跑道辨识算法在飞机防滑刹车中的应用研究
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摘要
机轮刹车系统是飞机的一个重要机载设备,对飞机的起飞和着陆起着重要的安全保障作用。飞机防滑刹车控制系统具有强实时性、强非线性和强不可测性,工作环境极其恶劣,极易受到跑道状况、机场侧风、不对称着陆等因素的影响,因此大吨位、高速度大飞机的防滑刹车控制系统要求具备一定的跑道自适应能力。目前,国内对防滑刹车控制算法虽然进行了较多较为深入的研究,但大多数都是以最佳滑移率为控制目标,并未对跑道状态辨识进行深入研究。因此,若要从根本上提高飞机的刹车效率,必须使防滑控制算法具备跑道辨识能力。
本文从分析飞机防滑刹车控制系统的原理出发,建立了以国产大型客机为对象的机轮刹车系统数学模型,并利用动态惯性试验验证了该模型的准确性。由于轮胎与跑道间相互作用机理较为复杂,对轮胎/跑道摩擦模型进行深入分析,在应用动态分布式LuGre摩擦模型的基础上建立了一个新型的非线性状态观测器,通过此观测器实时辨识跑道状态,以得到刹车过程中最佳滑移率。并将其应用于防滑控制算法中,使防滑控制算法具备跑道辨识能力,提高刹车效率。
最后,利用MATLAB软件中的Simulink仿真工具,对带跑道辨识功能的飞机防滑刹车控制算法进行仿真,考察了湿跑道、薄冰跑道及跑道状态突变情况下的飞机刹车性能,并将仿真结果与传统算法相比较,结果表明具有跑道辨识能力的防滑控制算法能够较好地改善飞机刹车性能。
Wheel braking system is one of the key airborne equipments which plays an important role in taking off and landing safely. In addition, aircraft antiskid braking system has a strong real-time, nonlinear and strong unpredictable nature.While affected by dreadful conditions and many critical factors such as runway conditions, airport cross-winds and asymmetric landing. The antiskid braking system must have the capability of runway adaptive in the large aircraft with large tonnage and high speed. Deep researches to the algorithm of antiskid braking system have been carried on by domestic researchers, but most of them lay emphasis more on the best slip rate than runway state identification. Therefore, runway state identification must be involved in the algorithm of antiskid braking system to improve braking efficiency essentially.
Based on the theory of the antiskid braking system in the paper, established in domestic large passenger aircraft braking system model, and the dynamic inertia test experiment has been used to verify the accuracy of the model. As the interaction between tyres and runway is so complex, the friction model for tyres and runway should be analyzed deeply. To achieve the best slip rate, a new type of nonlinear state observer which is based on the dynamic distributed LuGre friction model was designed. What's more, braking efficiency could be improved by applying the state observer to the antiskid control algorithm.
In the end, with the use of the SIMULINK toolbox in MATLAB software, the antiskid braking control algorithm is simulated on the model to study the antiskid braking performance in different conditions such as wet, icy runway and runway condition mutated. Comparing with the simulation results above to the proposed algorithm, it indicates that the antiskid control algorithm with capability of runaway state identification does well in improving the braking performance.
本文从分析飞机防滑刹车控制系统的原理出发,建立了以国产大型客机为对象的机轮刹车系统数学模型,并利用动态惯性试验验证了该模型的准确性。由于轮胎与跑道间相互作用机理较为复杂,对轮胎/跑道摩擦模型进行深入分析,在应用动态分布式LuGre摩擦模型的基础上建立了一个新型的非线性状态观测器,通过此观测器实时辨识跑道状态,以得到刹车过程中最佳滑移率。并将其应用于防滑控制算法中,使防滑控制算法具备跑道辨识能力,提高刹车效率。
最后,利用MATLAB软件中的Simulink仿真工具,对带跑道辨识功能的飞机防滑刹车控制算法进行仿真,考察了湿跑道、薄冰跑道及跑道状态突变情况下的飞机刹车性能,并将仿真结果与传统算法相比较,结果表明具有跑道辨识能力的防滑控制算法能够较好地改善飞机刹车性能。
Wheel braking system is one of the key airborne equipments which plays an important role in taking off and landing safely. In addition, aircraft antiskid braking system has a strong real-time, nonlinear and strong unpredictable nature.While affected by dreadful conditions and many critical factors such as runway conditions, airport cross-winds and asymmetric landing. The antiskid braking system must have the capability of runway adaptive in the large aircraft with large tonnage and high speed. Deep researches to the algorithm of antiskid braking system have been carried on by domestic researchers, but most of them lay emphasis more on the best slip rate than runway state identification. Therefore, runway state identification must be involved in the algorithm of antiskid braking system to improve braking efficiency essentially.
