王国丽 , 顾亮 , 孙逢春 . 车辆主动悬架技术的现状和发展趋势 [J ] . 兵工学报 , 2000 , 21 ( 增刊1 ): 80 - 83 .

WANG G L , GU L , SUN F C . Current status and tendency of development in vehicle active suspension [J ] . Acta Armamentarii , 2000 , 21 ( S1 ): 80 - 83 . (in Chinese)

喻凡 , 张勇超 , 张国光 . 车辆电磁悬架技术综述 [J ] . 汽车工程 , 2012 , 34 ( 7 ): 569 - 574 .

YU F , ZHANG Y C , ZHANG G G . Review on vehicle electromagnetic suspension technology [J ] . Automotive Engineering , 2012 , 34 ( 7 ): 569 - 574 . (in Chinese)

过学迅 , 彭明 , 邹俊逸 , 等 . 商用车悬架馈能潜力影响因素研究 [J ] . 中国公路学报 , 2016 , 29 ( 5 ): 151 - 158 . 为了给液电式馈能减振器的悬架匹配研究提供参考,基于仿真计算和实车道路试验分析了行驶工况和整车参数对商用车馈能悬架振动能量回收潜力的影响;并采用实车道路试验验证了MATLAB/Simulink路面模型和悬架动力学仿真模型的正确性;最后结合减振器台架试验结果,非线性回归拟合了液电式馈能减振器样机的馈能效率曲线。结果表明:整车参数对商用车减振器耗散功率的影响显著性从大到小依次为轮胎刚度、非簧载质量、簧载质量、悬架刚度和悬架阻尼;减振器耗散功率与路面等级、车速、轮胎刚度、非簧载质量和簧载质量的变化成正比,而随着悬架刚度和悬架阻尼的增大而减小。

GUO X X , PENG M , ZOU J Y , et al. Study on factors influencing energy regenerative suspension potential for commercial vehicles [J ] . China Journal of Highway and Transport , 2016 , 29 ( 5 ): 151 - 158 . (in Chinese)

庞辉 , 陈嘉楠 , 刘凯 . 汽车磁流变半主动悬架系统自适应反推跟踪控制 [J ] . 兵工学报 , 2017 , 38 ( 7 ): 1430 - 1442 . DOI: 10.3969/j.issn.1000-1093.2017.07.023 http://doi.org/10.3969/j.issn.1000-1093.2017.07.023 针对汽车磁流变半主动悬架系统非线性和模型不确定性所引起的控制稳定性及优化问题，考虑被控悬架综合控制目标的安全约束，建立1/2车辆悬架系统的非线性动力学模型。基于被控悬架系统与参考轨迹之间的跟踪误差，使用自适应反推方法和Lyapunov理论，设计被控悬架系统的磁流变阻尼器控制输入函数，提出基于投影算子的自适应控制律，进而设计一种能够处理安全约束问题的自适应反推控制器；为验证所提出控制策略的可行性和有效性，基于Matlab/Simulink建立磁流变悬架控制系统的仿真模型，并分别在随机路面和凸块路面上对该控制策略进行仿真验证。仿真结果表明，所提出的自适应反推控制策略能使磁流变悬架车辆在行驶稳定性方面具有较好的全局渐进稳定性，并能明显提高车辆行驶平顺性，满足悬架系统各方面的安全约束。

PANG H , CHEN J L , LIU K . Adaptive backstepping tracking control for vehicle semi-active suspension system with magnetorheological damper [J ] . Acta Armamentarii , 2017 , 38 ( 7 ): 1430 - 1442 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2017.07.023 http://doi.org/10.3969/j.issn.1000-1093.2017.07.023 As for the control optimization and stability caused by the nonlinearities and uncertainties of vehicle semi-active suspension systems with magnetorheological (MR) damper, a nonlinear dynamics model of one-half vehicle suspension system is established with consideration of the security constraints of comprehensive control objectives for the controlled vehicle semi-active suspension. The tracking error between controlled plant and reference trajectory is constructed, and the corresponding control input functions of controlled plant are designed based on backstepping control method and Lyapunov stability theory. The adaptive control law based on projection operator is investigated, and further a kind of adaptive backstepping controller is developed, which can deal with constraint problem of vehicle suspension system. In order to validate the feasibility and effectiveness of the proposed control algorithm, a control simulation framework of vehicle vibration control system is established based on Matlab/Simulink software, and the proposed adaptive backstepping control algorithm is verified on this control simulation framework under the conditions of random and bump roads. The results show that the proposed control approach has better global asymptotic stability for control stability problem of vehicle semi-active suspension systems, and it can not only obviously improve the performance of ride comfort, but also ensure the various required safety performances of vehicle semi-active suspension.Key

