并联混合电动卡车制动性能研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
所谓制动就是利用制动装置使车辆减慢或者停止的过程。就混合动力汽车而言,制动装置主要分为两种:传统的机械式和能量再生式。前者是利用摩擦原理将反相制动力矩直接施加在车轮上,后者是电机产生的反相制动力矩通过传动系统最终传递到半轴上。在制动过程中如何合理地操作两个制动系统,是车辆安全稳定运行的前提。也是目前混合动力汽车研究的关键内容之一。
     本文以并联混合电动卡车为主要研究对象,从分析再生制动模式为出发点,针对带有换挡操作的制动过程,鉴于以往控制策略的不足,着力改善混合电动卡车的制动性能,在深入分析各部件的特性基础上,提出适合本课题特定需求的控制方案和策略。集中表现为在制动过程中满足车辆安全性及驾驶员舒适性要求前提下同时尽可能多的回收能量。本文研究工作如下:
     (一)根据混合电动卡车制动控制问题的要求,主要对混合动力汽车的传统机械制动系统、再生制动系统(电机、超级电容、逆变器)传动系(电机减速器、手自一体化机械变速箱、主减速器、传动轴)和车轮建立数学模型。为混合动力汽车制动力矩控制和模拟仿真提供基础。
     (二)根据制动系统模型设计了电机和传统机械制动系统的力矩匹配协调控制策略,并从理论上对稳定性加以证明。具体是将制动过程分别处理,划分为制动无换挡和制动有换挡阶段两个阶段。在前一个阶段,分别对制动力矩在可测与不可测条件下,设计近似比例-积分的反馈控制器,并对其稳定性做了证明。在后一个阶段,分别采用两种控制策略:电机提前补偿策略和电机同步器、同步器齿轮压力同时补偿策略。从而保证了车辆换挡的顺利完成并减少在换挡过程中制动力矩的波动。
     (三)根据超级电容等价模型对实际电容两端电压利用观测器进行估计。在模型参数已知的条件下,运用类似Luenberger观测器估计实际电容端电压,并分析了估计结果关于观测器模型参数的敏感性以及观测器关于标称模型参数变化的敏感性。在模型参数未知的情况下,运用带有遗忘因子的最小二乘离线辨识方法来估计模型的参数,从而我们可以利用被辨识的参数作为上述观测器模型参数估计实际电容端电压。考虑到实际过程中扰动的影响,引入高斯白噪声作为状态过程扰动和输出测量扰动,并根据滤波理论设计了拓展的Kalman滤波器并对模型参数和实际电容端电压同时进行估计。
The process that using brake devices makes the vehicle slow down or stop is called braking. As far as hybrid electric vehicles, the brake system consists of two kinds:the traditional mechanical and energy regenerative brake system. The torque generated by the former can be acted on wheels, directly; Torque generated by the latter is transmitted to wheels by transmission. During braking, how to distribute properly brake torque between the two devices is premise of stability of vehicle and also one of the important content of study for hybrid electric vehicle.
     In this paper, parallel hybrid electric trucks can be considered as the main object of the research. Consider the analysis of the regenerative brake mode as starting point, point to brake process with gear shifting, find shortage of preceding control scheme, make efforts to improve braking performance of hybrid electric trucks, analyze deeply the properties of brake devices, and present control schemes and strategies for the sub-ject. The research problems embody retrieving the kinetic energy of vehicle as much as possible satisfying vehicle safety and the comfort requirement of driver. The main research work is as follows:
     (1) According to requirements of brake control of hybrid electric truck, the pa-per will give the mathematical model of the conventional mechanical brake system, the regenerative brake system (electrical, super capacitors, inverters) driveline (motor re-ducer, automated manual mechanical gearbox, main gear, drive shaft) and wheels. This provides the basis for brake torque control and simulation for hybrid electric truck.
     (2) Based on the brake system model, the coordinated torque control scheme is p-resented between the conventional mechanical brake system and the regenerative brake system, and the stability of the closed system is proved. The braking process can be divided into brake with no gear shifting and brake with gear shifting. In the former stage, approximate proportional-integral feedback controller is designed and stability is proved under the condition of the measurable brake torque and unmeasurable brake torque. In the latter stage, the two strategies are presented:motor advanced compensa-tion strategy and motor-synchronizer gears pressure compensation strategy, which en-sures successful completion of gear shifting and reduces the vibration of brake torque.