Based on the theory of the antiskid braking system in the paper, established in domestic large passenger aircraft braking system model, and the dynamic inertia test experiment has been used to verify the accuracy of the model. As the interaction between tyres and runway is so complex, the friction model for tyres and runway should be analyzed deeply. To achieve the best slip rate, a new type of nonlinear state observer which is based on the dynamic distributed LuGre friction model was designed. What's more, braking efficiency could be improved by applying the state observer to the antiskid control algorithm.
In the end, with the use of the SIMULINK toolbox in MATLAB software, the antiskid braking control algorithm is simulated on the model to study the antiskid braking performance in different conditions such as wet, icy runway and runway condition mutated. Comparing with the simulation results above to the proposed algorithm, it indicates that the antiskid control algorithm with capability of runaway state identification does well in improving the braking performance.
引文
[1]Statistical Summary of Commercial Jet Airplane Accidents Worldwide Operations 1959-2008[R]. Seattle:Aviation Safety Boeing Commercial Airplanes,2009.
[2]温兴清,廖力清.机轮防滑刹车控制方法的研究[J].飞机设计,2008,28(1)：23-27.
[3]余驰,贾玉红.飞机防滑刹车系统存在的问题及其解决方法[J].飞机设计,2006,3：44-47.
[4]宋砚玉.国外航空刹车材料的发展[J].航空精密机械工程,1989,4：73-77.
[5]于川江,姚萍屏.现代制动用刹车材料的应用研究和展望[J].润滑与密封,2010,35(2)：103-106.
[6]雷宝灵,易茂中,徐惠娟.C/C复合材料飞机刹车盘地三维温度场[J].复合材料学报,2009,26(1)：113-117.
[7]郭领军,潘小娟,李贺军,等.国内外C/C复合材料疲劳性能的研究发展[C].第22届炭-石墨材料学术会议论文集.宁波,2010：60-64.
[8]姚萍屏,熊翔,黄伯云.粉末冶金航空刹车材料的应用现状与发展[J].粉末冶金工业,2000,10(6)：34-38.
[9]罗瑞盈,向巧,李进松,等.先进碳/碳复合飞机刹车材料关键技术研究和应用进展[J].航空制造技术,2010,(1)：56-58.
[10]严爱军,王普,安晓辉.飞机防滑刹车控制方法综述[J].控制工程,2008,15(1)： 1-4.
[11]陈娟,宋国彪,王占林.飞机防滑刹车系统自适应控制器的设计与实现[J].机床与液压,2002,(6)：152-154.
[12]郑永安,史忠科.飞机起落架防滑刹车系统鲁棒故障诊断方法[J].2008,26(2)： 16-19.
[13]李玉忍,薛晶,马瑞卿.飞机制动过程滑移率寻优方法研究[J].西北工业大学学报,2008,26(4)：488-491.
[14]阳波,黄佑,黄超,等.飞机刹车系统集成研究[J].机床与液压,2008,36(10)：174-175.
[15]智维列夫,科柯宁.航空机轮和刹车系统设计[M].(邓启明,陈金祥等).北京：国防工业出版社,1980.
[16]何永乐.飞机刹车系统设计[M].西安：西北工业大学出版社,2007.
[17]高泽迥.飞机设计手册·起飞着落系统设计[M].北京：航空工业出版社,2002.
[18]Peter B. Ladkin. Analysis of a technical description of the airbus A320 braking system[J]. High Integrity Systems,1995,9 (13):1-29.
[19]Pascal Traverse, Isabelle Lacaze, Jean Souyris. Airbus fly-by-wire:A total approach to dependability[J]. Building the Information Society,2004, (156): 191-212.
