Optimal Control Strategy for BEV with CVT Using Dynamic Programming Method
Authors: Hanqing Zhao, Yasuo Moriyoshi, Tatsuya Kuboyama
Abstract
Battery electric vehicles (BEVs) equipped with high-speed, low-torque motors can benefit greatly from the use of continuously variable transmissions (CVTs). This study aims to reduce energy consumption by adjusting the CVT ratio to ensure that the motor operates in its optimal efficiency range during both traction and regenerative braking, while delivering the required power with minimal power loss. A detailed mathematical model of a dual motor, single CVT EV powertrain and transmission structure was developed to establish an optimal control problem aimed at minimizing energy consumption. Three methods were compared to evaluate their effectiveness: (1) The basic simulation method, which directly uses the existing control map to control the CVT ratio based on torque, vehicle speed, and motor speed; (2) The steady-state method, which searches all possible CVT ratio and torque combinations at each instant to find the most efficient combination for the required speed, and then performs simulation based on the stored results; (3) The dynamic programming (DP) method, which applies Bellman's optimality principle to determine the cumulative optimal control combinations for all SOC states and generates an optimal control map for simulation.
The results demonstrate the optimal control strategy for both single motor CVT and dual motor CVT configurations under the WLTC driving cycle. The optimal solutions were used to improve the control map, achieving improved overall efficiency, reduced SOC depletion and maintaining real-time applicability.
This research demonstrates the potential of CVT-equipped EVs and provides effective improvement strategies through improved control maps, ensuring feasible control implementation to improve efficiency and reduce SOC depletion.
Keywords: Electric Vehicles, Continuously Variable Transmission, Dynamic Programming, Optimal Control, Energy Efficiency, Real-Time Control