     (3) Based on equivalent model of super-capacitor, observer to estimate voltage of real capacitor is presented. Under the condition of known model parameter, the actual capacitor voltage is estimated by using observer similar to Luenberger type, and the estimated results is analyzed on sensitivity of observer parameters and the model param-eters. Under the condition of unknown model parameter, the least squares identification method with forgetting factor is used to estimate the real model parameters, and then the estimated parameters can be used as parameters of above observer to estimate real capacitor terminal voltage. With the consideration of disturbance effect in real process, Gaussian white noise is considered as real state disturbance and output measurement disturbance. The extended Kalman filter is designed to estimate simultaneously mod-el parameters and real capacitor terminal voltage.
引文
[1]R. Graham. Comparing the Benefits and Impacts of Hybrid Electric Vehicle Options. Technical Report 2001.
    [2]K. Bennion and M. Thornton. Fuel Savings from Hybrid Electric Vehicles. Technical Report NREL/TP-540-42681March 2009.
    [3]L. Guzzella and A. Sciarretta. Vehicle propulsion system, springer,2005.
    [4]M. Ehsani; Y.M. Gao; A. Emadi. Modern electric, hybrid electric, and fuel cell vehicles:fundamentals, theory, and design.2nd edition,Boca Raton:CRC Press,2010.
    [5]H.K. Khalil Nonlinear system (3rd edition). New Jersey, Prentice-hall,2002.
    [6]K. Koprubasi Modeling and control of a hybrid-electric vehicle for drivability and fuel economy improvements. Doctoral dissertation, Ohio State University,2008.
    [7]H. B. Pacejka Tyre and Vehicle Dynamics. Butterworth-Heinemann,2002.
    [8]G. Lucente, M. Montanari, C. Rossi Modelling of an automated manual transmission system. Mechatronics, Vol.17, No.2, pp.73-91,2007.
    [9]B.K. Powell, K.E. Bailey,S.R. Cikanek'Dynamic modeling and control of hybrid electric vehicle powertrain systems. IEEE Control System Magazine, pp.17-33.
    [10]D.T. Qin, M. Ye, Z. J. Liu Regenerative braking control strategy in mild hybrid electric vehicles equipped with automatic manual transmission. Front. Mech. Eng. China, Vol.2, No.3, pp.364-369.
    [11]Y.C. Youk Synchronizer for a manual transmission. Patent No:US006848554B2,2005.
    [12]M.H. Kim Synchronizer for manual transmission and a method thereof. Patent No:US006244404B1,2001.
    [13]M. Inui, S. Okuda, M. Hosono Gear synchronizer mechanism. Patent No:US004875566A,1989.
    [14]D.S. Park Synchronizer for automobile transmission. Patent No:US005701984A,1997.
    [15]R. Olsson Synchronizer device in a vehicle transmission. Patent No:US006053294A,2000.
    [16]A. Borg Synchronizer device in a vehicle transmission. Patent No:US006724818B1,2002.
    [17]K. B. Wipke, M. R. Cuddy, S. D. Burch ADVISOR 2.1:a user-friendly advanced powertrain simulation using a combined backward/forward approach. IEEE Transaction on Vehicular Technology, Vol.48, No.6, pp.1751-1761,1999.
    [18]K. Wipke, T. Markel, D. Nelson Optimizing energy management strategy and degree of hybridization for a hydrogen fuel cell SUV Proc. Of the 18th Electric Vehicles Symposium, Berlin, Germany,2001.
    [19]C. Liang, W. Qingnian, L. Youde, M. Zhimin, Z.Ziliang, L.Di Study of the electronic control strategy for the power train of hybrid electric vehicle Proc. Of the 19th IEEE Vehicle Electronics Conference, Changchun, China,1999.
    [20]Z. Rahman, K. Butler, M. Ehsani A comparative study between two parallel hybrid control concepts SAE Paper 2002.
