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Cooperative Adaptive Cruise Control and exhaust emission evaluation under heterogeneous connected vehicle network environment in urban city
Journal of Environmental Management 256 (2020) 109975
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Journal of Environmental Management journal homepage: http://www.elsevier.com/locate/jenvman
Research article
Cooperative Adaptive Cruise Control and exhaust emission evaluation under heterogeneous connected vehicle network environment in urban city Ling Huang a, 1, Cong Zhai b, 1, Haiwei Wang c, Ronghui Zhang d, *, Zhijun Qiu e, Jianping Wu f a
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, 510640, China School of Transportation and Civil Engineering and Architecture, Foshan University, Foshan, Guangdong, 528000, China c School of Transport and Economic Management, Guangdong Communication Polytechnic, Guangzhou, 510650, China d Guangdong Key Laboratory of Intelligent Transportation System, School of Engineering, Sun Yat-sen University, Guangzhou, 510275, China e Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Alberta, Canada f Department of Civil Engineering, Tsinghua University, Beijing, 100084, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Intelligent connected vehicle Cooperative adaptive cruise control Heterogeneous Exhaust emission evaluation Transportation simulation and environment Smart city
With the development of information communication and artificial intelligence, the ICV (intelligent connected vehicle) will inevitably play an important part in future urban transport system. In this paper, we study the car following behaviour under the heterogeneous ICV environment. The time to receive information varies from vehicle to vehicle, since the manual vehicles and autonomous vehicles co-exist on the road. By introducing timevarying lags function, a new car following model is proposed, and the cooperative control strategy of this model is studied. Based on Lyapunov function theory and linear matrix inequality (LMI) approach, the sufficient condition that the existence of the feedback controller is given, which makes the closed-loop system asymp totically stable under mixed traffic flow environment. That is to say, traffic congestion phenomenon under heterogeneous traffic flow can be effectively suppressed, and the feedback controller gain matrix can be obtained via solving linear matrix inequality. Finally, by simulation the method is verified effective in alleviating traffic congestions and reducing fuel consumption and exhaust emissions. It could be a useful reference to Cooperative Vehicle Infrastructure System and Smart City.
1. Introduction Recently, with the economic growth, more and more motorized cars are running on urban roads (Zhang et al., 2017a, 2017b). This exacer bates traffic congestion and brings many related environmental issues, such as noise pollution, air pollution, and energy consumption. Gov ernments are eager to find ways to alleviate traffic congestion effec tively. In the past few decades, people tried to use traffic organization and traffic demand management (TDM) to alleviate traffic congestion, yet the effect is not significant. Recently, under the impetus of the electronic information and wireless communication technology, the internet of things (IoT) technology has rapidly developed, making it possible to use car networking technology to alleviate traffic congestion (Knorr and Schreckenberg, 2012). Vehicle network, as the core of the Internet of things, makes real-time interconnection of vehicle-vehicle (V2V) and vehicle-infrastructure (V2I) possible to be implemented.
Based on the IoT technology, drivers can obtain the specific information of surrounding vehicles in real time, such as speed, headway etc., and thereby achieve communication with other vehicles. Because this technology can effectively improve the current deteriorating traffic environment, scholars conduct researches focused on this technology (Tang et al., 2014; You et al., 2015; Zhang et al., 2017a, 2017b). With the development of artificial intelligence (AI) and automatic technology, the autonomous vehicles (AV) will inevitably become the mainstream of future cars, scholars has focused on the topic of the traffic flow of the ACC vehicles (Nilsson et al., 2016). It’s found that based on the differences of all vehicles, the traffic performance of the road didn’t realized the optimum under each vehicles regards as the separate in dividuals. To solve this problem, the CACC (Cooperative Adaptive Cruise Control) arises. Considering the key factors such as current ac celeration, safety deceleration, space headway, and relative speed, a new CACC control logic is proposed by Van Arem et al. (2006). Wang
* Corresponding author. E-mail address: [email protected] (R. Zhang). 1 These authors contributed equally to this work. https://doi.org/10.1016/j.jenvman.2019.109975 Received 29 September 2018; Received in revised form 7 October 2019; Accepted 6 December 2019 Available online 14 December 2019 0301-4797/© 2019 Elsevier Ltd. All rights reserved.
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Journal of Environmental Management 256 (2020) 109975
et al. (2014) take advantage of the model predictive control to improve the Van Arem et al. (2006). In order to investigated the effect of the market penetration rate of ACC vehicles and the platoon sizes, a simu lation framework based on VISSIM considering ACC vehicles was pro posed by Wang et al. (2013), and the results show that urban traffic status is effective improved. Though the car-following models in connected-vehicle network en vironments have attracted a number of scholars’ attention (Wu et al., 2011; Tang et al., 2013; Ahn et al., 2014; Zhai and Wu, 2018a, 2018b; Sun et al., 2018; Francesco et al., 2018), there are still some limitations in current researches. Firstly, these previous works did not consider the influence of the difference of receiving information in conventional human-driven vehicles (also called manual vehicles). The manual vehi cles receive information mainly through the driver’s observation of the outside world. Responses to external stimuli vary from driver to driver, while some drivers have radar or infrared technology giving assistance to observation. AVs can communicate with other car via WIFI or local network, for which they also called intelligent connected vehicle (ICV). For the same stimulus, different ways of receiving external information would result in different response time. In this paper, we mainly use the lag function to represent the various response time. Secondly, consid ering the complexity of car networking and driverless technology, the public accept new technologies with varying degrees, which means the popularity of technology will take a long time. In other words, for a long time, there are both manual vehicles and ICVs running on the same traffic infrastructure. This paper mainly studied the car-following problem in this kind of heterogeneous traffic flow. In order to solve these problems, the mechanism of vehicle intelli gent control under the “semi-unicom status” has been studied. Before the start of the study, we first consider manual vehicles as controller fail ures. We assume the vehicles include the AVs implementing networking communication and the conventional human-driven vehicles not implementing the networking communication. Compared with the AVs, the manual vehicles require longer reflection time. For convenient, by treating the different receiver pattern as different lag, we introduce the lag function to represent the differences between these two different types of vehicles (AVs and manual vehicles). In this way, we propose an improved car-following model with multiple time lags. Based on the Lypunov function mentioned by Zhai and Liu (2016), the sufficient condition, where the designed feedback controller exists, is presented, and the heterogeneous traffic flow model under the designed controller satisfied the asymptotical stability. Then the controller is proved to be obtained by solving LMI. Last, simulation tests verified the effectiveness of the controller in both suppressing traffic oscillation and reducing the emission of CO2. The findings will give some inspirations for future study of AV driving strategy and environmental management in het erogeneous traffic flow with conventional manual vehicles and AVs. The structure of the paper is as follows: Section 2 introduces the improved car-following model; Section 3 is the stability analysis of the car-following model; Section 4 presents the design of the feedback controller; Section 5 is the simulation test results. Conclusions and future works are in Section 6.
