Realization of PMP-based Control for Hybrid Electric Vehicles in a Backward-Looking Simulation
N. W. KIM, D. H. LEE, C. ZHENG, C. SHIN, H. SEO, S. W. CHA
Optimal control is generally not possible without information about the future coming up, and it is not easy toobtain an optimal solution even though the information is given a priori. In this paper, a control concept based on Pontryagin’sMinimum Principle (PMP) is introduced as an efficient solution to generate an optimal control trajectory for Hybrid ElectricVehicles (HVEs) when the performance of the vehicles is evaluated on scheduled driving cycles at a simulation level. Themain idea of the control concept is to minimize Hamiltonian, which is interpreted as equivalent fuel consumption, and theHamiltonian is characterized by a co-state, which is interpreted as a weighting factor for the electrical usage. A key aspect ofthe control problem is that an appropriate initial condition of the co-state is required to satisfy the boundary condition of theproblem. In this study, techniques to calculate the Hamiltonian in different hybrid configurations are introduced, and amethodology to look for the initial condition of the co-state is studied, so that the controller is able to realize a desired StateOf Charge (SOC) trajectory. To address the issue, we utilize a shooting method with multiple initial conditions based on theconcept of the Newton-Raphson method, and all these techniques are realized in a backward looking simulator. The simulationresults show that the PMP-based control is a very efficient approach to produce the optimal control trajectory, and theperformance is compared to the optimal solution solved by Dynamic Programming (DP).