汽车操纵稳定性和平顺性中逆问题的研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
汽车操纵动力学特性影响汽车驾驶的操纵轻便程度,也是高速汽车安全行驶的一个主要性能。汽车在高速转向行驶时,驾驶员模型参数不易确定,从而导致驾驶员模型建立困难。为了避开驾驶员建模困难问题,本文运用操纵逆动力学方法,反求出驾驶员的操纵输入。
     针对目前路面不平度研究方法的局限性,本文运用逆问题的思想研究了路面不平度的识别方法,为汽车平顺性分析研究奠定了基础,为路面性能的分析提供了依据。
     (1)提出了一种基于径向基函数神经网络在频域范围内识别路面不平度的仿真研究方法。该方法以4自由度和7自由度汽车振动模型为基础,以Matlab软件仿真得到的汽车车身质心垂直加速度和俯仰角加速度作为神经网络理想输入样本,拟合的路面不平度为神经网络理想输出样本,应用RBF神经网络建立汽车车身质心垂直加速度、俯仰角加速度和路面不平度之间的非线性映射模型。另取一组仿真得到的车身质心垂直加速度和俯仰角加速度代入已训练好的网络进行路面不平度的识别。结果表明,该方法具有较强的抗噪声能力和较理想的识别精度,识别的路面不平度与拟合的路面不平度吻合较好。
     (2)提出了一种基于径向基函数神经网络在时域范围内识别路面不平度的仿真研究方法。在时域范围内建立RBF神经网络非线性映射模型,另取一组仿真得到的车身质心垂直加速度和俯仰角加速度代入已训练好的网络识别路面不平度。最后以ADAMS/View虚拟试验仿真得到的车身质心垂直加速度和俯仰角加速度来识别路面不平度,从而验证了运用RBF神经网络识别路面不平度的有效性。
     (3)提出了在不同汽车跟踪同一指定路径的情况下,汽车操纵逆动力学角输入识别和力输入识别的仿真研究方法。该方法以线性2自由度汽车方向盘转角输入和线性3自由度汽车方向盘转矩输入为数学模型,运用最优控制理论识别方向盘转角输入和方向盘转矩输入。用直接配置方法将最优控制问题转化为非线性规划问题,用序列二次规划方法对转化后的非线性规划问题进行求解。结果表明:利用该方法计算出来的路径跟踪性良好,且可以比较跟踪同一路径的不同汽车的操纵性能,且仿真结果与实车试验结果运动趋势相似。
     (4)提出了一种解决汽车最速操纵问题的仿真研究方法。该方法基于最优控制理论,以驾驶员对汽车施加的转角输入和驱动力/制动力为控制变量,以最短时间完成双移线和蛇行线过程为控制目标。通过直接配置方法将最优控制问题转化为非线性规划问题之后,运用序列二次规划方法求解。采用该方法计算了不同汽车在同样给定路径边界时的Matlab仿真结果。结果表明,该方法能够解决汽车的最速操纵问题,可以比较不同汽车以最短时间完成双移线和蛇行线过程的操纵性能,且仿真结果与ADAMS/Car虚拟样机试验结果具有良好的一致性。
The character of vehicle handling dynamics affects vehicle handling handiness, and is a main performance index determining safe running for high speed vehicle. In the case of vehicle high speed turning, driver model parameters are not easy to determine, which makes driver model difficult to bulid. In order to avoid the problem, driver handling input is calculated by the handling inverse dynamics method.
     Aiming at the limitation of current research method for road surface roughness, the road surface roughness identification method is studied by the thinking of inverse problem. It establishs the foundation for vehicle ride comfort , and provides the basis for the anlysis of road surface performance.
     (1)Based on RBF neural networks, a simulation research method of road surface roughness identification in the field of frequency is put forward. Based on four degree-of-freedom and seven degree-of-freedom vehicle vibration model, the vehicle body centroid vertical acceleration and pitching angular acceleration which are got through Matlab simulation are regarded as neural networks ideal input sample, the imitated road surface roughness is regarded as neural networks ideal output sample. The nonlinear mapping relations among vehicle body centroid vertical acceleration, pitching angular acceleration and the road surface roughness are found by RBF neural networks. Another vehicle body centroid vertical acceleration and pitching angular acceleration which are calculated by simulation are used to identify road surface roughness by trained networks. Simulated results show that the method has better ability of anti-noise and ideal identification accuracy, the road surface roughness of identification fits the imitated road surface roughness.
