# Efficient Simulation and Optimal Control for Vehicle Propulsion

Sammanfattning: Efficient drive cycle simulation of longitudinal vehicle propulsion models is an important aid for design and analysis of power trains. Tools on the market today mainly use two different methods for such simulations, forward dynamic or quasi-static inverse simulation. Here known theory for stable inversion of non linear systems is used in order to combine the fast simulation times of the quasi-static inverse simulation with the ability of including transient dynamics as in the forward dynamic simulation. The stable inversion technique with a new implicit driver model together forms a new concept, inverse dynamic simulation. This technique is demonstrated feasible for vehicle propulsion simulation and specifically on three powertrain applications that include important dynamics that can not be handled using quasi-static inverse simulation. The extensions are engine dynamics, drive line dynamics, and gas flow dynamics for diesel engines, which also are selected to represent important properties such as zero dynamics, resonances, and non-minimum phase systems. It is shown that inverse dynamic simulation is easy to set up, gives short simulation times, and gives consistent results for design space exploration. This makes inverse dynamic simulation a suitable method to use for drive cycle simulation, especially in situations requiring many simulations, such as optimization over design space, powertrain configuration optimization, or development of powertrain control strategies.Optimal vehicle propulsion control is developed with special focus on heavy trucks used for long haulage. The power to mass ratio for a typical heavy duty truck makes even moderate road slopes significant in the sense that it is impossible to keep a constant cruising speed. This gives an interesting problem how to control vehicle speed such that fuel consumption is minimized. Todays telematic systems together with three dimensional roadmaps can provide the vehicle control system with information of the road topography. This enables intelligent cruise controllers that utilize this information to control engine fueling and gear shifting such that an optimal speed trajectory is obtained.First the optimal control problem is solved numerically by dynamic programming, giving a controller with real time capabilities that can be used on-line in the vehicles control system. Simulations of such a system on authentic road profiles show that it has potential for significant fuel savings. To achieve knowledge about the underlying physics that affects the optimal solution, the optimal control problem is solved in detail and analytical expressions for the conditions of optimality are derived. Those expressions are then used to find optimal solutions on constructed test road profiles. Such test cases point out the typical behavior of an optimal solution and also which parameters that are decisive for the fuel minimization problem, and also how they quantitatively influence the behavior. It is for example shown that small non-linearities in the engine torque characteristics have significant effect on the optimal control strategy. The solutions for the non linear engine model have a smoother character but also require longer prediction horizons. For optimal gear ratio control it is shown that the maximum fueling function is essential for the solution. For example, in the case of a continuously variable transmission it is shown that the gear ratio never is chosen such that engine speed exceeds the speed of maximum engine power. For a discrete step transmission the gear shifting losses are essential for the optimal shift positions, but over all the solutions are close to continuous solutions.

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