Approximation state-space model for 2×2 hyperbolic systems with collocated boundary inputs

Abstract

The paper discusses an approximation model developed for linear hyperbolic DPS with two state variables and two collocated boundary inputs, expressed in classical, finite-dimensional state-space framework. Using the method of lines approach with the backward difference scheme, the original PDEs are transformed into a set of ODEs and expressed in the form of the state-space equations with matrix-valued state, input and output operators. The eigenvalues and the steady-state solutions of the approximation model are analyzed. The considerations are illustrated with a parallel-flow double-pipe heat exchanger. Steady-state and frequency-domain responses obtained from its original PDE model are compared with those calculated from its ODE approximations of different orders.