Optimal Control Utilizing Analytical Solutions for Heavy Truck Cruise Control
The problem addressed is how to control vehicle speed over a given
distance on a given time such that fuel consumption is
minimized. Analytical expressions for the necessary optimality
conditions are derived. These expressions are essential for the
understanding of the decisive parameters affecting fuel optimal
driving and the analytical optimality conditions make it possible to
see how each parameter affects the optimal solution. Optimal solutions
for an affine engine torque model are compared to solutions for a
piece-wise affine model, and it is shown that small non-linearities
have significant effect on the optimal control strategy. The solutions
for the non linear engine model has a smoother character but also
requires longer prediction horizons.
Assuming a continuously variable
transmission, optimal gear ratio control is presented, and it is shown
how the maximum fueling function is essential for the solution. It is
also shown that the gear ratio never is chosen such that engine speed
exceeds the speed of maximum engine power. Those results are then
extended to include a discrete stepped transmission, and it is
demonstrated how gear shifting losses affect optimal gear shifting
positions.
The theory presented is a good base to formalize the
intuition of fuel efficient driving. To show this, optimal solutions
are presented in simulations of some constructed test road profiles,
where the typical behavior of an optimal solution is pointed out, and
also which parameters that are decisive for the fuel minimization
problem. This is then used to design a simple low-complexity
computationally efficient rule-based look ahead cruise controller, and
it is demonstrated that simple parametrized quantitative rules have
potential for significant fuel savings.
Anders Fröberg and Lars Nielsen
2008
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