Fuel optimal control of hybrid vehicles

Hybrid vehicles have, at least, two power converters. Usually a prime mover, which can provide tractive power, consuming fuel with an irreversible proces, and secondary power converter(s), which convert tractive power, reversibly, into a power quantity suitable for a storage device, or visa versa. The fuel optimal control of hybrid vehicles involves the control of vehicle velocity, transmission ratio, power split between the prime mover and secondary power converter(s), and stop-start of the prime mover. The potential of hybrid vehicles has not been fully realized due to a lack of control methods that can cope with the unknown future power requests, can be embedded in industry standard hardware, and can obtain fuel use close to a global minimum. The control objective is to drive the vehicle to the next destination with a minimum of fuel subject to a time constraint. The combined control of vehicle velocity, transmission ratio and power split is approximated with a piecewise continuous scalar control signal the combined power request- and optimized with non-smooth optimal control theory. The stop-start of the prime mover and capacity boundaries of the storage device are hereby neglected. Using data from an onboard navigation system, providing information for the upcoming route, e.g., road curvature, road grade, and velocity limitations, the optimal power request, vehicle velocity, transmission ratio and power split trajectories for the upcoming route are obtained. The optimal velocity and transmission ratio trajectories can be used as set points for the real-time velocity (cruise) control and gearshift strategy, also for non-hybrid vehicles. The optimal power request and velocity trajectory can be applied to more involved optimization methods that obtain the optimal power split trajectory, including stop-start of the prime mover, subject to constraints on the storage device capacity boundaries. In case the power split cost function can be approximated with a convex function and there is a monotonically increasing relation between the storage power and the output power of the secondary power converter, a novel numerical approach is applied which is based on observations obtained with the -in optimal control theory well known Pontryagin Maximum Principle. The resulting optimal power split trajectory can be used as set point for the real-time power split controller which gives a robustness against errors in the predicted trajectories. Optimal trajectories can also be used to benchmark and design real-time implementable power split controls, or to derive optimal technology, topology, and component sizes in the design of hybrid vehicle drive trains. In this thesis the optimal hybridization ratio for a long-haul truck is derived for a 513 km long input trajectory. The design of a real-time implementable strategy takes advantage of the results obtained from the necessary conditions of optimality from the previously mentioned Maximum Principle, and boils down to: i) estimation of a multiplier function, that adjoins the energy stored in the storage device to the fuel cost, using real-time available information, and ii) optimization of a locally approximated Hamiltonian like function, given the limited available onboard computational capacity. The optimal control based real-time power split control estimates the multiplier function using linear feedback on an adaptive set point which is based on the energy currently stored in the storage device and the actual kinetic and potential energy of the vehicle. The strategy is implemented in a hybrid electric truck on standard industry hardware. This control is evaluated with experiments on a chassis dynamometer. The controller is easy to tune and obtains a fuel consumption, without a priori knowledge of future power requests, within 1.5% of the global optimum on routes where the capacity boundaries of the storage device are not reached. In case the storage device boundaries are reached, optimal power split trajectories, obtained with data coming from navigation systems, can enhance the performance to become close to optimal. The calculation of optimal trajectories, based on information from a navigation system, the novel numerical solution for scalar optimal control problems with state constraints, and the implemented power split controller adaptive for vehicle mass, vehicle velocity and elevation, together with the observations when predictive information is beneficial, can be seen as the main results of this research.