     (2)Based on RBF neural networks, a simulation research method of road surface roughness identification in the field of time is put forward. The nonlinear mapping relations in the field of time are found by RBF neural networks . Another vehicle body centroid vertical acceleration and pitching angular acceleration which are calculated by simulation are used to identify road surface roughness by trained networks. Finally another vehicle body centroid vertical acceleration and pitching angular acceleration which are got by ADAMS/View virtual experment simulation are used to identify road surface roughness. So the availability of road surface roughness identification by RBF neural networks is validated .
     (3)A simulation research method for identifying the angle input and the force input in vehicle handling inverse dynamics is proposed under the condition of different vehicles tracking the same given path. In this method, the linear vehicle model of steering angle input with two degree-of-freedom and steering momemt input with three degree-of-freedom are adopted, and the optimal control theory is used to identify the steering angle input and the steering moment input. By using the direct parallel method, the optimal control problem is converted into a nonlinear programming problem that is then solved by means of the sequential quadratic programming. Simulated results show that the proposed method is of good path-tracking ability; is able to compare the maneuverability of different vehicles that track the same path; and the movement trend of simulated results is similar to that of actually experiment.
     (4)A simulation research method for solving vehicle minimum time maneuver problem is proposed. Based on optimal control theory, steering angle input and traction/brake force imposed by driver are control variables, the minimum time required to complete the double lane change and slalom is control object. By using the direct parallel method, the optimal control problem is converted into a nonlinear programming problem that is then solved by means of the sequential quadratic programming. Matlab simulation results are obtained for two different vehicles performing similar given path boundary by the method. Simulated results show that the proposed method can solve vehicle minimum time maneuver problem; compare maneuverability of two different vehicles that complete double lane change and slalom with the minimum time; and the results fit the results of ADAMS/Car virtual experment.
引文
[1]余志生.汽车理论[M].第3版.北京:机械工业出版社,2000.
    [2]许锋,陈怀海,鲍明.机械振动载荷识别研究的现状与未来[J].中国机械工程,2002,13(6):526-531.
    [3]赵又群,尹浩,张丽霞,等.汽车操纵逆动力学的现状与发展[J].中国机械工程,2005,16(1):77-82.
    [4] Heath A N. Application of the Isotropic Road Roughness Assumption [J]. J. of Sound & Vibration, 1987, 115(1):14-131.
    [5] Dodds C J. BSI Document 72/34562/(ISO/TC/108/WG9)[R]. Generalised Terrain Dynamic Inputs to Vehicles.
    [6] Dodds C J, Robson J D. The Description of Road Surface Roughness [J]. J. of Sound & Vibration , 1973, 31(2):18-175.
    [7] Kamash K M A, Robson J D. Implications of Isotropic in Random Surfaces [J]. J. of Sound & Vibration, 1977, 54(1):131-145.
    [8] Kamash K M A, Robson J D. The Application of Isotropic in Road Surface Modeling [J]. J. of Sound& Vibration, 1978, 57(1):89-100.
    [9]郭孔辉.汽车振动与载荷的统计分析及悬挂系统的参数选择[J].汽车技术,1976,(4):1-14.
    [10]裘熙定,李志敏,高义民,童利.汽车悬架和轮胎参数的最佳匹配的研究[J].吉林工业大学学报,1991,(2):31-41.
    [11]史广奎,李槟,孟宪民.汽车设计中减震器相对阻尼系数的确定[J].汽车工程,1995,17(6):367-373.
    [12] Cebon D, Newland E. The Artificial Generation of Road Surface Topography by the Inverse FFT Method [C]. Proc. of the 8th IAVSD Symposium on the Dynamics of Vehicles on Roads and Tracks, Cambridge Massachusetts, 1982:29-41.
    [13] Heath A N. Modeling and Simulation of Road Roughness [C]. Proc. Of the 11th IAVSD Symposium, Ontaris,Canada,1989:274-284.
    [14] Kropá? O, Mú?ka P. Be Careful When Using the International Roughness Index as an Indicator of Road Unevenness [J]. Journal of Sound and Vibration, 2005,287 (4/5):989-1003.
