Velocity Profile optimization of an Electric Vehicle (EV) with Battery Constraint Using Pontryagin's Minimum Principle (PMP)

Electric vehicles (EVs) powered by electric motors and batteries have solved the issues related to the environmental pollution. The major concern with electric vehicles is their short range, which is due to the limited capacity of a battery installed in the system. Limited range issue can be solved or minimized through eco-driving; an optimization technique in which a driver is advised to follow a velocity profile that consumes minimum energy. In the recent past, eco-driving problem with an online requirement using the static model of a battery has been discussed. Eco-driving problem has been formulated as an optimal control problem, where the goal is to minimize vehicle power consumption only. In this work, the goal is extended to increase the life cycle of battery along with power consumption. For this purpose, battery dynamics are included along with vehicle dynamics. To increase the battery's life cycle constraints are applied to avoid the battery from getting fully charged and discharged. Problem is solved using pontryagin's minimum principle (PMP), where initial and final position of a vehicle, initial velocity of a vehicle and total trip time is fixed. Optimal torque, optimized velocity trajectory and constrained state of charge during a trip are generated that in turn minimize the energy consumption of the battery. The results have shown that constrained case is approximately 7 percent more efficient in terms of energy consumption than an unconstrained case. Reduction in energy consumption, coupled with battery constraints result in proper charging and discharging of the battery thereby extending battery life.