基于微分几何的非线性主动空气悬架仿真
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摘要
针对被动空气悬架系统不能很好解决车辆乘坐舒适性和操控稳定性问题,基于空气悬架的非线性特点有针对性的研究主动控制策略,以进一步提高其性能,使车辆在各种路面条件下实现主动调节。开展了大客车用空气弹簧试验,获得空气弹簧的非线性弹性力及非线性阻尼力数据,并在实测数据的基础上,采用MATLAB/Simulink建立了1/4非线性主动空气悬架模型。应用微分几何理论中的输出-干扰解耦方法,通过适当的坐标变换将1/4非线性主动空气悬架模型简化为线性系统并实施线性二次型调节器(LQR)最优控制,尝试将自适应遗传算法应用于LQR最优控制权阵的确定。通过分析主动空气悬架性能评价指标的特点设置适当的适应度函数,再利用自适应遗传算法的全局寻优能力得到最优控制权阵,从而获得非线性主动空气悬架的最优反馈控制力。以模拟产生的不同路面的不平度曲线和不同车速作为激励作用于车辆模型进行仿真试验,并对仿真结果进行了分析。结果表明:设计的基于微分几何理论的最优控制器获得了良好的控制效果,对车身垂直振动加速度、悬架动挠度及轮胎形变的改善效果明显,有效提高了汽车行驶平顺性和安全性。研究结果可为非线性汽车悬架的控制提供理论参考。
Aim at the passive air suspension systems cannot solve the problem of vehicle ride comfort and handling stability well,a targeted active control strategy was researched based on the nonlinear characteristics of air suspension,to improve performance further and realize better adjustment of the vehicles under various road conditions.The bus-with-air-spring experiment was carried out,and the nonlinear elastic force of the air spring and nonlinear damping force data,which was based on the measured data,were obtained.The nonlinear active air suspension model was established using MATLAB/Simulink.The output-interference decoupling method for differential geometry theory was used,1/4 nonlinear active air suspension model was simplified into a linear system using appropriate coordinate transformation,and linear quadratic regulator(LQR)optimal control was implemented.The adaptive genetic algorithm was used to determinethe optimal LQR control matrix.The characteristics of the active air suspension performance evaluation index were analyzed to formulate the appropriate fitness functions,and the adaptive global optimization ability of the genetic algorithm was used to obtain the optimal control matrix.The optimal feedback control of the nonlinear active air suspension was thus obtained.Simulation experiments were carried out on vehicle models with different road surface roughness curves and different speeds as incentives,and the simulation results were analyzed.The results show that the design of the optimal controller based on differential geometry theory obtains good control.The body vertical vibration acceleration,suspension dynamic deflection,and improvement in the tire deformation are evident.This can improve the vehicle riding comfort and safety effectively.The results can also provide a useful theoretical reference for the control of nonlinear automobile suspensions.
Aim at the passive air suspension systems cannot solve the problem of vehicle ride comfort and handling stability well,a targeted active control strategy was researched based on the nonlinear characteristics of air suspension,to improve performance further and realize better adjustment of the vehicles under various road conditions.The bus-with-air-spring experiment was carried out,and the nonlinear elastic force of the air spring and nonlinear damping force data,which was based on the measured data,were obtained.The nonlinear active air suspension model was established using MATLAB/Simulink.The output-interference decoupling method for differential geometry theory was used,1/4 nonlinear active air suspension model was simplified into a linear system using appropriate coordinate transformation,and linear quadratic regulator(LQR)optimal control was implemented.The adaptive genetic algorithm was used to determinethe optimal LQR control matrix.The characteristics of the active air suspension performance evaluation index were analyzed to formulate the appropriate fitness functions,and the adaptive global optimization ability of the genetic algorithm was used to obtain the optimal control matrix.The optimal feedback control of the nonlinear active air suspension was thus obtained.Simulation experiments were carried out on vehicle models with different road surface roughness curves and different speeds as incentives,and the simulation results were analyzed.The results show that the design of the optimal controller based on differential geometry theory obtains good control.The body vertical vibration acceleration,suspension dynamic deflection,and improvement in the tire deformation are evident.This can improve the vehicle riding comfort and safety effectively.The results can also provide a useful theoretical reference for the control of nonlinear automobile suspensions.
引文
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[2]王伟,钟益民.公路客车空气悬架的发展趋势及在我国的应用前景分析[J].汽车实用技术,2013(11):97-101.WANG Wei,ZHONG Yi-min.The development trend of air suspension of road bus and its application prospect in China[J].Automotive Practical Technology,2013(11):97-101.
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[4]陆文昌,杨帆,汪少华,等.气动可调阻尼同轴一体式减振支柱阻尼特性研究[J].振动与冲击,2015,34(20):115-119,128.LU Wen-chang,YANG Fan,WANG Shao-hua,et al.Research on damping characteristics of pneumatic adjustable damping coaxial one-body vibration reduction pillar[J].Vibration and Impact,2015,34(20):115-119,128.
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[7]江浩斌,杜滢君,叶燊辰.新型一体式悬架减振支柱行程相关刚度特性研究[J].振动与冲击,2012,31(22):66-70.JIANG Hao-bin,DU Ying-jun,YE Shen-chen.Strokedependent stiffness characteristics of a new type of integrated suspension strut[J].Journal of Vibration and Shock,2012,31(22):66-70.
