Philipp Zagar, Rudolf Scheidl,
"The Connection Between Sliding Mode Analysis and Singular Perturbation Theory for Modelling Fast Hydraulically Fed-Back Switching Valves"
: Proceedings of the 2022 ASME on Fluid Power and Motion Control FPMC2022, September 14-16, 2022, Bath, United Kingdom., 9-2022
The Connection Between Sliding Mode Analysis and Singular Perturbation Theory for Modelling Fast Hydraulically Fed-Back Switching Valves
Sprache des Titels:
Proceedings of the 2022 ASME on Fluid Power and Motion Control FPMC2022, September 14-16, 2022, Bath, United Kingdom.
In most cases modeling of fast switching valves in hydraulics
results in fast and slow subsystems. System equations which incorporate
fast and slow dynamics are called stiff systems and one
can apply singular perturbation theory to reduce the system order
and get handy approximate expressions in a lower-order description.
This is not only useful to reduce complexity to numerically
solve the system efficiently, but also to understand the system?s
key parameters and how they affect the behavior which is of great
interest during design phase.
In a previous paper the authors published an approach which
uses switched systems and sliding modes to get a reduced system
description of hydraulically fed-back switching. There, one
models a hydraulic valve as either completely open or closed. A
partially opened valve is then modelled as a sliding mode which
can be interpreted as a pulse-width modulation of a fast switching
digital valve. Even though, the resulting sliding mode dynamics
approximation does not preserve topological properties of the full
system dynamics an advantage of this approach is that the system
incorporates the nonlinearities which arise due to end-stops of
valves in a very natural way. Therefore, it is capable of describing
system dynamics which results from such non-smooth properties.
In this paper the authors work out the naturally suggested - even
though not obvious - connection between both approaches for
reducing systems with hydraulically fed-back switching valves.