潘凤文等：基于鲁棒H滤波的锂离子电池SOC估计 ·701· (谈发明，赵俊杰，王琪.动力电池SOC估计的一种新型鲁棒 [17]Zhang Y,Zhang C H,Zhang X F.State-of-charge estimation of the UKF算法.汽车工程，2019,41(8)：944) lithium-ion battery system with time-varying parameter for hybrid [8]Cheng K W E,Divakar B P,Wu H J,et al.Battery-management electric vehicles.IET Control Theory Appl,2013,8(3):160 system (BMS)and SOC development for electrical vehicles.IEEE [18]Liu C Z,Zhu Q,Li L,et al.A state of charge estimation method Trans Veh Technol,2011,60(1)上：76 based on Hoo observer for switched systems of lithium-ion nickel- [9]Dey S.Ayalew B.Nonlinear observer designs for state-of-charge manganese-cobalt batteries.IEEE Trans Ind Electron,2017, estimation of lithium-ion batteries /2014 American Control 64(10):8128 Conference.Portland,2014:248 [19]Dey S,Ayalew B,Pisu P.Nonlinear robust observers for state-of- [10]Bhangu B S,Bentley P,Stone D A,et al.Nonlinear observers for charge estimation of lithium-ion cells based on a reduced predicting state-of-charge and state-of-health of lead-acid batteries electrochemical model.IEEE Trans Control Syst Technol,2015, for hybrid-electric vehicles.IEEE Trans Veh Technol,2005 23(5):1935 54(3):783 [20]Wang T H,Martinez-Molina J J,Sename O.H observer-based [11]He H W,Xiong R,Fan J X.Evaluation of lithium-ion battery battery fault estimation for HEV application.IFAC Proc Vol, equivalent circuit models for state of charge estimation by an 2012,45(30):206 experimental approach.Energies,2011,4(4):582 [21]Zhu Q,Li L,Hu X S,et al.H,-based nonlinear observer design for [12]Ding Z T.Deng T.LiZ F,et al.SOC estimation of lithium-ion state of charge estimation of lithium-ion battery with polynomial battery based on ampere hour integral and unscented Kalman filter. parameters.IEEE Trans Veh Technol,2017,66(12):10853 China Mech Eng,2020,31(15):1823 [22]Dreef H J,Beelen H P G J,Donkers M C F.LMI-based robust (丁镇涛，邓涛，李志飞，等.基于安时积分和无迹卡尔曼滤波的 observer design for battery state-of-charge estimation //2018 /EEE 锂离子电池SOC估算方法研究.中国机械工程，2020,31(15)： Conference on Decision and Control (CDC).Miami Beach,2018: 1823) 5716 [13]Jin B W,Qiao H M,Pan T H,et al.Lithium battery SOC [23]Wang B J,Liu Z Y,Li S E,et al.State-of-charge estimation for estimation based on interal resistance power consumption.Aufom Eng,2020,42(8):1008 lithium-ion batteries based on a nonlinear fractional model.IEEE (新博文，乔慧敏，潘天红，等.基于内阻功率消耗的锂电池 Trans Control Syst Technol,2017,25(1):3 S0C估计.汽车工程，2020,42(8)：1008) [24]Lu W,Xu D,Yang Q X,et al.Fractional model and state-of- [14]Codeca F,Savaresi S M,Rizzoni G.On battery state of charge charge of lithium battery.J Xi'an Jiaotong Univ,2017,51(7):124 estimation:A new mixed algorithm /2008 IEEE International (鲁伟，续丹，杨晴霞，等.锂电池分数阶建模与荷电状态研究 Conference on Control Applications.San Antonio,2008:102 西安交通大学学报，2017,51(7)：124) [15]Hu Y R,Yurkovich S.Battery state of charge estimation in [25]Lofberg J.YALMIP:A toolbox for modeling and optimization in automotive applications using LPV techniques /Proceedings of MATLAB /2004 IEEE International Conference on Robotics and the 2010 American Control Conference.Baltimore,2010:5043 Automation.New Orleans,2004:284 [16]Hu Y,Yurkovich S.Battery cell state-of-charge estimation using [26]Lofberg J.Modeling and solving uncertain optimization problems linear parameter varying system techniques.J Power Sources, in YALMIP II Proceedings of the 17th IFAC World Congress. 2012,198:338 Seoul,2008:1337（谈发明, 赵俊杰, 王琪. 动力电池SOC估计的一种新型鲁棒 UKF算法. 