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Stochastic sampled-data multi-objective control of active suspension systems for in-wheel motor driven electric vehicles
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作者 Iftikhar Ahmad Xiaohua Ge Qing-Long Han 《Journal of Automation and Intelligence》 2024年第1期2-18,共17页
This paper addresses the sampled-data multi-objective active suspension control problem for an in-wheel motor driven electric vehicle subject to stochastic sampling periods and asynchronous premise variables.The focus... This paper addresses the sampled-data multi-objective active suspension control problem for an in-wheel motor driven electric vehicle subject to stochastic sampling periods and asynchronous premise variables.The focus is placed on the scenario that the dynamical state of the half-vehicle active suspension system is transmitted over an in-vehicle controller area network that only permits the transmission of sampled data packets.For this purpose,a stochastic sampling mechanism is developed such that the sampling periods can randomly switch among different values with certain mathematical probabilities.Then,an asynchronous fuzzy sampled-data controller,featuring distinct premise variables from the active suspension system,is constructed to eliminate the stringent requirement that the sampled-data controller has to share the same grades of membership.Furthermore,novel criteria for both stability analysis and controller design are derived in order to guarantee that the resultant closed-loop active suspension system is stochastically stable with simultaneous𝐻2 and𝐻∞performance requirements.Finally,the effectiveness of the proposed stochastic sampled-data multi-objective control method is verified via several numerical cases studies in both time domain and frequency domain under various road disturbance profiles. 展开更多
关键词 Active suspension system Electric vehicles In-wheel motor Stochastic sampling Dynamic dampers Sampled-data control Multi-objective control
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MPC-based Torque Distribution for Planar Motion of Four-wheel Independently Driven Electric Vehicles:Considering Motor Models and Iron Losses 被引量:3
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作者 Yiyan Su Deliang Liang Peng Kou 《CES Transactions on Electrical Machines and Systems》 CSCD 2023年第1期45-53,共9页
The most critical obstacle for four-wheel independently driven electric vehicles(4WID-EVs)is the driving range.Being the actuators of 4WID-EVs,motors account for its major power consumption.In this sense,by properly d... The most critical obstacle for four-wheel independently driven electric vehicles(4WID-EVs)is the driving range.Being the actuators of 4WID-EVs,motors account for its major power consumption.In this sense,by properly distributing torques to minimize the power consumption,the driving range of 4WID-EV can be effectively improved.This paper proposes a model predictive control(MPC)-based torque distribution scheme,which minimizes the power consumption of 4WID-EVs while guaranteeing its tracking performance of planar motions.By incorporating the motor model considering iron losses,the optimal torque distribution can be achieved without an additional torque controller.Also,for this reason,the proposed control scheme is computationally efficient,since the power consumption term to be optimized,which is expressed as the product of the motor voltages and currents,is much simpler than that derived from the efficiency map.With reasonable simplification and linearization,the MPC problem is converted to a quadratic programming problem,which can be solved efficiently.The simulation results in MATLAB and CarSim co-simulation environments demonstrate that the proposed scheme effectively reduces power consumption with guaranteed tracking performance. 展开更多
关键词 four-wheel independently driven electric vehicles Model predictive control motor models Iron losses
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Design and Optimization of Interior Permanent Magnet(IPM)Motor for Electric Vehicle Applications 被引量:2
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作者 Lavanya Balasubramanian Nurul Azim Bhuiyan +3 位作者 Asad Javied Ashraf A.Fahmy Fawzi Belblidia Johann Sienz 《CES Transactions on Electrical Machines and Systems》 CSCD 2023年第2期202-209,共8页
This paper explores some design parameters of an interior permanent magnet synchronous motor that contribute to enhancing motor performance.Various geometry parameters such as magnet dimension,machine diameter,stator ... This paper explores some design parameters of an interior permanent magnet synchronous motor that contribute to enhancing motor performance.Various geometry parameters such as magnet dimension,machine diameter,stator teeth height,and number of poles are analyzed to compare overall torque,power,and torque ripples in order to select the best design parameters and their ranges.Pyleecan,an open-source software,is used to design and optimize the motor for electric vehicle applications.Following optimization with Non-dominated Sorting Genetic Algorithm(NSGA-Ⅱ),two designs A and B were obtained for two objective functions and the corresponding torque ripples values of the design A and B were later reduced by 32%and 77%.Additionally,the impact of different magnet grades on the output performances is analyzed. 展开更多
关键词 Electric vehicles IPM motor Magnet grade OPTIMIZATION Permanent magnet motor Torque ripple