[20]刘国良,廖力清,凌玉华.带自调整因子的防滑刹车系统模糊控制器研究[J].飞机设计,2007,27(2)：46-50.
[21]曾小信,凌玉华,廖力清.飞机防滑刹车系统自适应模糊控制的应用研究[J].航空精密制造技术,2008,44(1)：32-34.
[22]韦凌峰,董新民,程建峰.飞机防滑刹车模糊控制器的改进研究[J].微计算机信息,2010,26(3)：176-177.
[23]Amir Poursamad. Adaptive feedback linearization control of antilock braking systems using neural networks[J]. Mechatronics,2009,19 (5):767-773.
[24]P.J.Costa Branco, J.A. Dente. Design and experimental evaluation of a fuzzy logic pressure controller for Airbus 310/320 braking control system[J]. Engineering Applications of Artificial Intelligence,2010,23 (6): 989-999.
[25]Andon V. Topalov, Yesim Oniz, Erdal Kayacan et al. Neuro-fuzzy control of antilock braking system using sliding mode incremental learning algorithm[J]. Neurocomputing,2011,7(3):1-11.
[26]刘泽华,高亚奎.CMAC-PID控制在飞机防滑刹车中的应用[J].海军航空工程学院学报,2010,25(2)：181-184.
[27]刘泽华,高亚奎.RBF-PID控制在防滑刹车系统中的应用研究[J].2010,27(10)：24-28.
[28]刘泽华,李振水,贾爱绒.免疫模糊控制算法在飞机防滑刹车系统中的应用研究[J].计算机测量与控制,2009,19(8)：1562-1564.
[29]李玉忍,马瑞卿,薛晶,等.飞机防滑刹车系统的变结构控制研究[J].西北工业大学学报,2008,26(6)：752-755.
[30]李波,焦宗夏.基于广义卡尔曼滤波的飞机防滑刹车变结构控制[J].系统仿真学报,2007,19(3)：585-592.
[31]Y Oniz, E Kayacan, O Kaynak. Simulated and Experimental Study of Antilock Braking System Using Grey Sliding Mode Control[C]. IEEE International Conference on Systems, Man and Cybernetics,2007:90-95.
[32]王天娇,袁朝晖,张谦.基于神经网络的飞机静液刹车系统设计[J].计算机测量与控制,2008,16(10)：1427-1429.
[33]李潇,吴瑞祥.基于补偿神经网络的模糊飞机刹车控制系统研究[J].计算机仿真,2006,23(1)：59-61.
[34]祝知富,曹克强,胡良谋.基于LQ最优控制理论的飞机刹车系统仿真研究[J].机床与液压,2005,13(1)：138-140.
[35]HaibinSong, Bin Fang, Pu Wang. Research and applications of immune PID adaptive controller in anti-skid braking system for aircraft[C].2009 International Conference on Information Engineering and Computer Science. Wuhan:IEEE,2009:1-5.
[36]Bakker, Eqbert, Nyborg et al. Tyre Modelling for Use in Vehicle Dynamics Studies[C]. SAE Technical Paper Series. Seattle,1987.
[37]Besselink IJM, Schmeitz AJC, Pacejka HB. An improved Magic Formula/Swift tyre model that can handle inflation pressure changes[J], VEHICLE SYSTEM DYNAMICS,2010,48(1):337-352.
[38]Kiencke.U, Realtime Estimation of Adhesion Characteristic Between Tyres and Road[C]. Proceeding of the 12th Triennial World Congress of the International Federation fo Automatic Control. Sydney:Pergamon,1993:15-18.
[39]张乐祎,余卓平,熊璐.基于广义卡尔曼滤波器的路面辨识[J].计算机辅助工程,2008,17(3)：32-35.
[40]L.R.Ray. Nonlinear Tire Force Estimation and Road Friction Identification: Simulation and Experiments[J]. Automatica,1997,33(10):1819-1833.
[41]刘冠志,林辉.飞机全电刹车驱动器设计与关键技术研究[J].计算机测量与控制,2010,18(2)：326-328.
[42]杨伟,章卫国,杨朝旭,等.容错飞行控制系统[M].西安：西北工业大学出版社,2007.
