The parallel hybrid electric vehicle (HEV) with a single pre-transmission electric motor (the P2 configuration) has a challenging drivability issue during engine-starts because the motor must simultaneously provide the propulsion torque demand and start the engine. The goal of this study is to present a design process to achieve optimal balance between these two conflicting goals. We first develop a control-oriented HEV powertrain model to accurately predict the engine, clutch, and vehicle dynamics. Assuming that the clutch torque can be accurately estimated and perfectly cancelled, an optimal engine-start control problem is formulated to minimize engine-start time while accurately supplying the driver torque demand simultaneously. This nonlinear constrained optimal control problem is solved numerically using Dynamic Programming (DP). DP results show that a proper constant clutch pressure level, which leads to constant torque disturbance that is easy to cancel out using the motor, can achieve near-optimal performance. Furthermore, 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.

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