    [15] Sprinc J, Kropá? O, Sprinc M . Characterization of Longitudinal Road Unevenness in the Light of the International PIARC - EVEN Experiment 1998 [J].Vehicle System Dynamics, 2002 , 37(4):263-281.
    [16] Kropá? O, Mú?ka P. Non-standard Longitudinal Profiles of Roads and Indicators for Their Characterization [J]. International Journal of Vehicle Design, 2004, 36 (2/3):149-172.
    [17] Kropá? O, Mú?ka P. Longitudinal Road Unevenness with Periodic Components: Characterization and Effects on People in a Traversing Vehicle and the Loading of the Pavement [J]. Institution of Mechanical Engineers, Part D, Journal of automobile Engineering, 2005, 219(6):773-790 .
    [18] Cebon D. Interaction Between Heavy Vehicles and Roads [C]. The Thirty-ninth L.Ray Buckendale Lecture, SAE paper , 1993.
    [19]檀润华,陈鹰,路甬祥.路面对汽车激励的时域模型建立及计算机仿真[J].中国公路学报,1998,11(3):96-102..
    [20]陈果,翟婉明.铁路轨道不平顺随机过程的数值模拟[J].西南交通大学学报,1999,34(2):138-142
    [21]赵衍,卢士富.路面对四轮汽车输入的时域模型[J].汽车工程,1999,21(6):112-117.
    [22]张永林,钟毅芳.车辆路面不平度输入的随机激励时域模型[J].农业机械学报,2000,35(2):9-12.
    [23]唐光武,贺学锋,颜永福.路面不平度的数学模型及计算机模拟研究[J].中国公路学报,2000,13(1):112-117.
    [24]刘献栋,邓志党,高峰.公路路面不平度的数值模拟方法研究[J].北京航空航天大学学报,2003,29(9):843-846.
    [25]常志权,罗虹,褚志刚,邓兆祥,等.谐波叠加路面输入模型的建立及数字模拟[J].重庆大学学报(自然科学版),2004,27(12):5-8.
    [26]张永林,钟毅芳.汽车道路双轮辙多点随机激励建模与仿真研究[J].系统仿真学报. 2004,16(6):1147-1150.
    [27] Fujikawa T, Koike H, Oshino Y, et al. Definition of Road Roughness Parameters for Tire Vibration Noise Control [J]. Applied Acoustics, 2005,66:501-512.
    [28]郭孔辉.汽车操纵动力学[M].长春:吉林科学技术出版社,1991.
    [29]赵又群,郭孔辉.稳态轮胎偏滑力学的发展极其展望[J].汽车技术,1997,(3):1-5.
    [30]赵又群,郭孔辉.汽车操纵性评价的发展、研究意义与基本问题[J].汽车技术,1998,(5):1-5.
    [31] Doebelin E O.系统的建模和响应[M].童钧芳等译.上海:上海科学技术文献出版社,1986.
    [32] Ellis J R. Vehicle Dynamics [M]. London:Business Books Ltd, 1969.
    [33] Steeds W. Mechanics of Road Vehicles [M]. London:Iliffe and Sons Ltd , 1960.
    [34]米奇克M.汽车动力学[M].桑杰译.北京:机械工业出版社,1972.
    [35] Okada T, Takiguchi T,Nishioka M. Evaluation of Vehicle Handling and Stability by Computer Simulation at the First Stage of Vehicle Planning [C]. SAE paper 730525,1973:1685-1707.
    [36]郭孔辉.汽车操纵稳定性[M].长春:吉林人民出版社,1983.
    [37]郭孔辉.长春汽车研究所近年来对汽车操纵稳定性的研究[J].汽车工程,1985,7(1):17-22.
    [38] Ellis J R. Vehicle Handling Dynamics [M]. London:Mechanical Engineering Publications Ltd, 1994.
    [39]阿达姆.汽车行驶性能[M].黄锡朋,解春阳译.北京:科学普及出版社,1992.
    [40] Mcruer D T, Allen R W, Weir D, et al. New Results in Driver Steering Control Models [J] .Human Factors, 1977, 19(4):381-397.
    [41] Macadam C C. Application of an Optimal Preview Control for Simulation of Closed-loop Automobile Driving [J]. IEEE Transaction on Systems, Man and Cybernetics, 1981, 11(6):393-399.