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Decentralized Dynamic Event-Triggered Communication and Active Suspension Control of In-Wheel Motor Driven Electric Vehicles with Dynamic Damping 被引量:14
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作者 Iftikhar Ahmad Xiaohua Ge Qing-Long Han 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第5期971-986,共16页
This paper addresses the co-design problem of decentralized dynamic event-triggered communication and active suspension control for an in-wheel motor driven electric vehicle equipped with a dynamic damper. The main ob... This paper addresses the co-design problem of decentralized dynamic event-triggered communication and active suspension control for an in-wheel motor driven electric vehicle equipped with a dynamic damper. The main objective is to simultaneously improve the desired suspension performance caused by various road disturbances and alleviate the network resource utilization for the concerned in-vehicle networked suspension system. First, a T-S fuzzy active suspension model of an electric vehicle under dynamic damping is established. Second,a novel decentralized dynamic event-triggered communication mechanism is developed to regulate each sensor's data transmissions such that sampled data packets on each sensor are scheduled in an independent manner. In contrast to the traditional static triggering mechanisms, a key feature of the proposed mechanism is that the threshold parameter in the event trigger is adjusted adaptively over time to reduce the network resources occupancy. Third, co-design criteria for the desired event-triggered fuzzy controller and dynamic triggering mechanisms are derived. Finally, comprehensive comparative simulation studies of a 3-degrees-of-freedom quarter suspension model are provided under both bump road disturbance and ISO-2631 classified random road disturbance to validate the effectiveness of the proposed co-design approach. It is shown that ride comfort can be greatly improved in either road disturbance case and the suspension deflection, dynamic tyre load and actuator control input are all kept below the prescribed maximum allowable limits, while simultaneously maintaining desirable communication efficiency. 展开更多
关键词 Active suspension control decentralized eventtriggered control dynamic damper dynamic eventtriggered communication in-wheel motor driven electric vehicle
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Auto-Test on Motor Temperature Rising in Electric Vehicles with Mutual MRAS 被引量:1
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作者 王志福 张承宁 《Journal of Beijing Institute of Technology》 EI CAS 2008年第4期395-399,共5页
A new method to calculate the motor temperature rising in electric vehicle (EV) is proposed based on the stator resistance identification. The measure theory of the motor temperature rising with the stator resistanc... A new method to calculate the motor temperature rising in electric vehicle (EV) is proposed based on the stator resistance identification. The measure theory of the motor temperature rising with the stator resistance is discussed at first. An enhanced magnetism motor dynamic math model is built which is the research object. Then the resistance identification system model is built on the mutual model reference adaptive,system (MRAS) theory. The simulation diagram of the mutual MRAS model is constructed and the resistance identification performance is studied in different motor states. Simulation results indicate that the stator resistance identification model with the mutual MRAS is effective. At the same time, the identification of motor temperature rising is possible with the identification of the stator resistance. 展开更多
关键词 electric vehicle (EV) motor's temperature rising model reference adaptive system (MARS) resistance identification
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Driving Range Parametric Analysis of Electric Vehicles Driven by Interior Permanent Magnet Motors Considering Driving Cycles 被引量:4
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作者 Le Tian Lijian Wu +1 位作者 Xiaoyan Huang Youtong Fang 《CES Transactions on Electrical Machines and Systems》 CSCD 2019年第4期377-381,共5页
This paper presents parametric analysis of driving range of electric vehicles driven by V-type interior permanent magnet motors aiming at maximum driving range,i.e.,minimal total energy consumption of the motors over ... This paper presents parametric analysis of driving range of electric vehicles driven by V-type interior permanent magnet motors aiming at maximum driving range,i.e.,minimal total energy consumption of the motors over a driving cycle.Influence of design parameters including tooth width,slot depth,split ratio(the ratio of inner diameter to outer diameter of the stator),and V-type magnet angle on the energy consumption of the motors and driving range of electric vehicles over a driving cycle is investigated in detail.The investigation is carried out for two typical driving cycles with different characteristics to represent different conditions:One is high-speed,low-torque cycle-Highway Fuel Economy Test and the other is low-speed,high-torque cycle-Artemis Urban Driving Cycle.It shows that for both driving cycles,the same parameters may have different influence on the energy consumption of the motors,as well as driving range of electric vehicles. 展开更多
关键词 Driving cycle driving range electrical vehicle interior permanent magnet motor.
