Model predictive control of hybrid electric vehicles for fuel economy, emission reductions, and inter-vehicle safety in car-following scenarios

Model predictive control of hybrid electric vehicles for fuel economy, emission reductions, and inter-vehicle safety in car-following scenarios

Journal Pre-proof Model predictive control of hybrid electric vehicles for fuel economy, emission reductions, and inter-vehicle safety in car-followin...

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Journal Pre-proof Model predictive control of hybrid electric vehicles for fuel economy, emission reductions, and inter-vehicle safety in car-following scenarios

Xiaosong Hu, Xiaoqian Zhang, Xiaolin Tang, Xianke Lin PII:

S0360-5442(20)30208-5

DOI:

https://doi.org/10.1016/j.energy.2020.117101

Reference:

EGY 117101

To appear in:

Energy

Received Date:

17 November 2019

Accepted Date:

04 February 2020

Please cite this article as: Xiaosong Hu, Xiaoqian Zhang, Xiaolin Tang, Xianke Lin, Model predictive control of hybrid electric vehicles for fuel economy, emission reductions, and inter-vehicle safety in car-following scenarios, Energy (2020), https://doi.org/10.1016/j.energy.2020.117101

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Journal Pre-proof Model predictive control of hybrid electric vehicles for fuel economy, emission reductions, and inter-vehicle safety in car-following scenarios Xiaosong Hua, *, Xiaoqian Zhanga, Xiaolin Tanga, *, Xianke Linb aState

Key Laboratory of Mechanical Transmissions, Department of Automotive Engineering, Chongqing University, Chongqing 400044, China bDepartment of Automotive, Mechanical and Manufacturing Engineering, University of Ontario Institute of Technology, 2000 Simcoe St N, Oshawa, ON L1G 0C5, Canada *Corresponding

author. State Key Laboratory of Mechanical Transmissions, Department of Automotive Engineering, Chongqing University, Chongqing 400044, China E-mail address: [email protected] (X. Tang); [email protected] (X. Hu);

Abstract: This paper develops a model predictive multi-objective control framework for HEVs in car-following scenarios to investigate the interplay between fuel economy, vehicle exhaust emissions, and inter-vehicle safety. Specifically, an MPC-based controller is developed to optimize the vehicle speed and engine torque for better fuel economy and fewer exhaust emissions while ensuring inter-vehicle safety. The engineout emission model and its impact on energy management are considered in the optimization. The proposed controller is evaluated at different driving conditions, such as urban driving and highway driving. The proposed controller is compared with conventional controllers used in ADVISOR. The comparison results demonstrate that the proposed controller can reduce fuel consumption by 10.49%, CO by 48.02%, HC by 55.38%, and NOx by 22.79% in the UDDS driving cycle. Keywords: Model predictive control, intelligent transportation system, car-following, energy-saving, vehicle-out emissions.

1

Journal Pre-proof Nomenclature ๐‘ ๐‘“ location of the following vehicle ๐‘ฃ๐‘“ velocity of the following vehicle ๐‘‡๐‘  sampling time ๐‘Ž๐‘“ acceleration of the vehicle ๐‘‡๐‘‘ torque demand at wheels ๐‘š๐‘ฃ vehicle mass gravitational constant ๐‘” rolling resistance coefficient ๐‘“ road slope ๐œƒ air density ฯ projected frontal area ๐ด ๐ถ๐ท air drag coefficient ๐‘Ÿ๐‘ค wheel radius engine torque motor torque AMT gear ratio final drive ratio AMT efficiency ๐‘ ๐‘–๐‘”๐‘› sign function ๐‘‡๐‘๐‘Ÿ๐‘˜ braking torque ๐‘š๐‘“๐‘ instantaneous fuel consumption ๐‘ƒ๐‘’๐‘›๐‘” engine power ๐‘„๐ต๐‘†๐น๐ถ fuel consumption rate ๐œ”๐‘’๐‘›๐‘” engine speed ๐‘š๐ป๐ถ instantaneous engine-out HC ๐‘š๐ถ๐‘‚ instantaneous engine-out CO ๐‘š๐‘๐‘‚๐‘ฅ instantaneous engine-out NOx ๐‘ƒ๐‘’๐‘š motor power ๐‘‡๐‘’๐‘š motor torque ๐œ”๐‘’๐‘š motor speed ๐œ‚๐‘’๐‘š motor efficiency ๐‘‡๐‘’๐‘›๐‘” ๐‘‡๐‘’๐‘š ๐‘–๐‘” ๐‘–0 ๐œ‚๐‘‡

๐‘ƒ๐‘๐‘Ž๐‘ก SoC ๐‘‰๐‘๐‘Ž๐‘ก ๐‘…๐‘๐‘Ž๐‘ก ๐‘„๐‘๐‘Ž๐‘ก ๐ฟ๐‘š๐‘–๐‘› ๐ฟ๐‘š๐‘Ž๐‘ฅ L๐‘™๐‘ ๐‘œ๐‘๐‘ก L๐‘ข๐‘ ๐‘œ๐‘๐‘ก L ๐ฝ๐‘  ๐‘ ๐‘’ ๐‘š๐‘’๐‘š ๐œ‚๐ธ๐‘€ ๐ฝ๐‘’๐‘๐‘œ ๐ฝ๐‘’๐‘š๐‘–๐‘  ๐ฝ๐‘œ๐‘๐‘ก ฮป ๐›ฝ N๐‘

battery power state of charge open-circuit voltage of the battery internal resistance of the battery battery capacity minimal inter-vehicle distance maximal inter-vehicle distance lower bound of optimal following zone upper bound of optimal following zone allowable tracking range driving safety cost equivalence factor instantaneous equivalent fuel consumption of motor average generation efficiency fuel economy cost vehicle emission cost overall cost weighting factor for ๐ฝ๐‘’๐‘๐‘œ weighting factor for ๐ฝ๐‘’๐‘š๐‘–๐‘ 

length of the receding horizon ๐œ”๐‘’๐‘›๐‘”,๐‘š๐‘–๐‘› minimum engine speed ๐œ”๐‘’๐‘›๐‘”,๐‘š๐‘Ž๐‘ฅ maximum engine speed ๐‘‡๐‘’๐‘›๐‘”,๐‘š๐‘–๐‘› minimum engine torque ๐‘‡๐‘’๐‘›๐‘”,๐‘š๐‘Ž๐‘ฅ maximum engine torque ๐œ”๐‘’๐‘š,๐‘š๐‘–๐‘› minimum motor speed ๐œ”๐‘’๐‘š,๐‘š๐‘Ž๐‘ฅ maximum motor speed ๐‘‡๐‘’๐‘š,๐‘š๐‘–๐‘› minimum motor torque ๐‘‡๐‘’๐‘š,๐‘š๐‘Ž๐‘ฅ maximum motor torque ๐‘Ž๐‘“,๐‘š๐‘–๐‘› minimum acceleration of the vehicle ๐‘Ž๐‘“,๐‘š๐‘Ž๐‘ฅ maximum acceleration of the vehicle ๐‘“(๐‘‡๐‘’๐‘›๐‘”,๐œ”๐‘’๐‘›๐‘”) instantaneous engine-out emissions rate