τ1 ðtÞÞÞ
v_i ðtÞ ¼ ai ðFðhi ðt h_i ðtÞ ¼ vi 1 ðtÞ
τ2 ðtÞÞÞ
vi ðt
(1)
vi ðtÞ
where: hi ðtÞ > 0 stands for the space headway of the adjacent vehicle i and i 1 at time t, i indicates the ID number of the vehicles, and i ¼ 1; 2; :::; N, vi ðtÞ stands for the speed of vehicle i at time t, ai stands for the driver’s reaction sensitivity of vehicle i, Fð �Þ stands for the optimal speed function, τ1 ðtÞ; τ2 ðtÞ stands for the sensing time lag function of the space headway and speed, respectively, and: 0 < τi ðtÞ < τi ;
(2)
τ_ i ðtÞ < di < 1;
where: τ1 ; τ2 ; d1 ; d2 is a known constant, τ1 ; τ2 stand for the maximum sensing lag of the space headway and the speed, respectively. The initialization of hi ðtÞ; vi ðtÞ are: hi ðtÞ ¼ φðtÞ;
t 2 ½0; τ1 �;
vi ðtÞ ¼ ψ ðtÞ;
(3)
t 2 ½0; τ2 �;
where: φðtÞ; ψ ðtÞ stand for the continuous differentiable functions. Regarding the optimal speed function, this paper still uses the function proposed by Yu and Shi (2014). Fðhi ðtÞÞ ¼
vmax ðtanhðhi ðtÞ 2
(4)
yc Þ þ tanhðhc ÞÞ
here: vmax , hc is the maximum velocity and safety distance, respectively. 3. Linear stability analysis Suppose the leading car moving at the speed of v0, then the steady state of Eq. (1) would be: � * * �T � �T vi ; hi ¼ v0 ; F 1 ðv0 Þ (5) Let the error variable hi ðtÞ, vi ðtÞ mentioned by Zhai and Wu (2019), the error dynamic equation would be: v_ i ðtÞ ¼ αi ðFðhi ðt h_ i ðtÞ ¼ vi 1 ðtÞ
τ1 ðtÞÞÞ
τ2 ðtÞÞÞ
vi ðt
(6)
vi ðtÞ
and the variable vi ðt τ2 ðtÞÞ , Fðhi ðt τ1 ðtÞÞÞ are consistent with Zhai and Wu (2019). is:
Let hðtÞ ¼ ½h1 ðtÞ;h2 ðtÞ;:::hn ðtÞ�;vðtÞ ¼ ½v1 ðtÞ;v2 ðtÞ;:::vn ðtÞ�, then Eq. (6)
_ ¼ AðFðhðt vðtÞ
τ1 ðtÞÞÞ
vðt
τ2 ðtÞÞÞ (7)
_ ¼ C vðtÞ hðtÞ 1 2
where: A ¼ diagfa1 ; a2 ; :::an g ;
1 6 1 6 C1 ¼ 4 0
0 1 ⋯ ⋯
0 0 ⋯ 1
3
⋯ ⋯7 7. 5 1
Theorem 1. Taking into account the model Eq. (1), if the time varying delay function τi ðtÞ satisfied (2), for any given scalar ε1 > 0, if exist α;β1 ; β2 > 0, the positive definite matrix Pi ; Qi ; Ri ði ¼ 1; 2Þ, and meeting the conditions:
2. Improved car-following model with lags Here, we improve car-following systems with multiple-lags from the one proposed by Zhai and Liu (2016). Parts of the formulas are similar, but for the sake of the integrity of the model description, we still present the whole model as:
β 1 P1 < R2 < β 2 P1
2
Journal of Environmental Management 256 (2020) 109975
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2
3 1 P1 A R2 P2 C 1 0 0 P1 A 0 6Σ1 7 τ2 6 7 6 7 6 7 0 0 0 0 β 2 P1 A 7 6 * ðd2 1ÞQ2 0 6 7 6 7 6 7 1 6* 7 * R 0 0 0 0 0 2 6 7 τ 2 6 7 6 7 6 7 1 1 6* 7 * * Q R 0 R 0 0 1 1 1 6 7 τ1 τ1 6 7 <0 6 7 6 7 2 6* 7 * * * ðd1 1ÞQ1 þ ε1 α 0 0 0 6 7 6 7 6 7 1 6* 7 * * * * R1 0 0 6 7 τ1 6 7 6 7 6 7 * * * * * ε1 I β2 P1 A 7 6* 6 7 6 7 4 5 1 * * * * * * * β 2 P1
Similarly Z
¼
V_ �
1
τ2 R2
K function mention by Zhai and Liu (2016):
T
Z
t
t
T
vT ðsÞQ2 vðsÞds
h ðsÞQ1 hðsÞds þ t τ1 ðtÞ
Z
t τ2 ðtÞ
Z
0
t
V3 ðtÞ ¼ τ1
T _ h_ ðsÞR1 hðsÞdsdθ þ
Z
0
Z
τ2
tþθ
where: Pi ; Qi ; Ri ði ¼ 1; 2Þ > 0. tions (2), we obtain
t
(9)
T _ v_ ðsÞR2 vðsÞdsdθ
tþθ
Derivative (9) under the given condi
Avðt
τ1 ðtÞÞÞ Avðt τ2 ðtÞÞÞT P1 vðtÞ þ vT ðtÞP1 ðAFðhðt τ1 ðtÞÞÞ τ2 ðtÞÞÞ
T _ h_ ðtÞR1 hðtÞ
T _ þ θÞ�dθ þ h_ ðt þ θÞR1 hðt
τ1
Z
T
_ þ τ v_ ðtÞR vðtÞ _ � τ1 h_ ðtÞR1 hðtÞ 2 2 T
Z
0
t
Via Jesen’s inequality, then �T � Z �Z t T 1 _ _ h_ ðθÞR1 hðθÞdθ � hðθÞdθ R1
τ1
t τ1
¼
1
τ1
ðhðtÞ
hðt
t τ1 T
τ1 ÞÞ R1 ðhðtÞ
t
T _ h_ ðθÞR1 hðθÞdθ
t
Z
t
τ1 ÞÞ
T V_ i þ ε1 α2 h ðt
τ1 ðtÞÞhðt
τ1 ðtÞÞ
FT ðhðt
τ1 ðtÞÞÞFðhðt
τ1 ðtÞÞÞ
�
(13)
T _ v_ ðθÞR2 vðθÞdθ
t τ2
don some drivers’ bad driving habits, which effectively reduce traffic accidents, and make traffic flow smoother. However, considering the current situation, AV technology is still immature and needs improve ment. In the future, there are two different types of vehicles on roads-the ACC vehicles and the vehicles unequipped the ACC system (Zhai et al., 2019). Based on this, this paper considers the manual vehicle as actuator failure, introducing a switch matrix, and the form M ¼ diagfm1 ; m2 ; :::mN g, where
� _ hðθÞdθ
t τ1
hðt
3 X
� T _ þ θÞ dθ v_ ðt þ θÞR2 vðt
T _ v_ ðtÞR2 vðtÞ
τ2
t τ1
Z
(11)
τ2 ÞÞ
With the rise of AI, more and more countries try to take advantage of computing machines replace manual operation. This principle mainly uses on-board sensors to sense the surrounding environment of vehicles, and adjusts the vehicle’s own speed in real time according to road conditions and other vehicle positions and speeds. Compared with manual vehicles, autonomous driving technology can effectively aban
T T V_ 2 ðtÞ ¼ h ðtÞQ1 hðtÞ þ vT ðtÞQ2 vðtÞ ð1 τ_ 1 ðtÞÞh ðt τ1 ðtÞÞQ1 hðt τ1 ðtÞÞ T ð1 τ_ 2 ðtÞÞv ðt τ2 ðtÞÞQ2 vðt τ2 ðtÞÞ T T � h ðtÞQ1 hðtÞ þ vT ðtÞQ2 vðtÞ ð1 d1 Þh ðt τ1 ðtÞÞQ1 hðt τ1 ðtÞÞ T ð1 d2 Þv ðt τ2 ðtÞÞQ2 vðt τ2 ðtÞÞ
0
vðt
4. Design of the feedback controller
T
Z
τ2 ÞÞ R2 ðvðtÞ
t τ2
_ < 0, namely the new model when condition (8) hold, then we know VðtÞ (1) is asymptotically stability, In other words, the traffic congestion will be not appear.
þ vT ðtÞCT1 P2 hðtÞ þ h ðtÞP2 C1 vðtÞ
V_ 3 ðtÞ ¼
vðt
_ vðθÞdθ
τ2
T T _ _ þ h_ ðtÞP2 hðtÞ þ hT ðtÞP2 hðtÞ V_ 1 ðtÞ ¼ v_ ðtÞP1 vðtÞ þ vT ðtÞP1 vðtÞ
¼ ðAFðhðt
ðvðtÞ
t τ2 T
�
t
Set ΠðtÞ ¼ ½vðtÞ;vðt τ2 ðtÞÞ;vðt τ2 Þ;hðtÞ;hðt τ1 ðtÞÞ;hðt τ1 Þ;Fð �Þ�, in view of the Schur complement lemma, we obtain V_ � Π T ðtÞΩΠðtÞ 2 3 1 P1 A R2 P2 C 1 0 0 P1 A 0 6Σ1 7 τ2 6 7 7 6 6 * ðd 1ÞQ 7 0 0 0 0 0 β P A 2 2 6 2 1 7 7 6 7 6 1 7 6* * R 0 0 0 0 0 2 7 6 τ 2 6 7 6 7 6 7 1 1 6* 7 * * Q R 0 R 0 0 1 1 1 6 7 τ τ 1 1 Ω¼ 6 7 6 7 2 7 6* * * * ðd1 1ÞQ1 þ ε1 α 0 0 0 6 7 7 6 7 6 1 7 6* * * * * R 0 0 1 7 6 τ1 7 6 6 7 6* ε * * * * * 1 I β 2 P1 A 7 6 7 6 7 1 4 5 * * * * * * * β2 P1
V1 ðtÞ ¼ vT ðtÞP1 vðtÞ þ h ðtÞP2 hðtÞ Z
τ2
�Z R2
i¼1
VðtÞ ¼ V1 ðtÞ þ V2 ðtÞ þ V3 ðtÞ
V2 ðtÞ ¼
_ vðθÞdθ
τ2
1
�T
t
Using the above inequalities, we got
Then said that the new model Eq. (1) is stable. Building the L
�Z
For any values of ε1 > 0, exist the α > 0, making the following expression is established: � T ε1 α2 h ðt τ1 ðtÞÞhðt τ1 ðtÞÞ FT ðhðt τ1 ðtÞÞÞFðhðt τ1 ðtÞÞÞ � 0 (12)
(8)
Prove.
1 T _ v_ ðθÞR2 vðθÞdθ �
t τ2
τ2
where: Σ 1 ¼ Q2 þ τ1 CT1 R1 C1
t
(10)
3
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� mi ¼
Journal of Environmental Management 256 (2020) 109975
2
1; represent thevehicle haveACC system 0; represent thevehicle unequiped the ACC system;namelymanualvehicle
6Σ 6 6 6 6 * ðd2 6 6 6 6* 6 6 6 6 6* 6 6 6 6 6* 6 6 6 6* 6 6 6 6 6* 6 6 4 *
(14) where: cles, if
PN i¼1
PNN
mi
i¼1
represent the penetration of the ACC vehicles in all vehi
mi
¼ 1, then represent all vehicles is ACC vehicles, mean
N P N mi while, if i¼1 ¼ 0 represent all vehicles is manual vehicles. N Then uðtÞ ¼ MuðtÞ, so the system transform into as following:
v_i ðtÞ ¼ αi ðFðhi ðt
τ1 ðtÞÞÞ
(15)
τ2 ðtÞÞÞ þ mi ui ðtÞ
vi ðt
In order to improve the robustness of the automatics vehicle, uti lizing the speed difference of successive vehicles, the state feedback controller is designed as follows ui ðtÞ ¼ ki ðvi 1 ðtÞ
(16)
vi ðtÞÞ
Here, ki stands for the gain coefficient. Applying the designed controller (13) to (14), then the close-loop car-following system is given: v_i ðtÞ ¼ αi ðFðhi ðt
τ1 ðtÞÞÞ
τ2 ðtÞÞÞ þ mi ki ðvi 1 ðtÞ
vi ðt
h_ i ðtÞ ¼ vi 1 ðtÞ
τ1 ðtÞÞÞ
τ2 ðtÞÞÞ þ mi ki ðvi 1 ðtÞ
vi ðt
τ1 ðtÞÞÞ
T _ h_ ðtÞR1 hðtÞ
T _ þ θÞ�dθ þ h_ ðt þ θÞR1 hðt
τ1 T _ þ τ v_ T ðtÞR vðtÞ _ � τ1 h_ ðtÞR1 hðtÞ 2 2
Z
Z
0
t
T _ h_ ðθÞR1 hðθÞdθ
t τ1
Z
*
*
*
ðd1 1ÞQ1 þ ε1 α2
*
*
*
*
*
*
*
*
*
*
*
*
Q1
τ1
R1
0
t
τ2
1
τ2 β1 P1 ; P1 MK
τ1 ðtÞÞÞ
¼L
τ2 ðtÞÞ þ MKC1 vðtÞÞT P1 vðtÞ τ1 ðtÞÞÞ Avðt τ2 ðtÞÞ þ MKC1 vðtÞÞ Avðt T
þvT ðtÞCT1 P2 hðtÞ þ h ðtÞP2 C1 vðtÞ
(22)
T T V_ 2 ðtÞ ¼ h ðtÞQ1 hðtÞ þ vT ðtÞQ2 vðtÞ ð1 τ_ 1 ðtÞÞh ðt τ1 ðtÞÞQ1 hðt τ1 ðtÞÞ T ð1 τ_ 2 ðtÞÞv ðt τ2 ðtÞÞQ2 vðt τ2 ðtÞÞ T T � h ðtÞQ1 hðtÞ þ vT ðtÞQ2 vðtÞ ð1 d1 Þh ðt τ1 ðtÞÞQ1 hðt τ1 ðtÞÞ T ð1 d2 Þv ðt τ2 ðtÞÞQ2 vðt τ2 ðtÞÞ (23)
(24)
T _ v_ ðθÞR2 vðθÞdθ
t τ2
priate dimension matrix L, make the following conditions hold:
Based on Eq. (10)–(12), we got
(20)
β1 P1 < R2 < β2 P1
1
*
� T _ þ θÞ dθ v_ ðt þ θÞR2 vðt
T _ v_ ðtÞR2 vðtÞ
τ2
0
þ v ðtÞP1 ðAFðhðt
Theorem 2. Based on the error dynamic Eq. (18), and the time varying lag function τi ðtÞ satisfying (2), for any given scalar ε1 > 0, if exist α; β1 ; β2 > 0, the positive definite matrix Pi ; Qi ; Ri ði ¼ 1; 2Þ, and the appro
0
0
*
T
where: K ¼ diagfk1 ; k2 ; :::; kn g.
