# American Institute of Mathematical Sciences

doi: 10.3934/dcdss.2022077
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## Design of the integrated AFS and DYC scheme for vehicles via FTSM and SOSM techniques

 School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, Jiangsu 212013, China

* Corresponding author: Li Ma

Received  October 2021 Revised  February 2022 Early access March 2022

Fund Project: This work is supported by the National Science Foundation of China under Grant 61973142, the Jiangsu Natural Science Foundation for Distinguished Young Scholars under Grant BK20180045 and the Priority Academic Program Development of Jiangsu Higher Education Institutions

Improving the stability and safety is of great significance for the in-wheel electric vehicle. There are many studies only concentrating on active front steering (AFS) control or direct yaw-moment control (DYC). However, When the in-wheel electric vehicle is under extreme conditions, AFS or DYC alone is not effective. In this paper, an integrated controller of AFS and DYC is proposed. Firstly, the ideal values of yaw rate and sideslip angle can be calculated based on the two-degree-of-freedom vehicle model. Secondly, the AFS controller is obtained according to the backstepping-based fast terminal sliding mode (FTSM). Then, the DYC controller which consists of the upper controller and the lower controller is constructed. The upper controller is developed via the integral-based second-order sliding mode (SOSM). The appropriate torque is outputted to each wheel by the lower controller. Finally, the simulation results show that the actual yaw rate and sideslip angle can approach the ideal ones as closely as possible under the proposed integrated controller.

Citation: Lina Zhang, Li Ma, Shan Chen. Design of the integrated AFS and DYC scheme for vehicles via FTSM and SOSM techniques. Discrete and Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2022077
##### References:
 [1] N. Ahmadian, A. Khosravi and P. Sarhadi, Adaptive yaw stability control by coordination of active steering and braking with an optimized lower-level controller, International Journal of Adaptive Control and Signal Processing, 34 (2020), 1242-1258.  doi: 10.1002/acs.3154. [2] N. Ahmadian, A. Khosravi and P. Sarhadi, Integrated model reference adaptive control to coordinate active front steering and direct yaw moment control, ISA Transactions, 106 (2020), 85-96.  doi: 10.1016/j.isatra.2020.06.020. [3] L. Basilio, Z. Mattia, S. Aldo, G. Patrick and D. Wouter, Yaw rate and sideslip angle control through single input single output direct yaw moment control, IEEE Transactions on Control Systems Technology, 29 (2021), 124-139. [4] X.-H. Chang, Y. Liu and M. Q. Shen, Resilient control design for lateral motion regulation of intelligent vehicle, IEEE/ASME Transactions on Mechatronics, 24 (2019), 2488-2497.  doi: 10.1109/TMECH.2019.2946895. [5] X.-H. Chang and G.-H. Yang, Nonfragile H-infty filter design for T-S fuzzy systems in standard form, IEEE Transactions on Industrial Electronics, 61 (2014), 3448-3458.  doi: 10.1109/TIE.2013.2278955. [6] L. Chen, P. S. Li, W. S. Lin and Q. Zhou, Observer-based fuzzy control for four-wheel independently driven electric vehicles with active steering systems, International Journal of Fuzzy Systems, 22 (2020), 89-100.  