2

Journal Pre-proof 1. INTRODUCTION A. Motivations and Technical Challenges Uncertainty in future oil supply, growing environmental awareness, and stricter standards for carbon footprint and toxic exhaust emissions provide a strong impetus for the development of sustainable transportation systems [1,2]. To alleviate growing concerns about global warming and air pollution, almost all global automakers are investing heavily in developing eco-friendly vehicles [3,4]. Hybrid electric vehicles (HEVs) have lower energy consumption and fewer harmful emissions than conventional fuel-powered vehicles due to the additional freedom provided by reversible energy storage devices and electric machines [5,6]. In HEVs, the energy management strategy (EMS) has a significant impact on fuel economy. The design and performance of EMS are affected by several external factors, such as traffic conditions, future traffic information, and road conditions [7,8]. Meanwhile, researchers are developing technologies for connected and automated vehicles (CAVs). These technologies enable vehicles to share and exchange information about current traffic conditions through inter-vehicle communications and vehicle-to-infrastructure (V2I) communications [9]. Fuel economy and vehicle performance can be further improved by developing EMSs based on the useful information provided by CAV technologies [10]. In this paper, by combining EMS and adaptive cruise control (ACC), inter-vehicle safety, fuel economy, and vehicle exhaust emissions are optimized in the car-following scenario. It is very important to develop a control framework that addresses the problems of inter-vehicle safety, fuel economy, 3

Journal Pre-proof and emission control simultaneously. It is a huge challenge for the traditional heuristic methods to optimize this constrained multi-objective problem in the car-following scenario. B. Literature Review In recent decades, various EMSs have been proposed for HEVs. There are mainly three categories of EMSs, namely heuristic/rule-based approaches, optimization-based approaches, and data-driven approaches [11]. An important advantage of rule-based methods is their excellent performance in real-time implementations. Unlike optimizations, a rule-based method uses a set of rules to determine the control actions at every time step, which is largely dependent on human expertise and intuitions. In optimization-based approaches, analytical or numerical optimization algorithms are used to determine the optimal control actions [12]. There is a trade-off between optimality and real-time performance. To fully explore the potential of HEVs, optimization-based control strategies can reduce dependence on expert experience and further improve vehicle performance. Optimization-based approaches include: 1) global optimization methods, such as dynamic programming (DP) [13], convex programming, and Pontryaginโ€™s minimum principle (PMP); and 2) instantaneous optimization methods, such as equivalent consumption minimization strategy (ECMS) and model predictive control (MPC). Moreover, data-driven approaches, such as particle swarm optimization (PSO) [14], genetic algorithm (GA) [15], simulated annealing (SA) [16], and machine learning (ML) [17], are also used in EMSs. DP can achieve global optimality, but it requires a priori information about the driving cycle 4

Journal Pre-proof and has high computational costs. Therefore, DP is usually implemented offline and used for benchmarking. ECMS is more suitable for real-time applications because it determines the control actions at each time step with a much lower computational cost. Unlike ECMS, MPC [18] solves the optimal problem over a finite receding horizon. With proper parameter tuning, MPC can achieve performance close to DP. In ACC, the speed of the vehicle is changed by adjusting the throttle or applying brakes based on the behavior of the leading car [19]. Researchers have recently worked on combining ACC and EMS to further improve inter-vehicle safety and energy saving. For instance, Luo et al [20] developed a non-linear MPC-based ACC for intelligent HEVs to achieve inter-vehicle safety, ride comfort and energy saving. In Ref [21], an active distance control strategy for driving safety, fuel economy, and driving comfort is proposed. In order to improve real-time performance and driving comfort, a hierarchical control structure is adopted. In this controller, driving safety and driving comfort are decoupled from the fuel economy. The first layer of the controller uses the DP algorithm to solve the multi-level constrained problem. Akhegaonkar et al. [22] applied a safe and efficient ACC-EMS to a hybrid electric vehicle, where ACC serves as a high-level controller to regulate the speed, and ECMS is the lower controller to determine the optimal power split ratio for energy saving. However, ACC and EMS are simply combined in series in their study. Li et al. [23] fused these two controllers in a smart-HEV to optimize fuel consumption while ensuring a safe headway spacing in the car-following scenario. The results showed a better overall performance of ACC and EMS. However, the speed profiles of their leading vehicles were predefined, which is 5

Journal Pre-proof not the case in reality. Xie et al. [24] used an artificial neural network to predict the front vehicle speed and optimized the SoC (state of charge) trajectory based on the predicted speed. The combined optimization of inter-vehicle safety and energy saving for a PHEV was then performed in the car-following scenario. Moreover, Sakhdari et al. [25] designed an ecological ACC system for plug-in hybrid electric vehicles (PHEVs) to optimize energy cost, driving safety and comfort. Their controller uses the traffic data from V2I communication to predict the front vehicle speed. The above studies have considered fuel economy in their adaptive cruise control designs. However, these studies ignored engine emissions. With the ever-tighter emission standards for environmental protection, reducing the toxic exhaust emissions, such as hydrocarbon (HC), carbon monoxide (CO) and nitrogen oxide (NOx), is becoming increasingly important. Fuel-efficient engine operating points do not necessarily result in low emissions. Therefore, it is very important to develop a control framework that achieves both fuel-saving and emission reduction. In order to solve the privacy problem in V2V communication, Zhang et al. [26] proposed a novel perturbation mechanism to ensure the privacy of communication. Their controller optimizes communication privacy, fuel consumption, and emission reduction simultaneously. However, this controller was designed for fuel-powered vehicles, not hybrid vehicles. To fully explore the energysaving potential of HEVs, this paper develops a multi-objective framework that addresses the problems of inter-vehicle safety, fuel-saving, and emission reduction for a parallel HEV in the car-following scenario. As mentioned earlier, the performance of EMS is affected by several external factors, 6

Journal Pre-proof including future traffic conditions. In ACC, MPC can use traffic information from V2V communications to optimize future vehicle speeds, thereby improving fuel economy and reducing emissions. Therefore, MPC is widely used in ACC-based EMSs. The multi-objective framework proposed in this paper is also based on MPC. The cost function is a weighted sum of inter-vehicle safety, fuel consumption, and engine emissions. Different weighting factors are examined to determine the optimal value for overall performance. C. Contributions The main purpose of this paper is to build a model predictive multi-objective control framework for fuel-saving and emission reduction while ensuring inter-vehicle safety in the car-following scenario. The effectiveness of the proposed method is demonstrated. The following three contributions are made. 1) First, a nonlinear model predictive multi-objective control framework is developed for a parallel hybrid electric vehicle in the car-following scenario, where inter-vehicle safety, fuel economy, and vehicle emissions are optimized simultaneously. 2) Second, tradeoffs between fuel economy and emissions are investigated. Different weighting factors for emissions are examined to determine an optimal value for better overall performance. 3) Third, comparisons with different vehicle models from ADVISOR are made to further demonstrate the improved performance of our method in terms of energy-saving and emission reduction. D. Outline of the paper 7

Journal Pre-proof The remainder of the paper is organized as follows: Section 2 introduces the modeling of a car-following system; the model predictive multi-objective control framework is formulated in Section 3, which considers inter-vehicle safety, fuel economy, and emissions; followed by the analysis of weighting factors, optimization results under different traffic conditions, and comparison results in Section 4; conclusions are drawn in Section 5. 2. CAR-FOLLOWING MODEL The car-following scenario considered in the study consists of two consecutive vehicles, i.e., a preceding vehicle and a following/host vehicle. The host vehicle is a single-shaft parallel HEV with a 63kW/1.9L gasoline engine, a 49kW electric motor (EM), an automatic mechanical transmission (AMT) and a battery pack [23]. The powertrain architecture is shown in Fig 1, and key parameters are listed in Table 1.

Fig.1. Powertrain configuration of the host vehicle.

8

Journal Pre-proof Table 1 Vehicle parameters [23]. Components

Specifications

Engine

FC_SI631 (ADVISOR) Displacement: 1.9 L

Electric Machine

MC_PM49 (ADVISOR) Maximum power: 49 kW

AMT

Gear ratio: [3.79, 2.17, 1.41, 1, 0.86]

Battery pack

ESS_NIMH61 (ADVISOR) Capacity: 13 Ah Nominal voltage: 288 V

1The

model data are from ADVISOR.