Z
β 1 P1
τ2
¼ ðAFðhðt
_ ¼ C vðtÞ hðtÞ 1
V_ 3 ðtÞ ¼
0
1
*
(19)
τ2 ðtÞÞÞ þ MKC1 vðtÞ
0
T T _ _ þ h_ ðtÞP2 hðtÞ þ hT ðtÞP2 hðtÞ V_ 1 ðtÞ ¼ v_ ðtÞP1 vðtÞ þ vT ðtÞP1 vðtÞ
(18)
vðt
0
3 P1 A β2 LC1 7 7 7 7 0 0 β 2 P1 A 7 7 7 7 7 0 0 0 7 7 7 7 1 7 R1 0 0 7 τ1 7 <0 7 7 7 0 0 0 7 7 7 1 7 R1 0 0 7 τ1 7 7 7 ε1 I β2 P1 A 7 * 7 7 5 1 * * β 2 P1 0
Prove. Considering the given condition (2) and the derivative of (12), we construct the Lyapunov Krasovskii function like (9) and obtain
Let hðtÞ ¼ ½h1 ðtÞ;h2 ðtÞ;:::hn ðtÞ�;vðtÞ ¼ ½v1 ðtÞ;v2 ðtÞ;:::vn ðtÞ�, then (17) is re-written as: _ ¼ AðFðhðt vðtÞ
0
Then with the controller of the formula (14) existing, the error dy namic system is still stable under the designed controller, which can be obtained based on the LMIs solution.
vi ðtÞÞ
vi ðtÞ
1ÞQ2
P2 C 1
where: Σ ¼ LC1 þ CT1 LT þ Q2 þ τ1 CT1 R1 C1
with the error hi ðtÞ; vi ðtÞ, then the error dynamic equation of above equation is: v_ i ðtÞ ¼ αi ðFðhi ðt
τ2
β1 P1
(21)
(17)
vi ðtÞÞ
1
P1 A
Manual Vehicles Automatic Vehicles
Automatic Vehicles
Regular Vehicles
Fig. 1. N cars driving in a single lane, the black solid line represents the communication between AVs, and the communication can be realized; the red dotted line represents the manual vehicle and the vehicle communication did not implemented. 4
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Journal of Environmental Management 256 (2020) 109975
Fig. 2. The velocity curve of all vehicles in (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon.
Fig. 3. The acceleration of all vehicles under (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon.
Fig. 4. The velocity of car 1, 6 and 11 simulated in (a) the manual vehicles platoon and (b) the heterogeneous vehicles platoon.
5
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Journal of Environmental Management 256 (2020) 109975
Fig. 5. The acceleration’ evolutions of car 1, 6 and 11 simulated in (a) the manual vehicles platoon and (b) the heterogeneous vehicles platoon.
V_ �
3 X
T V_ i þ ε1 α2 h ðt
τ1 ðtÞÞhðt
τ1 ðtÞÞ
FT ðhðt
τ1 ðtÞÞÞFðhðt
situations are analysed. Through the simulation tests we verify the feasibility and effectiveness of the method.
�
τ1 ðtÞÞÞ
i¼1
(25)
5.1. Braking process simulation
Then we know V_ � Π T ðtÞΩΠðtÞ 2 3 1 P1 A βP P2 C 1 0 0 P1 A β2 LC1 7 6Σ τ2 1 1 6 7 6 7 6 * ðd 1ÞQ 7 0 0 0 0 0 β P A 2 2 1 6 7 2 6 7 6 7 1 6* 7 * β1 P1 0 0 0 0 0 6 7 τ2 6 7 6 7 6 7 1 1 6* 7 * * Q1 R1 0 R1 0 0 6 7 τ1 τ1 Ω¼ 6 7 6 7 2 6* 7 * * * ðd 1ÞQ þ ε α 0 0 0 1 1 1 6 7 6 7 6 7 1 6* 7 * * * * R 0 0 1 6 7 τ 1 6 7 6 7 6* 7 * * * * * ε I β P A 1 2 1 6 7 6 7 1 4 5 * * * * * * * β 2 P1
We consider an arriving vehicle platoon with 11 vehicles on a single lane equipped with a traffic light. Followings are the assumed initial conditions: (1) the green traffic signal is on and the 11 vehicles are moving at a uniform speed of 0.964 m/s; (2) the 11th vehicle is at the starting point; (3) the distance between the first vehicle (the leader car of the platoon) and the traffic light is 2 m; (4) the distances between the rear and front ends of the successive vehicles are all 2 m. Then at time t ¼ 0, when the traffic light turned red, the first vehicle begins to decel erate at once, other vehicles also follow their front vehicle to decelerate. Finally, all vehicles stop in a line behind the stop line. For convenience, we assume that all vehicle control parameters and drivers’ sensitivity are homogeneous, the driver’s sensitivity is a ¼ 1; i ¼ 1; 2; :::11. Consistent with Zhai and Liu (2016), then the lag function is set as follows:
τ2
(27)
τ1 ¼ 0:25 þ 0:15 cosðtÞ; τ2 ¼ 0:25 þ 0:1 cosðtÞ
(26)
where: τ1 ¼ 0.4, τ2 ¼ 0.1, the initial speed and initial space headway of each vehicle are
_ Using Eqs. (20)–(21) we obtain VðtÞ<0, then the dynamic system Eq. (18) is stable.
hi ðtÞ ¼ 2; t 2 ½
5. Simulation tests
τ1 ; 0�;
vi ðtÞ ¼ 0:964; t 2 ½
τ2 ; 0�
(28)
It should be noted that the lag time consistent with the cosine function, for all function with meet condition (2) can be regarded as the lag function (see Fig. 1).
In this section, the vehicles following behaviours under different
Fig. 6. The headway’ evolutions of car 1, 6 and 11 simulated in (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon. 6
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Fig. 2 illustrates the speeds’ evolutions of 11 vehicles simulated by the proposed new car-following model in the situation of the manual vehicle platoon and the heterogeneous vehicle platoon. In heteroge neous platoon, car 1, 6, 11 are manual vehicles, and the rest are ACC vehicles. All ACC vehicles in both platoons are equipped with the controller, which can be obtained by solving theorem 3.2 via LMIs. The simulation results show that the manual vehicle has less ability to suppress traffic congestion due to the different speed adjustments of the manned car and the ACC vehicle (Fig. 2). It appears stronger overall shock, even the reverse phenomenon, in the manual vehicle platoon as shown in Fig. 2 (a). The ACC vehicles are able to quickly restore equi librium (Fig. 2 (b)), which means the ACC vehicles effectively alleviate traffic congestion phenomenon. Fig. 3 shows the acceleration curve of 11 cars simulated by the proposed car following model under manual traffic environment and the heterogeneous traffic environment respectively. In Fig. 3 (a), some ve hicles even appeared to accelerate. However, in Fig. 3 (b), we can see that the acceleration of the vehicles (excepting the head car) is small. Meanwhile, the differences of the acceleration of each vehicles is low, which further verify that the controller can effectively enhances the coordination between vehicles, making the platoon to effectively maintain steady. For further study the impact of the heterogeneous vehicles on the following vehicles’ speeds, accelerations and headways, we carry out the following comparative analysis between three vehicles in the manual vehicle platoon and the heterogeneous vehicle platoon. Fig. 4 compares the velocity curves between the manual vehicle platoon and the heterogeneous vehicle platoon, from which we can draw the following conclusions: the velocity curves of the 1st,6th,11th cars in the heterogeneous vehicle platoon are smoother, without obvious fluctuations. Fig. 5 compares the acceleration-time curve between the two pla toons. It is easy to found that the reverse phenomenon in (a) manual vehicle platoon has been disappear in (b) the heterogeneous vehicle platoon. What’s more, the amplitude of acceleration has been effectively reduced in the heterogeneous vehicle platoon (Fig. 5 (b)). It also shows that based on the cooperative control of our controller designed, the congestion can be relieved without experiencing obvious decelerations, and the consistency of the platoon can be maintained by coordination between vehicles. Fig. 6 compares the headway-time curve between the two platoons. The controller can widen the headway between adjacent vehicles and also reduce the interaction between the vehicles, so that the vehicles have enough headway to adjust its speed, thereby achieving the purpose of relieving congestion.
Fig. 7. The manual vehicles’ (a) velocity curve of three cars (b) velocity of all cars, and (c) space headway.
Fig. 8. The ACC vehicles’ (a) velocity curve of three cars, (b) velocity of all cars, and (c) space headway.
5.2. Traffic flow evolution simulation with external disturbance The simulation test represents the car following situation with an
Fig. 9. The CO emission of the 1st, 6th, 11th vehicles in (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon during periods of ½90s; 140s�. 7
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Fig. 10. The HC emission of the 1st, 6th, 11th vehicles in (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon during periods of ½90s; 140s�.
