Optimized engine transients
Recent development has renewed the interest in
drivetrain concepts which give a higher degree of freedom by
disconnecting the engine and vehicle speeds. This freedom raises
the demand for active control, which especially during transients
is not trivial but of which the quality is crucial for the success
of the drivetrain concept. This work attempts to analyze and
explain the fuel optimal solution for the simplest drivetrain
setup, which is an engine connected to a load which does not
restrict the engine speed. This is made by using a Willan’s model
for the engine and deriving the fuel optimal solution during
output power transients. The analysis is made with dynamic
programming, Pontryagin’s maximum principle and backward
simulation under a static optimal line restriction. The analysis
show that the optimal transients can be explained, visualized and,
in simple cases, derived from phase planes of the engine speed
and the Lagrange multiplier. In these cases the time needed for
computation was reduced a factor > 1000 compared to dynamic
programming. Restricting the engine to the static optimal line
turns out to be very close to optimal, even during highly transient
operation, while reducing the time needed for computation a
factor » 1000.
Tomas Nilsson, Anders Fröberg and Jan Åslund
2011
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