Mathematical Problems in Engineering

Volume 2015, Article ID 318025, 15 pages

http://dx.doi.org/10.1155/2015/318025

## Model Predictive Control for Connected Hybrid Electric Vehicles

^{1}School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China^{2}College of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China^{3}Graduate School of Integrated Frontier Sciences, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 8190395, Japan

Received 25 May 2015; Revised 12 July 2015; Accepted 21 July 2015

Academic Editor: Xiaosong Hu

Copyright © 2015 Kaijiang Yu 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

This paper presents a new model predictive control system for connected hybrid electric vehicles to improve fuel economy. The new features of this study are as follows. First, the battery charge and discharge profile and the driving velocity profile are simultaneously optimized. One is energy management for HEV for ; the other is for the energy consumption minimizing problem of acc control of two vehicles. Second, a system for connected hybrid electric vehicles has been developed considering varying drag coefficients and the road gradients. Third, the fuel model of a typical hybrid electric vehicle is developed using the maps of the engine efficiency characteristics. Fourth, simulations and analysis (under different parameters, i.e., road conditions, vehicle state of charge, etc.) are conducted to verify the effectiveness of the method to achieve higher fuel efficiency. The model predictive control problem is solved using numerical computation method: continuation and generalized minimum residual method. Computer simulation results reveal improvements in fuel economy using the proposed control method.

#### 1. Introduction

In recent years, the energy and environmental problems are emphasized. In particular, energy consumption of vehicles accounts for a substantial amount in the transportation sector. There are various approaches to reduce the fuel consumption of vehicles [1–5]. High efficient vehicles are being developed to increase fuel economy using lightweight automobiles, efficient power train systems, electric vehicles, and hybrid vehicles [1]. On the other hand, the so-called ecodriving can also reduce the fuel consumption [5–9]. Ecodriving can be characterized as avoiding aggressive acceleration or braking at any road-traffic situations, cruising at steady speed, decelerating smoothly at stops with little or no braking, and maintaining an optimal distance from the preceding vehicle. An ecological control of a single vehicle on a road with up-down shapes [2] and efficient spacing control of multiple vehicles [10] were presented.

A lot of works have been published on the energy management problem of hybrid electric vehicle (HEV) and plug-in hybrid electric vehicle (PHEV) systems. These approaches are typical in a family of optimal control techniques. They can be subdivided into four categories: numerical optimization, analytical optimal control theories, instantaneous optimization, and heuristic control techniques [11]. The most representative of numerical optimization is dynamic programming (DP) [11, 12]. However DP is based on fixed speed patterns which are impossible to get in reality. A kind of analytical optimal control techniques is Pontryagin’s minimum principle [13]. It gives necessary conditions that the optimal solution must satisfy. It also needs to know the entire driving cycle in advance. The convex optimization method [14] is also a kind of analytical optimal control techniques. The global optimality is guaranteed and the optimal solution can be rapidly and efficiently attained by solvers available. The instantaneous optimization includes the equivalent consumption minimization strategy (ECMS) [2, 15]. It is based on instantaneous optimization and is easy to implement in real-time. However it cannot guarantee the optimality over the whole driving cycle. Heuristic control techniques like rule-based control strategies [2] are robust, but they are impossible to guarantee the optimality.

To obtain even more fuel economy improvements, connected hybrid electric vehicles can be considered to reduce the air resistance. The air resistance of a vehicle is proportional to the square of the vehicle speed. When a vehicle runs at 100 km/h, its aerodynamic drag reaches more than sixty percent of total motion resistance forces [16]. It is obvious that its air resistance causes high fuel consumption. However, the air resistance can be reduced by maintaining a short spacing between two vehicles. Connected vehicles in an automated highway system can lead to increased driver safety, decreased road congestion, and improved fuel economy [17]. Connected vehicles can improve fuel economy through reduced wind resistance [18–20].

A low pressure area distributes in the rear of the lead vehicle. The size of the area can be different by changing the spacing between the vehicles. If the following vehicle runs at the back of the lead vehicle with a short spacing, its air resistance is decreased owing to improved airflow profile between the vehicles. Furthermore, the air resistance of the lead vehicle is also decreased by the smooth airflow [20]. Therefore, fuel consumption of both vehicles can be reduced. However, it is difficult to follow the lead vehicle with a short spacing at high speed by a human driver. Automated cruise control of the vehicle should be introduced to achieve this. Various conventional longitudinal control systems have been proposed such as vehicle following method using information of other vehicles [10] and point following method using a certain decided phase point [21]. A control law for internal combustion engine vehicles is proposed which uses relative speed and spacing information from the preceding and following vehicles in order to choose the proper control action for smooth vehicle following and for maintaining a desired intervehicle spacing specified by the driver [22]. Connected automatic guided electric vehicles to solve problems of traffic saturation, relying on GPS sensors and intervehicle communication, are addressed in [23]. However, these conventional methods consider string stability only. The quantitative effect of road shape and air resistance on fuel consumption for hybrid electric vehicles (HEVs) has not been researched.