    [42] Guo K H, Fancher P. Preview-Follower Method for Modeling Closed-loop Vehicle Directional Control [C]. Symposium of 19th Annual Conference on Manual Control, Cambridge, 1983:158-187.
    [43] Guo K, Guan H. Modeling of Driver/Vehicle Directional Control System [J]. Vehicle System Dynamics, 1993, 22(3/4):141-184.
    [44] Suetomi T, Yoshimoto K. Trend in R&D on Driving Simulators [J]. Journal of JSAE, 1986, 40(3):319-323.
    [45] Casali J G, Wierwille W W. The Effects of Various Design Alternatives on Moving-based Driving Simulator Discomfort [J]. Human Factors, 1980, 22(6):741-756.
    [46]赵又群,管欣,郭孔辉.开发型驾驶模拟器[J].公路交通科技,1995,12(3):64-66.
    [47]郭孔辉.人-车-路闭环系统主动安全性的综合评价指标与优化设计[J].汽车技术,1993,(4):4-12.
    [48] Harada H. Stability Criteria and Evaluation of Steering Maneuver in Driver-Vehicle System [J]. JSME Inter. J. Series, 1994, 37(1):115-122.
    [49]赵又群,王立功,何小明等.四轮转向汽车运动稳定性分析[J].中国机械工程,2003,14(14):1246-1248.
    [50]赵又群,郭孔辉.驾驶员统计特性对人-车闭环系统响应的影响与汽车主动安全性评价[J].汽车工程,1999,21(2):87-92.
    [51] Zhao Youqun, Zhang Guiyu, Guo Konghui. Handling Safety Simulation of Driver-Vehicle Closed-Loop System with Evolutionary Random Road Input [J]. Vehicle System Dynamics, 2000, 33(3):169-181.
    [52]赵又群,郭孔辉.汽车操纵性评价指标的研究[J].汽车工程,2001,23(1):1-4.
    [53]赵又群,郭孔辉.驾驶员-汽车闭环系统操纵动力学优化设计的二阶矩方法[J].机械科学与技术,1999,18(5):737-738.
    [54]赵又群,郭孔辉.汽车主动安全性的模糊优化设计[J].机械科学与技术,1999,18(6):919-921.
    [55]赵又群,何小明,郭孔辉.汽车由路面激发的演变随机响应预测[J].机械工程学报,2004,40(1):179-182.
    [56] Crolla D A, Chen D C,Vehicle Handling Assessment Using a Combined Subjective- objective Approach [C]. SAE paper 980226,1998:386-395.
    [57]郭孔辉,管欣.汽车性能设计技术的进展[J].中国机械工程,1997,8(1):94-96.
    [58] Hatwal H, Mikulcik E C. Some Inverse Solutions to an Automobile Path-Tracking Problem with Input Control of Steering and Brakes [J]. Vehicle System Dynamics, 1986, 15(2):61-71.
    [59] Bernard J, Pickelmann M. An Inverse Linear Model of a Vehicle [J]. Vehicle System Dynamics, 1986, 15(4):179-186.
    [60] Trom J, Vanderploeg M, Bernard J. Application of Inverse Models to Vehicle Optimization Problems [J]. Vehicle System Dynamics,1990,19(2):97-110.
    [61] Fujioka T, Kimura T. Numerical Simulation of Minimum-time Cornering Behaviour [J]. JSAE Review, 1992, 13(1):44-51.
    [62] Casanova D, Sharp R S, Symonds P. Minimum Time Manoeuvring :the Significance ofYaw Inertia [J]. Vehicle System Dynamics,2000,34(2):77-115.
    [63] Casanova D. On Minimum Time Vehicle Manoeuvring:the Theoretical Optimal Lap [D]. School of Mechanical Engineering, Cranfield University, 2000.
    [64] Sharp R S, Casanova D, Symonds P. A Mathematical Model for Driver Steering Control, with Design, Tuning and Performance Results [J]. Vehicle System Dynamics, 2000,23(5):289-326.
    [65] Casanova, D, Sharp, R S, Symonds P. Sensitivity to Mass Variations of the Fastest Possible Lap of a Formula One Car [J]. Supplement to Vehicle System Dynamics, 2001,35:119-134.