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Optimization of Vibration and Noise Performance of Permanent Magnet Synchronous Motor for Electric Vehicles 被引量:2
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作者 LIU Huijuan SONG Tengfei +1 位作者 ZHANG Zhenyang DU Jinwen 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2020年第2期332-342,共11页
In the design of the motor used for electric vehicles(EVS),vibration and noise problems are often ignored,which reduce the reliability and service life of the motor.In this paper,an interior permanent magnet synchrono... In the design of the motor used for electric vehicles(EVS),vibration and noise problems are often ignored,which reduce the reliability and service life of the motor.In this paper,an interior permanent magnet synchronous motor(IPMSM)with high power density is taken as an example,and its electromagnetic vibration and noise problem is investigated and optimized.Firstly,the factors that generate the electromagnetic force harmonic of IPMSM are analyzed by theoretical derivation.Furthermore,the mode and electromagnetic harmonic distribution of the motor are calculated and analyzed by establishing the electromagnetic-structure-sound coupling simulation model.Then,by combining finite element method(FEM)with modern optimization algorithm,an electromagnetic vibration and noise performance optimization method is proposed in the electromagnetic design stage of the motor.Finally,an IPMSM is optimized by this method for electromagnetic vibration and noise performance.The results of comparison between before and after optimization prove the feasibility of the method. 展开更多
关键词 electric vehicle(EV) vibration and noise performance optimization interior permanent magnet synchronous motor(IPMSM) finite element method(FEM)
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Comparison of the Mutagenicity of Exhaust Emissions From Motor Vehicles Using Leaded and Unleaded Gasoline as Fuel 被引量:1
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作者 YUANDONG ZHOUWEI 《Biomedical and Environmental Sciences》 SCIE CAS CSCD 1999年第2期136-143,共8页
While Unleaded gasoline has the advantage of eliminating lead from automobile exhaust, its potential to reduce the exhaust gas and particles, merits further examination. In the present studies,the concentrations of hy... While Unleaded gasoline has the advantage of eliminating lead from automobile exhaust, its potential to reduce the exhaust gas and particles, merits further examination. In the present studies,the concentrations of hydrocarbons (HC) and earbon monoxides (CO) in emissions were analyzed on Santana engine Dynamometer under a standard test cycle, and total exhaust particles were collected from engines using leaded and unleaded gasoline. It was found that unleaded gasoline reduced the emissions of CO and HC, and decreased the quantity of vehicle exhaust particulate matters by 60%.With the unlead gasoline, only 23 kinds of organic substances, adsorbed in the particles, were identified by gas chromatography/mass spectrometer (GC/MS) while 32 components were detected using the leaded gasoline. The results of in vitro Salmonella/ microsomal test and micronucleus induction assay in CHL cells indicated that both types of gasoline increased the number of histidine-independent colonies and the frequencies of micronucleus induction; no significant differellce was found in their mutagenicity. 展开更多
关键词 line Comparison of the Mutagenicity of Exhaust Emissions From motor vehicles Using Leaded and Unleaded Gasoline as Fuel PAHS
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Review of Three-phase Soft Switching Inverters and Challenges for Motor Drives
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作者 Haifeng Lu Qiao Wang +1 位作者 Jianyun Chai Yongdong Li 《CES Transactions on Electrical Machines and Systems》 EI CSCD 2024年第2期177-190,共14页
For electric vehicles (EVs),it is necessary to improve endurance mileage by improving the efficiency.There exists a trend towards increasing the system voltage and switching frequency,contributing to improve charging ... For electric vehicles (EVs),it is necessary to improve endurance mileage by improving the efficiency.There exists a trend towards increasing the system voltage and switching frequency,contributing to improve charging speed and power density.However,this trend poses significant challenges for high-voltage and high-frequency motor controllers,which are plagued by increased switching losses and pronounced switching oscillations as consequences of hard switching.The deployment of soft switching technology presents a viable solution to mitigate these issues.This paper reviews the applications of soft switching technologies for three-phase inverters and classifies them based on distinct characteristics.For each type of inverter,the advantages and disadvantages are evaluated.Then,the paper introduces the research progress and control methods of soft switching inverters (SSIs).Moreover,it presents a comparative analysis among the conventional hard switching inverters (HSIs),an active clamping resonant DC link inverter (ACRDCLI) and an auxiliary resonant commuted pole inverter (ARCPI).Finally,the problems and prospects of soft switching technology applied to motor controllers for EVs are put forward. 展开更多
关键词 Soft switching inverters Zero-voltage switching Electric vehicles motor drives
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Factors Influence Hanoians’ Choice of Non-Motorized Transport Mode to Access Bus Stations
