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

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.