr
dc.date.accessioned2021-05-06T06:27:49Z
dc.date.available2021-05-06T06:27:49Z
dc.date.issued2015
dc.description.abstractIt is well known that to synthesise a satisfactory control algorithm of a dynamical system a ,,good" mathematical model should be evaluated [5]. Also there is a trade off between the model accuracy and its complexity. In robotics the dynamical models of robot arms derived by Euler-Lagrange equations or Euler - Lagrange formalism are known [9]. Their complexity expressed by a large number of relevant parameters, often difficult to estimate forces a search for new solutions. The methodology proposed in the present paper allows one to find a simple model described by a variable-, fractional-order difference equation. The fractional calculus as a new mathematical tool generalising the commonly known calculus is becoming more and more popular in different research areas, ranging from electrical engineering, electromagnetism, electrochemistry, electronics, mechanics, rheology to biophysics and economy [6, 7, 8]. It seems to be very useful in complex unmodelable processes, for instance, in description the transient behaviour of a robot arm. The paper is organized as follows. In Section 2 the definition of the variable-, fractional-order backward difference is introduced. Next some discussion concerning the mathematical models of robot arms are given. Some rules for a choice of the differentiation order functions are given. Finally measured and simulated step responses of the robot arm are presented.[...]en_EN
dc.identifier.citationBąkała M., Duch P., Sankowski D., Ostalczyk P., Variable-, fractional-order simple model of the robot arm. W: Modelling and Identification Algorithms for Emerging Applications in Data and Signal Processing, Romanowski A. (red.), Sankowski D. (red.), Tadeusiewicz R. (red.), Wydawnictwo Politechniki Łódzkiej, Łódź 2015, s. 51-64, ISBN 978-83-7283-657-1.
dc.identifier.isbn978-83-7283-657-1
dc.identifier.urihttp://hdl.handle.net/11652/3421
dc.language.isoenen_EN
dc.publisherWydawnictwo Politechniki Łódzkiejpl_PL
dc.publisherLodz University of Technology Pressen_EN
dc.relation.ispartofRomanowski A. (red.), Sankowski D. (red.), Tadeusiewicz R. (red.), Modelling and Identification Algorithms for Emerging Applications in Data and Signal Processing, Wydawnictwo Politechniki Łódzkiej, Łódź 2015, ISBN 978-83-7283-657-1.
dc.relation.ispartofseriesMonografie Politechniki Łódzkiejpl_PL
dc.relation.ispartofseriesLodz University of Technology Monographsen_EN
dc.subjectvariable-fractional-order backward differenceen_EN
dc.subjectmathematical modelsen_EN
dc.subjectrobot arms - mathematical modelsen_EN
dc.subjectvariable fractional orderen_EN
dc.subjectrobot arm - modelen_EN
dc.subjectróżnica wsteczna o zmiennej ułamkowej kolejnościpl_PL
dc.subjectmodele matematycznepl_PL
dc.subjectramiona robotów - modele matematycznepl_PL
dc.subjectzmienna ułamkowa kolejnośćpl_PL
dc.subjectramie robota - modelpl_PL
dc.titleVariable-, fractional-order simple model of the robot armen_EN
dc.typerozdział książkipl_PL
dc.typebook chapteren_EN

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