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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


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Last updated: 2021-11-10