王会义 , 于良耀 , 宋健 . 汽车主动安全控制液压执行器的性能与原理 [J ] . 机械工程学报 , 2007 , 43 ( 9 ): 21 - 27 . 介绍目前汽车主动安全系统(汽车制动防抱系统、汽车驱动力控制系统、汽车电子稳定控制系统、汽车主动悬架、汽车四轮转向系统)上所应用的液压执行器，并重点分析目前先进的汽车主动安全系统——汽车电子稳定控制程序(Electronic stability program，ESP)上的液压执行器的结构、工作原理、工艺特点及其高速响应的性能特点。ESP所使用的液压执行器的响应速度在10 ms以内，其响应特性与液压执行器的各部分结构参数、被控车辆制动系统的参数等有紧密的联系，需要进行综合考虑和选择。介绍所采用的对汽车制动防抱系统液压执行器进行动态特性分析和参数匹配的建模分析方法，此方法同时也适用于对其他类型汽车主动安全系统的动态特性分析与参数匹配。最后对未来的汽车主动安全系统执行器的发展进行展望。

WANG H Y , YU L Y , SONG J . Performance and theory of the hydraulic actuators forautomotive active safety control system [J ] . Chinese Journal of Mechanical Engineering , 2007 , 43 ( 9 ): 21 - 27 . (in Chinese)

邓兆祥 , 来飞 . 车辆主动悬架用电磁直线作动器的研究 [J ] . 机械工程学报 , 2011 , 47 ( 14 ): 121 - 128 . 针对车辆主动悬架的使用要求，设计出一种具有行程大、推力大及响应快速特点的新型电磁直线作动器。结合有限元仿真软件，研究作动器的结构参数如气隙厚度、次级不锈钢管厚度、次级铜层厚度、绝缘挡圈导磁和导电性能及初级线圈的绕线方式等的变化对作动器电磁力大小和响应速度的影响规律，以及电源参数如电源电压、电源频率及电源加载方式的变化对作动器电磁力大小和响应速度的影响规律，结果表明，电磁力除与绝缘挡圈的导电性能无关外，而与气隙厚度等众多结构参数密切相关，电磁力与电源电压的平方成正比例关系，且随电源频率的增大而先增大后减小，在20 Hz左右存在电磁力响应峰值。在此基础上选取合理的参数，试制一款电磁直线作动器样机，并对样机模型进行稳态电磁力和相电流的相关试验测试，通过与有限元仿真结果比较，表明仿真分析结果和试验测试数据基本吻合，验证了有关设计分析的正确性。

DENG Z X , LAI F . Electromagnetic linear actuator for vehicle active suspension [J ] . Journal of Mechanical Engineering , 2011 , 47 ( 14 ): 121 - 128 . (in Chinese) A new type of electromagnetic linear actuator for vehicle active suspension is designed, with the characteristics of large stroke and force and fast response. Combined with the finite element analysis software, the effects of actuator structure parameters such as gap thickness, secondary stainless steel tube thickness, secondary copper layer thickness, magnetic permeability and electrical conductivity of insulated retainer ring and primary coil winding mode on actuator thrust size and response speed are studied. And the effects of actuator power parameters such as voltage, frequency and loading mode on actuator thrust size and response speed are also studied. The results show that the electromagnetic force is closely related to structural parameters such as the gap thickness, except for the conductivity of insulated retainer ring. And the electromagnetic force is proportional to the square of the voltage, and first increases and then decreases with the increase of frequency, getting the maximum at 20 Hz. Based on the simulation results, a prototype of electromagnetic linear actuator with appropriate parameters is developed. And the steady electromagnetic force and phase current test of the actuator is carried out. Comparison between the finite element simulation results and the experimental data shows they are basically consistent, thus verifying the correctness of the relevant design and analysis.