汽车工程, 2019, 41（8）：944） Cheng K W E, Divakar B P, Wu H J, et al. Battery-management system (BMS) and SOC development for electrical vehicles. IEEE Trans Veh Technol, 2011, 60（1）: 76 [8] Dey S, Ayalew B. Nonlinear observer designs for state-of-charge estimation  of  lithium-ion  batteries  //  2014 American Control Conference. Portland, 2014: 248 [9] Bhangu B S, Bentley P, Stone D A, et al. Nonlinear observers for predicting state-of-charge and state-of-health of lead-acid batteries for  hybrid-electric  vehicles. IEEE Trans Veh Technol,  2005, 54（3）: 783 [10] He  H  W,  Xiong  R,  Fan  J  X.  Evaluation  of  lithium-ion  battery equivalent  circuit  models  for  state  of  charge  estimation  by  an experimental approach. Energies, 2011, 4（4）: 582 [11] Ding  Z  T,  Deng  T,  Li  Z  F,  et  al.  SOC  estimation  of  lithium-ion battery based on ampere hour integral and unscented Kalman filter. China Mech Eng, 2020, 31（15）: 1823 （丁镇涛, 邓涛, 李志飞, 等. 基于安时积分和无迹卡尔曼滤波的 锂离子电池SOC估算方法研究. 中国机械工程, 2020, 31（15）： 1823） [12] Jin  B  W,  Qiao  H  M,  Pan  T  H,  et  al.  Lithium  battery  SOC estimation based on internal resistance power consumption. Autom Eng, 2020, 42（8）: 1008 （靳博文, 乔慧敏, 潘天红, 等. 基于内阻功率消耗的锂电池 SOC估计. 汽车工程, 2020, 42（8）：1008） [13] Codeca  F,  Savaresi  S  M,  Rizzoni  G.  On  battery  state  of  charge estimation:  A  new  mixed  algorithm  //  2008 IEEE International Conference on Control Applications. San Antonio, 2008: 102 [14] Hu  Y  R,  Yurkovich  S.  Battery  state  of  charge  estimation  in automotive  applications  using  LPV  techniques  // Proceedings of the 2010 American Control Conference. Baltimore, 2010: 5043 [15] Hu Y, Yurkovich S. Battery cell state-of-charge estimation using linear  parameter  varying  system  techniques. J Power Sources, 2012, 198: 338 [16] Zhang Y, Zhang C H, Zhang X F. State-of-charge estimation of the lithium-ion battery system with time-varying parameter for hybrid electric vehicles. IET Control Theory Appl, 2013, 8（3）: 160 [17] Liu C Z, Zhu Q, Li L, et al. A state of charge estimation method based on H∞ observer for switched systems of lithium-ion nickel￾manganese-cobalt  batteries. IEEE Trans Ind Electron,  2017, 64（10）: 8128 [18] Dey S, Ayalew B, Pisu P. Nonlinear robust observers for state-of￾charge  estimation  of  lithium-ion  cells  based  on  a  reduced electrochemical  model. IEEE Trans Control Syst Technol,  2015, 23（5）: 1935 [19] Wang  T  H,  Martinez-Molina  J  J,  Sename  O. H∞ observer-based battery  fault  estimation  for  HEV  application. IFAC Proc Vol, 2012, 45（30）: 206 [20] Zhu Q, Li L, Hu X S, et al. H∞-based nonlinear observer design for state  of  charge  estimation  of  lithium-ion  battery  with  polynomial parameters. IEEE Trans Veh Technol, 2017, 66（12）: 10853 [21] Dreef  H  J,  Beelen  H  P  G  J,  Donkers  M  C  F.  LMI-based  robust observer design for battery state-of-charge estimation // 2018 IEEE Conference on Decision and Control (CDC). Miami Beach, 2018: 5716 [22] Wang B J, Liu Z Y, Li S E, et al. State-of-charge estimation for lithium-ion batteries based on a nonlinear fractional model. IEEE Trans Control Syst Technol, 2017, 25（1）: 3 [23] Lu  W,  Xu  D,  Yang  Q  X,  et  al.  Fractional  model  and  state-of￾charge of lithium battery. J Xi'an Jiaotong Univ, 2017, 51（7）: 124 （鲁伟, 续丹, 杨晴霞, 等. 锂电池分数阶建模与荷电状态研究. 西安交通大学学报, 2017, 51（7）：124） [24] Lofberg J. YALMIP: A toolbox for modeling and optimization in MATLAB // 2004 IEEE International Conference on Robotics and Automation. New Orleans, 2004: 284 [25] Löfberg J. Modeling and solving uncertain optimization problems in  YALMIP  // Proceedings of the 17th IFAC World Congress. Seoul, 2008: 1337 [26] 潘凤文等： 基于鲁棒 H∞滤波的锂离子电池 SOC 估计 · 701 ·