    [66] Casanova D, Sharp R, Symonds P. On the Optimisation of the Longitudinal Location of the Mass Centre of a Formula One Car for Two Circuits [C]. Proceedings of AVEC’2002, International Symposium on Advanced Vehicle Control, Hiroshima, Japan, 2002.
    [67] Casanova D, Sharp R, Symonds P. On Minimum Time Optimisation of Formula One Cars:the Influence of Vehicle Mass [C]. Proceedings of AVEC’2000, International Symposium on Advanced Vehicle Control, Ann Arbor, Michigan, 2000.
    [68] Casanova D, Sharp R S, Final M, et al. Application of Automatic Diffentiation to Race Car Performance Optimisation [C]. Automatic Differentiation of Algorithms:From Simulation to Optimization, New York, NY, 2001, 117-124.
    [69] Velenis E, Tsiotras P. Optimal Velocity Profile Generation for Given Acceleration Limits:The Half-Car Model Case[C]. IEEE International Symposium on Industrial Electronics (ISIE05), Dubrovnik, Croatia, 2005.
    [70] Velenis E, Tsiotras P. Optimal Velocity Profile Generation for Given Acceleration Limits:Theoretical Analysis[C]. American Control Conference, Portland, OR, 2005:1478-1483.
    [71] Velenis E, Tsiotras P. Optimal Velocity Profile Generation for Given Acceleration Limits:Receding Horizon Implementation[C]. American Control Conference, Portland, OR, 2005:2147-2152.
    [72] Bünte T, Sahin A, Bajcinca N. Inversion of Vehicle Steering Dynamics with Modelica/Dymola [C]. Proceedings of the 4th International Modelica Conference, Hamburg, 2005:319-328.
    [73]吴淼,黄民.机械系统的载荷识别方法与应用[M].徐州:中国矿业大学出版社,1995.
    [74]张方,朱德懋.动态载荷时域识别的级数方法[J].振动工程学报,1996,9(1):1-5.
    [75]徐倩,文祥荣,孙守光.结构动态载荷识别的精细逐步积分法[J].计算力学学报,2002,19(1):53-57.
    [76]傅志方,饶柱石,周海亭.一种动态载荷的识别方法[J].上海交通大学学报,1997,31(3):5-7.
    [77] Sridhar J, Hatwal H. A Comparative Study of Four Wheel Steering Models Using the Inverse Solution [J]. Vehicle System Dynamics, 1992, 21(1):1-18.
    [78] Sridhar J. A Comparative Study of the Front Wheel Steered Vehicle and Four Wheeled Steered Vehicles Using the Inverse Solution [D]. Dept. of Mech. Eng., Indian Institute of Technology Kanpur , 1989.
    [79] Allen J. Computer Optimisation of Cornering Line [D]. School of Mechanical Engineering, Cranfield University, 1997.
    [80] Brayshaw D L , Harrison M F . A Quasi Steady State Approach to Race Car Lap Simulation in Order to Understand the Effects of Racing Line and Centre of Gravity Location [C]. Proc. IMechE, Part D:J. Automobile Engineering, 2005 , 219(6):725-739.
    [81]谢森,王玉.非线性系统完全线性化方法的研究[J].控制理论与应用,1997,14(1):139-143.
    [82] Hendrikx J P M, Meijlink T J J, Kriens R F C. Application of Optimal Control Theory to Inverse Simulation of Car Handling [J]. Vehicle System Dynamics, 1996, 26 (6):449-461.
    [83] Pvtlak R .Numerical Methods for Optimal Control Problems with State Constraints[M] . Berlin:Springer, 1999.
    [84] Sethi S, Thompson G. Optimal Control Theory [M] . US:Springer, 2000.
    [85] Bestaoui Y. An Optimal Velocity Generation of a Rear Wheel Drive Tricycle Along a Specified Path[C]. Proceedings of the American Control Conference. Chicago, 2000:2907-2911.
    [86] Cossalter V, Da Lio M, Biral F. Evaluation of Motorcycle Maneuverability with the Optimal Maneuver Method [C] .SAE paper 983022.
    [87] Cossalter V, DA Lio M, Lot R. A General Method for the Evaluation of Vehicle Maneuverability with Special Emphasis on Motorcycles [J]. Vehicle System Dynamics , 1999, 31(2):113-135.
    [88]张方,朱德懋.基于神经网络模型的动载荷识别[J].振动工程学报,1997,10(2):156-162.
