本論文針對混成車之關鍵零組件作多重領域之系統動態鍵結圖分析，此外並提出一以元件導向為基礎之模式簡化法則，有效率提升混成車模式模擬時之運算能力，並同時近似原系統之動態特性。論文中首先針對直噴式引擎、無刷直流馬達、質子交換膜燃料電池及無段變速傳動機構等關鍵零組件作鍵結圖建模，推導出其動態方程式。之後，分析各零組件(子系統)之時域或頻域響應，各子系統並整合成不同型態之混成車，如引擎-馬達混成車及燃料電池混成車等。由於混成車模式具高階非線性的動態，並不適用於車用(高階)控制器設計或即時模擬。因此，本論文提出一系統簡化（降階）法則，利用相似度指標，因果決定策略以及誤差動態模組合理刪減混成車鍵結圖模式中的系統元件。研究成果顯示，各關鍵零組件可透過鍵結圖動態分析法則，有效率整合不同物理領域並快速建模，各動態模組可適用於效能分析與零組件控制器設計。混成車動態特性可藉由合併關鍵零組件並採用規則庫控制法則加以評估。所提出之系統簡化法則可將混成車模式有系統的簡化，增加運算效能並保有原系統的特徵。當限制車用模擬器中每一個子系統精度於 5%之內時，利用系統簡化法則可使運算時間大幅減少40% 以上。車用即時模擬器因而完成。

This thesis aims to analyze the multi-disciplinary dynamics of key components in a hybrid electric vehicle (HEV) using bond graph unified approach. An element-oriented model simplification algorithm was also developed to enhance the computational ability for the HEV simulation but still remain the similar system dynamics of the original model. The key components including the direct injection spark ignition (DISI) engine, the brushless DC motor, the proton exchange membrane fuel cell (PEMFC) and the continuously variable transmission (CVT) have been modeled with a set of dynamic equations. Time-domain response and frequency-domain analysis for these key components (subsystems) then have been studied. These verified components were integrated into various types of HEVs, such as engine-motor HEVs or fuel cell HEVs. The highly-nonlinearity and high-order dynamics of a HEV make it improper for vehicle (high-level) controller designs or real-time simulation. A model simplification (order reduction) methodology was thereby proposed in this thesis using defined dynamics similarity, causality determination procedures and error dynamics modules to eliminate trivial states in the HEV bond graph model. Simulation results show that each subsystem can be modeled rapidly and multi-physical domains inside it can be integrated effectively using the bond graph approach. The dynamics analysis and controller designs for all bond graph models are accessible. Performance evaluations of hybrid vehicles are achieved by the combination of these subsystems and the developed rule-based control strategy. The proposed model simplification algorithm deduces complexity of HEV models systematically, enhances the computational efficiency and also keeps major characteristics of the original models. Results show that if the model fidelity of each subsystem in the automotive simulators is restricted within 5%, the computational time will decrease 40% via the proposed element-oriented model simplification algorithm. The automotive on-line simulators thus are completed.

[1]. Ye, Y., Youcef-Toumi, K., ”Model Reduction in the Physical Domain,” Proc. of the American Control. Conf., San Francisco, CA, pp. 4486-4490, June, 1999.
[2]. Rosenberg, R. C., Introduction to Physical System Dynamics. McGraw-Hill, 1996.
[3]. Karnopp, D. C., Margolis, D. L. and Rosenberg, R. C., System Dynamics: A Unified Approach. 2nd edition, John Wiley & Sons, Inc., 1990.
[4]. Filippo, J. M., Delgado, M., “A survey of bond graph: theory, applications and programs,” J. of the Franklin Inst., vol. 328, no. 5, pp. 565-606, 1991.
[5]. Dettmer, R., “Hybrid Pioneers”, IEE Review, vol. 49, pp. 42-45, 2003.
[6]. Purkrushpan J. T., Stefanopoulou A. G., Peng H., “Modeling and control for PEM fuel cell stack system.” Proc. of American Control Conference 2002; 4: pp.3117 -3122, 2002.