doi: 10.1007/s40815-019-00770-3. [7] J. Cheng, L. D. Liang, J. H. Park, H. C. Yan and K. Z. Li, A dynamic event-triggered approach to state estimation for switched memristive neural networks with nonhomogeneous sojourn probabilities, IEEE Transactions on Circuits and Systems-Ⅰ: Regular Papers, 68 (2021), 4924-4934.  doi: 10.1109/TCSI.2021.3117694. [8] J. Cheng, J. H. Park and Z. G. Wu, A hidden Markov model based control for periodic systems subject to singular perturbations, Systems Control Lett., 157 (2021), 8 pp. doi: 10.1016/j.sysconle.2021.105059. [9] S. H. Ding, L. Liu and W. X. Zheng, Sliding mode direct yaw moment control design for in-wheel electric vehicles, IEEE Transactions on Industrial Electronics, 64 (2017), 6752-6462.  doi: 10.1109/TIE.2017.2682024. [10] S. H. Ding, K. Q. Mei and X. H. Yu, Adaptive second-order sliding mode control: A Lyapunov approach, IEEE Transactions on Automatic Control, (2021), 1–1. doi: 10.1109/TAC.2021.3115447. [11] S. H. Ding, B. B. Zhang, K. Q. Mei and J. H. Park, Adaptive fuzzy SOSM controller design with output constraints, IEEE Transactions on Fuzzy Systems, (2021), 1–1, http://dx.doi.org/10.1109/TFUZZ.2021.3079506. [12] J. G. Guo, Y. G. Luo, K. Q. Li and Y. F. Dai, Coordinated path-following and direct yaw-moment control of autonomous electric vehicles with sideslip angle estimation, Mechanical Systems and Signal Processing, 105 (2018), 183-199.  doi: 10.1016/j.ymssp.2017.12.018. [13] J. H. Guo, Y. G. Luo, C. Hu, C. Tao and K. Q. Li, Robust combined lane keeping and direct yaw moment control for intelligent electric vehicles with time delay, International Journal of Automotive Technology, 20 (2019), 289-296.  doi: 10.1007/s12239-019-0028-5. [14] B. A. Guvenc, L. Guvenc and S. Karaman, Robust yaw stability controller design and hardware-in-the-loop testing for a road vehicle, IEEE Transactions on Vehicular Technology, 58 (2009), 555-571.  doi: 10.1109/TVT.2008.925312. [15] G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, 2d ed, Cambridge, at the University Press, 1952. [16] Q. K. Hou, S. H. Ding and X. H. Yu, A super-twisting-like fractional controller for SPMSM drive system, IEEE Transactions on Industrial Electronics, (2021), 1–1. doi: 10.1109/TIE.2021.3116585. [17] X. Jin, Y. Shi, Y. Tang and X. T. Wu, Event-triggered attitude consensus with absolute and relative attitude measurements, Automatica J. IFAC, 122 (2020), 109245, 10 pp. doi: 10.1016/j.automatica.2020.109245. [18] G. Li, C. F. Zong and L. Y. Jiang, Active front steering and direct yaw moment integrated control algorithm, Vehicle System Dynamics, 48 (2011). [19] X. D. Li and P. Li, Stability of time-delay systems with impulsive control involving stabilizing delays, Automatica J. IFAC, 124 (2021), 109336, 6 pp. doi: 10.1016/j.automatica.2020.109336. [20] X. Li, X. Yang and J. Cao, Event-triggered impulsive control for nonlinear delay systems, Automatica, 117 (2020), 108981, 7 pp. doi: 10.1016/j.automatica.2020.108981. [21] B. Li and F. Yu, Design of a vehicle lateral stability control system via a fuzzy logic control approach, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 224 (2010), 313-326.  