Transfer function–based impulse response analysis for a class of hyperbolic systems of balance laws

Results of the impulse response analysis for a class of dynamical systems, described by two weakly coupled linear partial differential equations of hyperbolic type, defined on a one-dimensional spatial domain are presented. For the case of two boundary inputs of the Dirichlet type, the analytical expressions for the impulse response functions are derived based on the inverse Laplace trans form of the 2×2 transfer function matrix of the system. The influence of the boundary inputs configuration on the impulse response functions is demonstrated. The considerations are illustrated with a practical example of a thin-walled double-pipe heat exchanger operating in parallel- and countercurrent-flow modes, which correspond to the analyzed boundary conditions.