[8]陈龙,喻力,崔晓利.阻尼多状态切换减振器的性能仿真与试验[J].江苏大学学报:自然科学版,2013,34(3):249-253.CHEN Long,YU Li,CUI Xiao-li.Performance simulation and test of damping multi-state switching damper[J].Journal of Jiangsu University:Natural Science Edition,2013,34(3):249-253.
[9]SUN X,CHEN L,WANG S H,et al.Vehicle height control of electronic air suspension system based on mixed logical dynamical modelling[J].Science China Technological Sciences,2015,58(11):1894-1904.
[10]张军,雷帅,段嗣盛.空气悬架大客车高度控制仿真与试验研究[J].武汉理工大学学报,2012,34(4):123-126.ZHANG Jun,LEI Shuai,DUAN Si-sheng.Simulation and experimental research on air suspension couch height control[J].Journal of Wuhan University of Technology,2012,34(4):123-126.
[11]卢胜文,贾启芬,于雯,等.汽车多自由度悬架的非线性振动特性[J].应用力学学报,2005,22(3):461-465,511-512.LU Sheng-wen,JIA Qi-fen,YU Wen,et al.Nonlinear dynamic characteristics of vehicle suspension system with multi-degrees of freedom[J].Journal of Applied Mechanics,2005,22(3):461-465,511-512.
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[13]杨柳青,陈无畏,汪洪波.基于H2/H∞控制的汽车主动悬架最优鲁棒容错控制[J].中国机械工程,2012,23(24):3013-3019.YANG Liu-qing,CHEN Wu-wei,WANG Hong-bo.Optimal robust fault tolerant control for vehicle active suspension system based on H2/H∞approach[J].China Mechanical Engineering,2012,23(24):3013-3019.
[14]陈龙,任皓,袁朝春,等.轮毂电动机HEV动力系统设计与仿真[J].江苏大学学报:自然科学版,2015,36(1):6-10,42.CHEN Long,REN Hao,YUAN Chao-chun,et al.Design and simulation power system for hybrid electric vehicles with wheel motors[J].Journal of Jiangsu University:Natural Science Edition,2015,36(1):6-10,42.
[15]王皓,周健,何志鹏,等.电流变客车减振器的力学分析与最优控制[J].电子科技大学学报,2015,44(4):631-635.WANG Hao,ZHOU Jian,HE Zhi-peng,et al.Linear quadratic optimal control theory applied to the damping system of the bus based on electrorheological fluid[J].Journal of University of Electronic Science&Technology of China,2015,44(4):631-635.
[16]寇发荣,范养强,张传伟,等.车辆电动静液压作动器的半主动悬架时滞补偿控制[J].中国机械工程,2016,27(15):2111-2117.KOU Fa-rong,FAN Yang-qiang,ZHANG Chuanwei,et al.Time delay compensation control of semiactive suspension with vehicle electro-hydrostatic actuator[J].China Mechanical Engineering,2016,27(15):2111-2117.
[17]么鸣涛,曹锋,阙瑞义,等.考虑汽车悬架动挠度的模糊PID控制[J].北京理工大学学报,2016,36(9):929-934.YAO Ming-tao,CAO Feng,QUE Rui-yi,et al.Fuzzy PID control considering vehicular suspension dynamic deflection[J].Transactions of Beijing Institute of Technology,2016,36(9):929-934.
[18]陈思忠,卢凡,吴志成,等.基于反馈线性化的非线性悬架系统振动状态观测[J].振动与冲击,2015,34(20):10-15.CHEN Si-zhong,LU Fan,WU Zhi-cheng,et al.Vibration state estimation of nonlinear suspension system based on feedback linearization[J].Journal of Vibration and Shock,2015,34(20):10-15.
[19]卢凡,陈思忠,刘畅,等.基于Kalman滤波器的车辆振动速度估计[J].振动与冲击,2014,33(13):111-116.LU Fan,CHEN Si-zhong,LIU Chang,et al.Vehicle vibration velocity estimation based on Kalman filter[J].Vibration and Impact,2014,33(13):111-116.
[20]庄德军,柳江,喻凡,等.汽车油气弹簧非线性数学模型及特性[J].上海交通大学学报,2005,39(4):1441-1444.ZHUANG De-jun,LIU Jiang,YU fan,et al.The nonlinear mathematical model and characteristics of hydro-pneumatic spring[J].Journal of Shanghai Jiao Tong University,2005,39(4):1441-1444.
[21]李以农,郑玲.基于磁流变减振器的汽车半主动悬架非线性控制方法[J].机械工程学报,2005,41(5):31-37.LI Yi-nong,ZHENG Ling.Nonlinear control methods of automotive semi-active suspension based on the MR damper magnetorheological damper[J].Chinese Journal of Mechanical Engineering,2005,41(5):31-37.
[22]李小伟,史俊武,张建武.主动油气悬架反馈线性化及PID控制[J].上海交通大学学报,2009,43(10):1521-1525.LI Xiao-wei,SHI Jun-wu,ZHANG Jian-wu.Feedback linearization and PID control for active hydro pneumatic suspension[J].Journal of Shanghai Jiao Tong University,2009,43(10):1521-1525.
[23]DANGOR M,DAHUNSI O A,PEDRO J O,et al.Evolutionary algorithm-based PID controller tuning for nonlinear quarter-car electrohydraulic vehicle suspensions[J].Nonlinear Dynamics,2014,78(4):2795-2810.
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