doi: 10.1243/09544070JAUTO1279. [22] X. D. Li and X. Y. Yang, Lyapunov stability analysis for nonlinear systems with state-dependent state delay, Automatica J. IFAC, 112 (2020), 108674, 6 pp. doi: 10.1016/j.automatica.2019.108674. [23] Y. Li, Y. Liu and S. Tong, Observer-based neuro-adaptive optimized control of strict-feedback nonlinear systems with state constraints, IEEE Transactions on Neural Networks and Learning Systems, (2021), 1–15. doi: 10.1109/TNNLS.2021.3051030. [24] X. T. Liang, Q. W. Wang, L. F. Zhao and X. Wang, Extension coordinated control of four wheel independent drive electric vehicles by AFS and DYC, Control Engineering Practice, 101 (2020), 1242-1258. [25] L. Liu, S. H. Ding and X. H. Yu, Second-order sliding mode control design subject to an asymmetric output constraint, IEEE Transactions on Circuits and Systems-Ⅱ: Express Briefs, 68 (2021), 1278-1282. [26] K. Q. Mei and S. H. Ding, HOSM controller design with asymmetric output constraints, SCIENCE CHINA Information Sciences, 65 (2022), 189202.  doi: 10.1007/s11432-020-3158-8. [27] K. Q. Mei, S. H. Ding and W. X. Zheng, Fuzzy adaptive SOSM based control of a type of nonlinear systems, IEEE Transactions on Circuits and Systems-Ⅱ: Express Briefs, 69 (2021), 1342-1346.  doi: 10.1109/TCSII.2021.3116812. [28] J. Ni, J. B. Hu and C. L. Xiang, Envelope control for four-wheel independently actuated autonomous ground vehicle through AFS/DYC integrated control, IEEE Transactions on Vehicular Technology, 66 (2017), 9712-9726.  doi: 10.1109/TVT.2017.2723418. [29] F. Paolo, B. Francesco, A. Jahan, T. Hongtei Eric and H. Davor, Predictive active steering control for autonomous vehicle systems, IEEE Transactions on Control Systems Technology, 15 (2007), 566-580. [30] X. D. Sun, L. Y. Feng, K. K. Diao and Z. B. Yang, An improved direct instantaneous torque control based on adaptive terminal sliding mode for a segmented-rotor SRM, IEEE Transactions on Industrial Electronics, 68 (2021), 10569-10579.  doi: 10.1109/TIE.2020.3029463. [31] X. D. Sun, J. L. Wu, G. Lei, Y. G. Guo and J. Z. Zhu, Torque ripple reduction of SRM drive using improved direct torque control with sliding mode controller and observer, Transactions on Industrial Electronics, 68 (2021), 9334-9345.  doi: 10.1109/TIE.2020.3020026. [32] Z.-Y. Sun, M.-M. Yun and T. Li, A new approach to fast global finite-time stabilization of high-order nonlinear system, Automatica J. IFAC, 81 (2017), 455-463.  doi: 10.1016/j.automatica.2017.04.024. [33] Y. Tang, X. T. Wu, P. Shi and F. Qian, Input-to-state stability for nonlinear systems with stochastic impulses, Automatica, 113 (2020), 108766, 12 pp. doi: 10.1016/j.automatica.2019.108766. [34] Y. Tang, D. D. Zhang, P. Shi, W. B. Zhang and F. Qian, Event-based formation control for nonlinear multiagent systems under DoS attacks, IEEE Transactions on Automatic Control, 66 (2021), 452-459.  doi: 10.1109/TAC.2020.2979936. [35] J. Wang, Z. G. Huang, Z. G. Wu, J. D. Cao and H. Shen, Extended dissipative control for singularly perturbed PDT switched systems and its application, IEEE Transactions on Circuits and Systems Ⅰ: Regular Papers, 67 (2020), 5281-5289.  