Optimal Control Utilizing Analytical Solutions for Heavy Truck Cruise Control LiTH-ISY-R-2842

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.