A. Longitudinal Dynamics of The Host Vehicle The discrete-time nonlinear longitudinal dynamics of the host vehicle can be formulated as follows, 1

๐‘ ๐‘“,๐‘˜ + 1 = ๐‘ ๐‘“,๐‘˜ + ๐‘ฃ๐‘“,๐‘˜ โ‹… ๐‘‡๐‘  + 2 โ‹… ๐‘Ž๐‘“,๐‘˜ โ‹… ๐‘‡2๐‘ 

(1)

๐‘ฃ๐‘“,๐‘˜ + 1 = ๐‘ฃ๐‘“,๐‘˜ + ๐‘Ž๐‘“,๐‘˜ โ‹… ๐‘‡๐‘ 

(2)

where the subscript ๐‘“ denotes the following vehicle, ๐‘˜ denotes time step, ๐‘ ๐‘“ is the location, ๐‘ฃ๐‘“ is the velocity, ๐‘‡๐‘  is the sampling time, and ๐‘Ž๐‘“ is the acceleration. The vehicle torque demand at wheels can be calculated by 1

๐‘‡๐‘‘ = (๐‘š๐‘ฃ๐‘”๐‘“๐‘๐‘œ๐‘ ๐œƒ + ๐‘š๐‘ฃ๐‘”๐‘ ๐‘–๐‘›๐œƒ + 2๐œŒ๐ด๐ถ๐ท๐‘ฃ2๐‘“,๐‘˜ + ๐‘š๐‘ฃ๐‘Ž๐‘“,๐‘˜) โ‹… ๐‘Ÿ๐‘ค

(3)

where ๐‘“ and ๐ถ๐ท are coefficients of the rolling resistance and the aerodynamic drag,

9

Journal Pre-proof respectively, ๐‘š๐‘ฃ is the vehicle mass, ๐ด is the projected frontal area, ๐œŒ is the air density, ๐‘” is the gravitational constant, ๐œƒ is the road slope, ๐‘Ÿ๐‘ค is the wheel radius. For the HEV in Fig.1, it can be propelled by the engine and the electric motor, together or separately. Therefore, the torque demand ๐‘‡๐‘‘ at the wheels is expressed by (

)

๐‘‡๐‘’๐‘š ๐‘‡๐‘‘ = (๐‘‡๐‘’๐‘›๐‘” + ๐‘‡๐‘’๐‘š)๐‘–๐‘”๐‘–0๐œ‚๐‘ ๐‘–๐‘”๐‘› + ๐‘‡๐‘๐‘Ÿ๐‘˜ ๐‘‡

(4)

where ๐‘‡๐‘’๐‘›๐‘” and ๐‘‡๐‘’๐‘š are the engine torque and the motor torque, respectively, ๐‘–๐‘” is the AMT ratio, ๐‘–0 is the final drive ratio, and ๐œ‚๐‘‡ represents the transmission efficiency, which is assumed to be a constant. For simplicity, the transmission gear ratio ๐‘–๐‘” is assumed to be the function of ๐‘ฃ๐‘“, and ๐‘‡๐‘๐‘Ÿ๐‘˜ is the braking torque and always 1 ๐‘‡๐‘’๐‘š > 0 negative, with ๐‘ ๐‘–๐‘”๐‘›(๐‘‡๐‘’๐‘š) = โ€•1๐‘‡ < 0 being a sign function. ๐‘’๐‘š

{

B. Engine Fuel Consumption Model and Engine-Out Emission Model CRUISE (developed by AVL), PSAT, and ADVISOR are commonly used simulation platforms to study vehicle dynamics performance, fuel economy, and emissions. These platforms provide great models for many important components in the vehicle, such as fuel converters, energy storage devices, transmissions, and vehicle dynamics models. Therefore, they are used by many researchers [27,28]. For instance, Zhang et. al [29] improved the HEV simulation accuracy by integrating Matlab/Simulink and AVL. In their study, an EMS was developed based on the powertrain and transmission models from AVL CRUISE. The results demonstrated the effectiveness of their proposed controller. In our study, the hybrid vehicle model is built based on the component models from ADVISOR A brake specific fuel consumption (BSFC) map in Fig.2 is used to calculate the fuel 10

Journal Pre-proof consumption rate, i.e., ๐‘„๐ต๐‘†๐น๐ถ(๐‘‡๐‘’๐‘›๐‘”,๐œ”๐‘’๐‘›๐‘”). It is a look-up table of the normalized fuel consumption rate as a function of the instantaneous engine torque ๐‘‡๐‘’๐‘›๐‘” and speed ๐œ”๐‘’๐‘›๐‘”. The fuel consumption per second ๐‘š๐‘“๐‘(๐‘”/๐‘ ), therefore, can be obtained as follows, ๐‘š๐‘“๐‘ =

๐‘ƒ๐‘’๐‘›๐‘” โ‹… ๐‘„๐ต๐‘†๐น๐ถ(๐‘‡๐‘’๐‘›๐‘”,๐œ”๐‘’๐‘›๐‘”)

(5)

3.6 ร— 106

where ๐‘ƒ๐‘’๐‘›๐‘” denotes the engine power.

Engine Torque Te [Nm]

160

BSFC [g/kWh] Maximum Torque

140 120 100 80 60 40 20 1000

2000

3000

4000

5000

Engine Speed e [rpm]

Fig. 2. BSFC map of the 63 kW/1.9L engine from ADVISOR. Similar to the engine fuel consumption model, the engine emission model used in this study also has a three-dimensional look-up table. In this look-up table, the engineout emissions rate, i.e. ๐‘“(๐‘‡๐‘’๐‘›๐‘”,๐œ”๐‘’๐‘›๐‘”) [๐‘”/๐‘˜๐‘Šโ„Ž], is determined by engine torque and engine speed. The pollutants, such as HC, CO and NOx, can be obtained according to the following equations,

{

๐‘š๐ป๐ถ = ๐‘š๐ถ๐‘‚ = ๐‘š๐‘๐‘‚๐‘ฅ =

๐‘ƒ๐‘’๐‘›๐‘” โ‹… ๐‘“๐ป๐ถ(๐‘‡๐‘’๐‘›๐‘”,๐œ”๐‘’๐‘›๐‘”) 3.6 ร— 106 ๐‘ƒ๐‘’๐‘›๐‘” โ‹… ๐‘“๐ถ๐‘‚(๐‘‡๐‘’๐‘›๐‘”,๐œ”๐‘’๐‘›๐‘”) 3.6 ร— 106 ๐‘ƒ๐‘’๐‘›๐‘” โ‹… ๐‘“๐‘๐‘‚๐‘ฅ(๐‘‡๐‘’๐‘›๐‘”,๐œ”๐‘’๐‘›๐‘”) 3.6 ร— 106

11

(6)

Journal Pre-proof where ๐‘š๐ป๐ถ, ๐‘š๐ถ๐‘‚ and ๐‘š๐‘๐‘‚๐‘ฅ are the instantaneous engine-out emissions, and their unit is g/s. C. EM Model As shown in Fig.3, the efficiency ๐œ‚๐‘’๐‘š of the electric machine is a function of the torque ๐‘‡๐‘’๐‘š and speed ๐œ”๐‘’๐‘š. The EM works as a motor (ฮฑ = 1) during driving or a generator (ฮฑ = โ€•1) during braking. The power to the EM can be represented by ๐‘ƒ๐‘’๐‘š = ๐‘‡๐‘’๐‘š โ‹… ๐œ”๐‘’๐‘š โ‹… ๐œ‚๐›ผ๐‘’๐‘š(๐‘‡๐‘’๐‘š,๐œ”๐‘’๐‘š)

(7)

300 Efficiency [% ] Maximum Torque

Motor Torque Tem [Nm]

250 200 150 100 50 0 -50 -100 -150 0

2000

4000

6000

8000

Motor Speed em [rpm]

Fig. 3. Efficiency map of the electric machine from ADVISOR.