[7]. National Renewable Energy Laboratory (NREL), Department of Energy (DOE), “Advisor 2002,”http://www.ctts.nrel.gov/analysis/advisor.html, 2002.
[8]. Cuddy, M., and Wipke, K., “Analysis of the fuel economy benefit of drivetrain hybridization,” SAE Paper No. 970289, 1997.
[9]. Mechanical Simulation Corporation, http://www.carsim.com/index.html, Last Revised, August 17, 2004.
[10]. Rizzoni, G., Guezennec, Y. Brahma, A., Wei, X., and Miller, T., “VP-SIM: a unified approach to energy and power flow modeling simulation and analysis of hybrid vehicles,” SAE Paper, No. 2000-01-1565, 2000.
[11]. Powell, B. K. and Pilutti, T. E., “A range extender hybrid electric vehicle dynamic model,” Proc. Of the 33rd IEEE Conf. on Decision and Control, LakeBuena Vista, FL, December, 1994.
[12]. Margolis, D. L., “Modeling of two-stroke internal combustion engine dynamics using bond graph technique,” SAE paper 75086, 1975.
[13]. Hung, Y. H. and Hong, C. W., “Dynamic modeling and powertrain management of a hybrid electric scooter”, AVEC’00 International Symposium on Advanced Vehicle Control (IEEE/ASME/JSAE/AVEC), Michgan, USA, August, 2000.
[14]. Hubbard, G. A., Youcef-Toumi, Kamal, “Modeling and simulation of a hybrid-electric vehicle drivetrain,” Proc. American Control Conference. Albuquerque, New Mexico, June 1997.
[15]. Delforce, C., Hecquet, M. and Brochet, P., “Bond-graph method applied to coupled electric and magnetic model of electrical devices,” IEEE Int. Conf. on Systems, Man and Cybernetics, vol. 1, pp. 573-578, 1993.
[16]. Delforce, C., Lemaire-semail, B., “Induction machine modeling using finite element and permeance network methods,” IEEE Transactions on Magnetics, Vol. 31, Issue 3, pp. 2092-2095, May, 1995.
[17]. Lee, B. K., Ehsani, M., “Advanced BLDC motor drive for low cost and high performance propulsion system in electric and hybrid vehicle,” IEEE Int. Electric Machines and Drives Conference, pp.246-251, 2000.
[18]. Karnopp, D. C., “Bond graph models for electrochemical energy storage: electrical, chemical and thermal effects,” J. of the Franklin Institute, vol. 327, no. 6, pp. 983-992, 1990.
[19]. Thoma, J., “Electric batteries and fuel cells modeled by bond graph,” J. of Power Sources, vol. 7, pp. 613-622, 1999.
[20]. Gerbert, B. G., “Adjustable speed V-belt drives – mechanical properties and design,” SAE No. 740747, 1974.
[21]. Hrovat, D. and Tobler, W. E., “Bond graph modeling of automotive power trains,” J. of the Franklin Institute, vol. 328, no. 5/6, pp. 623-662, 1991.
[22]. Drozdz, W. and Pacejka, H. B., “Development and validation of a bond graph handling model of an automobile,” J. of the Franklin Inst., vol. 328, no. 5/6, pp. 941-957, 1991.
[23]. Orbak, Y., “Physical domain model reduction for design and control of engineering systems,” PhD Thesis, Dept. of Mechanical Eng., Massachusetts Institute of Technology, U. S. A., 1998.
[24]. Bryson, E., Carrier, A., “Second-Order Algorithm for Optimal Model Order Reduction,” J. of Guidance, Control, and Dynamics, 13, pp. 887-892, 1990.
[25]. Elliot, H., Wolovich, W. A., “A Frequency Domain Model Reduction Procedure,” Automatica, vol. 16, pp. 167-177, 1980.