doi: 10.1109/TCSI.2020.3022729. [36] J. Wang, C. Y. Yang, J. W. Xia, Z. G. Wu and H. Shen, Observer-based sliding mode control for networked fuzzy singularly perturbed systems under weighted try-once-discard protocol, IEEE Transactions on Fuzzy Systems, (2021), http://dx.doi.org/10.1109/TFUZZ.2021.3070125. [37] Q. W. Wang, Y. Q. Zhao, Y. J. Deng, H. Xu, H. F. Deng and F. Lin, Optimal coordinated control of ARS and DYC for four-wheel steer and in-wheel motor drive electric vehicle with unknown tire model, IEEE Transactions on Vehicular Technology, 69 (2020), 10809-10819. [38] Y. Wang, J. Gao, K. Li and H. Chen, Integrated design of control allocation and triple-step control for over-actuated electric ground vehicles with actuator faults, Journal of the Franklin Institute, 357 (2020), 3150-3167.  doi: 10.1016/j.jfranklin.2019.07.035. [39] Z. Y. Wang, U. Montanaro, S. Fallah, A. Sorniotti and B. Lenzo, A gain scheduled robust linear quadratic regulator for vehicle direct yaw moment control, Mechatronics, 51 (2018), 31-45.  doi: 10.1016/j.mechatronics.2018.01.013. [40] S. J. Yim, Unified chassis control with electronic stability control and active front steering for under-steer prevention, International Journal of Automotive Technology, 16 (2015), 775-782.  doi: 10.1007/s12239-015-0078-2. [41] J. H. Yuan, S. H. Ding and K. Q. Mei, Fixed-time SOSM controller design with output constraint, Nonlinear Dynamics, 102 (2020), 1567-1583. [42] D. Zhang, Y. P. Shen, S. Q. Zhou, X. W. Dong and L. Yu, Distributed secure platoon control of connected vehicles subject to DoS attack: Theory and application, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51 (2021), 7269-7278.  doi: 10.1109/TSMC.2020.2968606. [43] H. Zhang and J. Wang, Vehicle lateral dynamics control through AFS/DYC and robust gain-scheduling approach, IEEE Transactions on Vehicular Technology, 65 (2016), 489-494.  doi: 10.1109/TVT.2015.2391184. [44] B. Zheng and S. Anwar, Yaw stability control of a steer-by-wire equipped vehicle via active front wheel steering, Mechatronics, 19 (2009), 799-804.  doi: 10.1016/j.mechatronics.2009.04.005.

show all references

##### References:
 [1] N. Ahmadian, A. Khosravi and P. Sarhadi, Adaptive yaw stability control by coordination of active steering and braking with an optimized lower-level controller, International Journal of Adaptive Control and Signal Processing, 34 (2020), 1242-1258.  doi: 10.1002/acs.3154. [2] N. Ahmadian, A. Khosravi and P. Sarhadi, Integrated model reference adaptive control to coordinate active front steering and direct yaw moment control, ISA Transactions, 106 (2020), 85-96.  doi: 10.1016/j.isatra.2020.06.020. [3] L. Basilio, Z. Mattia, S. Aldo, G. Patrick and D. Wouter, Yaw rate and sideslip angle control through single input single output direct yaw moment control, IEEE Transactions on Control Systems Technology, 29 (2021), 124-139. [4] X.-H. Chang, Y. Liu and M. Q. Shen, Resilient control design for lateral motion regulation of intelligent vehicle, IEEE/ASME Transactions on Mechatronics, 24 (2019), 2488-2497.  doi: 10.1109/TMECH.2019.2946895. [5] X.-H. Chang and G.-H. Yang, Nonfragile H-infty filter design for T-S fuzzy systems in standard form, IEEE Transactions on Industrial Electronics, 61 (2014), 3448-3458.  doi: 10.1109/TIE.2013.2278955. [6] L. Chen, P. S. Li, W. S. Lin and Q. Zhou, Observer-based fuzzy control for four-wheel independently driven electric vehicles with active steering systems, International Journal of Fuzzy Systems, 22 (2020), 89-100.  doi: 10.1007/s40815-019-00770-3. [7] J. Cheng, L. D. Liang, J. H. Park, H. C. Yan and K. Z. Li, A dynamic event-triggered approach to state estimation for switched memristive neural networks with nonhomogeneous sojourn probabilities, IEEE Transactions on Circuits and Systems-Ⅰ: Regular Papers, 68 (2021), 4924-4934.  