D. Battery Model The electrical power to the EM is provided by the battery, i.e., ๐‘ƒ๐‘๐‘Ž๐‘ก = ๐‘ƒ๐‘’๐‘š. The battery SoC is considered as a state variable in the proposed controller[30], and an equivalent electric circuit is used to model the dynamics of the battery [31] as follows, ๐‘†๐‘œ๐ถ๐‘˜ + 1 = ๐‘†๐‘œ๐ถ๐‘˜ โ€•

๐‘‰๐‘๐‘Ž๐‘ก โ€• ๐‘‰2๐‘๐‘Ž๐‘ก โ€• 4๐‘…๐‘๐‘Ž๐‘ก๐‘ƒ๐‘๐‘Ž๐‘ก,๐‘˜ 2๐‘…๐‘๐‘Ž๐‘ก๐‘„๐‘๐‘Ž๐‘ก

12

โ‹… ๐‘‡๐‘ 

(8)

Journal Pre-proof where ๐‘‰๐‘๐‘Ž๐‘ก is the open-circuit voltage, ๐‘…๐‘๐‘Ž๐‘ก is the internal resistance and ๐‘„๐‘๐‘Ž๐‘ก is the battery capacity. 3. MODEL PREDICTIVE MULTI-OBJECTIVE CONTROL FRAMEWORK In this section, the model predictive multi-objective control framework is developed to achieve optimal overall performance by optimizing trade-offs between tracking safety, energy-saving, and emission reduction during the car-following process. The EMS problem is formulated as a constrained nonlinear control system and is then solved by model predictive control. The performance indices for optimization are introduced below. 3.1. Driving safety index Based on Ref [23], the allowable tracking range ๐ฟ(๐ฟ = ๐‘ ๐‘™ โ€• ๐‘ ๐‘“) for the following vehicle should vary between a minimum and maximum, where ๐‘ ๐‘™ and ๐‘ ๐‘“ are the location of the leading vehicle and following vehicle. The minimal and maximal intervehicle distance, i.e., ๐ฟ๐‘š๐‘–๐‘› and ๐ฟ๐‘š๐‘Ž๐‘ฅ, are calculated as follows: ๐ฟ๐‘š๐‘–๐‘›(๐‘˜) = 2 + 0.5 โ‹… ๐‘ฃ๐‘“(๐‘˜) +0.0625 โ‹… ๐‘ฃ2๐‘“(๐‘˜)

(9)

๐ฟ๐‘š๐‘Ž๐‘ฅ(๐‘˜) = 10 + ๐‘ฃ๐‘“(๐‘˜) +0.0825 โ‹… ๐‘ฃ2๐‘“(๐‘˜).

(10)

In the meantime, an optimal following distance zone is defined accordingly. ๐ฟ๐‘™๐‘ ๐‘œ๐‘๐‘ก(๐‘˜) = 0.4 โ‹… ๐ฟ๐‘š๐‘–๐‘›(๐‘˜) +0.6 โ‹… ๐ฟ๐‘š๐‘Ž๐‘ฅ(๐‘˜)

(11)

๐ฟ๐‘ข๐‘ ๐‘œ๐‘๐‘ก(๐‘˜) = 0.4 โ‹… ๐ฟ๐‘š๐‘Ž๐‘ฅ(๐‘˜) +0.6 โ‹… ๐ฟ๐‘š๐‘–๐‘›(๐‘˜)

(12)

where the superscripts ๐‘™๐‘ and ๐‘ข๐‘ are the lower and upper bounds of the optimal following distance zone, respectively. The cost of driving safety can be calculated as follows, 13

Journal Pre-proof

๐ฝ๐‘  =

{

inf 0.2 โ‹… tan ๐ฟ(๐‘˜) โ€•

(โ‹… ๐œ‹ 2

|

๐ฟ(๐‘˜) โ€• ๐ฟ๐‘™๐‘ ๐‘œ๐‘๐‘ก(๐‘˜) ๐ฟ๐‘š๐‘–๐‘›(๐‘˜) โ€• ๐ฟ๐‘™๐‘ ๐‘œ๐‘๐‘ก(๐‘˜)

๐‘ข๐‘ ๐ฟ๐‘™๐‘ ๐‘œ๐‘๐‘ก(๐‘˜) + ๐ฟ๐‘œ๐‘๐‘ก(๐‘˜)

2

2 โ‹… (๐ฟ(๐‘˜) โ€• ๐ฟ๐‘ข๐‘ ๐‘œ๐‘๐‘ก(๐‘˜))

๐ฟ(๐‘˜) < ๐ฟ๐‘š๐‘–๐‘›(๐‘˜)

)

๐ฟ๐‘š๐‘–๐‘›(๐‘˜) โ‰ค ๐ฟ(๐‘˜) < ๐ฟ๐‘™๐‘ ๐‘œ๐‘๐‘ก(๐‘˜)

|

๐‘ข๐‘ ๐ฟ๐‘™๐‘ ๐‘œ๐‘๐‘ก(๐‘˜) โ‰ค ๐ฟ(๐‘˜) โ‰ค ๐ฟ๐‘œ๐‘๐‘ก(๐‘˜)

2

(13)

๐ฟ๐‘ข๐‘ ๐‘œ๐‘๐‘ก(๐‘˜) < ๐ฟ(๐‘˜) โ‰ค ๐ฟ๐‘š๐‘Ž๐‘ฅ(๐‘˜)

2

2 2 โ‹… (๐ฟ(๐‘˜) โ€• ๐ฟ๐‘ข๐‘ ๐‘œ๐‘๐‘ก(๐‘˜)) + 100 โ‹… (๐ฟ(๐‘˜) โ€• ๐ฟ๐‘š๐‘Ž๐‘ฅ(๐‘˜)) ๐ฟ(๐‘˜) > ๐ฟ๐‘š๐‘Ž๐‘ฅ(๐‘˜)

where ๐ฝ๐‘  is the inter-vehicle driving safety index at time step ๐‘˜. More details can be found in Ref [23]. 3.2. Fuel economy index The equivalent consumption minimization strategy (ECMS) has been demonstrated to be an effective approach for energy management problems of HEVs. The ECMS is used to address the optimal fuel consumption problem. The equivalence factor ๐‘ ๐‘’ is defined as

{

0.0001 ๐‘†๐‘œ๐ถ > 0.75 โ€•6 โˆ™ ๐‘†๐‘œ๐ถ + 15.4 0.55 < ๐‘†๐‘œ๐ถ โ‰ค 0.75 ๐‘ ๐‘’(๐‘†๐‘œ๐ถ) = 10 0.5 โ‰ค ๐‘†๐‘œ๐ถ โ‰ค 0.55 1000 ๐‘†๐‘œ๐ถ < 0.5.

(14)

The instantaneous equivalent fuel consumption of EM (๐‘š๐‘’๐‘š(๐‘”/๐‘ )) according to Ref [23] can be calculated by ๐‘„๐ต๐‘†๐น๐ถ โˆ™ ๐‘ƒ๐‘๐‘Ž๐‘ก

๐‘š๐‘’๐‘š = 3.6 ร— 106 โˆ™ ๐œ‚

๐ธ๐‘€

(15)

where ๐‘„๐ต๐‘†๐น๐ถ is the average fuel consumption rate, and its value is set to 240 ๐‘”/(๐‘˜๐‘Šโ„Ž). ๐œ‚๐ธ๐‘€ is the average generation efficiency which is assumed to be 88%. By summing up the total equivalent fuel consumption, we can get the fuel economy index ๐ฝ๐‘’๐‘๐‘œ at time step k, as follows: ๐ฝ๐‘’๐‘๐‘œ(๐‘˜) = ๐‘š๐‘“๐‘(๐‘˜) + ๐‘ ๐‘’ โˆ™ ๐‘š๐‘’๐‘š(๐‘˜).