    [21]P. Bowles, H. Peng, X. Zhang Energy management in a parallel hybrid electric vehicle with a continuously variable transmission Proc. of American control conference, pp.55-59,2000.
    [22]D. L. Buntin, J.W. Howze A switching logic controller for a hybrid electric/ICE vehicle Proc. of the American control conference, Vol.2, pp.1169-1175,1995.
    [23]S. Fish, T. Savoie, H. Vanicek Modeling hybrid electric HMMWV power system performance IEEE Transac-tions on Magnetics, Vol.37, No.1, pp.480-484,2001.
    [24]C. C. Lin, J. M. Kang, J. W. Grizzle, H. Peng Energy management strategy for a parallel hybrid electric truck Proc. of American control conference, Vol.4, pp.2878-2883,2001.
    [25]E. S. Koo, H. D. Lee, S. K. Sul, J. S. Kim, M. Kamiya Torque control strategy for a parallel hybrid vehicle using fuzzy logic IEEE Industry Applications Magazine, Vol.6, No.6, pp.33-38,2000.
    [26]M. Salman, N. J. Schouten, N. A. Kheir Control strategies for parallel hybrid vehicles Proc. of the American control conference, Vol.1, No.6, pp.524-528,2000.
    [27]N. J. Schouten, M. A. Salman, N. A. Kheir Energy management strategies for parallel hybrid vehicles using fuzzy logic Control Engineering Practice, Vol.11,No.2, pp.171-177,2003.
    [28]F. Gagliardi, A. Piccolo, A. Vaccaro, D. Villacci A fuzzy based control unit for the optimal power flow man-agement in parallel hybrid electric vehicles Proc. of the 19th Electric Vehicles Symposium, Busan, Korea.
    [29]B. M. Baumann, G. Washington, B. C. Glenn, G. Rizzoni Mechatronic design and control of hybrid electric vehicle IEEE/ASME Transactions on Mechatronics, Vol.5, No.l, pp.58-72,2000.
    [30]H. D. Lee, S. K. Sul Fuzzy-logic-based torque control strategy for parallel-type hybrid electric vehicle IEEE Transaction on Industrial Electronics, Vol.45, No.4, pp.625-632,1998.
    [31]A. S. Sarvestani, A. A. Safavi A novel optimal energy management strategy based on fuzzy logic for a Hybrid Electric Vehicle IEEE International Conference on Vehicular Electronics and Safety (ICVES), pp.141-145, 2009.
    [32]L. H. Xiao, P. Micheal, M. Tim Energy Management Strategies for a Hybrid Electric Vehicle IEEE conference on vehicle power and propulsion, pp.536-540,2005.
    [33]H. Hannoun, D. Diallo, C. Marchand Energy Management Strategy for a parallel Hybrid Electric Vehicle using Fuzzy Logic International Symposium on Power Electronics,Electrical Drives, Automation and Motion, pp.229-234,2006.
    [34]D. P. Bertsekas Dynamic programming and optimal control Athena Scientific, Nashua NH,1995.
    [35]E. Bryson, Y. C. Ho Applied Optimal Control Taylor and Francis, New York, NY,1975.
    [36]H. J. Yoon, S. J. Lee An optimized control strategy for parallel hybrid electric vehicle SAE Transactions, Vol.112, No.7, pp.579-586,2003.
    [37]F. Filipi, L. Louca, B. Daran, C. C. Lin, U. Yildir, B. Wu, M. Kokkolaras, D. Assanis, H. Peng, P. Papalambros, J. Stein, D. Szkubiel, R. Chapp Combined optimization of design and power management of the hydraulic hybrid propulsion system for the 6×6 medium truck International Journal of Heavy Vehicle systems, Vol.11, No.3/4, pp.373-402,2004.
    [38]A. Sciarretta, L. Guzzella, C. H. Onder On the power split control of parallel hybrid vehicles:from global optimization towards real-time control atAutomatisierungstechnik, Vol.51, No.5, pp.195-203,2003.
    [39]A. Sciarretta, L. Guzzella, M. Back Real-time optimal control strategy for parallel hybrid vehicles with on-board estimation of control parameters Proc. Of the IFAC Symposium on Advances in Automotive Control, Salerno, Italy,2004.