    [89] Bernard J, Gruening J, Hoffmeister K. Evaluation of Vehicle/Driver Performance UsingGenetic Algorithms [C]. SAE paper 980227,1998:73-85.
    [90]梁艳春.计算智能与力学反问题中的若干问题[J].力学学报,2000,30(3):321-331.
    [91]吴杰,赵又群,吴珂.基于逆问题求解的汽车操纵性能分析[J].中国机械工程,2006,17(4):435-439.
    [92]吴杰,赵又群,杨国权.汽车方向盘角输入识别的研究[J].机械科学与技术,2006,25(10):1175-1177.
    [93]张湘伟.一维Filtered Poisson Process路面模型及其数值模拟方法[J].重庆大学学报(自然科学版),1988,11(1):106-112.
    [94] Robert J, Schilling J, Carroll J. Approximation of Nonlinear Systems with Radial Basis Function Neural Networks [J]. IEEE Transactions on Neural Networks,2001,12(1):21 - 28.
    [95]王炜,吴耿锋,张博锋.径向基函数(RBF)神经网络及其应用[J].地震,2005,25(2):19 -25.
    [96] Matusko J, Petrovic I, Peric, N. Application of the RBF Neural Networks for Tire-road Friction Force Estimation [C]. IEEE International Symposium on Industrial Electronics ,Rio de Janeiro, Brazil, 2003:701-706.
    [97] Light W A. Some Aspects of Radial Basis Function Approximation [C]. Approximation Theory, Spline Functions and Applications, NATO ASI series. Boston:Kluwer Academic Publishers. 1992 , 256:163-190.
    [98]楼顺天,施阳.基于MATLAB的系统分析与设计-神经网络[M].西安:电子科技大学出版社,1999
    [99]王文成,神经网络及其在汽车工程中的应用[M].北京:北京理工大学出版,1998:15-89
    [100]徐昭鑫.随机振动[M].北京:高等教育出版社,1990.
    [101]赵济海.路面不平度谱分析应用研究报告[R].长春:长春汽车研究所整车研究室,1985.
    [102] Au F T K,Cheng Y S,Cheung Y K. Effects of Random Road Surface Roughness and Long-Term Deflection of Prestressed Concrete Girder and Cable-Stayed Bridges on Impact due to Moving Vehicles [J]. Computers and Structures,2001,79(8):853-872.
    [103]张丽霞,赵又群,徐培民,等.路面功率谱密度识别的仿真[J].农业机械学报,2007,38(5):15-18.
    [104]张丽霞,赵又群,吴杰,等.基于RBF神经网络识别路面谱的新方法[J].公路交通科技,2007,24(6):135-138.
    [105]吴元杰,徐博侯,陈宝莲.轿车悬架阻尼二阶最优控制设计方法研究[J].汽车工程,1999,21(6):353 -357.
    [106]谢伟东,王磊,佘翊妮.随机信号在路面不平度仿真中的应用[J].振动、测试与诊断,2005,25(2):126 - 130.
    [107]张洪欣.汽车行驶平顺性的计算机预测[J].汽车工程,1986,8(1):21 - 31.
    [108]王国强.虚拟样机技术及其在ADAMS上的实践[M].西安:西北工业大学出版社,2002.
    [109]李军,刑俊文,覃文洁. ADAMS实例教程[M].北京:北京理工大学出版社,2002:87-134.
    [110] Prashant S R, David R, Ron C . Developing an ADAMS Model of an Automobile Using Test Data [C]. SAE Paper 2002-01-1567,2002.
    [111] Vanderploeg M J, Trom J D, Bernard J . Evaluation of Four-Wheel Steer Path Following Performance Using a Linear Inverse Vehicle Method [C]. SAE Paper 880644, 1988.
    [112]张光澄.最优控制计算方法[M].成都:成都科技大学出版社,1991.
    [113]叶庆凯,王肇明.优化与最优控制中的计算方法[M].北京:科学出版社,1986.
    [114]宫锡芳.最优控制问题的计算方法[M].北京:科学出版社,1996.
    [115] Chen S H, Kang H Y, Lee H T. Dynamic Programming Approach for Analyzing Delayed Product Differentiation [J]. International Journal of Advanced Manufacturing Technology, 2006,28(5):445-449.
