Abstract
This paper is concerned with the yaw-moment stabilization for four-wheel independent-drive electric vehicle. A second-order sliding mode observer is first designed to estimate the required sideslip angle in a finite time. Then, the finite-time control technique and nonlinear disturbance observer are applied to construct the upper controller to drive both yaw rate and sideslip angle to their desired values. Finally, the lower controller is developed to distribute the torques to the independent four wheels according to the desired yaw moment obtained by the given upper controller. Comparisons among linear, discontinuous and nonsmooth controllers under different working conditions are given by using CarSim software.
Similar content being viewed by others
References
Zheng, Y., Dong, Z.Y., Xu, Y., Meng, K., Zhao, J.H., Qiu, J.: Electric vehicle battery charging/swap stations in distribution systems: comparison study and optimal planning. IEEE Trans. Power Syst. 29(1), 221–229 (2014)
Hori, Y.: Future vehicle driven by electricity and control-research on four-wheel-motored “UOT Electric March II”. IEEE Trans. Ind. Electron. 51(5), 954–962 (2004)
Roshanbin, A., Naraghi, M.: Adjustable robustness method for fuzzy logic integrated control of active steer angle and direct yaw moment. Int. J. Control Autom. 6(4), 329–346 (2013)
Chen, Y., Hedrick, J.K., Guo, K.: A novel direct yaw moment controller for in-wheel motor electric vehicles. Veh. Syst. Dyn. 51(6), 925–942 (2013)
Li, Y., Yin, G., Jin, X., Bian, C., Li, J.: Impact of delays for electric vehicles with direct yaw moment control. J. Dyn. Syst. Meas. Control 137(12), 121005 (2015)
Ding, N., Chen, W., Zhang, Y., Xu, G., Gao, F.: An extended Luenberger observer for estimation of vehicle sideslip angle and road friction. Int. J. Veh. Des. 66(4), 385–414 (2014)
Pi, D., Chen, N., Wang, J., Zhang, B.: Design and evaluation of sideslip angle observer for vehicle stability control. Int. J. Automot. Technol. 12(3), 391–399 (2011)
Nam, K., Fujimoto, H., Hori, Y.: Lateral stability control of in-wheel-motor-driven electric vehicles based on sideslip angle estimation using lateral tire force sensors. IEEE Trans. Veh. Technol. 61(5), 1972–1985 (2012)
Doumiati, M., Victorino, A.C., Charara, A., Lechner, D.: Onboard real-time estimation of vehicle lateral tire-road forces and sideslip angle. IEEE/ASME Trans. Mechatron. 16(4), 601–614 (2011)
Jia, G., Li, L., Cao, D.: Model-based estimation for vehicle dynamics states at the limit handling. J. Dyn. Syst. Meas. Control 137(10), 104501 (2015)
Melzi, S., Sabbioni, E.: On the vehicle sideslip angle estimation through neural networks: numerical and experimental results. Mech. Syst. Signal Process. 25(6), 2005–2019 (2011)
Chen, Y., Ji, Y., Guo, K.: A reduced-order nonlinear sliding mode observer for vehicle slip angle and tyre forces. Veh. Syst. Dyn. 52(12), 1716–1728 (2014)
Sun, H., Hou, L., Zong, G.: Continuous finite time control for static var compensator with mismatched disturbances. Nonlinear Dyn. Nonlinear Dyn. 85(4), 2159–2169 (2016)
Du, H., He, Y., Cheng, Y.: Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control. IEEE Trans. Circuits Syst. I Regul. Pap. 61(6), 1778–1788 (2014)
Kim, C.J., Mian, A.A., Kim, S.H., Back, S.H., Jang, H.B., Jang, J.H., Han, C.S.: Performance evaluation of integrated control of direct yaw moment and slip ratio control for electric vehicle with rear in-wheel motors on split-mu road. Int. J. Autom. Technol. 16(6), 939–946 (2015)
Zhang, H., Wang, J.: Vehicle lateral dynamics control through afs/dyc and robust gain-scheduling approach. IEEE Trans. Veh. Technol. 65(1), 489–494 (2015)
Zhu, B., Chen, Y., Zhao, J., Su, Y.: Design of an integrated vehicle chassis control system with driver behavior identification. Math. Probl. Eng. 2015, 1–12 (2015)