[43]惠晓强,周波,张磊,等.数字式防滑刹车综合控制器的设计[J].航空计算技术,2010,40(5)：126-130.
[44]李玉忍,魏寒冰,薛晶.基于MATLAB、MFC和Vega的飞机刹车视景仿真[J].研究与设计,2010,26(3)：12-15.
[45]刘国良,廖力清.飞机防滑刹车系统的工作原理与性能评估[J].飞机设计,2006,(4)：23-26.
[46]余驰,贾玉红.飞机防滑刹车系统的MATLAB/SINMULINK建模与仿真 [J].系统仿真学报,2007,19(5)：1144-1147.
[47]Ki-Chang Lee, Jeong-Woo Jeon, Don-Ha Hwang et al. Comparison between Software Simulation and HIL Simulation of Antiskid Brake System for Aircrafts[J]. Industrial Electonics Society,2005,12 (6):1993-1998.
[48]田广来,谢利理.航空机轮刹车系统的半实物仿真实现[J].航空精密制造技术,2006,42(3)：28-34.
[49]Ro K, Kamman J. W, Barlow J. B. Flight mechanics of a free-wing tilt-body aircraft[J]. Aeronautical Journal,2008,112 (1137):625-640.
[50]Guoqing Zhang, Shuxing Yang; Songhai Xue. Investigation of aerodynamic characteristics of blended-wing-body aircraft based on cluster system[C].2009 Second Pacific-Asia Conference on Web Mining and Web-based Application (WMWA). Piscataway:IEEE,2009:253-257.
[51]P. D. Khapane. Gear walk instability studies using flexible multibody dynamics simulation methods in SIMPACK[J]. Aerospace Science and Technology, 2006,10 (1):19-25.
[52]娄锐.飞机起落架着陆的多体系统动力学建模与仿真[D].南京：南京航空航天大学,2009.
[53]L. Lernbeiss, M. Plochl, Simulation model of an aircraft landing gear considering elastic properties of the shock absorber[C]. Proceedings of the Institution of Mechanical Engineers, Part K:Journal of Multi-body Dynamics Journal of Multi-body Dynamics. United Kingdom:Professional Engineering Publishing,2007:77-86.
[54]Lahargou Andre, Brune Marc, Robuchon Alain. Undercarriage shock absorber with positive petention in a petracted position and with crash overtravel:USA, US20090218444[P].2009-09-03.
[55]Lidner Lars. Experience with the magic formula tyre model [J]. Vehicle System Dynamics,1993,21(SUPPL):30-46.
[56]E. Bakker, L. Nyborg, H. B. Pacejka. Tire modeling for use in vehicle dynamic studies[J]. Society of Automotive Engineers,1987,4(21):68-74.
[57]王纪森.非线性控制理论在防滑刹车系统中的应用研究[D].西安：西北工业大学,2001.
[58]熊翔.炭/炭复合材料制动性能研究[D].长沙：中南大学,2004.
[59]李江鸿,熊翔,张红波,等.不同刹车压力下C/C复合材料的摩擦性能与摩擦面研究[J].润滑与密封,2007,32(4)：9-13.
[60]熊翔,黄伯云,徐惠娟,等.不同制动速度下炭/炭复合材料的摩擦磨损行为及机理[J].中国有色金属学报,2002,12(12)：255-259.
[61]Zhang Ming, Nie Hong, Wei Xiao-hui, et al. Research on Modelling and Simulation for Aircraft Anti-skid Braking[C]. ISSCAA 2008 2nd International Symposium on Systems and Control in Aerospace and Astronautics, Piscataway:IEEE,2008:1-5.
[62]Rao, K. V. Narasimha, Kumar, R. Krishna, Mukhopadhyay, R. et al. A study of the relationship between Magic Formula coefficients and tyre design attributes through finite element analysis[J]. Vehicle System Dynamics,2006, 44 (1):33-63.
[63]L. Alvarez, J Yi. Adaptive emergency braking control in automated highway systems[C]. Proceedings of the 38th IEEE Conference on Decision and Control.1999,4:3740-3745.
[64]U.Kiencke, A.Daiss. Observation of lateral vehicle dynamics[J]. Control Engineering Practice,1997,5 (8):1145-1150.