毛明 , 王乐 , 陈轶杰 , 等 . 惯容器及惯容器-弹簧-阻尼器悬架研究进展 [J ] . 兵工学报 , 2016 , 37 ( 3 ): 525 - 534 . DOI: 10.3969/j.issn.1000-1093.2016.03.019 http://doi.org/10.3969/j.issn.1000-1093.2016.03.019 介绍了惯容器和惯容器-弹簧-阻尼器（ISD）悬架的概念、提出背景及特点，总结了惯容器结构形式、动力学特征和非线性特性、频率响应特性和击穿现象。从ISD悬架结构形式、性能特点和网络综合理论的应用、ISD悬架空间布置和一体化设计等方面，系统说明了ISD悬架研究进展。归纳总结提出了惯容器及ISD悬架未来的5大研究方向，包括惯容器的创新设计、惯容器非线性研究、ISD悬 架网络综合、ISD悬架的应用研究及ISD悬架一体化融合设计。

MAO M , WANG L , CHEN Y J , et al. Research progress in inerter and inerter-spring-damper suspension [J ] . Acta Armamentarii , 2016 , 37 ( 3 ): 525 - 534 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2016.03.019 http://doi.org/10.3969/j.issn.1000-1093.2016.03.019 The appearance of inerter and its device greatly promote the development of electrical and mechanical analogy and inerter-spring-damper（ISD）suspension. The concept, background and characteristics of the inerter and ISD suspension are introduced. The structure types, dynamics, frequency responses, nonlinear characteristics and breakdown phenomena of the existing inerters at home and abroad are described. The research progress of ISD suspension are systematically explained by summarizing its structure types, performance, network synthesis theory and application, layout and integrated design. Five aspects of future application of inerter and ISD suspension, including innovative design of inerter, inerter nonlinear research, ISD suspension network synthesis, application and integrated design of ISD suspension, are presented.

曹民 , 刘为 , 喻凡 . 车辆主动悬架用电机作动器的研制 [J ] . 机械工程学报 , 2008 , 44 ( 11 ): 224 - 228 . 针对现有车用液力式主动悬架作动器普遍存在的响应慢、能耗大、蓄能效率低和结构复杂等不足，提出采用滚珠螺旋传动式无刷电机作动器的电机蓄能式主动悬架，并对该主动悬架的结构原理和电机作动器的创新设计方案。并以某中级轿车半独立后悬架作为试验对象，对电动机作动器的弹性元件、滚珠丝杠和无刷电动机等重要部件进行结构设计以及对输出特性进行分析推导。试制出电机作动器的功能样机，并对电气特性和被动响应特性进行测试分析，初步验证了该电机作动器的可行性和有效性，同时还阐述在有待进一步改进的设计缺陷，以及尚须进一步测试的主动控制响应和电磁蓄能特性等性能指标。

CAO M , LIU W , YU F . Development on electromotor actuator for active suspension of vehicle [J ] . Journal of Mechanical Engineering , 2008 , 44 ( 11 ): 224 - 228 . (in Chinese) In view of the shortcomings of actuator for hydraulic active suspension of vehicle, such as slow response, high energy consumption, low efficiency of energy accumulation, and complex structure, a novel design scheme of active suspension with energy accumulation by electromotor actuator (mainly composed of a brushless motor and a ball screw) is presented. Taking the semi-independent rear suspension of a certain intermediate car as example, structural designs of the important components of electromotor actuator, such as the elastic elements, ball screw and brushless motor are carried out, and the output characteristics are analyzed and derived. A functional prototype of actuator is trial-produced, and the electric and passive response characteristics of actuator are tested and analyzed. The feasibility and effectivity of actuator are proved. Moreover, the design defects that need to be further improved, and the performance indexes that need to be further tested, such as the active response and electromagnetic energy accumulation, are expounded.