[26]. Davison, E. J., “A Method for Simplifying Linear Dynamic Systems,” IEEE Trans. Aut. Control, AC-11, pp. 93-101, 1966.
[27]. Chen, C. F., and Shieh, J, L., “A novel approach to linear model simplification,” Int. J. Contr., vol. 8, pp. 561-570, Dec., 1968.
[28]. Hutton, M. F., and Friedland, B., “Routh approximations for reducing order of linear, time-invariant systems,” IEEE Transactions on Automatic Control, vol. AC-20, no. 3, June, 1975.
[29]. Wilson, B. H. and Stein, J. L., “An algorithm for obtaining minimum-order lumped parameter models of distributed and discrete systems,” Proc. of the 1992 ASME Winter Annual Meeting, November, Anaheim, CA, pp.47-58, 1992.
[30]. Desrochers, G., Saridis, N., “A Model for High Order Linear System Reduction and Nonlinear System Simplification,” Automatica, vol. 21, no.1, pp. 93-100, 1985.
[31]. Taylor, J. H., Wilson, B. H., “A frequency-domain model-order-deduction algorithm for nonlinear systems,” Proc. of the 4th IEEE Conference on Control Applications, Sept., pp. 1053-1058, 1995.
[32]. Orbak, Y., Youcef-Toumi, K., and Massaki Senga, “Model reduction and design of a power steering system,” Proc. of the American Control Conference, San Diego, California, June, pp. 4476-4481, 1999.
[33]. Louca, L. S., Stein, J. L., “Energy-based Model Reduction of Linear Systems,” Proc. of ICBGM’99, 4th Int. Conf. on Bond Graph Modeling and Simulation, San Francisco, CA, Jan, pp. 17-20, 1999.
[34]. Sendur, P., “Physical System Modeling: Algorithms for Assessing Model Quality Based on Design Specifications,” PhD Thesis, Dept. of Mechanical Eng., Univ. of Michigan, U. S. A., 2002.
[35]. Sueur, G., Dauphin, T., “Structural Controllability/Observability of Linear Systems Represented by Bond Graphs,” J. of the Franklin Inst., vol. 326, no. 6, pp. 869-883, 1989.
[36]. Yeh, T. J., “Backstepping control in the physical domain,” J. of the Franklin Inst., vol. 338, no. 4, pp. 455-479, 2001.
[37]. Gawthrop, P. J., “Physical model-based control: a bond graph approach,” J. of the Franklin Inst., vol. 332, no. 3, pp. 285-305, 1995.
[38]. Wilson, H. J., “A structurally based approach to model order reduction using bond graphs,” Proc. of the American Control Conf., Philadelphia, Pennsylvania. June, pp. 151-156, 1998
[39]. Mukherjee, S., Mishra, R. N., “Order reduction of linear systems using an error minimization technique,” J. of the Franklin Inst., vol. 323, pp. 23-32, 1987.
[40]. Wilson, H. J., Tayler, H., “A frequency domain model-order deduction algorithm for linear systems,” J. of Dyn. Sys,. Meas., and Contrl., vol. 120, pp. 185-192, 1998.
[41]. 20SIM, “20SIM pro user’s manual,” Version 3.1, The University of Twente- Controlab Products B. V. Enschede, The Netherlands, 2000.
[42]. Wu, S. T., Youcef-Toumi, K., “On relative degrees and zero dynamics from system configuration,” J. of Dynamic Systems Measurement and Control-Trans. of the ASME, vol. 177, no. 2, pp. 205-210, 1995.
[43]. Duindam, V., and Stramigioli, S., “Energy-based model-reduction of nonholonomic mechanical systems,” Submitted for Publication, 2003.
[44]. Coelingh, E., Vries, J. A., and Amerongen, J. V., “Automated performance assessment of mechatronic motion systems during the conceptual design stage,” Proc. of the 3rd Int. Conf. on Advanced Mechatronics, Okayama, Japan, Aug. 1998.
