| For the simultaneous optimization of fuel economy and emissions, we first develop a parallel Hybrid Electric Vehicles (HEVs) and Plug-in HEVs (PHEVs) model that can efficiently evaluate both fuel economy and tail-pipe emissions, and then solve the optimal control problem that minimizes fuel consumption and emissions for a cold-start driving cycle using Dynamic Programming (DP). Based on DP results, a comprehensive extraction method is developed to extract implementable optimal control strategies over the entire state space, instead of a single optimal trajectory. This method is applied to both HEVs and PHEVs to extract both optimal energy management and catalytic converter temperature management strategies. For the optimal energy management of PHEVs under known trip distances, a new variable Energy-to-Distance Ratio (EDR) is introduced to quantify the level of battery state-of-charge (SOC) with respect to the remaining distance. The extracted results show that the engine on/off, gear-shift, and power-split strategies must be properly adjusted to optimize fuel economy and tail-pipe emission. Based on the extracted results, a DP-based cold-start supervisory powertrain controller (SPC) is designed and compared with instantaneous optimization methods. Simulation results show that instantaneous optimization methods are good for the optimization of fuel economy despite frequent engine on/off and gear-shift events, but the DP-based SPC performs better when multiple objectives are considered.;For the engine-start control problem, a more detailed powertrain model, including clutch and crank-angle domain engine models, is developed. Assuming that the clutch torque can be accurately estimated and perfectly cancelled, the optimal engine-start control problem is formulated to minimize engine-start time while accurately supplying the driver torque demand. This nonlinear optimal control problem is solved both analytically and numerically. Under special cases, the optimization problem can be analytically solved to obtain a closed form solution. DP, on the other hand, is used to obtain numerical solutions for all cases, and the results confirm that the numerical solution matches with the analytical solution. More importantly, the DP control policy is found to be time-invariant, and thus can be directly implemented in the form of a full state feedback controller. |
