Model predictive control‐based eco‐driving strategy for CAV
2018; Institution of Engineering and Technology; Volume: 13; Issue: 2 Linguagem: Inglês
10.1049/iet-its.2018.5336
ISSN1751-9578
AutoresHongliang Wang, P Peng, Yanjun Huang, Xiaolin Tang,
Tópico(s)Vehicle Dynamics and Control Systems
ResumoIET Intelligent Transport SystemsVolume 13, Issue 2 p. 323-329 Research ArticleFree Access Model predictive control-based eco-driving strategy for CAV Hongliang Wang, Corresponding Author whl343@163.com Department of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094 Nanjing, People's Republic of ChinaSearch for more papers by this authorPai Peng, Department of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094 Nanjing, People's Republic of ChinaSearch for more papers by this authorYanjun Huang, Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, N2L3G1 CanadaSearch for more papers by this authorXiaolin Tang, State Key Laboratory of Mechanical Transmissions, College of Automotive Engineering, Chongqing University, Chongqing, 400044 Chongqing, People's Republic of ChinaSearch for more papers by this author Hongliang Wang, Corresponding Author whl343@163.com Department of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094 Nanjing, People's Republic of ChinaSearch for more papers by this authorPai Peng, Department of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094 Nanjing, People's Republic of ChinaSearch for more papers by this authorYanjun Huang, Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, N2L3G1 CanadaSearch for more papers by this authorXiaolin Tang, State Key Laboratory of Mechanical Transmissions, College of Automotive Engineering, Chongqing University, Chongqing, 400044 Chongqing, People's Republic of ChinaSearch for more papers by this author First published: 30 October 2018 https://doi.org/10.1049/iet-its.2018.5336Citations: 4AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract In this study, an eco-driving strategy is proposed to enhance the fuel efficiency of the connected autonomous vehicle (CAV) in car-following scenarios. First, the longitudinal dynamic model and fuel-consumption model of the vehicle are established. The speed trajectory of the preceding vehicles is obtained via vehicle-to-vehicle/vehicle-to-infrastructure communication function of CAVs, which is used as the reference of the following vehicles. Second, a model predictive controller is presented to optimise fuel consumption of the following vehicle. Finally, simulations in urban and highway driving conditions demonstrate that the proposed controller enables effective tracking of the preceding vehicle in an energy-efficient way. Comparisons between the second and the third following vehicles verify the fuel-saving benefits of the proposed method. 1 Introduction In recent years, due to the lack of oil fuel and people's increasing concern about the environmental pollution, more and more researchers have been involved in the study of improving the fuel economy of vehicles [1-4]. Besides the powertrain design and efficiency [5, 6], how the vehicles are operated [7, 8], especially traditional vehicles, play a great role on the fuel consumption of the vehicles [9]. Many works have been done on the correlation between driving style and fuel economy. The pulse-and-gliding (PnG) strategy has been widely studied in the eco-driving control during the past few years [10]. Xu et al. [11] researched PnG-type cruising strategy, in which the control action of engine and transmission is acquired via solving an optimal control problem. Li and Peng [12] investigated the fuel-optimal driving strategies during car-following manoeuvers and concluded that the optimal driving strategy would change from PnG to constant speed as the vehicle speed increases. On the basis of the optimisation outcomes in [12], Li et al. [13] make further efforts on a servo-loop control of PnG strategy. However, PnG strategy may not be an optimal one due to the poor comfort experience of the passengers. Model predictive control is an optimal control technique and suitable for vehicle driving control [14], it can be used to predict the vehicle states and optimise multiple control objectives under constraints [15]. Wu et al. [16] proposed a human–machine-cooperative-driving controller based on model predictive controller (MPC) to coordinate active front steering and direct yaw moment control. Wu et al. in [17] used MPC to recover more energy and minimise battery ageing in regenerative braking for hybrid electric vehicles. Many researchers have applied MPC to explore the fuel-saving potential without affecting the ride comfort of the passenger. Kamal et al. [18] used MPC with the continuation and generalised minimum residual methods to optimise fuel saving of ecological driving system. A non-linear MPC method in [19] is utilised to derive the