Mass- and Energy-Balance Relations in Lumped Parameter Hydraulic Modeling

Lumped parameter models are widely used as approximations of reality for system design and dynamic simulation due to their often simple and intuitive physical principles. This is particularly convenient, if the modeling is confined to one single physical domain, for instance, dynamic models of electronic circuits. Hydraulic drive technology is an interaction of physical effects from multiple domains such as mechanics, fluid dynamics and thermodynamics, which in turn makes the development of lumped parameter models more involved. In order to get simple models certain assumptions result in approximations that sometimes leave the correct physical context to some extent, which may lead to unexpected dynamic behaviour of certain models, like closed hydraulic systems. In this paper the problems of conventional hydraulic lumped parameter modeling regarding mass and energy conservation are addressed. The deficiencies of the established models from literature are investigated by simulations and analysed with an energy-based modeling framework from systems theory, which in turn enables the development of a simple strategy to adapt the original models in order to achieve a mass-conservative and energy-consistent behaviour under stated assumptions, even with existing simulation tools. Furthermore, the approximation of wave propagation effects in transmission lines by lumped parameter models is investigated by simulations.