3.3. Vehicle Emission index 14

(16)

Journal Pre-proof As mentioned earlier, the vehicle emissions evaluated in this study are CO, HC and NO๐‘ฅ. The emission index ๐ฝ๐‘’๐‘š๐‘–๐‘  at time step k is defined as ๐ฝ๐‘’๐‘š๐‘–๐‘ (๐‘˜) = ๐‘š๐‘๐‘œ(๐‘˜) + ๐‘š๐ป๐ถ(๐‘˜) + ๐‘š๐‘๐‘‚๐‘ฅ(๐‘˜).

(17)

3.4. Overall cost function The combined index ๐ฝ๐‘œ๐‘๐‘ก(๐‘˜) is used to evaluate the overall performance of intervehicle safety, energy-saving, and emissions. The cost function at time step k is expressed as follows, ๐ฝ๐‘œ๐‘๐‘ก(๐‘˜) = ๐ฝ๐‘ (๐‘˜) + ฮป โˆ™ ๐ฝ๐‘’๐‘๐‘œ(๐‘˜) + ฮฒ โˆ™ ๐ฝ๐‘’๐‘š๐‘–๐‘ (๐‘˜)

(18)

where ฮป and ฮฒ represent the weighting factors to regulate fuel economy and emissions in the overall cost function. 3.5. Optimization over the moving horizon The multi-objective optimization problem at time step k over the receding prediction horizon is formulated as follows: ๐‘˜+๐‘

1

๐ฝ๐‘œ๐‘๐‘ก(๐‘˜) = โˆ‘๐‘ก = ๐‘˜ ๐‘ - (๐ฝ๐‘ (๐‘˜) + ฮป โˆ™ ๐ฝ๐‘’๐‘๐‘œ(๐‘˜) + ฮฒ โˆ™ ๐ฝ๐‘’๐‘š๐‘–๐‘ (๐‘˜)) โˆ™ ๐‘‡๐‘ , ๐‘˜ = 0,1,2,โ€ฆ

(19)

where ๐‘๐‘ denotes the length of the receding horizon, and ๐ฝ๐‘œ๐‘๐‘ก is the overall cost function at the control variables ๐‘‡๐‘’๐‘š and ๐‘Ž๐‘“. It is worth noting that ๐‘Ž๐‘“ is assumed to be constant in the receding horizon. Meanwhile, the following inequality constraints need to be satisfied. ๐œ”๐‘’๐‘›๐‘”,๐‘š๐‘–๐‘› โ‰ค ๐œ”๐‘’๐‘›๐‘”,๐‘ก โ‰ค ๐œ”๐‘’๐‘›๐‘”,๐‘š๐‘Ž๐‘ฅ ๐‘‡๐‘’๐‘›๐‘”,๐‘š๐‘–๐‘› โ‰ค ๐‘‡๐‘’๐‘›๐‘”,๐‘ก โ‰ค ๐‘‡๐‘’๐‘›๐‘”,๐‘š๐‘Ž๐‘ฅ ๐œ”๐‘’๐‘š,๐‘š๐‘–๐‘› โ‰ค ๐œ”๐‘’๐‘š,๐‘ก โ‰ค ๐œ”๐‘’๐‘š,๐‘š๐‘Ž๐‘ฅ ๐‘‡๐‘’๐‘š,๐‘š๐‘–๐‘› โ‰ค ๐‘‡๐‘’๐‘š,๐‘ก โ‰ค ๐‘‡๐‘’๐‘š,๐‘š๐‘Ž๐‘ฅ ๐‘Ž๐‘“,๐‘š๐‘–๐‘› โ‰ค ๐‘Ž๐‘“,๐‘ก โ‰ค ๐‘Ž๐‘“,๐‘š๐‘Ž๐‘ฅ ๐ฟ๐‘š๐‘–๐‘› โ‰ค ๐ฟ๐‘ก โ‰ค ๐ฟ๐‘š๐‘Ž๐‘ฅ

(20)

where ๐œ”๐‘’๐‘›๐‘”,๐‘š๐‘–๐‘› and ๐œ”๐‘’๐‘›๐‘”,๐‘š๐‘Ž๐‘ฅ are the minimum and maximum limits of the engine speed; ๐‘‡๐‘’๐‘›๐‘”,๐‘š๐‘–๐‘› and ๐‘‡๐‘’๐‘›๐‘”,๐‘š๐‘Ž๐‘ฅ are the minimum and maximum engine torques 15

Journal Pre-proof (๐‘‡๐‘’๐‘›๐‘”,๐‘š๐‘Ž๐‘ฅ is a function of ๐œ”๐‘’๐‘›๐‘”, see Fig.2). Similarly, ๐œ”๐‘’๐‘š,๐‘š๐‘–๐‘› and ๐œ”๐‘’๐‘š,๐‘š๐‘Ž๐‘ฅ are the minimum and maximum motor speeds; ๐‘‡๐‘’๐‘š,๐‘š๐‘–๐‘› and ๐‘‡๐‘’๐‘š,๐‘š๐‘Ž๐‘ฅ are the minimum and maximum motor torques; ๐‘Ž๐‘“,๐‘š๐‘–๐‘› and ๐‘Ž๐‘“,๐‘š๐‘Ž๐‘ฅ are the minimum and maximum vehicle accelerations; ๐ฟ๐‘š๐‘–๐‘› and ๐ฟ๐‘š๐‘Ž๐‘ฅ are the minimum and maximum inter-vehicle distance, depending on the vehicular speed (see equation (9) and (10)). Model predictive control (MPC) is used to optimize the control problem as formulated below, ๐‘˜+๐‘

1

min ๐ฝ๐‘œ๐‘๐‘ก(๐‘˜) = โˆ‘๐‘ก = ๐‘˜ ๐‘ - (๐ฝ๐‘ (๐‘˜) + ฮป โˆ™ ๐ฝ๐‘’๐‘๐‘œ(๐‘˜) + ฮฒ โˆ™ ๐ฝ๐‘’๐‘š๐‘–๐‘ (๐‘˜)) โˆ™ ๐‘‡๐‘ 

(21)

๐‘‡๐‘’๐‘š,๐‘Ž๐‘“

which is subjected to:

{

1

๐‘ ๐‘“,๐‘˜ + 1 = ๐‘ ๐‘“,๐‘˜ + ๐‘ฃ๐‘“,๐‘˜ โ‹… ๐‘‡๐‘  + 2 โ‹… ๐‘Ž๐‘“,๐‘˜ โ‹… ๐‘‡2๐‘  ๐‘ฃ๐‘“,๐‘˜ + 1 = ๐‘ฃ๐‘“,๐‘˜ + ๐‘Ž๐‘“,๐‘˜ โ‹… ๐‘‡๐‘  1

๐‘‡๐‘‘ = (๐‘š๐‘ฃ๐‘”๐‘“๐‘๐‘œ๐‘ ๐œƒ + ๐‘š๐‘ฃ๐‘”๐‘ ๐‘–๐‘›๐œƒ + 2๐œŒ๐ด๐ถ๐ท๐‘ฃ2๐‘“,๐‘˜ + ๐‘š๐‘ฃ๐‘Ž๐‘“,๐‘˜) โ‹… ๐‘Ÿ๐‘ค (๐‘‡๐‘’๐‘š) + ๐‘‡๐‘๐‘Ÿ๐‘˜ = (๐‘‡๐‘’๐‘›๐‘” + ๐‘‡๐‘’๐‘š)๐‘–๐‘”๐‘–0๐œ‚๐‘ ๐‘–๐‘”๐‘› ๐‘‡

(22)