vehicle control inputs to build an eco-driving system for different traffic conditions. With information about the road geometry, Hellström et al. [20] proposed a dynamic programming algorithm in the predictive controller to optimise the speed trajectory, fuel economy and driving time of a real truck in highway driving. Lim et al. [21] developed a distance-based eco-driving controller, the vehicle speed was long-term optimised and local adapted according to the traffic conditions. Research in [22] presents a fuel-saving adaptive cruise control based on MPC to improve the fuel economy and tracking accuracy with consideration of the road elevation information. Yu et al. [23] investigated an ecological driving control scheme for hybrid vehicles and used MPC to obtain optimal vehicle input with the information of the traffic signal and road slope. However, these studies merely consider the driving control of a single vehicle in single driving condition. Furthermore, without vehicle-to-vehicle/vehicle-to-infrastructure (V2V/V2I) communication, the above methods may have some shortcomings such as loss or delay of accuracy in obtaining the speed trajectory of the preceding vehicle, leading to the decrease of optimal control. This work aims to develop a fuel-saving predictive control method to enhance the fuel efficiency of connected autonomous vehicles (CAVs) in car-following conditions. First, the vehicle longitudinal dynamic model is constructed, and a fuel-consumption model is introduced. Second, a model predictive control method is presented to optimise the fuel consumption of the vehicle, and the speed trajectory information of the preceding vehicle is sharing with the following vehicle via V2V/V2I communication. Finally, the effectiveness of the controller is sufficiently verified under the urban and highway car-following scenarios, and the fuel-saving characteristics of the proposed method are proved by comparing the second and third following vehicles on fuel consumption. The remaining part of this paper is structured as follows: the car-following model is constructed in Section 2. The fuel-saving predictive control is designed in Section 3, the simulations and analyses in Section 4, and Section 5 ultimately summarises the conclusions. 2 Car-following model The car-following scenario is depicted in Fig. 1, the following vehicle (V2) is under the control of the proposed method to follow the speed trajectory of the preceding vehicle (V1) in a more ecological way. More specifically, the location and speed control of V2 is realised by taking the driving information of V1 as the reference in the proposed controller via V2V/V2I communication. The powertrain of CAVs mainly consists of an internal combustion engine and a continuously variable transmission (CVT). Fig. 1Open in figure viewerPowerPoint Car-following scenario of CAVs 2.1 Longitudinal dynamics The vehicle longitudinal dynamics can be formulated as (1) where the equivalent mass is denoted by , consisting of the vehicle mass m and the inertia of the rotating parts on the powertrain. is the driving force (2) where the engine torque is represented by , the CVT ratio is denoted by , is the differential ratio, is the overall powertrain efficiency, and r is the tyre-rolling radius. The rolling resistance is the rolling-friction force between the road and the vehicle tyres (3) where g represents the gravitational acceleration, the road slope is denoted by , and the rolling resistance coefficient is represented by f. The air resistance is (4) where the air density is denoted by , the frontal area is represented by , the drag coefficient is represented by , and the vehicle speed is denoted by v. is the grade resistance (5) New variables are defined by combining (1)–(5) (6) (7) The longitudinal dynamic equation can be simplified as (8) is the brake force, actuated by the brake system. Moreover, (8) will be used for optimisation calculation in Section 3. The main parameters of the vehicle longitudinal dynamics model are shown in Table 1. Table 1. Main parameters of the vehicle model Parameter Value Parameter Value m 1573.5 kg g 9.81 m/s2 3.33 0 r 0.3284 m f 0.01 0.9 A 3.0 m2 1.2258 kg/m3 0.3 0.1 g/s 1s 2.2 Fuel-consumption model On the basis of Willans line approximation, the fuel-consumption model is developed for the test vehicle [24, 25] (9) where e denotes the global engine efficiency, the lower heating values of fuel are represented by , indicates the friction mean effective pressure, the engine displacement volume is denoted by , and the fuel-consumption rate at idle is . 