[45]. Blomen, LJMJ., Mugerwa, M. N., “Fuel Cell Systems,” New York, Plenum Press, 1993.
[46]. Bumby, J. R., Clarke, P. H., Forster, I., “Computer modeling of the automotive energy requirements for internal combustion engine and battery powered vehicles,” IEEE Trans. of Vehicle Technology, vol. 132, no. 5, pp. 265-279, 1985.
[47]. Bowles, P., Peng, H. and Zheng., X., “Energy management in a parallel hybrid electric vehicle with a continuous variable transmission,” Proc. of American Control Conf. Chicago, Illinois, June, 2000.
[48]. Heywood, J. B., “Internal Combustion Engine Fundamentals,” McGraw-Hill Book Co. 1998.
[49]. Hong, C. W., Shio, T. W., ”Fuzzy control strategy design for an autopilot on automotive chassis dynamometer test stands,” Mechatronics, vol. 6, no. 5, pp. 537-555, 1996.
[50]. Hung, Y. H., “CVT scooter powerrtrain dynamics using bond graph approach,” MSc Thesis, National Tsing Hua University, Hsinchu, Taiwan, 1999..
[51]. Hung, Y. H., Lin, B. S., Hong, C. W., “A rule-based control algorithm for hybrid electric motorcycle powertrain systems,” AVEC’02 International Symposium on Advanced Vehicle Control, Hiroshima, Japan, 2002.
[52]. Hung, Y. H., Hong, C. W., “Bond graph dynamics of a rubber-belt continuously variable transmission,” Int. J. of Vehicle Design, vol. 5, issue 31, 2004.
[53]. Worley, B. G., “Designing adjustable-speed V-belt drives for farm implements,” SAE Transactions, vol. 63, pp. 321-333, 1955.
[54]. Hung, Y. H., “Bond graph dynamics and real time control of fuel cell hybrid electric vehicles,” PhD Proposal, Dept. of power mechanical Engineering, National Tsing-Hua University, Hsingchu, Taiwan, 2002.
[55]. Marr, C., Li, X., “An engineering model of proton exchange membrane fuel cell performance,” An Interdisciplinary Journal of Physical and Engineering Science, Vol. 50, No. 4, pp. 190-200, 1998.
[56]. U. S. Department of Commerce PNGV Program Plan, http://www.ta.doc.gov/ PNGV-Archive/ default.htm, Washington, DC, 2002.
[57]. Zawodzinski T. A., Springer T. E., Gottesfeld S., “Polymer electrolyte fuel cell model,” J. the Electrochem. Society, 138 (8), pp. 2334-2342, 1991.
[58]. Mann, R. F., Amphlett, J. C., Hooper, M. A. I., Jensen, H. M., Peppley, B. A., Roberge, P. R., “Development and application of a generalized steady-state electrochemical model for a PEM fuel cell,” J. Power Sources, 86, pp. 173-180, 2000.
[59]. Rowe, A., Li, X., “Mathematical model of proton exchange membrane fuel cells,” J. Power Source, 102, pp. 82-96, 2001.
[60]. Hong, C. W., Cheng, C. H., Fei, K., “A three-dimensional CFD approach for PEMFC and DMFC design,” Proc. of ASME 1st Int. Conf. on Fuel Cell Science, Engineering and Technology; pp. 203-208, 2003.
[61]. Kim, Y. H., Kim, S. S., “An electrical modeling and fuzzy logic control of a fuel cell generation system,” IEEE Trans. on Energy Conversion, vol. 14, no. 2, pp. 239-244, 1999.
[62]. Heong, K. S., Oh, B. S., “Fuel economy and life-cycle cost analysis of a fuel cell hybrid vehicle,“ J. of Power Sources, vol. 105, pp. 58-65, 2002.
[63]. Dougal, R. A., Liu, S., Gao, L., Blackwelder M., “Virtual test bed for advanced power sources,” J. of Power Source, vol. 110, pp. 285-294, 2002.