doi: 10.1109/TCSI.2021.3117694. [8] J. Cheng, J. H. Park and Z. G. Wu, A hidden Markov model based control for periodic systems subject to singular perturbations, Systems Control Lett., 157 (2021), 8 pp. doi: 10.1016/j.sysconle.2021.105059. [9] S. H. Ding, L. Liu and W. X. Zheng, Sliding mode direct yaw moment control design for in-wheel electric vehicles, IEEE Transactions on Industrial Electronics, 64 (2017), 6752-6462.  doi: 10.1109/TIE.2017.2682024. [10] S. H. Ding, K. Q. Mei and X. H. Yu, Adaptive second-order sliding mode control: A Lyapunov approach, IEEE Transactions on Automatic Control, (2021), 1–1. doi: 10.1109/TAC.2021.3115447. [11] S. H. Ding, B. B. Zhang, K. Q. Mei and J. H. Park, Adaptive fuzzy SOSM controller design with output constraints, IEEE Transactions on Fuzzy Systems, (2021), 1–1, http://dx.doi.org/10.1109/TFUZZ.2021.3079506. [12] J. G. Guo, Y. G. Luo, K. Q. Li and Y. F. Dai, Coordinated path-following and direct yaw-moment control of autonomous electric vehicles with sideslip angle estimation, Mechanical Systems and Signal Processing, 105 (2018), 183-199.  doi: 10.1016/j.ymssp.2017.12.018. [13] J. H. Guo, Y. G. Luo, C. Hu, C. Tao and K. Q. Li, Robust combined lane keeping and direct yaw moment control for intelligent electric vehicles with time delay, International Journal of Automotive Technology, 20 (2019), 289-296.  doi: 10.1007/s12239-019-0028-5. [14] B. A. Guvenc, L. Guvenc and S. Karaman, Robust yaw stability controller design and hardware-in-the-loop testing for a road vehicle, IEEE Transactions on Vehicular Technology, 58 (2009), 555-571.  doi: 10.1109/TVT.2008.925312. [15] G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, 2d ed, Cambridge, at the University Press, 1952. [16] Q. K. Hou, S. H. Ding and X. H. Yu, A super-twisting-like fractional controller for SPMSM drive system, IEEE Transactions on Industrial Electronics, (2021), 1–1. doi: 10.1109/TIE.2021.3116585. [17] X. Jin, Y. Shi, Y. Tang and X. T. Wu, Event-triggered attitude consensus with absolute and relative attitude measurements, Automatica J. IFAC, 122 (2020), 109245, 10 pp. doi: 10.1016/j.automatica.2020.109245. [18] G. Li, C. F. Zong and L. Y. Jiang, Active front steering and direct yaw moment integrated control algorithm, Vehicle System Dynamics, 48 (2011). [19] X. D. Li and P. Li, Stability of time-delay systems with impulsive control involving stabilizing delays, Automatica J. IFAC, 124 (2021), 109336, 6 pp. doi: 10.1016/j.automatica.2020.109336. [20] X. Li, X. Yang and J. Cao, Event-triggered impulsive control for nonlinear delay systems, Automatica, 117 (2020), 108981, 7 pp. doi: 10.1016/j.automatica.2020.108981. [21] B. Li and F. Yu, Design of a vehicle lateral stability control system via a fuzzy logic control approach, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 224 (2010), 313-326.  