    [116] Pal B B, Basu I. A Goal Programming Method for Solving Fractional Programming Problems via Dynamic Programming [J]. Optimization, 1995, 35(2):145-157.
    [117]丁群燕,曾鑫.求解动态系统最优控制的主要数学方法.黄冈职业技术学院学报[J],2003,5(1):53-55.
    [118] Hargraves C R, Paris S W. Direct Trajectory Optimization Using Nonlinear Programming and Collocation [J]. J. Guidance, Control and Dynamics, 1987,10 (4):338-342.
    [119] Herman A L, Conway B A. Direct Optimization Using Collocation Based on High-order Gauss-Lobatto Quadrature Rules. J. Guidance, Control and Dynamics, 1996, 19(3) :592-599.
    [120] Goto N, Kawable H. Direct Optimization Methods Applied to a Nonlinear Optimal Control Problem [J]. Mathematics and Computers in Simulation, 2000,51(6):557-577.
    [121] von Stryk O. Numerical Solution of Optimal Control Problems by Direct Collocation[C] Proc. of the Optimal Control: Calculus of Variations, Optimal Control Theory and Numerical Methods . Basel:Birkh?user Verlag,1993:129-143.
    [122] von Stryk O, Bulirsch R. Direct and Indirect Methods for Trajectory Optimization [J]. Annals of Operations Research, 1992, 37:357-373.
    [123] Enright P J, Conway B A. Discrete Approximations to Optimal Trajectories Using Direct Transcription and Nonlinear Programming [C]. AIAA Paper 90-2963-CP.
    [124] Hu G S, Ong C J, Teo C L. Direct Collocation and Nonlinear Programming for Optimal Control Problem Using an Enhanced Transcribing Scheme [C]. Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Hawaii, USA, 1999:22-27.
    [125]袁亚湘,孙文瑜.最优化理论与方法[M].北京:科学出版社,1997 .
    [126] Enright P J , Conway B A. Optimal Finite-Thrust Spacecraft Trajectories Using Collocation and Nonlinear Programming [J] . Journal of Guidance , Control and Dynamics , 1991 , 14 (5):981 - 985.
    [127] Kraft D. Algorithm 733: TOMP-Fortran Modules for Optimal Control Calculations [J]. ACM Transactions on Mathematical Software, 1994, 20(3):262-281.
    [128] Betts T J. Issues in the Direct Transcription of Optimal Control Problems to Sparse Non-linear Programs [C]. Proc. of the Optimal Control: Calculus of Variations, Optimal Control Theory and Numerical Methods. Basel:Birkh?user Verlag,1994.
    [129] Gerdts M. Direct Shooting Method for the Numerical Solution of Higher-Index DAE Optimal Control Problems [J]. Journal of Optimization Theory and Applications, 2003,117(2):267-294 .
    [130]吴沧浦.最优控制的理论与方法[M].第2版.北京:国防工业出版社,2000.
    [131]张丽霞,赵又群,吴杰.基于最优控制的汽车操纵逆动力学的研究[J].中国机械工程,2007,18(16):2009-2011.
    [132]宗长富.开发型驾驶模拟器逼真度的改进与汽车操纵稳定性综合评价研究[D].长春:吉林大学,1998.
    [133]张丽霞,赵又群.汽车操纵逆动力学力输入识别研究[J].华南理工大学学报,2007,35(6):21-24.
    [134]汽车工程手册编辑委员会.汽车工程手册-试验篇[M] .北京:人民交通出版社,2000.
    [135]张丽霞,赵又群,宋桂霞,等.汽车最速操纵问题的逆动力学研究.中国机械工程2007,18(21):2628-2632.
    [136]时培成,陈黎卿.多功能车操纵稳定性的虚拟样机实验研究[J].汽车科技,2005,(3):45-48.
    [137] Drivet A, Ramirez M, Ricardo A, et al. A Mini-baja Active Suspension Modeling Using ADAMS/CAR [C]. Proceedings of the 16th IASTED International Conference on Modelling and Simulation, 2005, 80-84.
    [138]王树凤.汽车操纵稳定性虚拟试验系统的研究[D].北京:中国农业大学,2002.
    [139]王树凤,张俊友,余群.应用ADAMS设计车辆操纵稳定性试验[J].中国农业大学学报,2001,6(6):81-84.

© 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