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作者 Ngo Trung Phuong Masahiko Kikuchi +1 位作者 Aya Kojima Hisashi Kubota 《Journal of Transportation Technologies》 2024年第3期372-389,共18页
Hanoi’s rapid urbanization has led to a surge in private vehicle ownership, particularly motorcycles, amidst inadequate public transportation infrastructure. Despite government efforts, many still prefer motorized tr... Hanoi’s rapid urbanization has led to a surge in private vehicle ownership, particularly motorcycles, amidst inadequate public transportation infrastructure. Despite government efforts, many still prefer motorized transport, citing mobility and safety concerns, exacerbated by insufficient pedestrian infrastructure. This study examines the motivations behind this reliance on motorized vehicles, particularly motorcycles, in Hanoi. Findings reveal safety and convenience as primary factors driving motorized transport use, especially for accessing bus stations. Economic incentives could promote non-motorized travel and public transport adoption. Policy implications highlight the importance of addressing economic factors and improving access infrastructure to manage motorized vehicle reliance and foster sustainable urban mobility in Hanoi. 展开更多
关键词 Access Mode Choice Non-motorized vehicles motorized vehicles Bus User Urban Transport Behavior
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Analysis of 3D Static Temperature Field of Induction Motors With Different Cooling Structures in Mini Electric Vehicles 被引量:3
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作者 CHENG Shukang LI Cuiping CHAI Feng 《中国电机工程学报》 EI CSCD 北大核心 2012年第30期I0012-I0012,共1页
关键词 异步电动机 态温度场 电动汽车 冷却结构 三维 微型 异步电机 壳体材料
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Study on Modeling and Control Strategy for Electric Drive Motor of Tracked Vehicles 被引量:1
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作者 廖自力 黄苏融 +1 位作者 马晓军 庞宾宾 《Defence Technology(防务技术)》 CAS 2012年第2期65-69,共5页
Aimed at the requirements for electric transmission system of a military tracked vehicle, the motor's design indexes were analysed and calculated. A model based on saturate inductance parameter of interior permane... Aimed at the requirements for electric transmission system of a military tracked vehicle, the motor's design indexes were analysed and calculated. A model based on saturate inductance parameter of interior permanent magnet (IPM) synchronous motor was brought forward by using finite element analysis. And its control strategy based on the largest running capability was studied also. The experiment results for a scale model show that the modelling method improves the model's accuracy, and the motor's control strategy is effective. 展开更多
关键词 军用履带车辆 控制策略 驱动电机 建模方法 电传动系统 有限元分析 电感参数 同步电机
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Management of the Recall of Defective Motor Vehicles in China
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作者 Liu Xiang Yang Ying 《China Standardization》 2005年第3期20-23,共4页
The Administrative Regulation on the Recall of Defective Motor Vehicles has officially entered into force on October 1st, 2004, which means the management on defective products has made a substantive progress. The ena... The Administrative Regulation on the Recall of Defective Motor Vehicles has officially entered into force on October 1st, 2004, which means the management on defective products has made a substantive progress. The enactment and enforcement of the Administrative Regulation has generated active responses in our society and drawn much attention from the automobile industry. Up to March 2005, there have been 15 domestic and foreign auto manufacturers initiating voluntary recalls since the Administrative Regulation on the Recall of Defective Motor Vehicles was issued in March 2004, and 312864 vehicles have been recalled. All the relevant firms, types, models, numbers and the date are as the following table 1. 展开更多
关键词 SIQ Management of the Recall of Defective motor vehicles in China
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A Study on an Airgap Control System in a Rotary-Small-Scaled Linear Induction Motor for Railway Vehicles
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作者 C.B. Park B.S. Lee 《Journal of Energy and Power Engineering》 2011年第12期1193-1198,共6页
In general, it is important to operate the; airgap length uniformly for improving the system efficiency independent of the flatness of the reaction plate in a railway propulsion system by a linear induction motor (LI... In general, it is important to operate the; airgap length uniformly for improving the system efficiency independent of the flatness of the reaction plate in a railway propulsion system by a linear induction motor (LIM). And it is possible to operate the LIM propulsion system efficiently without a change of the LIM capacity through the airgap length control on the sloped rail. So, in this research, the authors introduce an airgap control system to control the airgap length which depends on the flatness of the secondary reaction plate when the LIM is operated, and design a rotary small-scaled LIM and its airgap control system before manufacturing the real system. Then, the authors analyze some characteristics of the LIM (thrust and normal force, input current, efficiency and power factor), and through the LIM control modeling, the authors finally analyze an effect of the airgap-length control of the LIM by the airgap control system. 展开更多
关键词 Airgap control system linear induction motor PROPULSION railway vehicles.