    [40]S. I. Jeon, S. T. Jo, Y. I. Park, J. M. Lee Multi-Mode Driving Control of a Parallel Hybrid Electric Vehicle Using Driving Pattern Recognition Journal of Dynamic System, Measurement, Control, Vol.124, No.1, pp.141-149, 2002.
    [41]A. Sciarretta, M. Back, L. Guzzella Optimal control of parallel hybrid electric vehicles IEEE Transaction on Control System Technology, Vol.12, No.3, pp.352-363,2004.
    [42]A. Sciarretta, L. Guzzella Control of hybrid electric vehicles IEEE control system magazine, Vol.27, No.2, pp.67-70,2007.
    [43]F. R. Salmasi Control strategies for hybrid electric vehicles:Evolution, classification, comparison, and future trends IEEE Transactions on Vehicular Technology, Vol.56, No.5, pp.2393-2404,2007.
    [44]H. Mosbech Optimal control of hybrid vehicle ISATA 80 proceedings, Vol.2, pp.303-20.
    [45]M. Oprean, V. lonescu, N. Mocanu, S. Beloiu, C. Stanciu Dynamic Programming applied to hybrid vehicle control Proc. International conference on electrical drives ICED 88, Vol.4, pp.1-20.
    [46]M. Cristian, R. Giorgio, S. Benedetto A-ECMS:an adaptive algorithm for hybrid electric vehicle energy management Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, pp.1816-1823,2005.
    [47]S. Delprat, J. Lauber, T. M. Guerra, J. Rimaux Control of a parallel powertrin:optimal control IEEE Transac-tions on Vehicular Technology, Vol.53, No.3, pp.872-881,2004.
    [48]N. Kim, S. Cha, H. Peng Optimal Control of Hybrid Electric Vehicles Based on Pontryagin's Minimum Principle IEEE Transaction on Control System Technology, Vol.19, No.5, pp.1279-1287,2011.
    [49]B. K. Powell, K. E. Bailey, S. R. Cikanek Dynamic modeling and control of hybrid electric vehicle powertrain systems IEEE Control System magazine, Vol.18, No.5, pp.17-33,1998.
    [50]G. Lucente, M. Mantanari, C. Rossi Modeling of an automated manual transmission system Mechatronics, Vol.17, No.2-3, pp.73-91,2007.
    [51]L. Guzzella, C. Onder Introduction to Modeling and Control of Internal Combustion Engine Systems 2th edition, springer,2010.
    [52]L. Guzzella, A. Sciarretta Control of Hybrid Electric Vehicles-A Survey of Optimal Energy-Management Strategies IEEE Control Systems Magazine, Vol.27, No.2, pp.60-70,2007.
    [53]J. Deur, J. Asgari, D. Hrovat Modeling and Analysis of Automatic Transmission Engagement Dynamics-Nonlinear Case Including Validation Journal of Dynamic System, Measurement, Control, Vol.128, No.2, pp.251-262,2006.
    [54]F. Vasca, L. Iannelli, A. Senatore, G. Reale Torque Transmissibility Assessment for Automotive Dry-Clutch Engagement IEEE/ASME Transactions On Mechatronics, Vol.16, No.3,2011.
    [55]M.J.W.H. Edelaar Model and control of a wet plate clutch Graduate report,1997.
    [56]D. H. Kim, J. M. Kim, S. H. Hwang Optimal brake torque distribution for a four-wheel-drive hybrid elec-tric vehicle stability enhancement Proceedings of the Institution of Mechanical Engineers Part D-Journal of Automobile Engineering, Vol.221, No.D11.pp.1357-1366.2007.
    [57]Z. F. Bai, S. X. Li, B. G. Cao H∞ control applied to electric torque control for regenerative braking of an electric vehicle Journal of Applied Sciences, Vol.5, No.6, pp.1103-1107,2005.
    [58]A. Fazeli, M. Zeinali, A. Khajepour Application of adaptive sliding control for regenerative braking torque control IEEE/AMSE Transaction on Mechatronics, Vol.17, No.4, pp.745-755,2011.