GYSEN B L J , VAN DER SANDE T P J , PAULIDES J J H , et al. Efficiency of a regenerative direct-drive electromagnetic active suspension [J ] . IEEE Transactions on Vehicular Technology , 2011 , 60 ( 4 ): 1384 - 1393 . DOI: 10.1109/TVT.2011.2131160 http://doi.org/10.1109/TVT.2011.2131160 http://ieeexplore.ieee.org/document/5737802/ http://ieeexplore.ieee.org/document/5737802/

SHEN Y M , LU Q , YE Y . Double-stator air-core tubular permanent magnet linear motor for vehicle active suspension systems [C ] //Proceedings of the 2016 IEEE Vehicle Power and Propulsion Conference . Zhejiang, China : IEEE , 2016 : 1 - 6 .

GYSEN B L J , JANSSEN J L G , PAULIDES J J H , et al. Design aspects of an active electromagnetic suspension. system for automotive applications [J ] . IEEE Transactions on Industry Applications , 2009 , 45 ( 5 ): 1589 - 1597 . DOI: 10.1109/TIA.2009.2027097 http://doi.org/10.1109/TIA.2009.2027097 http://ieeexplore.ieee.org/document/5165013/ http://ieeexplore.ieee.org/document/5165013/

ZHOU H W , ZHANG J J , LU Z , et al. A novel five-phase double-stator tubular fault-tolerant flux-modulation permanent magnet motor [J ] . IEEE Transactions on Applied Superconductivity , 2018 , 28 ( 3 ): 1 - 5 .

孙晓东 , 蔡峰 , 蔡英凤 , 等 . 主动悬架用直线电机模型预测推力控制 [J ] . 中国公路学报 , 2021 , 34 ( 9 ): 85 - 100 . DOI: 10.19721/j.cnki.1001-7372.2021.09.007 http://doi.org/10.19721/j.cnki.1001-7372.2021.09.007 针对主动悬架用直线电机高精度与高效率的控制需求，充分研究直线电机以及主动悬架动力学特性，建立直线电机驱动模型与主动悬架二自由度参考模型。为了改善传统直线电机直接推力控制的动态性能，提出一种改进的模型预测推力控制方法。该方法将逆变器产生的7个非零电压矢量作为备选矢量，并融合预测模型来计算出控制周期内的电机运行状态参数，基于成本函数最小值原理挑选出最优电压矢量，并将其作用于逆变器产生驱动电机所需的电压。为了解决数字控制系统的固有问题，提出延时补偿技术，保证对电机能够进行实时控制；对于逆变器开关频率不固定而引起的开关损耗等问题，通过在成本函数中加入开关频率项，在选择最优电压矢量的同时还降低了逆变器的整流频率与开关损耗；另外为了提高电机推力的效率以及减小推力与磁链波动，提出最大推力电流比与占空比优化控制技术，提高直线电机的动态控制性能。基于MATLAB/Simulink与dSPACE联合仿真，并搭建直线电机与主动悬架硬件测试平台，对所提出的控制方法进行验证，同时对主动悬架系统的动力学性能也进行了仿真与试验测试。试验结果表明：相较于传统的直接推力控制，所提出的控制策略使电机能够拥有更快的稳态速度、更小的电磁力与磁链波动以及更低的开关频率；各工况下，轮胎动载荷试验与仿真结果均方根值的相对误差分别为12.3%、4.47%、6.3%；悬架动行程试验与仿真结果均方根值的相对误差分别为10.3%、8.86%、10.6%；车身加速度试验与仿真结果均方根值的相对误差分别为6.23%、9.12%、7.2%。由计算结果可知，各评价指标的相对误差均在13%以内，验证了仿真结果的正确性，证明了模型预测推力控制对于提升电机与悬架动力学性能的有效性，能够实现对车辆悬架系统全局工况性能最优，协调控制悬架系统的动力学性能。

SUN X D , CAI F , CAI Y F , et al. Improved model predictive thrust-force control of linear motors for active suspensions [J ] . China Journal of Highway and Transport , 2021 , 34 ( 9 ): 85 - 100 . (in Chinese)

汪若尘 , 戴煜 , 丁仁凯 , 等 . 混合电磁悬架作动器设计与试验 [J ] . 农业机械学报 , 2019 , 50 ( 5 ): 385 - 393 .

