TIME DOMAIN FLUID TRANSMISSION LINE MODELLING USING A PASSIVITY PRESERVING RATIONAL APPROXIMATION OF THE FREQUENCY DEPENDENT TRANSFER MATRIX
Keywords:
fluid lines, transient response, modal analysis, transfer function, rational approximation, passivity enforcementAbstract
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.
Downloads
References
Book, W. J. and Watson, C. 2000. Alternatives in the
generation of time domain models of fluid lines using
frequency domain techniques. Mathematics and
Computers in Simulation, Vol. 53, pp. 353-365.
D’Souza, A. and Oldenberger, R. 1964. Dynamic
Response of Fluid Lines. ASME J. Basic Eng., Vol.
, pp. 589-598.
Franco, W. and Sorli M. 2004. Time-Domain Models
for Pneumatic Transmission Lines, Bath Workshop
on Power Transmission & Motion Control, PTMC2004, Bath, UK, Eds. C.R. Burrows, K.A. Edge,
and O.N. Johnston, pp. 257-269.
Gustavsen, B. and Semlyen, A. 1999. Rational approximation
of frequency domain responses by vector
fitting. IEEE Trans. Power Delivery, Vol. 14,
No.3, pp. 1052-1061.
Gustavsen, B. and Semlyen, A. 2001. Enforcing Passivity
for Admittance Matrices Approximated by
Rational Functions. IEEE Trans. Power Systems,
Vol. 16, No.3, pp. 97-104.
Hsue, C. and Hullender, D. 1983. Modal Approximation
for the Fluid Dynamics of Pneumatic and Hydraulic
Transmission Lines. Fluid Transmission
Line Dynamics, eds. ASME, pp.51-77.
Hullender, D. A. 1985. Modal Representations for
Fluid Transmission Line Dynamics. Proc. Int.
Symp. on Fluid Control and Measurement FLUCOME,
Tokyo, pp.93-99.
Khalil, H.K. 1996. Nonlinear Systems. Prentice Hall.
Kojima, E., Shinada, M. and Yu J. 2002. Development
of accurate and practical simulation technique
based on the modal approximations for fluid transients
in compound fluid lines systems (2ND Report).
Int. Journal of Fluid Power, Vol. 4, No.3, pp.
-45.
Kojima, E. and Shinada, M. 2003. Development of
accurate and practical simulation technique based
on the modal approximations for fluid transients in
compound fluid lines systems (1ST Report). Int.
Journal of Fluid Power, Vol. 3, No.2, pp. 5-15.
Krus, P., Jansson, A., Palmberg, J. and Weddfeld,
K., 1990. Distributed Simulation of Hydromechanical
Systems. Third Bath International Fluid Power
Workshop, Bath, UK.
Krus, P., Weddfeld, K., and Palmberg, J. 1994. Fast
Pipeline Models for Simulation of Hydraulic Systems.
ASME Journal of Dynamic Systems, Measurement
and Control, Vol 116, pp. 132-136.
Krus, P. 1999. Modelling of Mechanical Systems Using
Rigid Bodies and Transmission Line Joints.
ASME Journal of Dynamic Systems, Measurement
and Control, Vol 121.
Mäkinen, J., Piché, R. and Ellman, A. 2000. Fluid
Transmission Line Modeling Using a Variational
Method. ASME Journal of Dynamic Systems, Measurement
and Control, Vol 122, pp. 153-162.
Manhartsgruber, B. 2004. Passivity of fluid transmission
line models. Bath Workshop on Power Transmission
& Motion Control, PTMC 2004, Bath, UK,
Eds. C.R. Burrows, K.A. Edge, and O.N. Johnston,
pp. 99-108.
Stecki, J. S. and Davis, D. C. 1986a. Fluid Transmission
Lines-Distributed Parameter Models, Part 1: A
Review of the State of Art. Proc. Inst. Mech. Engrs.
Part A, Vol. 200, pp. 215-228.
Stecki, J. S. and Davis, D. C. 1986b. Fluid Transmission
Lines-Distributed Parameter Models, Part 2:
Comparison of Models. Proc. Inst. Mech. Engrs.
Part A, Vol. 200, pp. 229-236.
Tahmeen, M., Muto, T. and Yamada H. 2001. Simulation
of Dynamic Responses of Tapered Fluid
Lines. JSME International Journal, Series B, Vol.
, No. 2, pp. 247-254.
Watton, J. 1988. Modelling of Electrohydraulic Systems
with Transmission Lines Using Modal Approximations.
Proc. Instn. Mech. Engrs, Vol. 202,
n.B3, pp.153-163.
Wylie, E. B. and Streeter, V. L. 1978. Fluid Transients,
McGraw-Hill.
Yang, W. C. and Tobler, W. E. 1991. Dissipative
Modal Approximation of Fluid Transmission Lines
Using Linear Friction Model. ASME Journal of Dynamic
Systems, Measurement and Control, Vol 113,
pp. 152-162.