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Annual Report on Implementing Administrative Regulation on the Recall of Defective Motors Vehicles
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《China Standardization》 2006年第1期12-17,共6页
关键词 Annual Report on Implementing Administrative Regulation on the Recall of Defective motors vehicles
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New Method to Restrain Pumping Voltage of Braking Procedure for Brushless DC Motor of Electric Armored Vehicle 被引量:3
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作者 郑慕侨 宋小庆 +1 位作者 孙德福 臧克茂 《Journal of Beijing Institute of Technology》 EI CAS 2002年第2期137-141,共5页
In order to restrain the high pumping voltage of braking procedure which is harmful to the system of electric armored vehicle. Based on the analysis of pumping voltage of the braking procedure, the relation between pu... In order to restrain the high pumping voltage of braking procedure which is harmful to the system of electric armored vehicle. Based on the analysis of pumping voltage of the braking procedure, the relation between pumping voltage and PWM ratio is derived and a new digital control method to restrain the pumping voltage by changing PWM ratio is put forward. Because the capacitance is decreased effectively, the volume of controller is reduced and the performance to price ratio is improved. The results of computer simulation and experiment proved that this method is feasible and valid. 展开更多
关键词 electrical armored vehicle brushless DC motor regenerative braking
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A CONTROL STRATEGY OF SWITCHED RELUCTANCE MOTOR FOR ELECTRIC VEHICLE APPLICATION
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作者 冬雷 曹志亮 刘迪吉 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 1999年第2期120-124,共5页
A control strategy of switched reluctance motor (SRM)for electric vehicle applications is proposed. In electric vehicle application, the switched reluctance motor is a good choice with its flexible control method, com... A control strategy of switched reluctance motor (SRM)for electric vehicle applications is proposed. In electric vehicle application, the switched reluctance motor is a good choice with its flexible control method, compactness, robustness, high efficiency and high starting torque. In this paper, the control strategy of motoring and regenerative braking for electric vehicle application is presented. Computer simulations are employed to analyze the steady state behavior of SRM propulsion system. Experimental results in electric motorcycle are provided to demonstrate the validity of SRM propulsion system. 展开更多
关键词 switched reluctance motors electric vehicles regenerative braking self tuning
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Design and Development of the DTC Induction Motor Drive for Electric Vehicle
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作者 孙逢春 程夕明 《Journal of Beijing Institute of Technology》 EI CAS 2000年第4期415-421,共7页
The design and development of the traction controller for electric vehicle is introduced, which is based on the induction motor. This drive is developed by using a digital signal processor at low cost and carried out ... The design and development of the traction controller for electric vehicle is introduced, which is based on the induction motor. This drive is developed by using a digital signal processor at low cost and carried out with the module design concept of both software and hardware. Nevertheless, a scheme of the sensorless direct torque control is based on the developed hardware, of which the feasibility is tested by a trial program. Additionally, both the interface function of the drive hardware and the feasibility of its software are proved to be good by the trail programs. A test motor can run about 18?r/min by a variable frequency program with the space vector pulse width modulation technology, of which the torque is visible pulsatile. In this presentation, based on the theoretical approach, the sensorless torque control is to be studied and applied to electric vehicles, of which the quick, smooth and stable torque response is emphasized because it quite benefits improving the drive performance of electric vehicles. 展开更多
关键词 electric vehicle induction motor digital signal processor direct torque control
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Dynamic emission characteristics and control strategies of air pollutants from motor vehicles in downtown Beijing,China
