Time domain fluid transmission line modelling using a passivity preserving rational approximation of the frequency dependent transfer matrix

Flow and pressure transients in fluid transmission lines can be analysed starting from a modal approximation of the frequency domain irrational transfer matrix, relating pressure and flow rate at the line ends in Laplace transform. The obtained rational approximation can be converted in a state space representation and used in variable time step simulators to evaluate the influence of the line on fluid servosystems dynamics. Particular attention must be given to the causality, to the stability and to the energy passivity of the resulting line model. In this paper the application of a numerical approximation technique (Vector Fitting) to the frequency dependent transfer matrix describing the pipeline dynamics is proposed. The admittance matrix formulation is chosen, introducing an effective passivity enforcing technique, to ensure the energy passivity of the approximated matrix, thus preserving in the model the physical meaning of the real system. The rational approximation of the transfer matrix, combined with the passivity enforcement methodology, is applied to the study of the transient response of a single uniform line and of compound hydraulic line systems, showing the agreement between the simulation and the solution obtained with inverse fast Fourier transform.