Fig. 11. The Fuel consumption of the 1st, 6th, 11th vehicles in (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon during periods of ½90s;140s�.
external disturbance, by making the velocity of the leading vehicle reduced from v0 to 0 at [100s–102s]. Fig. 7 shows the velocities and the space headway of the manual vehicle platoon. Fig. 8 shows the speeds, the space headway of the heterogeneous vehicle platoon (with both manual vehicles and ACC controlled vehicles) (see Fig. 9). Simulation results show that in manual vehicle platoon situation, the velocity fluctuation of the leading car brought fluctuation to all the rear manual vehicles speeds and space headways. Moreover, the restoration time to the desired speed of each vehicle would be relatively larger than that in Fig. 8. Therefore, in manual vehicle platoon the oscillation of the traffic occurs more frequently. The comparisons of Figs. 7 and 8 demonstrated that the controller could effectively improve the convergence capability, reduce the restoration time to the desired speed of vehicles at the same time, and relieve the vibration range of all vehicles in the platoon. Though speeds and space headways continue to present vibrations in manual vehicles in the heterogeneous vehicle platoon, this method is nevertheless effective in reducing traffic congestion in a “heterogeneous” environment. Last, the simulation results verified the efficiency of the feedback controller in reducing fuel consumption and exhaust emission. Consid ering that the traffic emission model is time consuming (Tang et al., 2015), we applied the VT-Micro model in the present work (Zhai et al., 2019). This model mainly demonstrates the relationship of fuel con sumption and exhaust emission with the speed and acceleration of the vehicle. The relationship is derived from the following equation: InðMOEeÞ ¼
� �j � 3 X 3 � X dv K ei;j � vi � dt i¼0 j¼0
Fig. 10 demonstrates the curve of the cumulative fuel consumption with emission of CO, HC, and NOx in the manual vehicle platoon, the ACC vehicle platoon and the heterogeneous vehicle platoon, respec tively. Comparisons between the manual vehicle platoon and the het erogeneous vehicle platoon indicates that regardless of fuel consumption and emission of CO, HC, or NOx emission, the heteroge neous vehicle platoon perform better than the manual vehicle platoon in the amount of the exhaust emissions and fuel consumption, which verify that the controller is effective in reducing fuel consumption and emis sions (see Fig. 12) (see Fig. 11). 5.3. The exhaust emission of the vehicles under difference penetration Table 1 presents the amount of all vehicle exhaust emissions under different ACC penetration. Considering the position where the ACC ve hicles will influence the authenticity of the results, based on different penetration of ACC, statistics 100 times of all vehicles emissions under different ACC vehicle position in the platoon in the period of 100s–140s respectively. Finally, by the average we got the total emissions of the vehicles under difference ACC vehicles penetration. The method is effective to overcome the influence of ACC position distribution on all vehicles emissions, and is able to reflect the penetration of ACC vehicles’ impact on the exhaust emission (Bracha et al., 2018; Ross et al., 2018; Xiong et al., 2018; Noelia et al., 2018; Rathna et al., 2018; Wang et al., 2019). From Table 1, we can see that as the penetration of ACC vehicles increases, the amount of exhaust emissions gradually decreases. The minimal exhaust emission in the ACC vehicles is 100%, which also verifies the ACC vehicle’s ability to reduce vehicle emissions even dur ing normal driving process.
(29)
where: MOEe represents the instant emission or the instant fuel con sumption ratio. Kei;j represents the related regression coefficient, and the
specific value can be obtained from the work of Tang et al. (2015).
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Fig. 12. The NOx emission of the 1st, 6th, 11th vehicles in (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon during periods of ½90s; 140s�.
Acknowledgment
Table 1 The exhaust emission of the vehicles under difference penetration. The exhaust emission
The market penetration rate of the ACC Vehicles 0%
25%
50%
75%
100%
CO
1234.1 (100%) 171.25 (100%) 232.72 (100%) 242.35 (100%)
1204.9 (97.6%) 167.97 (98.0%) 228.41 (98.1%) 239.37 (98.7%)
1180.3 (95.6%) 164.33 (95.9%) 224.50 (96.5%) 237.44 (97.9%)
1172.8 (95.0%) 162.51 (94.9%) 223.67 (96.1%) 235.69 (97.2%)
1168.7 (94.7%) 161.83 (94.5%) 222.8 (95.7%) 234.9 (96.9%)
NOx HC Fuel
This work was partially supported by the Science and Technology Planning Project of Guangdong Province (Grant Nos. 2017A040405021), National Natural Science Foundation of China (Grant Nos. 51408237, 51808151, 51775565), Fundamental Research Funds for the Central Universities (Grant No.18LGPY83), and the Fundamental Research Funds for Guangdong Communication Poly technic(20181014). References Ahn, K., Rakha, H., Trani, A., et al., 2014. Estimating vehicle fuel consumption and emissions based on instantaneous speed and acceleration levels. Transp. Eng. J. ASCE 128 (2), 182–190. https://doi.org/10.1061/(ASCE)0733-947X(2002)128:2 (182). Bracha, Y., Schindler, B.Y., Leon, B., et al., 2018. Green roof and photovoltaic panel integration: effects on plant and arthropod diversity and electricity production. J. Environ. Manag. 225, 288–299. https://doi.org/10.1016/j.jenvman.2018.08.017. Deny, D.M., Teresa, A.B., Valentina, C., 2018. Energy efficiency and reduction of CO2 emissions from campsites management in a protected area. J. Environ. Manag. 222, 368–377. https://doi.org/10.1016/j.jenvman.2018.05.084. Francesco, F., Guido, P., Mariangela, R., et al., 2018. Car-sharing services: an annotated review. Sust. Cities Soc. 37, 501–518. https://doi.org/10.1016/j.scs.2017.09.020. Hong, T., Koo, C., Kim, H., 2012. A decision support model for improving a multi-family housing complex based on CO2 emission from electricity consumption. J. Environ. Manag. 112, 67–78. https://doi.org/10.1016/j.jenvman.2012.06.046. Knorr, F., Schreckenberg, M., 2012. Influence of inter-vehicle communication on peak hour traffic flow. Physica A 391 (6), 2225–2231. https://doi.org/10.1016/j. physa.2011.11.027. Nilsson, J., Brannstrom, M., Fredriksson, J., et al., 2016. Longitudinal and lateral control for automated yielding manoeuvres. IEEE Trans. Intell. Transp. Syst. 17 (5), 1–11. https://doi.org/10.1109/TITS.2015.2504718. Noelia, O.T., Lluc, C.C., Beatriz, A.G., 2018. Sustainable design of a thermosolar electricity generation power plant in Burkina Faso. J. Environ. Manag. 226, 428–436. https://doi.org/10.1016/j.jenvman.2018.08.043. Rathna, R., Sunita, V., Ekambaram, N., 2018. Recent developments and prospects of dioxins and furans remediation. J. Environ. Manag. 223, 797–806. https://doi.org/ 10.1016/j.jenvman.2018.06.095. Ross, G., Gordon, W., Paul, C., et al., 2018. Storying energy consumption: collective video storytelling in energy efficiency social marketing. J. Environ. Manag. 213, 1–10. https://doi.org/10.1016/j.jenvman.2018.02.046. Sun, X.J., Zhang, H., Meng, W.J., et al., 2018. Primary resonance analysis and vibration suppression for the harmonically excited nonlinear suspension system using a pair of symmetric viscoelastic buffers. Nonlinear Dyn. 94, 1243–1265. https://doi.org/ 10.1007/s11071-018-4421-9. Tang, T.Q., LI, Jingang, Wang, Y.P., et al., 2013. Vehicle’s fuel consumption of carfollowing models. Sci. China Technol. Sci. 56 (5), 1307–1312. https://doi.org/ 10.1007/s11431-013-5182-9. Tang, T.Q., Yu, Q., Yang, S.C., et al., 2015. Impacts of the vehicle’s fuel consumption and exhaust emissions on the trip cost allowing late arrival under car-following model. Physica A 431, 52–62. https://doi.org/10.1016/j.physa.2015.02.041. Tang, T.Q., Shi, W.F., Shang, H.Y., et al., 2014. An extended car-following model with consideration of the reliability of inter-vehicle communication. Measurement 58, 286–293. https://doi.org/10.1016/j.measurement.2014.08.051.
6. Conclusion and future works Considering different receiver pattern as different time-varying lags and regarding the manual operations as the actuator existing failure constraints, an improved car-following model is proposed. By the theory of Lyapunov function, the sufficient condition of the traffic flow stability is given. That means traffic congestion can be avoided, and when the above stability conditions are not met, a new feedback controller is designed, and the detailed design steps are given. By the controller, which can be obtained by solving the LMI, the car-following model can satisfy the asymptotic stability under the heterogeneous vehicles envi ronment (Hong et al., 2012; Deny et al., 2018). Finally, by comparing the velocities, accelerations and space headway of the following vehicles in manual controlled vehicle platoon and the heterogeneous vehicles platoon, we found that the speed fluctuations under the feedback controller can be restored to equilibrium faster than the manual vehicle without the controller. Meanwhile the controller in reducing the exhaust emission and fuel consumption also has a significant effect. Yet, our work only focused on the car-following behaviours in single-lane, and the behaviour of the lane changing and the passing through the pro posed model did not reflect. Moreover, the assumptions of drivers’ lag time and driver sensitivity in the heterogeneous connected vehicle network environment were rather simple compared to the realistic driving behaviours. Future work will focus on the car following be haviours in more complex environments, with more realistic assump tions and considerations on some issues such as drivers’ lag time, sensitivity and so on by obtaining extensive natural driving data. Declaration of competing interest The authors declare that there is no conflict of interests regarding the publication of this article.
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Journal of Environmental Management 256 (2020) 109975 Yu, S., Shi, Z., 2014. An improved car-following model considering headway changes with memory. Physica A 421, 1–14. https://doi.org/10.1016/j.physa.2014.11.008. Zhai, C., Liu, W., 2016. The fault-tolerant control strategy of the Takagi-Sugeno fuzzy car following model with two-delays. In: International Conference on Advanced Robotics & Mechatronics. IEEE, pp. 602–607. https://doi.org/10.1109/ ICARM.2016.7606989, 2016. Zhai, C., Wu, W.T., Huang, L., 2019. Collaborative control of coupled map car-following model under heterogeneous connected vehicle environment. Control Theory & Appl. 36 (1), 96–107. https://doi.org/10.7641/CTA.2018.70431. Zhai, C., Wu, W.T., 2018. Stability analysis of two-lane lattice hydrodynamic model considering lane-changing and memorial effects. Mod. Phys. Lett. B 32, 1850233. https://doi.org/10.1142/S0217984918502330. Zhai, C., Wu, W.T., 2018. An extended continuum model with consideration of the selfanticipative effect. Mod. Phys. Lett. B 32, 1850382. https://doi.org/10.1142/ S0217984918503827. Zhai, C., Wu, W.T., 2019. Lattice hydrodynamic model based feedback control method with traffic interrupt probability. Mod. Phys. Lett. B 33 (23), 1950273, 2019. Zhang, R., Wu, J., Huang, L., et al., 2017. Study of bicycle movements in conflicts at mixed traffic unsignalized intersections. IEEE Access 5, 10108–10117. https://doi. org/10.1109/ACCESS.2017.2703816. Zhang, R.H., He, Z.C., Wang, H.W., et al., 2017. Study on self-tuning tyre friction control for developing main-servo loop integrated chassis control system. IEEE Access 5, 6649–6660. https://doi.org/10.1109/ACCESS.2017.2669263.
