1. bookVolume 30 (2020): Issue 3 (September 2020)
    Big Data and Signal Processing (Special section, pp. 399-473), Joanna Kołodziej, Sabri Pllana, Salvatore Vitabile (Eds.)
Journal Details
First Published
05 Apr 2007
Publication timeframe
4 times per year
access type Open Access

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

Published Online: 29 Sep 2020
Page range: 475 - 491
Received: 12 Feb 2020
Accepted: 29 May 2020
Journal Details
First Published
05 Apr 2007
Publication timeframe
4 times per year

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.


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