๐œ”๐‘’๐‘›๐‘”,๐‘š๐‘–๐‘› โ‰ค ๐œ”๐‘’๐‘›๐‘”,๐‘ก โ‰ค ๐œ”๐‘’๐‘›๐‘”,๐‘š๐‘Ž๐‘ฅ ๐‘‡๐‘’๐‘›๐‘”,๐‘š๐‘–๐‘› โ‰ค ๐‘‡๐‘’๐‘›๐‘”,๐‘ก โ‰ค ๐‘‡๐‘’๐‘›๐‘”,๐‘š๐‘Ž๐‘ฅ ๐œ”๐‘’๐‘š,๐‘š๐‘–๐‘› โ‰ค ๐œ”๐‘’๐‘š,๐‘ก โ‰ค ๐œ”๐‘’๐‘š,๐‘š๐‘Ž๐‘ฅ ๐‘‡๐‘’๐‘š,๐‘š๐‘–๐‘› โ‰ค ๐‘‡๐‘’๐‘š,๐‘ก โ‰ค ๐‘‡๐‘’๐‘š,๐‘š๐‘Ž๐‘ฅ ๐‘Ž๐‘“,๐‘š๐‘–๐‘› โ‰ค ๐‘Ž๐‘“,๐‘ก โ‰ค ๐‘Ž๐‘“,๐‘š๐‘Ž๐‘ฅ ๐ฟ๐‘š๐‘–๐‘› โ‰ค ๐ฟ๐‘ก โ‰ค ๐ฟ๐‘š๐‘Ž๐‘ฅ

Optimization E.q.(21) min J opt ๏€ฝ J s ๏€ซ ๏ฌ ๏ƒ— J eco ๏€ซ ๏ข ๏ƒ— J emis

State Trajectories ๏ฎ l ,t , Sl ,t (t ๏€ฝ k ,๏‹, k ๏€ซ N p ๏€ญ 1)

V2V

Receding Horizon

a f ,k , Tem ,k

V2I

Leading Vehicle

Following Vehicle

Fig. 4. The model predictive multi-objective control framework. 4. SIMULATIONS AND ANALYSIS 16

Journal Pre-proof This section consists of three parts. First, different weighting factors are examined to determine the optimal values for better overall vehicular performance. Second, the proposed controller is assessed in two different drive cycles. Third, comparisons with conventional controllers are made to demonstrate the effectiveness of the proposed controller.

Table 2 Simulation parameters [23]. Name

Value

Name

Value

Vehicle mass ๐‘š๐‘ฃ(๐‘˜๐‘”)

2000

Road slope ๐œƒ(ยฐ)

0

Frontal area ๐ด(๐‘š2)

2.66

Initial SoC

0.65

Air resistance coefficient ๐ถ๐ท

0.44

Cost function efficient ฮป

1000

Air density ฯ(kg/๐‘š3)

1.2258

Gravity ๐‘”(๐‘š/๐‘ 2)

9.8

Road resistance coefficient ๐‘“

0.0125

Cost function efficient ฮฒ

125

Wheel radius ๐‘Ÿ๐‘ค(๐‘š)

0.343

Prediction horizon N๐‘

8

Final drive ratio ๐‘–0

4.55

Sampling time ๐‘‡๐‘ (๐‘ )

0.1

A. Weighting factors The control framework developed in this paper aims to find a tradeoff between energy-saving and engine-out emissions in the car-following process while ensuring the inter-vehicle safety. Different penalties on emissions are examined to determine the optimal values for an improved overall vehicular performance. A larger value of ๐œ† adds more weight to the energy-saving, whereas a larger value of ๐›ฝ adds more weight 17

Journal Pre-proof to the vehicle emissions. As shown in equation (19), the magnitudes of ๐ฝ๐‘ , ๐ฝ๐‘’๐‘๐‘œ and ๐ฝ๐‘’๐‘š๐‘–๐‘  remain 102, 10-1 and 10-1 in most cases, respectively. ๐œ† and ๐›ฝ should be set to 1000 so that the three cost terms have similar magnitudes. Since vehicles in urban conditions are more likely to run in car-following mode, the driving cycle UDDS (Urban Dynamometer Driving Schedule) is therefore chosen for the simulation tests. The value of ๐œ† is set to 1000. When emissions are not considered in the optimization, ๐›ฝ is set to 0. The simulation results are plotted. As shown in Figure 5, the actual following distance of the host vehicle does not exceed the car-following zone. In Figure 6, the host vehicle shows good performance in following the leading vehicle. The fuel consumption is 0.8097 L and the SoC at the end of the trip is 0.6498. The initial SoC value is 0.65. After including the equivalent fuel consumption of battery energy, the final fuel consumption per hundred kilometers is 6.75 L/(100km).

Following Distance [m]

100 Actual following distance Maximum following distance Minimum following distance

80

60

40

20

0

0

200

400

600

800

1000

1200

Time [s]

Fig. 5. Following distance when ๐›ฝ is 0 in UDDS.

18

1400

Journal Pre-proof

25

Leading vehicle Following vehicle

Speed [m/s]

20 15 10 5 0

0

200

400

600

800

1000

1200

1400

Time [s]

Fig. 6. Speed profiles of the leading vehicle and following vehicle when ๐›ฝ is 0 in UDDS. 1

J eco J emis

Normalized Cost

0.8

Js J opt

0.6

0.4

0.2

0

0

20

40

60

80

100

120

140

Weighting Factor

Fig. 7. Costs at different ๐›ฝ values in UDDS. To get an appropriate ๐›ฝ value for the emission index, different ๐›ฝ values between 0 and 145 are chosen to evaluate the overall operating cost. All the costs are normalized, including inter-vehicle safety, fuel consumption, emissions, and total cost. The result is shown in Figure 7. Based on the relationship between each cost and ๐›ฝ, the x-axis can be divided into three intervals. In the interval [0,65], the cost for emissions shows an obvious downward trend with the increase of ๐›ฝ, while the fuel consumption increases sharply. In the second interval [65,125], the rate of increase in fuel 19

Journal Pre-proof consumption and the rate of decrease in emissions are slower than that of the first interval. This shows that these three costs are in a relatively balanced state. However, in the third interval [125,145], as ๐›ฝ increases, safety cost grows significantly, and there is even an increasing trend in fuel consumption and emissions. Because the following distance becomes larger when the value ๐›ฝ is above 125, the safety cost also increases according to equation (13). In order to ensure the car-following performance, the following vehicle has to accelerate to catch up with the leading vehicle, resulting in increased fuel consumption and emissions. This shows that after ๐›ฝ exceeds 125, increasing ๐›ฝ will no longer reduce emissions. Instead, it causes an increase in fuel consumption and emissions. This is because the fuel consumption and emissions caused by acceleration are greater than the fuel consumption and emissions saved by increasing ๐›ฝ. As the weighting factor for emissions increases further, the following distance may exceed the maximum following distance (see in Figure 8). This is no longer a carfollowing scenario. Therefore, there is no need to evaluate ฮฒ greater than 145. 100

Actual following distance Maximum following distance Minimum following distance

Following Distance [m]

23

80

22.5 22

60

580

585

590

40

20

0

0

200

400

600

800

1000

1200

1400

Time [s]

Fig. 8. Following distance when ๐›ฝ is 200 in UDDS. Based on the above analysis, the weighting factor ๐œ† is set to 1000, and ๐›ฝ is set to 20

Journal Pre-proof 125. Fig. 9 shows the SoC trajectory of the battery and Fig. 10 shows the engine operating points. As shown in Fig. 10 (a), the engine operates mainly in the area where the fuel consumption rate is less than 240 [g/kWh]. Fig. 10 (b), (c) and (d) show that the operating points mainly concentrate on the low-emission areas. The engine operating points are affected by many factors, such as driving cycles, shifting strategies and equivalence factors in ECMS (see in equation(14)). In this optimization framework, the objective function considers both the fuel consumption and engine emission simultaneously. The optimized engine speed ranges between 1000 rpm and 3000 rpm, resulting in relatively low fuel consumption and engine emissions. The above factors together contribute to the distribution of engine operating points. The operating points of the electric motor are shown in Fig.11. To sum up, the engine shows good performance in both fuel-saving and emission reduction. 0.66 SoC 0.64

SoC

0.62 0.6 0.58 0.56 0.54

0

200

400

600

800

1000

Time [s]

Fig. 9. SoC of the following vehicle in UDDS.

