In addressing the issue of driving stability control for electric vehicles equipped with distributed four-wheel hub motor drives, this study first introduces a method for determining the stability region of vehicles in phase space, utilizing a Radial Basis Function (RBF) neural network algorithm. Building upon this foundation, an adaptive control weight calculation method for the coordination of Active front steering and the Direct Yaw Control system is proposed, grounded in the theory of extension. To tackle the challenges of vehicle stability in complex environments, a three-tier control system is proposed. The upper tier employs Adaptive Gain PID algorithm to design a vehicle speed tracking controller, while Adaptive Non-singular Integral Terminal Sliding Mode theory is utilized to develop a direct yaw moment controller, alongside Adaptive Robust Integral Sliding Mode theory for the active front steering controller. The middle tier incorporates a cost function for tire slip energy loss into an additional yaw moment optimization distribution function, employing a quadratic programing algorithm to derive the optimal tire driving force. Additionally, a PID algorithm is used to design a tire force closed-loop controller, facilitating the transmission of the ideal driving moment and the desired additional steering angle to the execution layer. Finally, the effectiveness of the proposed algorithm is verified by simulation and hardware-in-the-loop test. The simulation and test results based on the proposed algorithm are compared with other algorithms, and the results show that the proposed algorithm has better performance.
ZhaoYDengHLiY, et al. Coordinated control of stability and economy based on torque distribution of distributed drive electric vehicle. Proc Inst Mech Eng D J Automobile Eng2020; 234(6): 1792–1806.
2.
ZhangXGohlichDLiJ.Energy-efficient toque allocation design of traction and regenerative braking for distributed drive electric vehicles. IEEE Trans Vehicular Technol2018; 67(1): 285–295.
3.
CongGMostefaiLDenaiM, et al. Direct yaw-moment control of an in-wheel motored electric vehicle based on body slip angle fuzzy observer. IEEE Trans Ind Electron2009; 56(5): 1411–1419.
4.
ChenYHedrickJKGuoK.A novel direct yaw moment controller for in-wheel motor electric vehicles. Veh Syst Dyn2013; 51(6): 925–942.
5.
FallahSKhajepourAFidanB, et al. Vehicle optimal torque vectoring using state-derivative feedback and linear matrix inequality. IEEE Trans Vehicular Technol2013; 62(4): 1540–1552.
6.
MutohNHayanoYYahagiH, et al. Electric braking control methods for electric vehicles with independently driven front and rear wheels. IEEE Trans Vehicular Technol2007; 54(2): 1168–1176.
7.
YinDOhSHoriY.A novel traction control for EV based on maximum transmissible torque estimation. IEEE Trans Ind Electron2009; 56(6): 2086–2094.
8.
WangHWuSWangQ.Global sliding mode control for nonlinear vehicle antilock braking system. IEEE Access2021; 9: 40349–40359.
9.
ZhangJSunWJingH.Nonlinear robust control of antilock braking systems assisted by active suspensions for automobile. IEEE Trans Control Syst Technol2019; 27(3): 1352–1359.
10.
GadolaMChindamoDRomanoM, et al. Development and validation of a Kalman filter-based model for vehicle slip angle estimation. Veh Syst Dyn2014; 52(1): 68–84.
11.
LiuYHuangCZhouD, et al. Vehicle sideslip angle estimation based on strong tracking SCKF considering road inclinations. IEEE Trans Vehicular Technol2023; 72(12): 15535–15547.
12.
TianJWangQDingJ, et al. Integrated control with DYC and DSS for 4WID electric vehicles. IEEE Access2019; 7: 124077–124086.
13.
AhmadianNKhosraviASarhadiP.Driver assistant yaw stability control via integration of AFS and DYC. Veh Syst Dyn2022; 60(5): 1742–1762.
14.
LiangJLuYYinG, et al. A distributed integrated control architecture of AFS and DYC based on MAS for distributed drive electric vehicles. IEEE Trans Vehicular Technol2021; 70(6): 5565–5577.
15.
SelmanajDCornoMPanzaniG, et al. Vehicle sideslip estimation: a kinematic based approach. Control Eng Pract2017; 67: 1–12.
16.
BascettaLBaurMFerrettiG.A simple and reliable technique to design kinematic-based sideslip estimators. Control Eng Pract2020; 96: 104317.
17.
SunWWangZWangJ, et al. Research on a real-time estimation method of vehicle sideslip angle based on EKF. Sensors2022; 22: 3386.
18.
WangSYuQZhaoX, et al. Vehicle sideslip angle estimation based on SVD-UPF algorithm. J Intell Fuzzy Syst2019; 37(4): 4563–4573.
19.
LiJLuoJFengB, et al. Vehicle stability control based on vehicle motion state and tire force estimation. Trans Can Soc Mech Eng2025; 49: 207–219.
