Design and Comparative Analyses of Optimal Feedback Controllers for Hybrid Electric Vehicles

This paper presents an adaptive equivalent consumption minimization strategy (ECMS) and a linear quadratic tracking (LQT) method for optimal power-split control of a combustion engine and an electric machine in a hybrid electric vehicle (HEV). The objective is to deliver demanded torque and minimize fuel consumption and usage of service brakes, subject to constraints on actuator limits and battery state of charge (SOC). First, we derive a function for calculating maximum deliverable torque that is as close as possible to demanded torque and then reduce the number of control inputs to one while minimizing the usage of service brakes in the case of negative demanded torque. Next, we propose modeling SOC constraints by tangent or logarithm functions that provide an interior point to both the ECMS and the LQT. Then, we show that the resulting objective functions are convex, and we propose sub-optimal analytic solutions for the optimization problem by applying their second order approximation about a given reference. We also consider robustness of the controllers to measurement noise using a simple model of noise. Simulation results of the two controllers are compared, and their effectiveness is discussed.