2.3 V2V/V2I communication CAV technologies replace human drivers with robots that can precisely execute well-designed driving algorithms with real-time access to traffic information from V2V/V2I communications [26]. The preceding vehicle and following vehicle connect automatically and interchange their position and speed data to each other when they are in V2V communication range. In V2I, the infrastructure plays a coordination role by gathering the speed trajectory of the preceding vehicle and then delivering to the following vehicle with the goal of optimising the fuel consumption of the following vehicle. 3 Fuel-saving predictive control To optimise the fuel economy in the same mileage, and given the speed fluctuations between the preceding vehicle and the following vehicle, the cost function J of this optimal control problem can be written as (10) where is the size of the prediction horizon, is the speed of the preceding vehicle, and the location of the following vehicle and the preceding vehicle are represented by and , respectively (11) (12) (13) According to (1)–(9) and (11)–(13), J also can be described as functions of the engine torque , the CVT ratio , and the brake force which are selected as the decision variables. The constraints of this optimal control problem at every prediction step consist of the equality constraints (11)–(13) and the inequality ones (14) (14) where is the allowed speed difference between the preceding vehicle and the following vehicle; the engine speed is limited by and ; and (a function of ) indicate the range of engine torque; and is the limit value of the CVT ratio. and are the bounds for the brake force applied to the wheels. To improve the computational efficiency, the negative value of is substituted for the brake force ; so the bounds for the brake force and the engine torque can be merged into one. is a negative value, which can be equivalent to . The fuel-consumption optimal control problem with a prediction horizon from the current time step i to is characterised as the equation below: (15) Sequential quadratic programming algorithm is used to solve the optimal control problem for its effectiveness has been studied and proved in many MPC applications [27, 28]. For that it is a non-linear control system, Taylor expansion is used to linearise the system. The optimised input of the decision variables is obtained from (15), and is added to the former step variable and to get the value of and , which is retained as the actuation action to the following vehicle. Fig. 2 shows the schematic representation of the proposed fuel-saving predictive control in car-following scenarios. The threshold values of the control scheme are listed in Table 2. Table 2. Threshold values Parameter Value Parameter Value −1000 Nm 300 Nm 0.69 4.14 1000 r/min 5000 r/min 5 m/s — — Fig. 2Open in figure viewerPowerPoint Fuel-saving predictive control in a car-following scenario 4 Simulations and analyses 4.1 Effectiveness of the proposed scheme The MPC-based controller is tested in urban and highway driving modes. The size of the prediction horizon is designated as 3, the initial speed of the preceding vehicle is set to be 0, and the initial safety distance is 50 m. For simplicity, the speed profile of the preceding vehicle is extracted from the urban dynamometer driving schedule cycle and used to represent the one obtained by V2V/V2I in urban traffic scenario. The optimised result is shown In Fig. 3 ; it can be discerned that the proposed scheme can implement automatically tracking of the speed of the preceding vehicle, the safety distance between V1 and V2 varies with the speed, and no safety issue is observed in the whole horizon. A closer examination reveals that the speed of the following vehicle is higher than the preceding vehicle during each brake, which means the brake force of the following vehicle is smaller. It would be beneficial to apply a small brake force to avoid energy waste. The results of the decision variables are depicted in Fig. 4, both torque and CVT ratios are within the limits. Fig. 3Open in figure viewerPowerPoint V1 and V2 in the urban driving scenario (a) Speed, (b) Safety distance Fig. 4Open in figure viewerPowerPoint Decision variables of V2 in the urban driving scenario (a) Torque, (b) CVT ratio To emulate the highway driving scenario, the speed profile of the preceding vehicle is extracted from the highway fuel economy test cycle. Figs. 5 and 6 show the optimisation results, from which we can see that the proposed controller is equally effective in highway driving. Fig. 5Open in figure viewerPowerPoint V1 and V2 in highway driving scenario (a) Speed, (b) Safety distance Fig. 6Open in figure viewerPowerPoint Decision variables of V2 in highway driving scenario (a) Torque, (b) CVT ratio 4.2 Fuel-saving characteristic This section discusses the fuel-saving characteristic of the proposed controller. As the fuel consumption of V1 is unavailable, another vehicle (V3) is utilised to verify the proposed scheme by comparison with V2 in terms of fuel consumption. The same with V2, V3 obtains the speed trajectory of the preceding vehicle (V2) via V2V/V2I