Mirzaei, M.: A new strategy for minimum usage of external yaw moment in vehicle dynamic control system. Transp. Res. Part C Emerg. Technol. 18(2), 213–224 (2010)
Mashadi, B., Ahmadizadeh, P., Majidi, M., Mahmoodi-Kaleybar, M.: Integrated robust controller for vehicle path following. Multibody Syst. Dyn. 33(2), 207–228 (2015)
Song, J.: Development and comparison of integrated dynamics control systems with fuzzy logic control and sliding mode control. J. Mech. Sci. Technol. 27(6), 1853–1861 (2013)
Seongjin, Y., Jaewoong, C., Kyongsu, Y.: Coordinated control of hybrid 4wd vehicles for enhanced maneuverability and lateral stability. IEEE Trans. Veh. Technol. 61(4), 1946–1950 (2012)
Yin, C., Chen, Y., Zhong, S.: Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems. Automatica 50(12), 3173–3181 (2014)
Yin, C., Cheng, Y., Chen, Y., Stark, B., Zhong, S.: Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems. Nonlinear Dyn. 82(1), 39–52 (2015)
Yin, C., Stark, B., Chen, Y., Zhong, S., Lau, E.: Fractional-order adaptive minimum energy cognitive lighting control strategy for the hybrid lighting system. Energy Build. 87, 176–184 (2015)
Ding, S., Wang, J., Zheng, W.: Second-order sliding mode control for nonlinear uncertain systems bounded by positive functions. IEEE Trans. Ind. Electron. 62(9), 5899–5909 (2015)
Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)
Hong, Y.: Finite-time stabilization and stabilizability of a class of controllable systems. Syst. Control Lett. 46(4), 231–236 (2002)
Huang, X., Lin, W., Yang, B.: Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica 41(5), 881–888 (2005)
Li, J., Qian, C., Ding, S.H.: Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems. Int. J. Control 83(11), 2241–2252 (2010)
Qi, Z., Taheri, S., Wang, B., Yu, H.: Estimation of the tyre-road maximum friction coefficient and slip slope based on a novel tyre model. Veh. Syst. Dyn. 53(4), 506–525 (2015)
Maclaurin, B.: A skid steering model using the magic formula. J. Terramechanics 48(4), 247–263 (2011)
Guo, K., Yang, J.: Steady-state unitire lateral force model under sideslip combined with large camber condition. J. Mech. Eng. 50(8), 95–101 (2014)
Fu, C.: Direct yaw moment cControl for electric vehicles with independent motors. PhD thesis, RMIT University (2014)
Wu, J., Zhao, Y., Ji, X., Liu, Y., Yin, C.: A modified structure internal model robust control method for the integration of active front steering and direct yaw moment control. Sci. China Technol. Sci. 58(1), 75–85 (2015)
Shtessel, Y., Edwards, C., Fridman, L., Levant, A.: Sliding Mode Control and Observation. Springer, New York (2014)
Rajamani, R.: Vehicle Dynamics and Control. Mechanical Engineering Series. Springer, New York (2006)
Li, S., Yang, J., Chen, W., Chen, X.: Disturbance Observer Based Control Methods and Applications. CRC Press, Boca Raton (2014)
Ding, S., Levant, A., Li, S.: Simple homogeneous sliding-mode controller. Automatica 67(5), 22–32 (2016)
Zhang, J., Han Z, Z., Zhu, F.: Finite time control and L1-gain analysis for positive switched systems. Optim. Control Appl. Methods 36(4), 550–565 (2015)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by the NSF of China (Nos. 61573170, 61273154, 51375210) and the PAPD of Jiangsu Higher Education Institutions, the Postdoctoral Science Foundation of China (2015M571687), China Postdoctoral Science Special Foundation (2016T90427) and the Zhejiang Open Foundation of the Most Important Subjects.
Rights and permissions
About this article
Cite this article
Ding, S., Sun, J. Direct yaw-moment control for 4WID electric vehicle via finite-time control technique. Nonlinear Dyn 88, 239–254 (2017). https://doi.org/10.1007/s11071-016-3240-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-016-3240-0