Nonlinear Model Predictive Control for power-split Hybrid Electric Vehicles

In this paper, a causal optimal controller based on Nonlinear Model Predictive Control (NMPC) is developed for a power-split Hybrid Electric Vehicle (HEV). The global fuel minimization problem is converted to a finite horizon optimal control problem with an approximated cost-to-go, using the relationship between the Hamilton-Jacobi-Bellman (HJB) equation and the Pontryagin's minimum principle. A nonlinear MPC framework is employed to solve the problem online. Different methods for tuning the approximated minimum cost-to-go as a design parameter of the MPC are discussed. Simulation results on a validated high-fidelity closed-loop model of a power-split HEV over multiple driving cycles show that with the proposed strategy, the fuel economies are improved noticeably with respect to those of an available controller in the commercial Powertrain System Analysis Toolkit (PSAT) software and a linear time-varying MPC controller previously developed by the authors.

I. Introduction

A Hybrid Electric Vehicle (HEV) combines the mechanical energy produced by a combustion engine with the electrical energy of an energy storage system (usually a battery), hence providing extra degrees of freedom for operating the engine more efficiently. Another benefit of an HEV comes from its ability to capture the kinematic energy of the vehicle which is normally wasted during braking. Among different HEV configurations, the power-split type is the most versatile one having been used by several auto-makers. The Toyota Prius, Ford Escape, and Ford Fusion hybrids are all power-split HEVs currently in production. The versatility provided by a planetary gear set (a speed coupler) in a powerplit hybrid allows the engine operation to be completely decoupled from the vehicle motion. Also, the battery can assist the engine or it can store part of the mechanical energy from the engine or from braking. The challenge is to decide how to split the driver's demanded power between the engine and the battery and to select the system operation point such that the fuel consumption is minimized without sacrificing drivability.