doi: 10.1243/09544070JAUTO1279. [22] X. D. Li and X. Y. Yang, Lyapunov stability analysis for nonlinear systems with state-dependent state delay, Automatica J. IFAC, 112 (2020), 108674, 6 pp. doi: 10.1016/j.automatica.2019.108674. [23] Y. Li, Y. Liu and S. Tong, Observer-based neuro-adaptive optimized control of strict-feedback nonlinear systems with state constraints, IEEE Transactions on Neural Networks and Learning Systems, (2021), 1–15. doi: 10.1109/TNNLS.2021.3051030. [24] X. T. Liang, Q. W. Wang, L. F. Zhao and X. Wang, Extension coordinated control of four wheel independent drive electric vehicles by AFS and DYC, Control Engineering Practice, 101 (2020), 1242-1258. [25] L. Liu, S. H. Ding and X. H. Yu, Second-order sliding mode control design subject to an asymmetric output constraint, IEEE Transactions on Circuits and Systems-Ⅱ: Express Briefs, 68 (2021), 1278-1282. [26] K. Q. Mei and S. H. Ding, HOSM controller design with asymmetric output constraints, SCIENCE CHINA Information Sciences, 65 (2022), 189202.  doi: 10.1007/s11432-020-3158-8. [27] K. Q. Mei, S. H. Ding and W. X. Zheng, Fuzzy adaptive SOSM based control of a type of nonlinear systems, IEEE Transactions on Circuits and Systems-Ⅱ: Express Briefs, 69 (2021), 1342-1346.  doi: 10.1109/TCSII.2021.3116812. [28] J. Ni, J. B. Hu and C. L. Xiang, Envelope control for four-wheel independently actuated autonomous ground vehicle through AFS/DYC integrated control, IEEE Transactions on Vehicular Technology, 66 (2017), 9712-9726.  doi: 10.1109/TVT.2017.2723418. [29] F. Paolo, B. Francesco, A. Jahan, T. Hongtei Eric and H. Davor, Predictive active steering control for autonomous vehicle systems, IEEE Transactions on Control Systems Technology, 15 (2007), 566-580. [30] X. D. Sun, L. Y. Feng, K. K. Diao and Z. B. Yang, An improved direct instantaneous torque control based on adaptive terminal sliding mode for a segmented-rotor SRM, IEEE Transactions on Industrial Electronics, 68 (2021), 10569-10579.  doi: 10.1109/TIE.2020.3029463. [31] X. D. Sun, J. L. Wu, G. Lei, Y. G. Guo and J. Z. Zhu, Torque ripple reduction of SRM drive using improved direct torque control with sliding mode controller and observer, Transactions on Industrial Electronics, 68 (2021), 9334-9345.  doi: 10.1109/TIE.2020.3020026. [32] Z.-Y. Sun, M.-M. Yun and T. Li, A new approach to fast global finite-time stabilization of high-order nonlinear system, Automatica J. IFAC, 81 (2017), 455-463.  doi: 10.1016/j.automatica.2017.04.024. [33] Y. Tang, X. T. Wu, P. Shi and F. Qian, Input-to-state stability for nonlinear systems with stochastic impulses, Automatica, 113 (2020), 108766, 12 pp. doi: 10.1016/j.automatica.2019.108766. [34] Y. Tang, D. D. Zhang, P. Shi, W. B. Zhang and F. Qian, Event-based formation control for nonlinear multiagent systems under DoS attacks, IEEE Transactions on Automatic Control, 66 (2021), 452-459.  doi: 10.1109/TAC.2020.2979936. [35] J. Wang, Z. G. Huang, Z. G. Wu, J. D. Cao and H. Shen, Extended dissipative control for singularly perturbed PDT switched systems and its application, IEEE Transactions on Circuits and Systems Ⅰ: Regular Papers, 67 (2020), 5281-5289.  doi: 10.1109/TCSI.2020.3022729. [36] J. Wang, C. Y. Yang, J. W. Xia, Z. G. Wu and H. Shen, Observer-based sliding mode control for networked fuzzy singularly perturbed systems under weighted try-once-discard protocol, IEEE Transactions on Fuzzy Systems, (2021), http://dx.doi.org/10.1109/TFUZZ.2021.3070125. [37] Q. W. Wang, Y. Q. Zhao, Y. J. Deng, H. Xu, H. F. Deng and F. Lin, Optimal coordinated control of ARS and DYC for four-wheel steer and in-wheel motor drive electric vehicle with unknown tire model, IEEE Transactions on Vehicular Technology, 69 (2020), 10809-10819. [38] Y. Wang, J. Gao, K. Li and H. Chen, