Predictive optimal control based energy management of hybrid electric vehicles

Vehicle electrification is important for reducing the impact of fossil fuels on the planet and the hybrid electric vehicle is a critical stage on the path to the adoption of fully electric vehicles. It is therefore important to address the energy management problem that arises as a result of the availability of many power sources. The goal of the energy management strategies employed in supervisory control is to maximise the efficiency of the powertrain. This thesis explores a number of energy management strategies for the minimisation of energy consumption in a P2 plug-in hybrid electric vehicle.

A dynamic program was implemented to derive the globally optimal solution to the energy management problem and serve as the top benchmark for the development of novel energy management strategies which are optimal or near-optimal. A charge deplete and sustain strategy as well as an adaptive equivalent consumption minimisation strategy was implemented to serve as suitable lower benchmarks for the other proposed energy management strategies. The lower benchmarks are representative of the popular strategies implemented on current production vehicles and give a baseline for the quantification of any gains made in optimality by the proposed strategy.

A number of model predictive control formulations were explored for real-time energy management. The first formulation was configured to track the optimal trajectory prescribed by the dynamic program in convex optimisation. Another formulation was based on an online formulation of an equivalent consumption minimisation based model predictive control strategy with a hierarchical optimisation that includes the ICE startstop optimisation. This strategy leverages a quadratic formulation of the equivalent consumption minimisation cost function, as well as a reduction in the horizon of the discrete engine, and start-stop optimisation to keep the problem convex. The predicition horizon of the equivalent consumption minimisation based model predictive control strategy was extended using a variable sampling time model predictive controller so that the terminal state constraint coincides with the end of the drive.

The predictive energy management strategies discussed in this thesis all rely on some level of prediction. With a perfect forecast, the proposed strategies all perform near optimally within 2% to 3% of the global optimum. However, the performance of the aforementioned strategies degrades considerably by up to a 60% loss in fuel consumption when there is a mismatch between the prediction and the actual drive. To improve the robustness of the strategy to uncertainty in the prediction, a novel formulation of the equivalent consumption minimisation based model predictive control strategy was developed by combining the approach with a dynamic program cost-to-go function. This improves the robustness of the proposed strategy with regard to the end-state target and deviations from the optimal trajectory. In the proposed equivalent consumption minimisation based model predictive control strategies, the real-time optimisation of the torque split and engine start-stop variables rely on a forecast of the expected road load. A novel method for the analysis of prediction mismatch is presented and analysis is done to evaluate the sensitivity of the proposed strategy to inaccuracies in the forecasted information.