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Paper details
Number 3 - September 2020
Volume 30 - 2020
Approximate state-space and transfer function models for 2x2 linear hyperbolic systems with collocated boundary inputs
Krzysztof Bartecki
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.
Keywords
distributed parameter system, hyperbolic equations, approximation model, state space, transfer function