For connected hybrid electric vehicles, it is necessary to compute the optimum control inputs of the vehicles by anticipating the future situations including road shape, vehicles’ states, and road loads. Therefore, model predictive control (MPC) method can be used.

This paper extends HEV energy management research by adding two novel contributions. First, the battery charge and discharge profile and the driving velocity profile are simultaneously optimized. We make the two connected problems together: one is energy management for HEV for the battery; the other is for the energy consumption minimizing problem of speed control of two vehicles. In reality, the two connected problems are coupled together and affect each other always. The speed of the vehicle affects the charge and discharge profile of the battery. The charge and discharge profile of the battery affects the speed of the vehicle. Second, a new policy between the global optimization method and the instantaneous optimization method is developed. The global optimization method like dynamic programming needs all the information in the future to compute the global optimal control input. The instantaneous optimization method needs no information in the future to compute the control input. The easiest way to deal with the complicated control system is to divide the longitudinal vehicle control system into an upper and lower level controller. The upper level controller determines the desired acceleration of the vehicle on the basis of the position and velocity relative to the other vehicles in the string. The lower level controller determines the input commands to the engine and the braking system, to accomplish the desired acceleration. Also, there is possible to consider road slope, wind, and so forth as a disturbance for the problem. However, in this work we intended to optimize the fuel economy and the speed profile for high fuel efficiency and safety simultaneously. In the HEV operation it is desirable to charge or discharge the battery properly according to the road loads. There is a problem between the fast dynamics components like the engine and the slow dynamics components like the battery. The prediction horizon of the battery state is limited. We developed a new policy to predict the battery state in a longer future for better performance. The desired battery state of charge is designed according to the road slopes for better recuperation of free braking energy. The battery state of charge profile is scheduled systematically to improve fuel economy inside the HEV considering the effect of different parameters, that is, road conditions, battery state of charge, and real-time implementation ability. The quantitative analysis of the vehicle spacing influence and the battery state of charge profile influence for the fuel economy is presented. Performance of the proposed system has been evaluated by computer simulation. The proposed system is found to be more fuel efficient and safer for running over several typical roads with up-down slopes.

The rest of this paper is organized as follows. In Section 2, the nonlinear model of two connected power-split HEVs is derived. Section 3 formulates the nonlinear model predictive control algorithm. Section 4 presents comparative simulation results. Section 5 provides conclusions.

#### 2. Modeling of Two Connected HEVs

The configuration of the HEV system is shown in Figure 1. FD represents the final drive. The power-split device (PSD) is the key component of the power-split HEV system and has both functionality of speed coupler and continuously variable transmission (CVT). There are five dynamic components: the engine, the battery, two motor/generators (), and the wheels in this power-split HEV system. The only dynamic state to be considered in the optimal control problem based on known driving cycle is the battery state of charge (SOC) which can simplify the MPC algorithm for implementation. This simplification is possible because this paper introduces four constraints: the road load, the torque and speed relationship of the speed coupler, the power flow relationship among the five components, and the engine optimal operating line (OOL) using CVT. In this work, we assume that the engine works along its OOL using CVT. For simplicity, we assume the two vehicle configurations are the same. It is assumed that the central controller set in the lead vehicle controls the two vehicles. The central controller computes the control inputs of the two vehicles. The control inputs of the two vehicles are fed into the two vehicles, respectively. The states of the two vehicles are measured and sent to the central controller. In this way a closed control loop is formed. Here, we call it central control system of connected vehicles. In a distributed control system of connected vehicles [18–20], the individual vehicles are controlled separately by its own controller. It cannot predict other vehicles precisely. In a central control system of connected vehicles, all the information of the vehicles is shared, and the global optimality of all the vehicles can be obtained. The distance between the two vehicles changes (which affect the air drag coefficient) and the slope changes; therefore the stability of this controller is very important. However, the control scheme proposed in this work is brand new; the stability of this controller is completely different from that of the distributed control system of connected vehicles. Hence, we would like to add the stability problem as our future directions because of its complexity. The control signals are transmitted to the vehicles through intervehicle communication. It is assumed that there is no delay of the communication. The proposed methodology will work independently of other kinds of vehicles on the roadway in the network if the vehicle has the functionality of CVT. This paper divided the optimal control problem into two levels. The high-level controller determines the optimal battery power and the low-level controller determines the optimal torque and speed of the engine and the motor/generators. This paper focuses on the high-level controller.