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Wybrane zagadnienia z zakresu liniowych ciągłych układów niecałkowitego rzędu

100%

Busłowicz M.

2010

tom R. 14, nr 2

93-114

W pracy dokonano przeglądu wybranych zagadnień z zakresu rachunku niecałkowitego rzędu oraz teorii ciągłych układów liniowych stacjonarnych rzędu niecałkowitego, takich jak metody opisu, synteza regulatorów niecałkowitego rzędu, ich modelowanie oraz realizacja praktyczna, a także badanie stabilności układów regulacji. Rozważania zilustrowano przykładami liczbowymi.

The paper gives the review of the selected problems from calculus of non-integer order and theory of continuous-time linear systems of non-integer order such as description methods, synthesis of non-integer controllers, their modelling and practical realization and also stability checking of the control systems. The considerations are illustrated by examples.

Non-integer viscoelastic constitutive law to model soft biological tissues to in-vivo indentation

63%

Demirci N. , Tönük E.

Acta of Bioengineering and Biomechanics

2014

tom Vol. 16, no. 4

13--21

Purpose: During the last decades, derivatives and integrals of non-integer orders are being more commonly used for the description of constitutive behavior of various viscoelastic materials including soft biological tissues. Compared to integer order constitutive relations, non-integer order viscoelastic material models of soft biological tissues are capable of capturing a wider range of viscoelastic behavior obtained from experiments. Although integer order models may yield comparably accurate results, non-integer order material models have less number of parameters to be identified in addition to description of an intermediate material that can monotonically and continuously be adjusted in between an ideal elastic solid and an ideal viscous fluid.Methods: In this work, starting with some preliminaries on non-integer (fractional) calculus, the “spring-pot”, (intermediate mechanical element between a solid and a fluid), non-integer order three element (Zener) solid model, finally a user-defined large strain non-integer order viscoelastic constitutive model was constructed to be used in finite element simulations. Using the constitutive equation developed, by utilizing inverse finite element method and in vivo indentation experiments, soft tissue material identification was performed. Results: The results indicate that material coefficients obtained from relaxation experiments, when optimized with creep experimental data could simulate relaxation, creep and cyclic loading and unloading experiments accurately.Conclusions: Non-integer calculus viscoelastic constitutive models, having physical interpretation and modeling experimental data accurately is a good alternative to classical phenomenological viscoelastic constitutive equations.

Fractional-order digital filter approximation method for embedded control applications

63%

Tepljakov A. , Petlenkov E. , Belikov J.

International Journal of Microelectronics and Computer Science

2014

tom Vol. 5, nr 2

54--60

Fractional-order calculus presents a novel modeling approach for systems with extraordinary dynamical properties by introducing the notions of derivatives and integrals of noninteger order. In system theory this gives rise to extensions to linear, time invariant systems to enhance the description of complex phenomena involving memory or hereditary properties of systems. Standard industrial controllers, such as the PID controller and lead-lag compensator, have also been updated to beneﬁt from the effects of noninteger integration and differentiation, and have advantages over classical controllers in case of both conventional and fractional-order process control. However, given the deﬁnitions of fractional operators, accurate digital implementation of fractional-order systems and controllers is difﬁcult because it requires inﬁnite memory. In this work we study the speciﬁc implementation of a fractional-order PID controller and fractional-order lead-lag compensator based on an inﬁnite impulse response (IIR) ﬁlter structure obtained by applying the Oustaloup recursive ﬁlter synthesis technique. Software for generating digital fractional-order is developed and tested on an Atmel AVR microcontroller. The results are veriﬁed using a MATLAB/Simulink based real-time prototyping platform.