Fuel Minimization of a Hybrid Electric Racing Carby Quasi-Pontryagin’s Minimum Principle

This paper improves the fuel efficiency of a student-made parallel hybrid electric racing car whose internal combustion engine (ICE) either operates with peak efficiency or is turned off. The control to the ICE thus becomes a binary problem. Owing to the very limited computation resource onboard, the energy management strategy (EMS) for this car must have small time and space complexities. A computationally efficient controller that combines the advantages of dynamic programming (DP) and Pontryagins minimum principle (PMP) is developed to run on a low-cost microprocessor. DP is employed offline to calculate the optimal speed trajectory, which is used as the reference for the online PMP to determine the real-time ICE on/off status and the electric motor (EM) torques. The normal PMP derives the optimal costate trajectory through solving partial differential equations. The proposed quasi-PMP (Q-PMP) method finds the costate from the value function obtained by DP. The fuel efficiency and computational complexity of the proposed controller are compared against several state of art methods through both model-in-the-loop (MIL) and processor-in-the-loop (PIL) simulations. The new method reaches similar fuel efficiency as the explicit DP, but requires less than 1% onboard flash memory. The performance of the Q-PMP controller is compared between binary-controlled and continuously controlled engines. It achieves roughly 12% higher fuel efficiency for the binary engine with only approximately 1/3 CPU utilization.