    [59]H. Yeo, S. Hwang, H. Kim Regenerative braking algorithm for a HEV with CVT ratio control during deceler-ation Proc. Int. Continuously Variable Hybrid Transm. Congr.,2004.
    [60]M.1. Shang, L. Chu, J. H. Guo, Y. Fang Braking force dynamic coordinated control for hybrid electric vehicles 2th International Conference on Advanced Computer Control, pp.411-416,2010.
    [61]J. K. Hedrick, J. C. Gerdes, D. B. Maciuca, D. Swaroop Brake system modeling, control and integrated brake/throttle switching:phase I UCB-ITS-PRR-97-21 California PATH Research Report, Universtiy of Cali-fornia, Berkeley,1997.
    [62]X. D. Wang, Y. L. Hu, C. G. Li, X. L. Wang Modelling and analysis of an air-over-hydraulic brake system Proc. IMechE, D, Journal of Automobile Engineering, pp.805-815,2004.
    [63]K. Zheng, T. L. Shen, K. Hikiri, M. Sasaki, Y. Yao Modeling and control of regenerative braking system in heavy duty hybrid electrical vehicles SAE Paper, no.2008-01-1569,2008.
    [64]F. P. Bu, H. S. Tan Pneumatic brake control for precision stopping of heavy-duty vehicles IEEE Transaction on control system technology, Vol.15, No.1, pp.53-64,2007.
    [65]R. A. Masmoudi, J. K. Hedrick Estamation of Vehicle Shaft Torque Using Nonlinear Observers Journal of Dynamic systems, Measurement, and control, Vol.114, No.3, pp.394-400,1992.
    [66]X. P. Yu, T. L. Shen, G. Y. Li, K. Hikiri Model-based drive shaft torque estimation and control of a hybrid electric vehicle in energy regeneration mode ICCAS-SICE, pp.3543-3548,2009.
    [67]X. P. Yu, T. L. Shen, G. Y. Li, K. Hikiri Regenerative braking torque estimation and control approaches for a hybrid electric truck American Control Conference, pp.5832-5837,2010.
    [68]M. Pettersson Driveline Modeling and principles for speed control and gear-shift control Licentiate thesis, Department of electrical engineering, Linkoping University,1996.
    [69]J. Fredriksson, B. Egardt Nonlinear control applied to gear shifting in automated manual transmissions Proc. IEEE Conf. Decision Contr., vol,1, pp.444-449,2000.
    [70]A. Haj-Fraj, F. Pfeiffer Optimization of gear shift operations in automatic transmissions Proc.6th Int. Workshop on Advanced Motion Control, pp.469-473,2000.
    [71]G. Lucente, M. Mantanari, C. Rossi Hybrid optimal control of an automated manual transmission system 7th IFAC symposium on nonlinear control systems, pp.1127-1132,2007.
    [72]H. D. Lee, S. K. Sul, H. S. Cho, J. M. Lee Advanced gear-shifting and clutching strategy for a Parallel-hybrid electric vehicle IEEE Industry Applications Magazine, Vol.6, No.6, pp.26-32,2000.
    [73]R. C. Baraszu, S. R. Cikanek Torque Fill-In for an Automated Shift Manual Transmission in a Parallel Hybrid Electric Vehicle Proc. of American control conference, pp.1431-1436,2002.
    [74]N. D. Viet, T. Hofman, M. Steinbuck, A. Serrarens Optimal shifting strategy for a parallel hybrid electric vehicle EVS-25, pp.1-8,2010.
    [75]J. S. Won, R. Langari, M. Ehsani An energy management and charge sustaining strategy for a parallel hybrid vehicle with CVT IEEE Transaction on Control System Technology, vol.13, No.2, pp.313-320,2005.
    [76]F. Wang, X. J. Mao, H. Zhong, Z. L. Ma Parallel hybrid electric system energy optimization control with automated mechanical transmission Proceedings of the Institution of Mechanical Engineers, Part D:Journal of Automobile Engineering,Vol.223,No.2 pp.151-167,2009.
    [77]A. Ibranhim, D. T. Qin, Z. J. Liu A control strategy on starting up of vehicle with automated manual trans-mission Journal of Information Technology, Vol4, No.2, pp.140-145.2005.
