H 2-Optimal Low Order Transmission Line Models

Transmission line modeling has played a crucial role in understanding the dynamics of fluid power systems. A vast body of literature exists from simple lumped parameter approaches to fully coupled three-dimensional fluid structure interaction models. When it comes to computationally efficient, yet physically sound low order models needed for fast computations iteratively called by optimization codes or for the purpose of model based control design, there is still room for improvement. Modal approximations of the input-output behaviour of liquid transmission lines have been around for decades. The basic idea of tuning the parameters of a canonical linear time invariant state space model to fit the transfer functions of a transmission line model in the H2-optimal sense under passivity constraints has been published by the author of the present paper in the past. However, the method so far was barely usable due to numerical difficulties in the underlying optimization process. A new implementation of the method employing quadruple-precision floating point numbers has recently been found to resolve the convergence problems and is reported in the present paper. The new version of the method is based on analytic computation of the cost and constraint functions as well as their gradients in the computer algebra package Maple and automatic code generation for compilation in FORTRAN. Results are very promising because both the entire low frequency behaviour and the first three eigenmodes of a transmission line model can be accurately covered by a model of order eight only.