communication and follows V2 in a fuel-efficient way under the proposed controller, as shown in Fig. 7. Fig. 7Open in figure viewerPowerPoint Car-following scenarios of three CAVs The optimisation outcomes of V3 in urban driving are illustrated in Figs. 8 and 9. It can be seen from Fig. 8 that the MPC controller ensures effective tracking of the speed of V2. The engine torque, as well as CVT ratio of V3, is depicted in Fig. 9. Similar optimisation results of V3 in highway driving can be found in Figs. 10 and 11. Fig. 8Open in figure viewerPowerPoint V2 and V3 in the urban driving scenario (a) Speed, (b) Safety distance Fig. 9Open in figure viewerPowerPoint Decision variables of V3 in the urban driving scenario (a) Torque, (b) CVT ratio Fig. 10Open in figure viewerPowerPoint V2 and V3 in highway driving scenario (a) Speed, (b) Safety distance Fig. 11Open in figure viewerPowerPoint Decision variables of V3 in highway driving scenario (a) Torque, (b) CVT ratio Fig. 12 shows the fuel consumption and driving distance of V2 and V3 in urban and highway conditions, from which we can see that the fuel consumption of V3 is no more than V2 at the same driving distance. The fuel consumptions of V2 and V3 in two different driving modes are presented in Table 3, the fuel consumption of V3 is decreased by 2.63% in urban driving condition and 1.14% in highway driving condition compared with V2, identifying that the proposed controller is able to effectively improve the fuel economy of the following vehicle in car-following scenarios. Table 3. Fuel consumption for the proposed controller Driving condition CAV Fuel consumption, g/km urban V2 45.59 V3 44.42 highway V2 43.66 V3 43.17 Fig. 12Open in figure viewerPowerPoint Fuel consumption and distance of V2 and V3 (a) Urban, (b) Highway 5 Conclusion In this paper, an eco-driving strategy was put forward to enhance the fuel efficiency in car-following scenarios for CAVs. In the control synthesis, the vehicle longitudinal dynamic model was developed, and the fuel-consumption model was introduced. Then, the MPC was constructed to optimise the speed and fuel economy of the following vehicle. V2V/V2I communication is utilised to gather the speed trajectory of the preceding vehicle and then deliver it to the following vehicle. Simulation results in urban and highway driving conditions verified that the following vehicles can effectively track the speed trajectory of the preceding vehicle under our proposed scheme. As the fuel consumption is unavailable, the comparison between V2 and V3 was made to prove the fuel-saving characteristic of the proposed controller. The comparative outcomes revealed that the fuel consumption of V3 is decreased by 2.63 and 1.14% than V2 in urban and highway driving conditions, respectively, which demonstrated that the proposed controller was capable of improving the fuel economy of the following vehicle in the car-following scenarios. 6 Acknowledgments This work was supported by the Project of Jiangsu Provincial Six Talent Peaks (Grant no. 2016-JXQC-020), the Fundamental Research Funds for the Central Universities (Grant no. 309171B8811), the National Natural Science Fund of China (Grant nos. 51205209 and 51205204), and the China Scholarship Council Funds (Grant no. 201606845008). 7 References 1Huang Y. Khajepour A. Ding H. et al.: ' An energy-saving set-point optimiser with a sliding mode controller for automotive air-conditioning/refrigeration systems', Appl. Energy, 2017, 188, pp. 576– 585CrossrefWeb of Science®Google Scholar 2Zhang S. Wu Y. Un P. et al.: ' Modeling real-world fuel consumption and carbon dioxide emissions with high resolution for light-duty passenger vehicles in a traffic populated city', Energy, 2016, 113, pp. 461– 471CrossrefCASWeb of Science®Google Scholar 3Li L. Wang X. Song J.: ' Fuel consumption optimization for smart hybrid electric vehicle during a car following process', Mech. Syst. Signal Process., 2016, 87, (1), pp. 17– 29Google Scholar 4Wang H. Huang Y. Khajepour A.: ' Cyber-physical control for energy management of off-road vehicles with hybrid energy storage systems', IEEE-ASME Trans. Mechatronics., 2018, DOI: 10.1109/TMECH.2018.2832019 CrossrefWeb of Science®Google Scholar 5Tang X. Yang W. Hu X. et al.: ' A novel simplified model for torsional vibration analysis of a series–parallel hybrid electric vehicle', Mech. Syst. Signal Process., 2017, 85, pp. 329– 338CrossrefWeb of Science®Google Scholar 6Tang X. Hu X. Yang W. et al.: ' Novel torsional vibration modeling and assessment of a power-split hybrid electric vehicle equipped with a dual mass flywheel', IEEE Trans. Veh. Technol., 2018, 67, (3), pp. 1990– 2000CrossrefWeb of Science®Google Scholar 7Li C. Jing H. Wang R. et al.: ' Vehicle lateral motion regulation under unreliable communication links based on robust h ∞ output-feedback control schema', Mech. Syst. Signal