Van Arem, B., van Driel, C.J.G., Visser, R., 2006. The impact of cooperative adaptive cruise control on traffic-flow characteristics. IEEE Trans. Intell. Transp. Syst. 7 (4), 429–436. https://doi.org/10.1109/TITS.2006.884615. Wang, L., Zhang, L.B., Li, H.Y., et al., 2019. High selective production of 5-hydroxyme thylfurfural from fructose by sulfonic acid functionalized SBA-15 catalyst. Compos. B Eng. 156, 88–94. https://doi.org/10.1016/j.compositesb.2018.08.044. Wang, M., Daamen, W., Hoogendoorn, S.P., et al., 2014. Rolling horizon control framework for driver assistance systems. Part II: cooperative sensing and cooperative control. Transp. Res. C Emerg. Technol. 40, 290–311. https://doi.org/10.1016/j. trc.2013.11.024. Wang, M., Treiber, M., Daamen, W., et al., 2013. Modelling supported driving as an optimal control cycle: framework and model characteristics. Transp. Res. C Emerg. Technol. 36, 547–563. https://doi.org/10.1016/j.trc.2013.06.012. Wu, C., Zhao, G., Ou, B., 2011. A fuel economy optimization system with applications in vehicles with human drivers and autonomous vehicles. Transp. Res. Part DTransport. Environ. 16 (7), 515–524. https://doi.org/10.1016/j.trd.2011.06.002. Xiong, H.Y., Zhu, X.L., Zhang, R.H., 2018. Energy recovery strategy numerical simulation for dual axle drive pure electric vehicle based on motor loss model and big data calculation. Complexity 2018, 4071743. https://doi.org/10.1155/2018/4071743. You, F., Zhang, R.H., Guo, L., et al., 2015. Trajectory planning and tracking control for autonomous lane change maneuver based on the cooperative vehicle infrastructure system. Expert Syst. Appl. 42 (14), 5932–5946. https://doi.org/10.1016/j. eswa.2015.03.022.
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Research article
Cooperative Adaptive Cruise Control and exhaust emission evaluation under heterogeneous connected vehicle network environment in urban city Ling Huang a, 1, Cong Zhai b, 1, Haiwei Wang c, Ronghui Zhang d, *, Zhijun Qiu e, Jianping Wu f a
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, 510640, China School of Transportation and Civil Engineering and Architecture, Foshan University, Foshan, Guangdong, 528000, China c School of Transport and Economic Management, Guangdong Communication Polytechnic, Guangzhou, 510650, China d Guangdong Key Laboratory of Intelligent Transportation System, School of Engineering, Sun Yat-sen University, Guangzhou, 510275, China e Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Alberta, Canada f Department of Civil Engineering, Tsinghua University, Beijing, 100084, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Intelligent connected vehicle Cooperative adaptive cruise control Heterogeneous Exhaust emission evaluation Transportation simulation and environment Smart city
With the development of information communication and artificial intelligence, the ICV (intelligent connected vehicle) will inevitably play an important part in future urban transport system. In this paper, we study the car following behaviour under the heterogeneous ICV environment. The time to receive information varies from vehicle to vehicle, since the manual vehicles and autonomous vehicles co-exist on the road. By introducing timevarying lags function, a new car following model is proposed, and the cooperative control strategy of this model is studied. Based on Lyapunov function theory and linear matrix inequality (LMI) approach, the sufficient condition that the existence of the feedback controller is given, which makes the closed-loop system asymp totically stable under mixed traffic flow environment. That is to say, traffic congestion phenomenon under heterogeneous traffic flow can be effectively suppressed, and the feedback controller gain matrix can be obtained via solving linear matrix inequality. Finally, by simulation the method is verified effective in alleviating traffic congestions and reducing fuel consumption and exhaust emissions. It could be a useful reference to Cooperative Vehicle Infrastructure System and Smart City.
1. Introduction Recently, with the economic growth, more and more motorized cars are running on urban roads (Zhang et al., 2017a, 2017b). This exacer bates traffic congestion and brings many related environmental issues, such as noise pollution, air pollution, and energy consumption. Gov ernments are eager to find ways to alleviate traffic congestion effec tively. In the past few decades, people tried to use traffic organization and traffic demand management (TDM) to alleviate traffic congestion, yet the effect is not significant. Recently, under the impetus of the electronic information and wireless communication technology, the internet of things (IoT) technology has rapidly developed, making it possible to use car networking technology to alleviate traffic congestion (Knorr and Schreckenberg, 2012). Vehicle network, as the core of the Internet of things, makes real-time interconnection of vehicle-vehicle (V2V) and vehicle-infrastructure (V2I) possible to be implemented.
Based on the IoT technology, drivers can obtain the specific information of surrounding vehicles in real time, such as speed, headway etc., and thereby achieve communication with other vehicles. Because this technology can effectively improve the current deteriorating traffic environment, scholars conduct researches focused on this technology (Tang et al., 2014; You et al., 2015; Zhang et al., 2017a, 2017b). With the development of artificial intelligence (AI) and automatic technology, the autonomous vehicles (AV) will inevitably become the mainstream of future cars, scholars has focused on the topic of the traffic flow of the ACC vehicles (Nilsson et al., 2016). It’s found that based on the differences of all vehicles, the traffic performance of the road didn’t realized the optimum under each vehicles regards as the separate in dividuals. To solve this problem, the CACC (Cooperative Adaptive Cruise Control) arises. Considering the key factors such as current ac celeration, safety deceleration, space headway, and relative speed, a new CACC control logic is proposed by Van Arem et al. (2006). Wang
* Corresponding author. E-mail address: [email protected] (R. Zhang). 1 These authors contributed equally to this work. https://doi.org/10.1016/j.jenvman.2019.109975 Received 29 September 2018; Received in revised form 7 October 2019; Accepted 6 December 2019 Available online 14 December 2019 0301-4797/© 2019 Elsevier Ltd. All rights reserved.
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et al. (2014) take advantage of the model predictive control to improve the Van Arem et al. (2006). In order to investigated the effect of the market penetration rate of ACC vehicles and the platoon sizes, a simu lation framework based on VISSIM considering ACC vehicles was pro posed by Wang et al. (2013), and the results show that urban traffic status is effective improved. Though the car-following models in connected-vehicle network en vironments have attracted a number of scholars’ attention (Wu et al., 2011; Tang et al., 2013; Ahn et al., 2014; Zhai and Wu, 2018a, 2018b; Sun et al., 2018; Francesco et al., 2018), there are still some limitations in current researches. Firstly, these previous works did not consider the influence of the difference of receiving information in conventional human-driven vehicles (also called manual vehicles). The manual vehi cles receive information mainly through the driver’s observation of the outside world. Responses to external stimuli vary from driver to driver, while some drivers have radar or infrared technology giving assistance to observation. AVs can communicate with other car via WIFI or local network, for which they also called intelligent connected vehicle (ICV). For the same stimulus, different ways of receiving external information would result in different response time. In this paper, we mainly use the lag function to represent the various response time. Secondly, consid ering the complexity of car networking and driverless technology, the public accept new technologies with varying degrees, which means the popularity of technology will take a long time. In other words, for a long time, there are both manual vehicles and ICVs running on the same traffic infrastructure. This paper mainly studied the car-following problem in this kind of heterogeneous traffic flow. In order to solve these problems, the mechanism of vehicle intelli gent control under the “semi-unicom status” has been studied. Before the start of the study, we first consider manual vehicles as controller fail ures. We assume the vehicles include the AVs implementing networking communication and the conventional human-driven vehicles not implementing the networking communication. Compared with the AVs, the manual vehicles require longer reflection time. For convenient, by treating the different receiver pattern as different lag, we introduce the lag function to represent the differences between these two different types of vehicles (AVs and manual vehicles). In this way, we propose an improved car-following model with multiple time lags. Based on the Lypunov function mentioned by Zhai and Liu (2016), the sufficient condition, where the designed feedback controller exists, is presented, and the heterogeneous traffic flow model under the designed controller satisfied the asymptotical stability. Then the controller is proved to be obtained by solving LMI. Last, simulation tests verified the effectiveness of the controller in both suppressing traffic oscillation and reducing the emission of CO2. The findings will give some inspirations for future study of AV driving strategy and environmental management in het erogeneous traffic flow with conventional manual vehicles and AVs. The structure of the paper is as follows: Section 2 introduces the improved car-following model; Section 3 is the stability analysis of the car-following model; Section 4 presents the design of the feedback controller; Section 5 is the simulation test results. Conclusions and future works are in Section 6.
τ1 ðtÞÞÞ
v_i ðtÞ ¼ ai ðFðhi ðt h_i ðtÞ ¼ vi 1 ðtÞ
τ2 ðtÞÞÞ
vi ðt
(1)
vi ðtÞ
where: hi ðtÞ > 0 stands for the space headway of the adjacent vehicle i and i 1 at time t, i indicates the ID number of the vehicles, and i ¼ 1; 2; :::; N, vi ðtÞ stands for the speed of vehicle i at time t, ai stands for the driver’s reaction sensitivity of vehicle i, Fð �Þ stands for the optimal speed function, τ1 ðtÞ; τ2 ðtÞ stands for the sensing time lag function of the space headway and speed, respectively, and: 0 < τi ðtÞ < τi ;
(2)
τ_ i ðtÞ < di < 1;
where: τ1 ; τ2 ; d1 ; d2 is a known constant, τ1 ; τ2 stand for the maximum sensing lag of the space headway and the speed, respectively. The initialization of hi ðtÞ; vi ðtÞ are: hi ðtÞ ¼ φðtÞ;
t 2 ½0; τ1 �;
vi ðtÞ ¼ ψ ðtÞ;
(3)
t 2 ½0; τ2 �;
where: φðtÞ; ψ ðtÞ stand for the continuous differentiable functions. Regarding the optimal speed function, this paper still uses the function proposed by Yu and Shi (2014). Fðhi ðtÞÞ ¼
vmax ðtanhðhi ðtÞ 2
(4)
yc Þ þ tanhðhc ÞÞ
here: vmax , hc is the maximum velocity and safety distance, respectively. 3. Linear stability analysis Suppose the leading car moving at the speed of v0, then the steady state of Eq. (1) would be: � * * �T � �T vi ; hi ¼ v0 ; F 1 ðv0 Þ (5) Let the error variable hi ðtÞ, vi ðtÞ mentioned by Zhai and Wu (2019), the error dynamic equation would be: v_ i ðtÞ ¼ αi ðFðhi ðt h_ i ðtÞ ¼ vi 1 ðtÞ
τ1 ðtÞÞÞ
τ2 ðtÞÞÞ
vi ðt
(6)
vi ðtÞ
and the variable vi ðt τ2 ðtÞÞ , Fðhi ðt τ1 ðtÞÞÞ are consistent with Zhai and Wu (2019). is:
Let hðtÞ ¼ ½h1 ðtÞ;h2 ðtÞ;:::hn ðtÞ�;vðtÞ ¼ ½v1 ðtÞ;v2 ðtÞ;:::vn ðtÞ�, then Eq. (6)
_ ¼ AðFðhðt vðtÞ
τ1 ðtÞÞÞ
vðt
τ2 ðtÞÞÞ (7)
_ ¼ C vðtÞ hðtÞ 1 2
where: A ¼ diagfa1 ; a2 ; :::an g ;
1 6 1 6 C1 ¼ 4 0
0 1 ⋯ ⋯
0 0 ⋯ 1
3
⋯ ⋯7 7. 5 1
Theorem 1. Taking into account the model Eq. (1), if the time varying delay function τi ðtÞ satisfied (2), for any given scalar ε1 > 0, if exist α;β1 ; β2 > 0, the positive definite matrix Pi ; Qi ; Ri ði ¼ 1; 2Þ, and meeting the conditions:
2. Improved car-following model with lags Here, we improve car-following systems with multiple-lags from the one proposed by Zhai and Liu (2016). Parts of the formulas are similar, but for the sake of the integrity of the model description, we still present the whole model as:
β 1 P1 < R2 < β 2 P1
2
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L. Huang et al.