20.
GuoK.Principles of automotive dynamics. Jiangsu Science and Technology Publishing House, 2011.
21.
LiuFXiongLDengL, et al. A method for determining vehicle driving stability based on the phase plane method. J South China Univ Technol (Nat Sci Ed)2014; 42(11): 63–70.
22.
ChenYChenYQueR, et al. Research on the mechanism of vehicle instability based on Lyapunov and phase plane diagrams. Veh Power Technol2021; 4: 11–14+22.
23.
LuoYLaiE.Research on vehicle stability judgment based on energy method. Automot Eng2014; 36(12): 1534–1538.
24.
HuangMZhengMZhangB, et al. Research on vehicle rollover stability dynamics based on energy method. J Vib Shock2016; 35(24): 164–174.
25.
SamsundarJHustonJ.Estimating lateral stability region of a nonlinear 2 degree-of-freedom vehicle. SAE technical paper981172, 1988.
26.
PacejkaHB.Tire and vehicle dynamics. Butterworth-Heinemann, 2002.
27.
OnoEHosoeSDoiS. Bifurcation in vehicle dynamics and robust front wheel steering control. IEEE Trans Control Syst Technol1998; 6(3): 412–420.
28.
InagakiSKshiroIYamamotoM.Analysis on vehicle stability in critical cornering using phase plane method. JSAE Rev1995; 16(2): 287–292.
29.
ZhuZZhangYHuangY, et al. Sum-of-squares based vehicle dynamic stability method and its applications in ADAS. In: >2022 IEEE intelligent vehicles symposium (IV), 4–9 June 2022.
30.
LiXXuNGuoK, et al. An adaptive SMC controller for EVs with four IWMs handling and stability enhancement based on a stability index. Veh Syst Dyn2021; 59(10): 1509–1532.
31.
SuDZhaoZZhaoK, et al. Tube-MPC vehicle stability control based on the partitioning of stability regions in the extended state space. Automot Eng2024; 46(09): 1654–1667.
32.
LaiFHuangCQ.Path tracking and stability integrated control of intelligent vehicles under steering collision avoidance. Proc Inst Mech Eng D J Automobile Eng2023; 237(8): 1868–1884.
33.
JinXJYinGChenN.Gain-scheduled robust control for lateral stability of four-wheel-independent-drive electric vehicles via linear parameter-varying technique. Mechatronics2015; 30: 286–296.
34.
ZhangNWangJLiZ, et al. Coordinated optimal control of AFS and DYC for four-wheel independent drive electric vehicles based on MAS model. Sensors2023; 23: 3505.
35.
ChengSLiLLiuCZ, et al. Robust LMI-based H-infinite controller integrating AFS and DYC of autonomous vehicles with parametric uncertainties. IEEE Trans Syst Man Cybern Syst2021; 51(11): 6901–6910.
36.
JinXYuZYinG, et al. Improving vehicle handling stability based on combined AFS and DYC system via robust Takagi-Sugeno fuzzy control. IEEE Trans Intell Transp Syst2018; 19(8): 2696–2707.
37.
LiuHLiuCHanL, et al. Handling and stability integrated control of AFS and DYC for distributed drive electric vehicles based on risk assessment and prediction. IEEE Trans Intell Transp Syst2022; 23(12): 23148–23163.
38.
LiJLuoJGuoS, et al. Research on yaw stability control strategy based on direct slip rate allocation. Electronics2024; 13: 193.
39.
SeoYChoKNamK.Integrated yaw stability control of electric vehicle equipped with front/rear steer-by-wire systems and four in-wheel motors. Electronics2022; 11: 1277.
40.
ZhangJLiJ.Integrated vehicle chassis control for active front steering and direct yaw moment control based on hierarchical structure. Trans Inst Meas Contr2019; 41(9): 2428–2440.
41.
LiuYZongCZhangD, et al. Fault-tolerant control approach based on constraint control allocation for 4WIS/4WID vehicles. Proc Inst Mech Eng D J Automobile Eng2021; 235: 2281–2295.
42.
ZhuSWeiBLiuD, et al. A dynamics coordinated control system for 4WD-4WS electric vehicles. Electronics2022; 11: 3731.
43.
LiuZLiYLiW, et al. Research on control strategy of vehicle stability based on dynamic stable region regression analysis. Front Neurorobot2023; 17: 1149201.
44.
ChenWLiangXWangQ, et al. Extension coordinated control of four wheel independent drive electric vehicles by AFS and DYC. Control Eng Pract2020; 101: 104504.
45.
LiJFengBLiangZ, et al. Vehicle lateral control based on dynamic boundary of phase plane based on tire characteristics. Electronics2023; 12: 5012.