Process., 2018, 104, pp. 171– 187CrossrefWeb of Science®Google Scholar 8Wang R. Jing H. Wang J. et al.: ' Robust output-feedback based vehicle lateral motion control considering network-induced delay and tire force saturation', Neurocomputing, 2016, 214, pp. 409– 419CrossrefWeb of Science®Google Scholar 9Van Mierlo J. Maggetto G. Van Burgwal E. et al.: ' Driving style and traffic measures - influence on vehicle emissions and fuel consumption', Proc. Inst. Mech. Eng. D., J. Automob., 2005, 218, (1), pp. 43– 50CrossrefGoogle Scholar 10Li S.E. Hu X. Li K. et al.: ' Mechanism of vehicular periodic operation for optimal fuel economy in free-driving scenarios', IET Intell. Transp. Syst., 2015, 9, (3), pp. 306– 313Wiley Online LibraryWeb of Science®Google Scholar 11Xu S. Li S.E. Zhang X. et al.: ' Fuel-optimal cruising strategy for road vehicles with step-gear mechanical transmission', IEEE Trans. Intell. Transp. Syst., 2015, 16, (6), pp. 3496– 3507CrossrefWeb of Science®Google Scholar 12Li S.E. Peng H.: ' Strategies to minimize fuel consumption of passenger cars during car following scenarios', Proc. Inst. Mech. Eng. D., J. Automob., 2011, 226, (3), pp. 2107– 2112Google Scholar 13Li S.E. Peng H. Li K. et al.: ' Minimum fuel control strategy in automated car following scenarios', IEEE Trans. Veh. Technol., 2012 61, (3), pp. 998– 1007CrossrefWeb of Science®Google Scholar 14Huang Y. Wang H. Khajepour A. et al.: ' Model predictive control power management strategies for HEVs: a review', J. Power Source, 2017, 341, pp. 91– 106CrossrefCASWeb of Science®Google Scholar 15Li L. Lu Y. Wang R. et al.: ' A 3-dimensional dynamics control framework of vehicle lateral stability and rollover prevention via active braking with MPC', IEEE Trans. Ind. Electron., 2016, 64, pp. 3389– 3401CrossrefWeb of Science®Google Scholar 16Wu J. Cheng S. Liu B. et al.: ' A human–machine-cooperative-driving controller based on AFS and DYC for vehicle dynamic stability', Energies, 2017, 10, (11), pp. 1737– 1746CrossrefWeb of Science®Google Scholar 17Wu J. Wang X. Li L. et al.: ' Hierarchical control strategy with battery aging consideration for hybrid electric vehicle regenerative braking control', Energy, 2018, 145, (2), pp. 301– 312CrossrefGoogle Scholar 18Kamal M.A.S. Mukai M. Murata J. et al.: ' On board eco-driving system for varying road-traffic environments using model predictive control'. IEEE Int. Conf. Control Applications, Yokohama, Japan, September 2010, pp. 1636– 1641CrossrefGoogle Scholar 19Kamal M.A.S. Mukai M. Murata J. et al.: ' Ecological vehicle control on roads with up–down slopes', IEEE Trans. Intell. Transp. Syst., 2011, 12, (3), pp. 783– 794CrossrefWeb of Science®Google Scholar 20Hellström E. Ivarsson M. Âslund J. et al.: ' Look-ahead control for heavy trucks to minimize trip time and fuel consumption', Control Eng. Pract., 2009, 17, (2), pp. 245– 254CrossrefWeb of Science®Google Scholar 21Lim H. Su W. Mi C.C.: ' Distance-based ecological driving scheme using a two-stage hierarchy for long-term optimization and short-term adaptation', IEEE Trans. Veh. Technol., 2017, 66, (3), pp. 1940– 1949CrossrefWeb of Science®Google Scholar 22Li S.E. Guo Q. Xu S. et al.: ' Performance enhanced predictive control for adaptive cruise control system considering road elevation information', IEEE Trans. Intell. Veh., 2017, 2, (3), pp. 150– 160CrossrefCASGoogle Scholar 23Yu K. Yang J. Yamaguchi D.: ' Model predictive control for hybrid vehicle ecological driving using traffic signal and road slope information', Control Theory Technol., 2015, 13, (1), pp. 17– 28CrossrefGoogle Scholar 24Ozatay E. Ozguner U. Filev D. et al.: ' Analytical and numerical solutions for energy minimization of road vehicles with the existence of multiple traffic lights'. IEEE Conf. Decision and Control, Palazzo dei Congressi, Florence, Italy, December 2013, pp. 7137– 7142CrossrefGoogle Scholar 25Jing J.: ' Vehicle fuel consumption optimization using model predictive control based on V2V communication', Master's thesis, The Ohio State University, 2014Google Scholar 26Masikos M. Demestichas K. Adamopoulou E. et al.: ' Machine-learning methodology for energy efficient routing', IET Intell. Transp. Syst., 8, 2013, (3), pp. 255– 265Wiley Online LibraryWeb of Science®Google Scholar 27Xie W. Bonis I. Theodoropoulos C.: ' Data-driven model reduction-based nonlinear MPC for large-scale distributed parameter systems', J. Process Control, 2015, 35, pp. 50– 58CrossrefCASWeb of Science®Google Scholar 28Torrisi G. Grammatico S. Cortinovis A. et al.: ' Model predictive approaches for active surge control in centrifugal compressors', IEEE Trans. Control Syst. Technol., 2016, 25, (6), pp. 1947– 1960CrossrefWeb of Science®Google Scholar Citing Literature Volume13, Issue2February 2019Pages 323-329 FiguresReferencesRelatedInformation
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