    [78]Y. L. Lei, M. K. Niu, A. L. Ge A Research on Starting Control Strategy of Vehicle with AMT Seoul FISITA World Automotive Congress, pp.1-4,2000.
    [79]M. S. James, N. K. Robert Design of Robust Vehicle Launch Control system IEEE Transaction On Control Systems Technology, Vol.4, No.4, pp.326-335,2000.
    [80]A. L. Ge, H. Jin, Y. L. Lei Engine Constant Speed Control in Starting and Shifting Process of Automated Mechanical Transmission Seoul FISITA World Automotive Congress,2000.
    [81]C. C. Lin, H. Peng, J. W. Grizzle A Stochastic Control Strategy for Hybrid Electric Vehicles American Control Conference, Boston,2004.
    [82]S. J. Moura. H. K. Fathy, D. S. Callaway, J. L. Stein A Stochastic Optimal Control Approach for Power Management in Plug-In Hybrid Electric Vehicles IEEE Transactions On Control Systems Technology. Vol.19, No.3, pp.545-555,2011.
    [83]张炳力,代康伟,赵韩,江昊,胡先锋 基于随机动态规划的燃料电池城市客车能量管理策略优化系统仿真学报,20(17):4664-4667,2008.
    [84]L. C. Buckman Commercial vehicle braking systems:Air brakes, ABS and beyond the 43rd L. Ray Buckendale Lecture, International Trucks and Bus Meeting and Exposition Society of Automotive Engineers, Indianapolis, 1998.
    [85]S. C. Subramanian. D. Swaroop. K. R. Rajagopal A diagnostic system for air brakes in commercial vehicles IEEE Transactions on Intelligent Transportation System, vol.7, No.3, pp.360-376,2006.
    [86]M. Sorli, G. Figliolini, and S. Pastorelli Dynamic model and experimental investigation of a pneumatic pro-portional pressure valve IEEE/ASME Transactions on Mechatronics, Vol.9. No.1, pp.78-86,2004.
    [87]H. M. Handroos and M. J. Vilenius The unitlization of experimental data in modelling hydraulic single stage pressure control valves ASME Journal of Dynamic Systems, Measurement and Control, Vol.112, No.3, pp. 482-488,1990.
    [88]O. OLABY, X. BRUN. S. SESMAT, T. REDARCE, E. BIDEAUX Characterization And Modeling Of A Proportional Valve For Control Synthesis Proceedings of the 6th JFPS International Symposium on Fluid Power, pp.771-776,2005.
    [89]D. Cristofori, A. Vacca The Modeling of Electrohydraulic Proportional Valves ASME Journal of Dynamic Systems. Measurement and Control, Vol.134, No.2.2012.
    [90]M. Moran. H. N. Shapiro Fundamentals of Engineering Thermodynamics Wiley. New York.1992.
    [91]S.V. Natarajan, S.C. Subramanian, S. Darbha. K.R. Rajagopal A model of the relay valve used in an air brake system Nonlinear Analysis:Hybrid Systems, Vol.1. No.3. pp.430-442,2007.
    [92]P. Karthikeyan, C. S. Chaitanya, N. J. Raju, S.C. Subramanian Modelling an electropneumatic brake system for commercial vehicles Nonlinear Analysis:Hybrid Systems, Vol.1,No.3, pp.430-442,2007.
    [93]X. C. Xiong, J. H. Wei, J. Chen Modeling, Experimentation, and Simulation of an Air-Over-Hydraulic Brake System ASME Journal of Dynamic Systems, Measurement and Control, Vol.131, No.3,2012.
    [94]J.K. Hedrick, J.C. Gerdes, D.B. Maciuca, D. Swaroop Brake System Modeling, Control and Integrated Brake/Throttle Switching:Phase I California PATH Research Report, UCB-ITS-PRR-97-21,1997.
    [95]P. Pillay, R. Krishnan Modeling, simulation, and analysis of permanent-magnet motor drives. Ⅰ. The permanent-magnet synchronous motor drive IEEE Transactions on Industry Applications, Vol.25. No.2. pp.265-273,1989.
