<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Two approximate representations are proposed for distributed parameter systems described by two linear hyperbolic PDEs with two time- and space-dependent state variables and two collocated boundary inputs. Using the method of lines with the backward difference scheme, the original PDEs are transformed into a set of ODEs and expressed in the form of a finite number of dynamical subsystems (sections). Each section of the approximation model is described by state-space equations with matrix-valued state, input and output operators, or, equivalently, by a rational transfer function matrix. The cascade interconnection of a number of sections results in the overall approximation model expressed in finite-dimensional state-space or rational transfer function domains, respectively. The discussion is illustrated with a practical example of a parallel-flow double-pipe heat exchanger. Its steady-state, frequency and impulse responses obtained from the original infinite-dimensional representation are compared with those resulting from its approximate models of different orders. The results show better approximation quality for the “crossover” input–output channels where the in-domain effects prevail as compared with the “straightforward” channels, where the time-delay phenomena are dominating.</p></abstract>

Two approximate representations are proposed for distributed parameter systems described by two linear hyperbolic PDEs with two time- and space-dependent state variables and two collocated boundary inputs. Using the method of lines with the backward difference scheme, the original PDEs are transformed into a set of ODEs and expressed in the form of a finite number of dynamical subsystems (sections). Each section of the approximation model is described by state-space equations with matrix-valued state, input and output operators, or, equivalently, by a rational transfer function matrix. The cascade interconnection of a number of sections results in the overall approximation model expressed in finite-dimensional state-space or rational transfer function domains, respectively. The discussion is illustrated with a practical example of a parallel-flow double-pipe heat exchanger. Its steady-state, frequency and impulse responses obtained from the original infinite-dimensional representation are compared with those resulting from its approximate models of different orders. The results show better approximation quality for the “crossover” input–output channels where the in-domain effects prevail as compared with the “straightforward” channels, where the time-delay phenomena are dominating.

Approximate State–Space and Transfer Function Models for 2×2 Linear Hyperbolic Systems with Collocated Boundary Inputs

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Two approximate representations are proposed for distributed parameter systems described by two linear hyperbolic PDEs with two time- and space-dependent state...

Approximate State–Space and Transfer Function Models for 2×2 Linear Hyperbolic Systems with Collocated Boundary Inputs

Publié en ligne: 29 sept. 2020

Pages: 475 - 491

Reçu: 12 févr. 2020

Accepté: 29 mai 2020

DOI: https://doi.org/10.34768/amcs-2020-0035

Mots clés
distributed parameter system, hyperbolic equations, approximation model, state space, transfer function

© 2020 Krzysztof Bartecki, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Approximate State–Space and Transfer Function Models for 2×2 Linear Hyperbolic Systems with Collocated Boundary Inputs

Publié en ligne: 29 sept. 2020

Pages: 475 - 491

Reçu: 12 févr. 2020

Accepté: 29 mai 2020

DOI: https://doi.org/10.34768/amcs-2020-0035

Mots clésdistributed parameter system, hyperbolic equations, approximation model, state space, transfer function

© 2020 Krzysztof Bartecki, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
distributed parameter system, hyperbolic equations, approximation model, state space, transfer function