Rational Transfer Function Approximation Model for \(2 \times 2\) Hyperbolic Systems with Collocated Boundary Inputs

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1196)


Rational transfer function approximation model for distributed parameter systems described by two weakly coupled linear hyperbolic PDEs with the boundary conditions representing two collocated external inputs to the system is considered. 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 cascade interconnection of N subsystems, each described by \(2 \times 2\) rational transfer function matrix. The considerations are illustrated with a parallel-flow double-pipe heat exchanger. The frequency and impulse responses obtained from its original irrational transfer functions are compared with those calculated from its rational approximations of different orders.


Distributed parameter system Hyperbolic equations Transfer function Approximation model Method of lines Frequency response Impulse response Heat exchange 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Control EngineeringOpole University of TechnologyOpolePoland

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