WANG R C , DAI Y , DING R K , et al. Design and experiment on actuator for hybrid electromagnetic suspension [J ] . Transactions of the Chinese Society for Agricultural Machinery , 2019 , 50 ( 5 ): 385 - 393 . (in Chinese)

秦武 , 上官文斌 , 吕辉 . 非线性二自由度主动悬架滑模控制方法的研究 [J ] . 机械工程学报 , 2020 , 56 ( 1 ): 58 - 68 . DOI: 10.3901/JME.2020.01.058 http://doi.org/10.3901/JME.2020.01.058 以非线性二自由度主动悬架模型为研究对象，分析与验证了基于参考天棚模型的滑模控制算法在非线性悬架控制中的有效性。根据参考天棚模型和非线性二自由度模型中簧载质量位移和速度相等，利用滑模控制方法，给出了非线性二自由度主动悬架的控制力的计算方法。试验测试了有无控制时非线性二自由度主动悬架系统中簧载质量的加速度，验证了主动悬架的控制力的计算方法的有效性。给出了参考天棚模型中天棚阻尼系数的选择方法，研究了控制参数对非线性二自由度主动悬架控制效果的影响。基于非线性二自由度主动悬架模型，计算分析了滑模控制和线性二次型最优（Linear quadratic regulator，LQR）控制的主动悬架性能指标。结果表明：对于非线性二自由度悬架系统，基于参考天棚滑模控制的主动悬架系统可以获得更优的性能指标。

QIN W , SHANGGUAN W B , LÜ H . Research on sliding mode control for nonlinear active suspension system with two degrees of freedom [J ] . Journal of Mechanical Engineering , 2020 , 56 ( 1 ): 58 - 68 . (in Chinese) DOI: 10.3901/JME.2020.01.058 http://doi.org/10.3901/JME.2020.01.058 Based on the nonlinear model of two degrees of freedom (2DOF), the sliding mode control (SMC) algorithm based on reference sky-hook model for active suspension system is proposed. The effectiveness of the algorithm applied in the nonlinear 2DOF control system of active suspension is validated by the active suspension plant. In the reference sky-hook model and the nonlinear 2DOF control model of active suspension, the displacement and the velocity of sprung mass assumed to be equal by using the control force. The calculation method for control force of active suspension is developed by using the SMC algorithm based on reference sky-hook model. Through the measured acceleration of sprung mass in nonlinear 2DOF model with SMC, the effectiveness of the calculated method for the control force is verified. The method for selecting damping coefficient in reference sky-hook model is proposed. The influence of the selected parameters in reference sky-hook model on the controlling performance of the nonlinear 2DOF control system of active suspension is analyzed. Based on the nonlinear 2DOF suspension model, the performance indexes of active suspension system with SMC and linear quadratic regulator (LQR) control are calculated and compared. It is shown that the nonlinear active suspension control system with SMC based on reference sky-hook model can obtain the better performance indexes.