2
3 1 P1 A R2 P2 C 1 0 0 P1 A 0 6Σ1 7 τ2 6 7 6 7 6 7 0 0 0 0 β 2 P1 A 7 6 * ðd2 1ÞQ2 0 6 7 6 7 6 7 1 6* 7 * R 0 0 0 0 0 2 6 7 τ 2 6 7 6 7 6 7 1 1 6* 7 * * Q R 0 R 0 0 1 1 1 6 7 τ1 τ1 6 7 <0 6 7 6 7 2 6* 7 * * * ðd1 1ÞQ1 þ ε1 α 0 0 0 6 7 6 7 6 7 1 6* 7 * * * * R1 0 0 6 7 τ1 6 7 6 7 6 7 * * * * * ε1 I β2 P1 A 7 6* 6 7 6 7 4 5 1 * * * * * * * β 2 P1
Similarly Z
¼
V_ �
1
τ2 R2
K function mention by Zhai and Liu (2016):
T
Z
t
t
T
vT ðsÞQ2 vðsÞds
h ðsÞQ1 hðsÞds þ t τ1 ðtÞ
Z
t τ2 ðtÞ
Z
0
t
V3 ðtÞ ¼ τ1
T _ h_ ðsÞR1 hðsÞdsdθ þ
Z
0
Z
τ2
tþθ
where: Pi ; Qi ; Ri ði ¼ 1; 2Þ > 0. tions (2), we obtain
t
(9)
T _ v_ ðsÞR2 vðsÞdsdθ
tþθ
Derivative (9) under the given condi
Avðt
τ1 ðtÞÞÞ Avðt τ2 ðtÞÞÞT P1 vðtÞ þ vT ðtÞP1 ðAFðhðt τ1 ðtÞÞÞ τ2 ðtÞÞÞ
T _ h_ ðtÞR1 hðtÞ
T _ þ θÞ�dθ þ h_ ðt þ θÞR1 hðt
τ1
Z
T
_ þ τ v_ ðtÞR vðtÞ _ � τ1 h_ ðtÞR1 hðtÞ 2 2 T
Z
0
t
Via Jesen’s inequality, then �T � Z �Z t T 1 _ _ h_ ðθÞR1 hðθÞdθ � hðθÞdθ R1
τ1
t τ1
¼
1
τ1
ðhðtÞ
hðt
t τ1 T
τ1 ÞÞ R1 ðhðtÞ
t
T _ h_ ðθÞR1 hðθÞdθ
t
Z
t
τ1 ÞÞ
T V_ i þ ε1 α2 h ðt
τ1 ðtÞÞhðt
τ1 ðtÞÞ
FT ðhðt
τ1 ðtÞÞÞFðhðt
τ1 ðtÞÞÞ
�
(13)
T _ v_ ðθÞR2 vðθÞdθ
t τ2
don some drivers’ bad driving habits, which effectively reduce traffic accidents, and make traffic flow smoother. However, considering the current situation, AV technology is still immature and needs improve ment. In the future, there are two different types of vehicles on roads-the ACC vehicles and the vehicles unequipped the ACC system (Zhai et al., 2019). Based on this, this paper considers the manual vehicle as actuator failure, introducing a switch matrix, and the form M ¼ diagfm1 ; m2 ; :::mN g, where
� _ hðθÞdθ
t τ1
hðt
3 X
� T _ þ θÞ dθ v_ ðt þ θÞR2 vðt
T _ v_ ðtÞR2 vðtÞ
τ2
t τ1
Z
(11)
τ2 ÞÞ
With the rise of AI, more and more countries try to take advantage of computing machines replace manual operation. This principle mainly uses on-board sensors to sense the surrounding environment of vehicles, and adjusts the vehicle’s own speed in real time according to road conditions and other vehicle positions and speeds. Compared with manual vehicles, autonomous driving technology can effectively aban
T T V_ 2 ðtÞ ¼ h ðtÞQ1 hðtÞ þ vT ðtÞQ2 vðtÞ ð1 τ_ 1 ðtÞÞh ðt τ1 ðtÞÞQ1 hðt τ1 ðtÞÞ T ð1 τ_ 2 ðtÞÞv ðt τ2 ðtÞÞQ2 vðt τ2 ðtÞÞ T T � h ðtÞQ1 hðtÞ þ vT ðtÞQ2 vðtÞ ð1 d1 Þh ðt τ1 ðtÞÞQ1 hðt τ1 ðtÞÞ T ð1 d2 Þv ðt τ2 ðtÞÞQ2 vðt τ2 ðtÞÞ
0
vðt
4. Design of the feedback controller
T
Z
τ2 ÞÞ R2 ðvðtÞ
t τ2
_ < 0, namely the new model when condition (8) hold, then we know VðtÞ (1) is asymptotically stability, In other words, the traffic congestion will be not appear.
þ vT ðtÞCT1 P2 hðtÞ þ h ðtÞP2 C1 vðtÞ
V_ 3 ðtÞ ¼
vðt
_ vðθÞdθ
τ2
T T _ _ þ h_ ðtÞP2 hðtÞ þ hT ðtÞP2 hðtÞ V_ 1 ðtÞ ¼ v_ ðtÞP1 vðtÞ þ vT ðtÞP1 vðtÞ
¼ ðAFðhðt
ðvðtÞ
t τ2 T
�
t
Set ΠðtÞ ¼ ½vðtÞ;vðt τ2 ðtÞÞ;vðt τ2 Þ;hðtÞ;hðt τ1 ðtÞÞ;hðt τ1 Þ;Fð �Þ�, in view of the Schur complement lemma, we obtain V_ � Π T ðtÞΩΠðtÞ 2 3 1 P1 A R2 P2 C 1 0 0 P1 A 0 6Σ1 7 τ2 6 7 7 6 6 * ðd 1ÞQ 7 0 0 0 0 0 β P A 2 2 6 2 1 7 7 6 7 6 1 7 6* * R 0 0 0 0 0 2 7 6 τ 2 6 7 6 7 6 7 1 1 6* 7 * * Q R 0 R 0 0 1 1 1 6 7 τ τ 1 1 Ω¼ 6 7 6 7 2 7 6* * * * ðd1 1ÞQ1 þ ε1 α 0 0 0 6 7 7 6 7 6 1 7 6* * * * * R 0 0 1 7 6 τ1 7 6 6 7 6* ε * * * * * 1 I β 2 P1 A 7 6 7 6 7 1 4 5 * * * * * * * β2 P1
V1 ðtÞ ¼ vT ðtÞP1 vðtÞ þ h ðtÞP2 hðtÞ Z
τ2
�Z R2
i¼1
VðtÞ ¼ V1 ðtÞ þ V2 ðtÞ þ V3 ðtÞ
V2 ðtÞ ¼
_ vðθÞdθ
τ2
1
�T
t
Using the above inequalities, we got
Then said that the new model Eq. (1) is stable. Building the L
�Z
For any values of ε1 > 0, exist the α > 0, making the following expression is established: � T ε1 α2 h ðt τ1 ðtÞÞhðt τ1 ðtÞÞ FT ðhðt τ1 ðtÞÞÞFðhðt τ1 ðtÞÞÞ � 0 (12)
(8)
Prove.