21

1200

1400

Journal Pre-proof

160

BSFC [g/kWh] Maximum Torque

140

Engine Torque Te [Nm]

Engine Torque Te [Nm]

160

120 100 80 60 40

fCO [g/kWh] Maximum Torque

140 120 100 80 60 40

20

20 1000

2000

3000

4000

5000

1000

2000

Engine Speed e [rpm]

(a) 160

fHC [g/kWh] Maximum Torque

140

4000

5000

e [rpm]

(b)

Engine Torque Te [Nm]

Engine Torque Te [Nm]

160

3000

Engine Speed

120 100 80 60 40

f NOx [g/kWh] Maximum Torque

140 120 100 80 60 40

20

20 1000

2000

3000

Engine Speed

(c)

4000

5000

1000

2000

e [rpm]

3000

Engine Speed

(d)

4000

5000

e [rpm]

Fig. 10. Engine operating points in UDDS on (a) BSFC map; (b) CO emission map; (c) HC emission map; (d) NOx emission map. 300 Efficiency [% ] Maximum Torque

Motor Torque T em [Nm]

250 200 150 100 50 0 -50 -100 -150 0

2000

4000

6000

Motor Speed em [rpm]

Fig.11. EM operating points in UDDS. 22

8000

Journal Pre-proof

Table 3 Results at two different ๐›ฝ values. Weighting factor

Fuel consumption (L)

CO (g/km)

HC (g/km)

NOx (g/km)

Final SOC

0

0.8098

3.3981

0.3340

0.9316

0.6498

125

0.8807

3.1187

0.3066

0.9504

0.6493

Emission values of CO, HC and NO๐‘ฅ, at ๐›ฝ = 0 and ๐›ฝ = 125 are shown in Table 3. The fuel consumption is 7.34 L/(100km) when ๐›ฝ is 125, which is an 8.74% increase compared with ๐›ฝ = 0. Compared with the optimization without penalty on emission (๐›ฝ = 0), CO and HC are reduced by 8.22% and 8.20%, respectively, while NO๐‘ฅ is slightly increased by 2.20%. From Figure 7, it can be found that it is impossible to achieve the minimum of fuel consumption and emissions simultaneously. Therefore, better emission reduction performance can be achieved only by sacrificing some fuel consumption performance.

B. Results Under Different Driving Cycles The proposed controller is examined in two different types of driving conditions, that is, urban driving and highway driving. The details of the drive cycles are listed in Table 4. The drive cycle UDDS is chosen to be the speed profile of the preceding car. The optimized speed of the host vehicle and the following distance are shown in Fig. 12 and Fig. 13. It can be clearly seen that the host vehicle follows the leading vehicle while ensuring a satisfactory inter-vehicle distance. 23

Journal Pre-proof

Table 4 Two driving cycles Driving Cycle

Time(s)

Distance(km)

Max.Speed(m/s)

Ave.Speed(m/s)

UDDS

1370

12.0

25.3

8.8

HWFET

765

16.5

26.8

21.5

25

Leading vehicle Following vehicle

Speed [m/s]

20 15 10 5 0

0

200

400

600

800

1000

1200

1400

Time [s]

Fig.12. Speed profiles of the leading vehicle and following vehicle in UDDS.

Following Distance [m]

100 Actual following distance Maximum following distance Minimum following distance

80

60

40

20

0

0

200

400

600

800

1000

1200

Time [s]

Fig.13. The inter-vehicle following distance in UDDS.

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1400

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Leading vehicle Following vehicle

25

Speed [m/s]

20 15 10 5 0

0

100

200

300

400

500

600

700

Time [s]

Fig.14. Speed profiles of the leading vehicle and following vehicle in HWFET. 120

Actual following distance Maximum following distance Minimum following distance

Following Distance [m]

100 80 60 40 20 0

0

100

200

300

400

500

600

Time [s]

Fig.15. The inter-vehicle following distance in HWFET.

25

700

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0.66 SoC 0.65

SoC

0.64

0.63

0.62

0.61

0

100

200

300

400

500

600

700

Time [s]

Fig.16. SoC of the following vehicle in HWFET. 160

BSFC [g/kWh] Maximum Torque

140

Engine Torque Te [Nm]

Engine Torque Te [Nm]

160

120 100 80 60 40

fCO [g/kWh] Maximum Torque

140 120 100 80 60 40

20

20 1000

2000

3000

4000

5000

1000

Engine Speed e [rpm]

2000

(a) 160

fHC [g/kWh] Maximum Torque

140

4000

5000

(b)

Engine Torque Te [Nm]

Engine Torque Te [Nm]

160

3000

Engine Speed e [rpm]

120 100 80 60 40

f NOx [g/kWh] Maximum Torque

140 120 100 80 60 40

20

20 1000

2000

3000

4000

5000

1000

Engine Speed e [rpm]

2000

3000

4000

5000

Engine Speed e [rpm]

(d)

(c)

Fig.17. Operating points of the engine in HWFET on (a) BSFC map; (b) CO emission map; (c) HC emission map; (d) NO๐‘ฅ emission map.

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Journal Pre-proof 300 Efficiency [% ] Maximum Torque

Motor Torque T em [Nm]

250 200 150 100 50 0 -50 -100 -150 0

2000

4000

6000

8000

Motor Speed em [rpm]

Fig.18. EM operating points in HWFET. To simulate highway driving, the HWFET (Highway Fuel Economy Test cycle) driving cycle is selected as the leading vehicle speed profile. The car-following optimization results are shown in Figs. 14 and 15. Figure 16 shows the SoC trajectory over HWFET. Operating points of the engine and the electric motor are shown in Fig.17 and Fig.18. From the results, we can see that the proposed controller is also effective in highway driving. The fuel consumption and vehicle emissions CO, HC and NO๐‘ฅ, are shown in Table 5. The fuel economy under highway cycles is greater than that of urban driving. Since there is no frequent start and stop in highway driving, it is easier for the engine to operate in the high-efficiency area. However, the emissions are greater in highway driving cycles. This is because, in highway driving, the power demand and the temperature in the engine cylinder are higher, which results in more NO๐‘ฅ. In addition, the fuel combustion time is short, and lack of oxygen causes insufficient fuel combustion, which leads to more CO and HC.

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Table 5 Results in urban and highway driving cycles. Driving cycle

UDDS

HWFET

CO (g/km)

3.1187

4.3763

HC (g/km)

0.3066

0.4302

NOx (g/km)

0.9504

1.4089

SoC(end)

0.6493

0.6487

Total fuel (L)

0.8810

1.1051

Fuel (L/100km)

7.34

6.70

B. Comparisons with Conventional Controllers To evaluate the effectiveness of the proposed control scheme, the leading vehicle in the car-following model is selected as the counterpart for comparison. Two different preceding vehicles are used. They have different powertrains, including a conventional fuel vehicle and a parallel HEV from ADVISOR. The above two vehicle models are systematically compared in terms of energy-saving and consequent engine-out emissions, in both urban and highway conditions. For a fair comparison, the aftertreatment model is removed from ADVISOR, because ADVISOR adopts a tail gas after-treatment model, while our proposed engine-out emissions model does not consider exhaust after-treatment technologies. The optimization results are shown in Table 6. It is obvious that the fuel-saving and emissions reduction by our controller is better than the conventional controllers no matter what driving cycles are used. Compared with the traditional fuel-powered vehicle in urban driving, CO, HC and NO๐‘ฅ are reduced by 56.79%, 62.34%, and 36.70%, respectively, and the fuel consumption is reduced by 27.33%. Compared with