[65]Dahl, P. R. Dynamic hysteresis model application to stiction type problems [C]. Advances in the Astronautical Sciences. Brechenridge, CO, United States: Univelt Inc,2001:95-111.
[66]Johanastrom, K. Canudas-de-Wit, C. Revisiting the LuGre friction model[J]. IEEE Control Systems Magazine,2008,28 (6):101-114.
[67]C Canudas de Wit, H Olsson, K J Astrom, et al. A new model for control of systems with friction[J]. IEEE Transactions on Automatic Control,1995,40 (3):419-425.
[68]唐志云,廖力清,欧阳昌华.基于PLC的SY02机轮联合加载试验控制系统[J].可编程控制器与工厂自动化,2008,(4)：38-40.
[2]温兴清,廖力清.机轮防滑刹车控制方法的研究[J].飞机设计,2008,28(1)：23-27.
[3]余驰,贾玉红.飞机防滑刹车系统存在的问题及其解决方法[J].飞机设计,2006,3：44-47.
[4]宋砚玉.国外航空刹车材料的发展[J].航空精密机械工程,1989,4：73-77.
[5]于川江,姚萍屏.现代制动用刹车材料的应用研究和展望[J].润滑与密封,2010,35(2)：103-106.
[6]雷宝灵,易茂中,徐惠娟.C/C复合材料飞机刹车盘地三维温度场[J].复合材料学报,2009,26(1)：113-117.
[7]郭领军,潘小娟,李贺军,等.国内外C/C复合材料疲劳性能的研究发展[C].第22届炭-石墨材料学术会议论文集.宁波,2010：60-64.
[8]姚萍屏,熊翔,黄伯云.粉末冶金航空刹车材料的应用现状与发展[J].粉末冶金工业,2000,10(6)：34-38.
[9]罗瑞盈,向巧,李进松,等.先进碳/碳复合飞机刹车材料关键技术研究和应用进展[J].航空制造技术,2010,(1)：56-58.
[10]严爱军,王普,安晓辉.飞机防滑刹车控制方法综述[J].控制工程,2008,15(1)： 1-4.
[11]陈娟,宋国彪,王占林.飞机防滑刹车系统自适应控制器的设计与实现[J].机床与液压,2002,(6)：152-154.
[12]郑永安,史忠科.飞机起落架防滑刹车系统鲁棒故障诊断方法[J].2008,26(2)： 16-19.
[13]李玉忍,薛晶,马瑞卿.飞机制动过程滑移率寻优方法研究[J].西北工业大学学报,2008,26(4)：488-491.
[14]阳波,黄佑,黄超,等.飞机刹车系统集成研究[J].机床与液压,2008,36(10)：174-175.
[15]智维列夫,科柯宁.航空机轮和刹车系统设计[M].(邓启明,陈金祥等).北京：国防工业出版社,1980.
[16]何永乐.飞机刹车系统设计[M].西安：西北工业大学出版社,2007.
[17]高泽迥.飞机设计手册·起飞着落系统设计[M].北京：航空工业出版社,2002.
[18]Peter B. Ladkin. Analysis of a technical description of the airbus A320 braking system[J]. High Integrity Systems,1995,9 (13):1-29.
[19]Pascal Traverse, Isabelle Lacaze, Jean Souyris. Airbus fly-by-wire:A total approach to dependability[J]. Building the Information Society,2004, (156): 191-212.
[20]刘国良,廖力清,凌玉华.带自调整因子的防滑刹车系统模糊控制器研究[J].飞机设计,2007,27(2)：46-50.
[21]曾小信,凌玉华,廖力清.飞机防滑刹车系统自适应模糊控制的应用研究[J].航空精密制造技术,2008,44(1)：32-34.
[22]韦凌峰,董新民,程建峰.飞机防滑刹车模糊控制器的改进研究[J].微计算机信息,2010,26(3)：176-177.
[23]Amir Poursamad. Adaptive feedback linearization control of antilock braking systems using neural networks[J]. Mechatronics,2009,19 (5):767-773.