1 T _ v_ ðθÞR2 vðθÞdθ �
t τ2
τ2
where: Σ 1 ¼ Q2 þ τ1 CT1 R1 C1
t
(10)
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� mi ¼
Journal of Environmental Management 256 (2020) 109975
2
1; represent thevehicle haveACC system 0; represent thevehicle unequiped the ACC system;namelymanualvehicle
6Σ 6 6 6 6 * ðd2 6 6 6 6* 6 6 6 6 6* 6 6 6 6 6* 6 6 6 6* 6 6 6 6 6* 6 6 4 *
(14) where: cles, if
PN i¼1
PNN
mi
i¼1
represent the penetration of the ACC vehicles in all vehi
mi
¼ 1, then represent all vehicles is ACC vehicles, mean
N P N mi while, if i¼1 ¼ 0 represent all vehicles is manual vehicles. N Then uðtÞ ¼ MuðtÞ, so the system transform into as following:
v_i ðtÞ ¼ αi ðFðhi ðt
τ1 ðtÞÞÞ
(15)
τ2 ðtÞÞÞ þ mi ui ðtÞ
vi ðt
In order to improve the robustness of the automatics vehicle, uti lizing the speed difference of successive vehicles, the state feedback controller is designed as follows ui ðtÞ ¼ ki ðvi 1 ðtÞ
(16)
vi ðtÞÞ
Here, ki stands for the gain coefficient. Applying the designed controller (13) to (14), then the close-loop car-following system is given: v_i ðtÞ ¼ αi ðFðhi ðt
τ1 ðtÞÞÞ
τ2 ðtÞÞÞ þ mi ki ðvi 1 ðtÞ
vi ðt
h_ i ðtÞ ¼ vi 1 ðtÞ
τ1 ðtÞÞÞ
τ2 ðtÞÞÞ þ mi ki ðvi 1 ðtÞ
vi ðt
τ1 ðtÞÞÞ
T _ h_ ðtÞR1 hðtÞ
T _ þ θÞ�dθ þ h_ ðt þ θÞR1 hðt
τ1 T _ þ τ v_ T ðtÞR vðtÞ _ � τ1 h_ ðtÞR1 hðtÞ 2 2
Z
Z
0
t
T _ h_ ðθÞR1 hðθÞdθ
t τ1
Z
*
*
*
ðd1 1ÞQ1 þ ε1 α2
*
*
*
*
*
*
*
*
*
*
*
*
Q1
τ1
R1
0
t
τ2
1
τ2 β1 P1 ; P1 MK
τ1 ðtÞÞÞ
¼L
τ2 ðtÞÞ þ MKC1 vðtÞÞT P1 vðtÞ τ1 ðtÞÞÞ Avðt τ2 ðtÞÞ þ MKC1 vðtÞÞ Avðt T
þvT ðtÞCT1 P2 hðtÞ þ h ðtÞP2 C1 vðtÞ
(22)
T T V_ 2 ðtÞ ¼ h ðtÞQ1 hðtÞ þ vT ðtÞQ2 vðtÞ ð1 τ_ 1 ðtÞÞh ðt τ1 ðtÞÞQ1 hðt τ1 ðtÞÞ T ð1 τ_ 2 ðtÞÞv ðt τ2 ðtÞÞQ2 vðt τ2 ðtÞÞ T T � h ðtÞQ1 hðtÞ þ vT ðtÞQ2 vðtÞ ð1 d1 Þh ðt τ1 ðtÞÞQ1 hðt τ1 ðtÞÞ T ð1 d2 Þv ðt τ2 ðtÞÞQ2 vðt τ2 ðtÞÞ (23)
(24)
T _ v_ ðθÞR2 vðθÞdθ
t τ2
priate dimension matrix L, make the following conditions hold:
Based on Eq. (10)–(12), we got
(20)
β1 P1 < R2 < β2 P1
1
*
� T _ þ θÞ dθ v_ ðt þ θÞR2 vðt
T _ v_ ðtÞR2 vðtÞ
τ2
0
þ v ðtÞP1 ðAFðhðt
Theorem 2. Based on the error dynamic Eq. (18), and the time varying lag function τi ðtÞ satisfying (2), for any given scalar ε1 > 0, if exist α; β1 ; β2 > 0, the positive definite matrix Pi ; Qi ; Ri ði ¼ 1; 2Þ, and the appro
0
0
*
T
where: K ¼ diagfk1 ; k2 ; :::; kn g.
Z
β 1 P1
τ2
¼ ðAFðhðt
_ ¼ C vðtÞ hðtÞ 1
V_ 3 ðtÞ ¼
0
1
*
(19)
τ2 ðtÞÞÞ þ MKC1 vðtÞ
0
T T _ _ þ h_ ðtÞP2 hðtÞ þ hT ðtÞP2 hðtÞ V_ 1 ðtÞ ¼ v_ ðtÞP1 vðtÞ þ vT ðtÞP1 vðtÞ
(18)
vðt
0
3 P1 A β2 LC1 7 7 7 7 0 0 β 2 P1 A 7 7 7 7 7 0 0 0 7 7 7 7 1 7 R1 0 0 7 τ1 7 <0 7 7 7 0 0 0 7 7 7 1 7 R1 0 0 7 τ1 7 7 7 ε1 I β2 P1 A 7 * 7 7 5 1 * * β 2 P1 0
Prove. Considering the given condition (2) and the derivative of (12), we construct the Lyapunov Krasovskii function like (9) and obtain
Let hðtÞ ¼ ½h1 ðtÞ;h2 ðtÞ;:::hn ðtÞ�;vðtÞ ¼ ½v1 ðtÞ;v2 ðtÞ;:::vn ðtÞ�, then (17) is re-written as: _ ¼ AðFðhðt vðtÞ
0
Then with the controller of the formula (14) existing, the error dy namic system is still stable under the designed controller, which can be obtained based on the LMIs solution.
vi ðtÞÞ
vi ðtÞ
1ÞQ2
P2 C 1
where: Σ ¼ LC1 þ CT1 LT þ Q2 þ τ1 CT1 R1 C1
with the error hi ðtÞ; vi ðtÞ, then the error dynamic equation of above equation is: v_ i ðtÞ ¼ αi ðFðhi ðt
τ2
β1 P1
(21)
(17)
vi ðtÞÞ
1
P1 A
Manual Vehicles Automatic Vehicles
Automatic Vehicles
Regular Vehicles
Fig. 1. N cars driving in a single lane, the black solid line represents the communication between AVs, and the communication can be realized; the red dotted line represents the manual vehicle and the vehicle communication did not implemented. 4
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Journal of Environmental Management 256 (2020) 109975
Fig. 2. The velocity curve of all vehicles in (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon.
Fig. 3. The acceleration of all vehicles under (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon.
Fig. 4. The velocity of car 1, 6 and 11 simulated in (a) the manual vehicles platoon and (b) the heterogeneous vehicles platoon.
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Journal of Environmental Management 256 (2020) 109975
Fig. 5. The acceleration’ evolutions of car 1, 6 and 11 simulated in (a) the manual vehicles platoon and (b) the heterogeneous vehicles platoon.
V_ �
3 X
T V_ i þ ε1 α2 h ðt
τ1 ðtÞÞhðt
τ1 ðtÞÞ
FT ðhðt
τ1 ðtÞÞÞFðhðt
situations are analysed. Through the simulation tests we verify the feasibility and effectiveness of the method.
�
τ1 ðtÞÞÞ
i¼1
(25)
5.1. Braking process simulation
Then we know V_ � Π T ðtÞΩΠðtÞ 2 3 1 P1 A βP P2 C 1 0 0 P1 A β2 LC1 7 6Σ τ2 1 1 6 7 6 7 6 * ðd 1ÞQ 7 0 0 0 0 0 β P A 2 2 1 6 7 2 6 7 6 7 1 6* 7 * β1 P1 0 0 0 0 0 6 7 τ2 6 7 6 7 6 7 1 1 6* 7 * * Q1 R1 0 R1 0 0 6 7 τ1 τ1 Ω¼ 6 7 6 7 2 6* 7 * * * ðd 1ÞQ þ ε α 0 0 0 1 1 1 6 7 6 7 6 7 1 6* 7 * * * * R 0 0 1 6 7 τ 1 6 7 6 7 6* 7 * * * * * ε I β P A 1 2 1 6 7 6 7 1 4 5 * * * * * * * β 2 P1
We consider an arriving vehicle platoon with 11 vehicles on a single lane equipped with a traffic light. Followings are the assumed initial conditions: (1) the green traffic signal is on and the 11 vehicles are moving at a uniform speed of 0.964 m/s; (2) the 11th vehicle is at the starting point; (3) the distance between the first vehicle (the leader car of the platoon) and the traffic light is 2 m; (4) the distances between the rear and front ends of the successive vehicles are all 2 m. Then at time t ¼ 0, when the traffic light turned red, the first vehicle begins to decel erate at once, other vehicles also follow their front vehicle to decelerate. Finally, all vehicles stop in a line behind the stop line. For convenience, we assume that all vehicle control parameters and drivers’ sensitivity are homogeneous, the driver’s sensitivity is a ¼ 1; i ¼ 1; 2; :::11. Consistent with Zhai and Liu (2016), then the lag function is set as follows:
τ2
(27)
τ1 ¼ 0:25 þ 0:15 cosðtÞ; τ2 ¼ 0:25 þ 0:1 cosðtÞ
(26)
where: τ1 ¼ 0.4, τ2 ¼ 0.1, the initial speed and initial space headway of each vehicle are
_ Using Eqs. (20)–(21) we obtain VðtÞ<0, then the dynamic system Eq. (18) is stable.
hi ðtÞ ¼ 2; t 2 ½
5. Simulation tests
τ1 ; 0�;
vi ðtÞ ¼ 0:964; t 2 ½
τ2 ; 0�
(28)
It should be noted that the lag time consistent with the cosine function, for all function with meet condition (2) can be regarded as the lag function (see Fig. 1).
In this section, the vehicles following behaviours under different
Fig. 6. The headway’ evolutions of car 1, 6 and 11 simulated in (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon. 6
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Journal of Environmental Management 256 (2020) 109975
Fig. 2 illustrates the speeds’ evolutions of 11 vehicles simulated by the proposed new car-following model in the situation of the manual vehicle platoon and the heterogeneous vehicle platoon. In heteroge neous platoon, car 1, 6, 11 are manual vehicles, and the rest are ACC vehicles. All ACC vehicles in both platoons are equipped with the controller, which can be obtained by solving theorem 3.2 via LMIs. The simulation results show that the manual vehicle has less ability to suppress traffic congestion due to the different speed adjustments of the manned car and the ACC vehicle (Fig. 2). It appears stronger overall shock, even the reverse phenomenon, in the manual vehicle platoon as shown in Fig. 2 (a). The ACC vehicles are able to quickly restore equi librium (Fig. 2 (b)), which means the ACC vehicles effectively alleviate traffic congestion phenomenon. Fig. 3 shows the acceleration curve of 11 cars simulated by the proposed car following model under manual traffic environment and the heterogeneous traffic environment respectively. In Fig. 3 (a), some ve hicles even appeared to accelerate. However, in Fig. 3 (b), we can see that the acceleration of the vehicles (excepting the head car) is small. Meanwhile, the differences of the acceleration of each vehicles is low, which further verify that the controller can effectively enhances the coordination between vehicles, making the platoon to effectively maintain steady. For further study the impact of the heterogeneous vehicles on the following vehicles’ speeds, accelerations and headways, we carry out the following comparative analysis between three vehicles in the manual vehicle platoon and the heterogeneous vehicle platoon. Fig. 4 compares the velocity curves between the manual vehicle platoon and the heterogeneous vehicle platoon, from which we can draw the following conclusions: the velocity curves of the 1st,6th,11th cars in the heterogeneous vehicle platoon are smoother, without obvious fluctuations. Fig. 5 compares the acceleration-time curve between the two pla toons. It is easy to found that the reverse phenomenon in (a) manual vehicle platoon has been disappear in (b) the heterogeneous vehicle platoon. What’s more, the amplitude of acceleration has been effectively reduced in the heterogeneous vehicle platoon (Fig. 5 (b)). It also shows that based on the cooperative control of our controller designed, the congestion can be relieved without experiencing obvious decelerations, and the consistency of the platoon can be maintained by coordination between vehicles. Fig. 6 compares the headway-time curve between the two platoons. The controller can widen the headway between adjacent vehicles and also reduce the interaction between the vehicles, so that the vehicles have enough headway to adjust its speed, thereby achieving the purpose of relieving congestion.