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作者 Yan Shen Tongran Wu +9 位作者 Aiping Lian Jie Gao Fei Peng Guohua Song Xuefang Wu Yangyang Cui Xinyu Liu Yunfei Wan Jing Yan Yifeng Xue 《Journal of Environmental Sciences》 SCIE EI CAS CSCD 2024年第2期637-646,共10页
This study combined the real-time monitoring and investigation of traffic flows to comprehensively analyze the road traffic flow and vehicle structure in downtown Beijing.A dynamic emission inventory of motor vehicle ... This study combined the real-time monitoring and investigation of traffic flows to comprehensively analyze the road traffic flow and vehicle structure in downtown Beijing.A dynamic emission inventory of motor vehicle air pollutants in downtown Beijing in 2021 was established,and the impact of these emissions on air quality was simulated and quantified,and different emission reduction control scenarios were proposed to evaluate their environmental improvement effects and explore measures to mitigate the impact of pollution emissions.The results show that the high traffic flow and the structure of the motor vehicle emissions in downtown Beijing are the main causes of severe motor vehicle pollution.Monitoring data shows that traffic flow in central Beijing is dominated by small passenger vehicles,while the vehicle mix is better than in other regions,with 72.0%of vehicles meeting"National V"or higher emission standards.However,to achieve higher air quality goals,further reducing vehicle emissions is necessary.Based on dynamic traffic flow,the average daily emissions of nitrogen oxides(NOX),particulate matters(PM_(2.5))and volatile organic compounds(VOC)from motor vehicles in central Beijing are 17.7 tons,0.6 tons and 14.0 tons,respectively,accounting for 23.0%of the city’s average daily motor vehicle emissions.If a zero-emission zone for motor vehicles were implemented in central Beijing,the annual average emission level of pollutants will be reduced by 10.4%to 21.0%.The designation of ultra-low emission zones for motor vehicles could be effective in improving the air quality in the center of Beijing. 展开更多
关键词 motor vehicle Air pollutant Emission characteristics Control strategy BEIJING
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A novel predictive braking energy recovery strategy for electric vehicles considering motor thermal protection
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作者 YANG Chao SUN TongLin +2 位作者 YANG LiuQuan ZHANG YuHang WANG WeiDa 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2024年第4期1253-1269,共17页
Braking energy recovery(BER)aims to recover the vehicle's kinetic energy by coordinating the motor and mechanical braking torque to extend the driving range of the electric vehicle(EV).To achieve this goal,the mot... Braking energy recovery(BER)aims to recover the vehicle's kinetic energy by coordinating the motor and mechanical braking torque to extend the driving range of the electric vehicle(EV).To achieve this goal,the motor/generator mode requires frequent switching and prolonged operation during driving.In this case,the motor temperature will unavoidably rise,potentially triggering motor thermal protection(MTP).Activating MTP increases the risk of motor component failure,and the EV typically disables the BER function.Thus,maximizing BER while reducing the risk of motor overheating is a challenging problem.To address this issue,this article proposes a predictive BER strategy with MTP using the non-smooth Pontryagin Minimum Principle(NSPMP)for EVs.Firstly,a Markov long short-term memory(MLSTM)model is designed to obtain future velocity information.Secondly,the BER problem with MTP in the studied EV is embedded in a model predictive control(MPC)framework.Then,under the MPC framework,the NSPMP strategy is proposed to resolve the problem of MTP.Finally,the performance of the proposed strategy is verified through simulation and a hardware-in-loop test.The results show that in two real-world driving cycles,compared to the rule-based strategy,the proposed strategy reduced power consumption by 1.24%and0.96%,respectively,and effectively limited motor temperature.Additionally,under global cycle conditions,this strategy demonstrated better MTP control performance compared to other benchmark strategies. 展开更多
关键词 electric vehicle braking energy recovery strategy motor thermal protection non-smooth PMP
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