[64]. Jiang, R., Chu, D., “Voltage-time behavior of a polymer electrolyte membrane fuel cells,” J. of Power Sources, vol. 92, pp. 193-198, 2001.
[65]. Lee, W. Y., Park, G. G., Yang, T. H., Yoon, Y. G. and Kim, C. S., “Empirical modeling of polymer electrolyte membrane fuel cell performance using artificial neural networks,’ Int J. of Hydrogen Energy, vol. 29:, pp. 961-966, 2004.
[66]. Amphlett, J. C., Mann, R. F., Peppley, B. A., Roberge, P. R., and Rodrigues, A., “A model predicting transient response of proton exchange membrane fuel cells,” J. Power Sources , vol. 61, pp. 183-188, 1996.
[67]. Moraal, P. and Kolmanovsky, I., “Turbocharger modeling for Automotive Control Applications,” SAE Paper No. 1999-01-0908, 1999.
[68]. Mayer, U., Groll, M., and Supper, W., “Heat and mass transfer in metal hydride reaction beds: experimental and theoretical results,” J. of Less-Common Met., vol. 131, pp. 235-244, 1987.
[69]. Askri, F., Jemni, A. and Nasrakkah, S. B., “Prediction of transient heat and mass transfer in a closed metal-hydrogen reactor,” Int. J. of Hydrogen Energy, vol. 29, pp. 195-208, 2004.
[70]. Pukrushpan, J. T., Modeling and control of fuel cell systems and fuel processors, Ph.D. Dissertation, University of Michigan, USA, 2003.
[71]. Pukrushpan, J. T., Peng, H., and Stefanopoulou, A. G., “Simulation and analysis of transient fuel cell performance based on a dynamic reactant flow model,” Proc. of 2002 ASME International Mechatronical Engineering Congress and Exposition (IMECE ’02), New Orleans, Louisiana, November, 2002.
[72]. Pan, C, H., “Control and hardware-in-the-loop simulation of hybrid electric scooters,” Master Thesis, National Tsing Hua Univ., Taiwan, 2004.
[73]. Lin, P. H., Hung, Y. H., Hong, C. W., “A Rule-Based Control Algorithm for Hybrid Electric Motorcycle Powertrain Systems”, AVEC’02 International Symposium on Advanced Vehicle Control, Hiroshima, Japan, Sept., 2002 .
[74]. Liang, C., Qingnian, W., Youde, L., Zhimin, M., Ziliang, ., and Di, L., “Study of the electric control strategy for the power train of hybrid electric vehicles,” Proc. of IEEE Int. Vehicle Electronics Conf. (IVEC ‘99), vol. 1, pp. 383-386, 1999.
[75]. Lin, C. C., Kang, J., Grizzle, J. W., and Peng, H., “Energy mamagement strategy for a parallel hybrid electric truck,” Proc. Of the 2001 American Control Conference, Arlington, VA, USA, June, 2001, pp. 2878-2883.
[76]. Sebastien, D., Marie, G. T., Gino, P., Jimmy, L., and Michel, D., “Control strategy optimization for a hybrid parallel powertrain,” Proc. of American Control Conf., Arington, VA, June 25-27, 2001.
[77]. Wong, J. Y., Theory of Ground Vehicles. 2nd Edit., John Wiley & Sons, Inc., 1993.
[78]. Lewis, F. L., and Syrmos, V. L., Optimal Control. 2nd Edit., John Wiley & Sons, Inc., 1995.
[79]. Engstorm, J., and Victor, T., “Real-time recognition of large-scale driving patterns,” Proc. of 2001 IEEE Intelligent Transportation Systems Conference, Oakland, CA, USA, August, 2001.
[80]. Hung, Y. H., Wu, C. H., and Hong, C. W., “An adaptive-sized real-time hybrid electric vehicle simulator using on-line identification method,” International Symposium on Advanced Vehicle Control (AVEC’04), Arhem, Netherlands, Sept. 23-27, 2004.