    [96]A. B. Dehkordi, A. M. Gole. T. L. Maguire Permanent magnet synchronous machine model for real-time simulation In International conference on power systems transients,2005.
    [97]A. F. Burke Batteries and ultracapacitors for electric, hybrid, and fuel cell vehicles Proceedings of the IEEE, Vol.95, No.4, pp.806-820,2007.
    [98]S. H. Marin, C. E. James Supercapacitors:A Brief Overview Report No. MP 05W0000272. The MITRE Corporation, McLean, Virginia,2006.
    [99]K. Youngho Ultracapacitor technology powers electronic circuits Power Electronics Technology, Vol.29, No.10, pp.34-39,2003.
    [100]D. W. Z. Gao, C. Mi, A. Emadi Modeling and Simulation of Electric and Hybrid Vehicles Proceedings of the IEEE, Vol.95, No.4, pp.729-745,2007.
    [101]K. Koprubasi Modeling And Control Of A Hybrid-Electric Vehicle For Drivability And Fuel Economy Improvements Dissertation for Ph.D, Ohio State University,2008.
    [102]D. Maclay, R. Dorey Alpplying Genetic Search Techniques to Drivetrain Modeling IEEE Control System Magazines, Vol.13, No.3, pp.50-55,1993.
    [103]M. H. M. Dassen Modelling and control of automotive clutch systems Report number 2003.73.
    [104]K. S. Narendra, J. Balakrishnan A Common Lyapunov Function for Stable LTI Systems with Commuting A-Matrices IEEE Transactions On Automatic Control, Vol.39, No.12, pp.2469-2471,1994.
    [105]L. Vu, D. Liberzon Common Lyapunov functions for families of commuting nonlinear systems System Control Letter, Vol.54, pp.405-416,2005.
    [106]D. Liberzon, J. P. Hespanha, A. S. Morse Stability of switched systems:A Lie-algebraic condition System Control Letter,Vol.37, No.3, pp.117-122,1999.
    [107]D. Liberzon, A. S. Morse Basic problems in stability and design of switched systems IEEE Control System Magazine, Vol.19, No.5, pp.59-70,1999.
    [108]H. Lin, P. J. Antsaklis Stability And Stabilizability Of Switched Linear System:A Survey Of Recent Results IEEE Transaction On Automatic Control, Vol.54, No.2, pp.308-322,2009.
    [109]M. Margaliot Stability Analysis of Switched Systems Using Variational Priciples:An Introduction Automat-ica, Vol.42, No.12, pp.2059-2077,2006.
    [110]D. Liberson Switching in Systems and Control Boston, MA:Birkhauser,2003.
    [111]M.Johansson piecewise linear control systems-A computational approach New York:Springer-Verlag,2002.
    [112]S. Roman Advanced Linear Algebra 3rd edition, Springer Verlag,2008.
    [113]L. L. Dines, Systems of linear inequalities, Annals of Mathematics,1919,20(3):191-199.
    [114]W. P. Dayawansa, C. F. Martin A converse Lyapunov theorem for a class of dynamical systems which undergo switching IEEE Transaction on Automatic Control, Vol.44, No.4, pp.751-760,1999.
    [115]A. P. Molchanov, Y. S. Pyatnitskiy Criteria of asymptotic stability of differential and difference inclusions encountered in control theory Systems Control Letter, Vol.13, No.1, pp.59-64,1989.
    [116]D. Cheng, L. Guo, J. Huang On quadratic Lyapunov functions IEEE Transaction Automatic Control, Vol.48, No.5, pp.885-890,2003.
    [117]R. Shorten, F. Wirth, O. Mason, K.Wulff, C. King Stability criteria for switched and hybrid systems SIAM Review, Vol.49, No.4, pp.549-592,2007.
    [118]A. Sasane Stability of switching infinite-dimensional systems Automatica, Vol.41, No.1, pp.75-78,2005.
    [119]F. Hante, M. Sigalotti Existence of common Lyapunov functions for infinite-dimensional switched linear systems 49th IEEE Conference on Decision and Control, pp.5668-5673,2010.
    [120]G. Welch, G. Bishop An Introduction to the Kalman Filter Proceedings of SIGGRAPH, Course,2001.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700