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1
Content available Divisibility of the second-order minors of the nominators by minimal denominators of transfer matrices of cyclic fractional linear systems
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
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2021
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Vol. 31, no. 4
627--633
EN
The divisibility of the second-order minors of the numerators of transfer matrices by their minimal denominators for cyclic fractional linear systems is analyzed. It is shown that all nonzero second-order minors of the numerators of the transfer matrices are divisible by their minimal denominators if and only if the system matrices of fractional standard and descriptor linear systems are cyclic. The theorems are illustrated by examples of fractional standard and descriptor linear systems.
2
Content available High-performance quasi one-dimensional mirrors of mechanical waves built of periodic and aperiodic structures
Garus S., Sochacki W.
Journal of Applied Mathematics and Computational Mechanics
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2018
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Vol. 17, nr 4
19--24
EN
The work studied the reflectance for quasi one-dimensional phononical structures. In composite superlattices, the thickness of the layers, their arrangement and selection of constituent materials with appropriate properties such as the density and velocity of mechanical waves propagation allows for the creation of a phononic band gap (PhBG) phenomenon. PhBG is characterized by high reflectance of the mechanical wave incident on the analyzed structure, which means that the wave does not propagate in the superlattice. The paper proposes periodic and aperiodic structures characterized by a wide range of reflectance for the ultrasonic frequencies of mechanical waves and shows how the change the thickness of the layer affects the properties of the analyzed structures.
3
Content available Computation of positive realizations for descriptor linear continuoustime systems
Kaczorek T.
Autobusy : technika, eksploatacja, systemy transportowe
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2018
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R. 19, nr 12
428--432
EN
A new method for computation of positive realizations of given transfer matrices of descriptor linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.
PL
W pracy podano nową metodę wyznaczania dodatnich realizacji dla zadanych macierzy transmitacji operatorowych deskryptowych( singularnych) ciągłych układów liniowych. Sformułowano warunki konieczne i wystarczające istnienia dodatnich realizacji dla tej klasy deskryptowych ciągłych układów liniowych. Podano procedurę wyznaczania tych realizacji. Procedura ta została zlustrowana przykładami liczbowymi.
4
Content available remote Application of transfer relations to structural analysis of arch bridges
Zhang J.-L., Hellmich C., Mang H. A., Yuan Y., Pichler B.
Computer Assisted Methods in Engineering and Science
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2017
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Vol. 24, no. 3
199--215
EN
Transfer relations, representing analytical solutions of the linear theory of slender circular arches, have facilitated structural analysis of segmented tunnel linings. This is the motivation to apply such relations to two examples of circular arch bridges in which the bridge deck is held from the arch by equally spaced hangers. First, the number of hangers is optimized to minimize the maximum bending moment of the arch, thus allowing the latter to come as close as possible to the desired thrust-line behavior. Next, analytical solutions for a “uniform temperature change” are derived and used to demonstrate that a temperature increase of 30 K results in minor redistributions of the inner forces but in significant additional deflections. The two examples have shown that the transfer relations are useful for structural analysis of circular arch bridges, because they reduce the complexity of the analysis to that of structural systems consisting of straight beams.
5
Content available A new approach to the realization problem for fractional discrete-time linear systems
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2016
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Vol. 64, nr 1
9--14
EN
A new approach to the realization problem for fractional discrete-time linear systems is proposed. A procedure for computation of fractional realizations of given transfer matrices is presented and illustrated by numerical examples.
6
Content available Transfer function matrix model of the bubbling fluidized bed boiler
Porzuczek J.
Archives of Thermodynamics
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2011
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Vol. 32, no. 3
245-31
EN
The paper presents proposal of a model of the fluidized bed boiler adapted for use in model-based controllers e.g. predictive, adaptive or internal model control (IMC). The model has been derived in the form of transfer function matrix which allows its direct implementation in the controller structure. Formulated model takes into consideration the principal cross-coupling between process variables which enables the opportunity to search for feasibility of decoupling control. The results of the identification of the dynamics of the 2 MW industrial bubbling fluidized bed boiler using the proposed model form was presented. According to the experimental data it was found that despite of introduced simplifications presented model allows the boiler behavior prediction.
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