余曼 , 周辰雨 , 魏朗 , 等 . 基于T-S模糊模型的车辆电液悬架系统H_∞控制 [J ] . 中国公路学报 , 2018 , 31 ( 8 ): 205 - 217 . 为了进一步降低主动悬架作动器输出力并优化控制系统鲁棒性，建立车辆7自由度整车模型，采用Takagi-Sugeno （T-S）模糊建模技术，设计主动悬架外环H_{∞}控制器，从而根据路面输入调节主动悬架性能，提升作动器能效。通过构建一个包括控制器稳定性分析、悬架运动空间及力的限值问题的线性矩阵不等式组，将控制器的优化问题转换为此线性不等式组的求解问题，并结合并行分配补偿控制技术，得到此控制器状态反馈系数。针对系统不确定性参数，内环采用自适应鲁棒控制方法，提升控制力的跟踪性能。通过对不同路面轮廓激励工况、交叉轴双轮激励工况以及控制力跟踪性能进行仿真试验，分析被动悬架和主动悬架性能评价指标，并对其作动器输出力进行对比研究。研究结果表明：在小激励下，基于T-S模糊模型的H_{∞}控制主动悬架相比被动悬架，各车轮处加速度均方根值可降低80%以上，与最优控制相比可降低47%以上；而在大激励时，虽然其加速度均方根值有所上升，但其悬架动挠度峰值较被动悬架有所下降；通过路面交叉轴激励对比可以看出，针对整车平顺性参数，该方法可在路面小激励时较被动悬架降低质心、俯仰以及侧倾加速度均方根值达55%、83%以及90%以上；与反演作动器输出力及最优控制作动器输出力对比结果表明，该控制方法可有效降低主动悬架控制力峰值20%以上，并提升控制力的跟踪性能；基于T-S模糊模型的H_{∞}控制可以在保证车辆悬架性能的基础上有效降低系统能耗。

YU M , ZHOU C Y , WEI L , et al. Takagi-Sugeno fuzzy-model-based automobile electrohydraulic active suspension H-infinity control [J ] . China Journal of Highway and Transport , 2018 , 31 ( 8 ): 205 - 217 . (in Chinese)

韩雪岩 , 祁坤 , 张哲 , 等 . 永磁同步直线电机磁阻力分析及抑制措施 [J ] . 电工技术学报 , 2015 , 30 ( 6 ): 70 - 76 .

HAN X Y , QI K , ZHANG Z , et al. Analysis and suppression measures of magnetic resistance force in permanent magnet linear synchronous motors [J ] . Transactions of China Electrotechnical Society , 2015 , 30 ( 6 ): 70 - 76 . (in Chinese)

卢琴芬 , 沈燚明 , 叶云岳 . 永磁直线电动机结构及研究发展综述 [J ] . 中国电机工程学报 , 2019 , 39 ( 9 ): 2575 - 2588 .

LU Q F , SHEN Y M , YE Y Y . Development of permanent magnet linear synchronous motors structure and research [J ] . Proceedings of the CSEE , 2019 , 39 ( 9 ): 2575 - 2588 . (in Chinese)

彭兵 , 张囡 , 夏加宽 , 等 . 永磁直线电机端部效应力的解析计算 [J ] . 中国电机工程学报 , 2016 , 36 ( 2 ): 547 - 553 .

PENG B , ZHANG N , XIA J K , et al. Analytical calculation for end effect forces in permanent magnet linear motors [J ] . Proceedings of the CSEE , 2016 , 36 ( 2 ): 547 - 553 . (in Chinese)

YAO Y H , LU Q . Comparative study of e-core and c-core modular pm linear machines with different slot/pole combinations [J ] . IEEE Transactions on Magnetics , 2017 , 53 ( 11 ): 1 - 7 .

HU H Z , LIU X D , ZHAO J , et al. Analysis and minimization of detent end force in linear permanent magnet synchronous machines [J ] . IEEE Transactions on Industrial Electronics , 2018 , 65 ( 3 ): 2475 - 2486 . DOI: 10.1109/TIE.2017.2740851 http://doi.org/10.1109/TIE.2017.2740851 http://ieeexplore.ieee.org/document/8012418/ http://ieeexplore.ieee.org/document/8012418/

张鲁 , 寇宝泉 , 赵斌超 , 等 . 新型Halbach次级结构永磁同步直线电机 [J ] . 电工技术学报 , 2013 , 28 ( 7 ): 39 - 45 .

ZHANG L , KOU B Q , ZHAO B C , et al. A novel synchronous permanent magnet linear motor with Halbach secondary structure [J ] . Proceedings of the CSEE , 2013 , 28 ( 7 ): 39 - 45 . (in Chinese)