[24]P.J.Costa Branco, J.A. Dente. Design and experimental evaluation of a fuzzy logic pressure controller for Airbus 310/320 braking control system[J]. Engineering Applications of Artificial Intelligence,2010,23 (6): 989-999.
[25]Andon V. Topalov, Yesim Oniz, Erdal Kayacan et al. Neuro-fuzzy control of antilock braking system using sliding mode incremental learning algorithm[J]. Neurocomputing,2011,7(3):1-11.
[26]刘泽华,高亚奎.CMAC-PID控制在飞机防滑刹车中的应用[J].海军航空工程学院学报,2010,25(2)：181-184.
[27]刘泽华,高亚奎.RBF-PID控制在防滑刹车系统中的应用研究[J].2010,27(10)：24-28.
[28]刘泽华,李振水,贾爱绒.免疫模糊控制算法在飞机防滑刹车系统中的应用研究[J].计算机测量与控制,2009,19(8)：1562-1564.
[29]李玉忍,马瑞卿,薛晶,等.飞机防滑刹车系统的变结构控制研究[J].西北工业大学学报,2008,26(6)：752-755.
[30]李波,焦宗夏.基于广义卡尔曼滤波的飞机防滑刹车变结构控制[J].系统仿真学报,2007,19(3)：585-592.
[31]Y Oniz, E Kayacan, O Kaynak. Simulated and Experimental Study of Antilock Braking System Using Grey Sliding Mode Control[C]. IEEE International Conference on Systems, Man and Cybernetics,2007:90-95.
[32]王天娇,袁朝晖,张谦.基于神经网络的飞机静液刹车系统设计[J].计算机测量与控制,2008,16(10)：1427-1429.
[33]李潇,吴瑞祥.基于补偿神经网络的模糊飞机刹车控制系统研究[J].计算机仿真,2006,23(1)：59-61.
[34]祝知富,曹克强,胡良谋.基于LQ最优控制理论的飞机刹车系统仿真研究[J].机床与液压,2005,13(1)：138-140.
[35]HaibinSong, Bin Fang, Pu Wang. Research and applications of immune PID adaptive controller in anti-skid braking system for aircraft[C].2009 International Conference on Information Engineering and Computer Science. Wuhan:IEEE,2009:1-5.
[36]Bakker, Eqbert, Nyborg et al. Tyre Modelling for Use in Vehicle Dynamics Studies[C]. SAE Technical Paper Series. Seattle,1987.
[37]Besselink IJM, Schmeitz AJC, Pacejka HB. An improved Magic Formula/Swift tyre model that can handle inflation pressure changes[J], VEHICLE SYSTEM DYNAMICS,2010,48(1):337-352.
[38]Kiencke.U, Realtime Estimation of Adhesion Characteristic Between Tyres and Road[C]. Proceeding of the 12th Triennial World Congress of the International Federation fo Automatic Control. Sydney:Pergamon,1993:15-18.
[39]张乐祎,余卓平,熊璐.基于广义卡尔曼滤波器的路面辨识[J].计算机辅助工程,2008,17(3)：32-35.
[40]L.R.Ray. Nonlinear Tire Force Estimation and Road Friction Identification: Simulation and Experiments[J]. Automatica,1997,33(10):1819-1833.
[41]刘冠志,林辉.飞机全电刹车驱动器设计与关键技术研究[J].计算机测量与控制,2010,18(2)：326-328.
[42]杨伟,章卫国,杨朝旭,等.容错飞行控制系统[M].西安：西北工业大学出版社,2007.
[43]惠晓强,周波,张磊,等.数字式防滑刹车综合控制器的设计[J].航空计算技术,2010,40(5)：126-130.
[44]李玉忍,魏寒冰,薛晶.基于MATLAB、MFC和Vega的飞机刹车视景仿真[J].研究与设计,2010,26(3)：12-15.
[45]刘国良,廖力清.飞机防滑刹车系统的工作原理与性能评估[J].飞机设计,2006,(4)：23-26.
[46]余驰,贾玉红.飞机防滑刹车系统的MATLAB/SINMULINK建模与仿真 [J].系统仿真学报,2007,19(5)：1144-1147.
[47]Ki-Chang Lee, Jeong-Woo Jeon, Don-Ha Hwang et al. Comparison between Software Simulation and HIL Simulation of Antiskid Brake System for Aircrafts[J]. Industrial Electonics Society,2005,12 (6):1993-1998.
