Mathematical Problems in Engineering

Volume 2017, Article ID 3095347, 13 pages

https://doi.org/10.1155/2017/3095347

## Design and Validation of Real-Time Optimal Control with ECMS to Minimize Energy Consumption for Parallel Hybrid Electric Vehicles

^{1}School of Mechatronics, Northwestern Polytechnical University, Xi’an 710072, China^{2}Henan Collaborative Innovation Center of Machinery Equipment Advanced Manufacturing, Henan University of Science and Technology, Luoyang 471003, China^{3}School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang 471003, China^{4}School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China

Correspondence should be addressed to Xiaozhong Deng; nc.ude.tsuah@duolcelgae

Received 27 September 2016; Accepted 13 December 2016; Published 26 January 2017

Academic Editor: Michele Betti

Copyright © 2017 Aiyun Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A real-time optimal control of parallel hybrid electric vehicles (PHEVs) with the equivalent consumption minimization strategy (ECMS) is presented in this paper, whose purpose is to achieve the total equivalent fuel consumption minimization and to maintain the battery state of charge () within its operation range at all times simultaneously. Vehicle and assembly models of PHEVs are established, which provide the foundation for the following calculations. The ECMS is described in detail, in which an instantaneous cost function including the fuel energy and the electrical energy is proposed, whose emphasis is the computation of the equivalent factor. The real-time optimal control strategy is designed through regarding the minimum of the total equivalent fuel consumption as the control objective and the torque split factor as the control variable. The validation of the control strategy proposed is demonstrated both in the MATLAB/Simulink/Advisor environment and under actual transportation conditions by comparing the fuel economy, the charge sustainability, and parts performance with other three control strategies under different driving cycles including standard, actual, and real-time road conditions. Through numerical simulations and real vehicle tests, the accuracy of the approach used for the evaluation of the equivalent factor is confirmed, and the potential of the proposed control strategy in terms of fuel economy and keeping the deviations of at a low level is illustrated.

#### 1. Introduction

Hybrid electric vehicles (HEVs) are most promising among all the new energy vehicles including battery electric vehicles and fuel cell vehicles to better fuel economy and emissions without compromising vehicle performances [1, 2]. In the last few decades, many automobile manufacturers have been researching HEVs and have obtained several configurations for practical applications [3, 4]. There are many methods to improve fuel economy of HEVs, such as optimizing their mechanical construction, matching the powertrain parameters, and lighting the body. This paper will optimize the energy management strategy, which distributes the total torque demanded at wheels between the ICE and the electric motor (EM) to minimize the fuel consumption and maintain the battery state of charge (SOC) simultaneously.

Many energy management strategies have been proposed for efficient energy usage, which can be classified into four types, namely, the rule-based control strategy, the global optimal strategy, the real-time optimization control strategy, and the fuzzy logic control strategy. The rule-based control strategy sets the initial value of the parameters by mostly relying on engineering experience and then adjusts these parameters by adopting the trial-and-error method. Although this strategy can offer a prominent improvement in energy efficiency and is also adopted widely in the commercial HEV, it is clear that the strategy does not guarantee an optimal value in all cases or allow the vehicle to run at maximum efficiency when the parameters are fixed [5, 6]. Although the fuzzy logic control strategy is good at dealing with model uncertainty and complex decisions, the formulation of its fuzzy rules is lack of system approach and mainly depends on engineering experience, which leads to loss of control accuracy [7, 8].

The papers [9, 10] propose a global optimal strategy based on dynamic programming methods for parallel hybrid electric vehicles (PHEVs) and parallel-series HEV, respectively. These techniques can find a global optimal solution to the control parameters, such as the ICE/EM torque, but cannot offer an online solution because they assume that the future driving cycle is entirely known. This method can be a good analysis and assessment tool for other control strategies. However, due to computational complexity, it is not easily implemented for practical applications.

Due to the causal nature of global optimization technique, it is not suitable for real-time analysis, because the main aim of the real-time analysis is to reduce global criterion to an instantaneous optimization by introducing a cost function that depends only on the present state of the system parameters [11, 12]. Moreover, global optimization technique does not consider variations of battery in the problem. Hence, in order to derive cost functions for instantaneous optimization of power split, while maintaining battery , real-time optimization is performed.

The real-time control strategy is based on instantaneous optimization and defines a cost function which is guaranteed to be minimum at each instant depending upon system current variables. Various attempts have been made to propose real-time control based on instantaneous optimization [13–15]. The more promising approach of the real-time optimization is used in [16], which is defined as equivalent consumption minimization strategy (ECMS). Its cost function is a sum of the ICE fuel consumption and the EM equivalent fuel consumption. To be distinguished, the real-time control strategy without ECMS is defined as the simpler real-time strategy.

The ECMS is supposing that the energy consumption from the battery at present is supplemented by the ICE in the future. Thus, battery discharging at any time is equivalent to fuel consumption of the ICE in the future. Due to the small computational time, near-optimal characteristics, and the feasibility of online implementation, ECMS has widely been used to address the energy management control problem for both HEVs [17, 18] and PHEVs [19, 20]. The key problem of the ECMS design is the calculation of the equivalent factor between fuel and electrical energy based on the available vehicle information, because it has a major influence on the fuel economy and the charge sustainability of PHEVs.

In this paper, a real-time control strategy with ECMS for a PHEV is proposed, which is based on a new method for evaluating the equivalent factor between fuel and electrical energy in order to regulate SOC at a constant reference point with the minimum fuel consumption simultaneously. Based on the models established of the PHEV, computation and optimization of the total equivalent fuel consumption are discussed in detail in the paper.

The remainder of this paper is organized as follows. Section 2 introduces the vehicle configuration and models of the parallel hybrid electric vehicle. Section 3 then describes the novel ECMS algorithm. The design of the real-time optimal control is presented in Section 4. Validation of the control strategy proposed and optimization results are discussed in Section 5. Section 6 highlights this paper’s key conclusions.

#### 2. Configuration and Models of the PHEV

##### 2.1. Configuration of the PHEV

The principal schematic of the PHEV is shown in Figure 1. Both the output torque of the ICE and the EM are coupled by the torque coupling mechanism (TCM), whose output torque is then transmitted into the gearbox and final drive, through which the vehicle is ultimately propelled. A friction clutch is located between the ICE and the TCM, and an autoclutch is located between the EM and the TCM. The main component specifications of the hybrid powertrain system are listed in Table 1.