Fig. 7. The manual vehicles’ (a) velocity curve of three cars (b) velocity of all cars, and (c) space headway.
Fig. 8. The ACC vehicles’ (a) velocity curve of three cars, (b) velocity of all cars, and (c) space headway.
5.2. Traffic flow evolution simulation with external disturbance The simulation test represents the car following situation with an
Fig. 9. The CO emission of the 1st, 6th, 11th vehicles in (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon during periods of ½90s; 140s�. 7
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Journal of Environmental Management 256 (2020) 109975
Fig. 10. The HC emission of the 1st, 6th, 11th vehicles in (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon during periods of ½90s; 140s�.
Fig. 11. The Fuel consumption of the 1st, 6th, 11th vehicles in (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon during periods of ½90s;140s�.
external disturbance, by making the velocity of the leading vehicle reduced from v0 to 0 at [100s–102s]. Fig. 7 shows the velocities and the space headway of the manual vehicle platoon. Fig. 8 shows the speeds, the space headway of the heterogeneous vehicle platoon (with both manual vehicles and ACC controlled vehicles) (see Fig. 9). Simulation results show that in manual vehicle platoon situation, the velocity fluctuation of the leading car brought fluctuation to all the rear manual vehicles speeds and space headways. Moreover, the restoration time to the desired speed of each vehicle would be relatively larger than that in Fig. 8. Therefore, in manual vehicle platoon the oscillation of the traffic occurs more frequently. The comparisons of Figs. 7 and 8 demonstrated that the controller could effectively improve the convergence capability, reduce the restoration time to the desired speed of vehicles at the same time, and relieve the vibration range of all vehicles in the platoon. Though speeds and space headways continue to present vibrations in manual vehicles in the heterogeneous vehicle platoon, this method is nevertheless effective in reducing traffic congestion in a “heterogeneous” environment. Last, the simulation results verified the efficiency of the feedback controller in reducing fuel consumption and exhaust emission. Consid ering that the traffic emission model is time consuming (Tang et al., 2015), we applied the VT-Micro model in the present work (Zhai et al., 2019). This model mainly demonstrates the relationship of fuel con sumption and exhaust emission with the speed and acceleration of the vehicle. The relationship is derived from the following equation: InðMOEeÞ ¼
� �j � 3 X 3 � X dv K ei;j � vi � dt i¼0 j¼0
Fig. 10 demonstrates the curve of the cumulative fuel consumption with emission of CO, HC, and NOx in the manual vehicle platoon, the ACC vehicle platoon and the heterogeneous vehicle platoon, respec tively. Comparisons between the manual vehicle platoon and the het erogeneous vehicle platoon indicates that regardless of fuel consumption and emission of CO, HC, or NOx emission, the heteroge neous vehicle platoon perform better than the manual vehicle platoon in the amount of the exhaust emissions and fuel consumption, which verify that the controller is effective in reducing fuel consumption and emis sions (see Fig. 12) (see Fig. 11). 5.3. The exhaust emission of the vehicles under difference penetration Table 1 presents the amount of all vehicle exhaust emissions under different ACC penetration. Considering the position where the ACC ve hicles will influence the authenticity of the results, based on different penetration of ACC, statistics 100 times of all vehicles emissions under different ACC vehicle position in the platoon in the period of 100s–140s respectively. Finally, by the average we got the total emissions of the vehicles under difference ACC vehicles penetration. The method is effective to overcome the influence of ACC position distribution on all vehicles emissions, and is able to reflect the penetration of ACC vehicles’ impact on the exhaust emission (Bracha et al., 2018; Ross et al., 2018; Xiong et al., 2018; Noelia et al., 2018; Rathna et al., 2018; Wang et al., 2019). From Table 1, we can see that as the penetration of ACC vehicles increases, the amount of exhaust emissions gradually decreases. The minimal exhaust emission in the ACC vehicles is 100%, which also verifies the ACC vehicle’s ability to reduce vehicle emissions even dur ing normal driving process.
(29)
where: MOEe represents the instant emission or the instant fuel con sumption ratio. Kei;j represents the related regression coefficient, and the
specific value can be obtained from the work of Tang et al. (2015).
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Fig. 12. The NOx emission of the 1st, 6th, 11th vehicles in (a) the manual vehicle platoon and (b) the heterogeneous vehicle platoon during periods of ½90s; 140s�.
Acknowledgment
Table 1 The exhaust emission of the vehicles under difference penetration. The exhaust emission
The market penetration rate of the ACC Vehicles 0%
25%
50%
75%
100%
CO
1234.1 (100%) 171.25 (100%) 232.72 (100%) 242.35 (100%)
1204.9 (97.6%) 167.97 (98.0%) 228.41 (98.1%) 239.37 (98.7%)
1180.3 (95.6%) 164.33 (95.9%) 224.50 (96.5%) 237.44 (97.9%)
1172.8 (95.0%) 162.51 (94.9%) 223.67 (96.1%) 235.69 (97.2%)
1168.7 (94.7%) 161.83 (94.5%) 222.8 (95.7%) 234.9 (96.9%)
NOx HC Fuel
This work was partially supported by the Science and Technology Planning Project of Guangdong Province (Grant Nos. 2017A040405021), National Natural Science Foundation of China (Grant Nos. 51408237, 51808151, 51775565), Fundamental Research Funds for the Central Universities (Grant No.18LGPY83), and the Fundamental Research Funds for Guangdong Communication Poly technic(20181014). References Ahn, K., Rakha, H., Trani, A., et al., 2014. Estimating vehicle fuel consumption and emissions based on instantaneous speed and acceleration levels. Transp. Eng. J. ASCE 128 (2), 182–190. https://doi.org/10.1061/(ASCE)0733-947X(2002)128:2 (182). Bracha, Y., Schindler, B.Y., Leon, B., et al., 2018. Green roof and photovoltaic panel integration: effects on plant and arthropod diversity and electricity production. J. Environ. Manag. 225, 288–299. https://doi.org/10.1016/j.jenvman.2018.08.017. Deny, D.M., Teresa, A.B., Valentina, C., 2018. Energy efficiency and reduction of CO2 emissions from campsites management in a protected area. J. Environ. Manag. 222, 368–377. https://doi.org/10.1016/j.jenvman.2018.05.084. Francesco, F., Guido, P., Mariangela, R., et al., 2018. Car-sharing services: an annotated review. Sust. Cities Soc. 37, 501–518. https://doi.org/10.1016/j.scs.2017.09.020. Hong, T., Koo, C., Kim, H., 2012. A decision support model for improving a multi-family housing complex based on CO2 emission from electricity consumption. J. Environ. Manag. 112, 67–78. https://doi.org/10.1016/j.jenvman.2012.06.046. Knorr, F., Schreckenberg, M., 2012. Influence of inter-vehicle communication on peak hour traffic flow. Physica A 391 (6), 2225–2231. https://doi.org/10.1016/j. physa.2011.11.027. Nilsson, J., Brannstrom, M., Fredriksson, J., et al., 2016. Longitudinal and lateral control for automated yielding manoeuvres. IEEE Trans. Intell. Transp. Syst. 17 (5), 1–11. https://doi.org/10.1109/TITS.2015.2504718. Noelia, O.T., Lluc, C.C., Beatriz, A.G., 2018. Sustainable design of a thermosolar electricity generation power plant in Burkina Faso. J. Environ. Manag. 226, 428–436. https://doi.org/10.1016/j.jenvman.2018.08.043. Rathna, R., Sunita, V., Ekambaram, N., 2018. Recent developments and prospects of dioxins and furans remediation. J. Environ. Manag. 223, 797–806. https://doi.org/ 10.1016/j.jenvman.2018.06.095. Ross, G., Gordon, W., Paul, C., et al., 2018. Storying energy consumption: collective video storytelling in energy efficiency social marketing. J. Environ. Manag. 213, 1–10. https://doi.org/10.1016/j.jenvman.2018.02.046. Sun, X.J., Zhang, H., Meng, W.J., et al., 2018. Primary resonance analysis and vibration suppression for the harmonically excited nonlinear suspension system using a pair of symmetric viscoelastic buffers. Nonlinear Dyn. 94, 1243–1265. https://doi.org/ 10.1007/s11071-018-4421-9. Tang, T.Q., LI, Jingang, Wang, Y.P., et al., 2013. Vehicle’s fuel consumption of carfollowing models. Sci. China Technol. Sci. 56 (5), 1307–1312. https://doi.org/ 10.1007/s11431-013-5182-9. Tang, T.Q., Yu, Q., Yang, S.C., et al., 2015. Impacts of the vehicle’s fuel consumption and exhaust emissions on the trip cost allowing late arrival under car-following model. Physica A 431, 52–62. https://doi.org/10.1016/j.physa.2015.02.041. Tang, T.Q., Shi, W.F., Shang, H.Y., et al., 2014. An extended car-following model with consideration of the reliability of inter-vehicle communication. Measurement 58, 286–293. https://doi.org/10.1016/j.measurement.2014.08.051.
6. Conclusion and future works Considering different receiver pattern as different time-varying lags and regarding the manual operations as the actuator existing failure constraints, an improved car-following model is proposed. By the theory of Lyapunov function, the sufficient condition of the traffic flow stability is given. That means traffic congestion can be avoided, and when the above stability conditions are not met, a new feedback controller is designed, and the detailed design steps are given. By the controller, which can be obtained by solving the LMI, the car-following model can satisfy the asymptotic stability under the heterogeneous vehicles envi ronment (Hong et al., 2012; Deny et al., 2018). Finally, by comparing the velocities, accelerations and space headway of the following vehicles in manual controlled vehicle platoon and the heterogeneous vehicles platoon, we found that the speed fluctuations under the feedback controller can be restored to equilibrium faster than the manual vehicle without the controller. Meanwhile the controller in reducing the exhaust emission and fuel consumption also has a significant effect. Yet, our work only focused on the car-following behaviours in single-lane, and the behaviour of the lane changing and the passing through the pro posed model did not reflect. Moreover, the assumptions of drivers’ lag time and driver sensitivity in the heterogeneous connected vehicle network environment were rather simple compared to the realistic driving behaviours. Future work will focus on the car following be haviours in more complex environments, with more realistic assump tions and considerations on some issues such as drivers’ lag time, sensitivity and so on by obtaining extensive natural driving data. Declaration of competing interest The authors declare that there is no conflict of interests regarding the publication of this article.
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