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Journal Pre-proof the same vehicle using the conventional controller in ADVISOR, CO, HC and NO๐‘ฅ are reduced by 48.02%, 55.38%, and 22.79% in urban driving, respectively, and the fuel consumption is reduced by 10.49%. Since the control strategy used in ADVISOR is rule-based, it cannot guarantee the optimal results, whereas the MPC based controller operates the engine in the highefficiency area. The speed profile of the leading car is predefined, and the following vehicle considers the interactions of both vehicles for speed planning. As mentioned earlier, the vehicle speed has a significant impact on the performance of the energy management. The energy-saving of the host vehicle, as a result, is much better than that of the preceding vehicle. Table 6 Optimization results of different controllers. Driving Cycle

Type

UDDS

HWFET

Conventional Car

Fuel (L/100km) 10.1

CO (g/km) 7.2181

HC (g/km) 0.8142

NOx (g/km) 1.5014

HEV

8.2

5.9996

0.6872

1.2309

Actual

7.34

3.1187

0.3066

0.9504

Conventional Car

7.9

5.6642

0.6553

1.5342

HEV

7.03

5.0303

0.5815

1.3012

Actual

6.70

4.3763

0.4302

1.4089

C. Computational Efficiency In practice, the computational efficiency of the control strategy is also very important. As a result, it is of great importance to evaluate the computational efficiency of our proposed optimization controller. The sampling time in our optimization method is 0.1s. As shown in Table 7, the controller is able to solve the optimization problem within 29

Journal Pre-proof only 65.18 s and 36.29 s under the UDDS and HWFET cycles, respectively, and the durations of UDDS and HWFET are 1370 s and 765 s. This demonstrates the high computational efficiency of the proposed algorithm.

Table 7 Calculation Time. Driving cycle

UDDS

HWFET

2Time

65.18

36.29

2A

[s]

3.40 GHz CPU with 32 GB RAM was used.

5. CONCLUSIONS This paper develops a model predictive multi-objective control framework in the carfollowing scenario, which optimizes fuel consumption and vehicle-out emissions simultaneously while ensuring inter-vehicle safety. The proposed control framework explores the interplay between fuel economy and vehicle emission reduction while ensuring inter-vehicle safety. Furthermore, its effectiveness is evaluated in two different driving conditions, including urban and highway drive cycles. Its real-time performance is also discussed. The comparison results show that the engine CO and HC are reduced by 8.22% and 8.20%, respectively when sacrificing a little fuel consumption performance. Comparisons with conventional controllers in ADVISOR are also performed. The results show that the developed MPC-based strategy is superior to traditional strategies in terms of both energy saving and vehicle emissions. The fuel consumption is reduced by 10.49%, and CO, HC and NO๐‘ฅ are reduced by 48.02%, 55.38%, and 22.79% in urban driving, respectively. In highway driving, CO and HC are reduced by 13%, 26.02%, respectively, and fuel consumption is reduced by 4.69%. 30

Journal Pre-proof Future work will consider the cold start-up of the engine and its effect on fuel consumption and emissions. Furthermore, the transmission shifting process will be optimized in the EMS to improve the ride comfort in car-following scenarios. ACKNOWLEDGMENTS This work was supported in part by the National Natural Science Foundation of China (Grant No. 51875054 and No. 51705044), and Natural Sciences and Engineering Research Council of Canada (NSERC) through the Discovery Grant Program (RGPIN2018-05471).

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Journal Pre-proof management for a plug-in hybrid electric bus with an adaptive reference state-ofcharge advisory. IEEE Transactions on Vehicular Technology, 2018, 67(7): 56715682. [7] Hu X, Zou C, Tang X, Liu T, Hu L. Cost-optimal energy management of hybrid electric vehicles using fuel cell/battery health-aware predictive control. IEEE Transactions on Power Electronics, 2020, 35(1):382-392. [8] Xie S, Hu X, Tang X, Xin Z, Qi S, Lang K, Brighton J. Model predictive energy management for plug-in hybrid electric vehicles considering optimal battery depth of discharge. Energy, 2019, 173:667-678. [9] Li S, Li K, Rajamani R, Wang J. Model predictive multi-objective vehicular adaptive cruise control. IEEE Transactions on Control Systems Technology, 2010, 19(3): 556-566. [10] Zhang F, Hu X, Langari R, Cao D. Energy management strategies of connected HEVs and PHEVs: Recent progress and outlook. Progress in Energy and Combustion Science, 2019, 73: 235-256. [11] Hu X, Liu T, Qi X, Matthew B. Reinforcement learning for hybrid and plug-in hybrid electric vehicle energy management: Recent advances and prospects. IEEE Industrial Electronics Magazine, 2019, 13(3):16-25. [12] Tang X, Zhang D, Liu T, Khajepour A, Yu H, Wang H. Research on the energy control of a dual-motor hybrid vehicle during engine start-stop process. Energy, 2019, 166:1181-1193. [13] Lin C C, Peng H, Grizzle J W, Kang J M. Power management strategy for a parallel hybrid electric truck. IEEE Transactions on Control Systems Technology, 2003, 11(6), 839-849. [14] Yang C, Du S, Li L, You S, Yang Y, Zhao Y. Adaptive real-time optimal energy 32

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Journal Pre-proof [23] Li L, Wang X, Song J. Fuel consumption optimization for smart hybrid electric vehicle during a car-following process. Mechanical Systems and Signal Processing, 2017, 87: 17-29. [24] Xie S, Hu X, Liu T, Qi S, Lang K, Li H. Predictive vehicle-following power management for plug-in hybrid electric vehicles. Energy, 2019, 166:701-714. [25] Sakhdari B, Vajedi M, Azad N L. Ecological Adaptive Cruise Control of a plugin hybrid electric vehicle for urban driving. IEEE International Conference on Intelligent Transportation Systems. 2016:1739-1744. [26] Zhang X, Huang C, Liu M, Stefanopoulou, A, Ersal, T. Predictive cruise control with private vehicle-to-vehicle communication for improving fuel consumption and emissions. IEEE Communications Magazine, 2019, 57(10):91-97. [27] Xi J, Zhou Z, Li Y. The Simulation Study of Vehicle Hydro-Mechanical Continuously Variable Transmission Test Based on AVL CRUISE. 2015 7th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC). IEEE, 2015:117-121. [28] Saju C, Lydia M. A Comprehensive Review on Hybrid Electic Vehicles: Power Train Configurations, Modelling Approaches, Control Techniques. 2018 Second International Conference on Inventive Communication and Computational Technologies (ICICCT). Coimbatore, India. 20-21 April 2018: 925-930. [29] Zhang Q, Cui N, Li K, Shang Y, Zhang C. Co-simulation of energy management strategy for hybrid electric vehicle in AVL InMotion. 2017 Chinese Automation Congress (CAC). IEEE, 2017:4932-4937. [30] Hu X, Yuan H, Zou C, Li Z, Zhang L. Co-estimation of state of charge and state of health for lithium-ion batteries based on fractional-order calculus. IEEE Transactions on Vehicular Technology, 2018, 67(11):10319-10329. 34

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Declaration of interests โ˜’ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. โ˜The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Journal Pre-proof Title: Model Predictive Control of Hybrid Electric Vehicles for Fuel Economy, Emission Reduction, and Inter-vehicle Safety in The Car-following Scenario

Highlights ๏ฌ

An online multi-objective optimization framework for HEV in car-following scenarios

๏ฌ

The interplay between fuel economy and vehicle exhaust emissions is investigated

๏ฌ

The designed controller is evaluated at different traffic conditions

๏ฌ

Comparisons with conventional control methods are made

๏ฌ

Improved performance of fuel economy and emission reduction is achieved