[48]田广来,谢利理.航空机轮刹车系统的半实物仿真实现[J].航空精密制造技术,2006,42(3)：28-34.
[49]Ro K, Kamman J. W, Barlow J. B. Flight mechanics of a free-wing tilt-body aircraft[J]. Aeronautical Journal,2008,112 (1137):625-640.
[50]Guoqing Zhang, Shuxing Yang; Songhai Xue. Investigation of aerodynamic characteristics of blended-wing-body aircraft based on cluster system[C].2009 Second Pacific-Asia Conference on Web Mining and Web-based Application (WMWA). Piscataway:IEEE,2009:253-257.
[51]P. D. Khapane. Gear walk instability studies using flexible multibody dynamics simulation methods in SIMPACK[J]. Aerospace Science and Technology, 2006,10 (1):19-25.
[52]娄锐.飞机起落架着陆的多体系统动力学建模与仿真[D].南京：南京航空航天大学,2009.
[53]L. Lernbeiss, M. Plochl, Simulation model of an aircraft landing gear considering elastic properties of the shock absorber[C]. Proceedings of the Institution of Mechanical Engineers, Part K:Journal of Multi-body Dynamics Journal of Multi-body Dynamics. United Kingdom:Professional Engineering Publishing,2007:77-86.
[54]Lahargou Andre, Brune Marc, Robuchon Alain. Undercarriage shock absorber with positive petention in a petracted position and with crash overtravel:USA, US20090218444[P].2009-09-03.
[55]Lidner Lars. Experience with the magic formula tyre model [J]. Vehicle System Dynamics,1993,21(SUPPL):30-46.
[56]E. Bakker, L. Nyborg, H. B. Pacejka. Tire modeling for use in vehicle dynamic studies[J]. Society of Automotive Engineers,1987,4(21):68-74.
[57]王纪森.非线性控制理论在防滑刹车系统中的应用研究[D].西安：西北工业大学,2001.
[58]熊翔.炭/炭复合材料制动性能研究[D].长沙：中南大学,2004.
[59]李江鸿,熊翔,张红波,等.不同刹车压力下C/C复合材料的摩擦性能与摩擦面研究[J].润滑与密封,2007,32(4)：9-13.
[60]熊翔,黄伯云,徐惠娟,等.不同制动速度下炭/炭复合材料的摩擦磨损行为及机理[J].中国有色金属学报,2002,12(12)：255-259.
[61]Zhang Ming, Nie Hong, Wei Xiao-hui, et al. Research on Modelling and Simulation for Aircraft Anti-skid Braking[C]. ISSCAA 2008 2nd International Symposium on Systems and Control in Aerospace and Astronautics, Piscataway:IEEE,2008:1-5.
[62]Rao, K. V. Narasimha, Kumar, R. Krishna, Mukhopadhyay, R. et al. A study of the relationship between Magic Formula coefficients and tyre design attributes through finite element analysis[J]. Vehicle System Dynamics,2006, 44 (1):33-63.
[63]L. Alvarez, J Yi. Adaptive emergency braking control in automated highway systems[C]. Proceedings of the 38th IEEE Conference on Decision and Control.1999,4:3740-3745.
[64]U.Kiencke, A.Daiss. Observation of lateral vehicle dynamics[J]. Control Engineering Practice,1997,5 (8):1145-1150.
[65]Dahl, P. R. Dynamic hysteresis model application to stiction type problems [C]. Advances in the Astronautical Sciences. Brechenridge, CO, United States: Univelt Inc,2001:95-111.
[66]Johanastrom, K. Canudas-de-Wit, C. Revisiting the LuGre friction model[J]. IEEE Control Systems Magazine,2008,28 (6):101-114.
[67]C Canudas de Wit, H Olsson, K J Astrom, et al. A new model for control of systems with friction[J]. IEEE Transactions on Automatic Control,1995,40 (3):419-425.
[68]唐志云,廖力清,欧阳昌华.基于PLC的SY02机轮联合加载试验控制系统[J].可编程控制器与工厂自动化,2008,(4)：38-40.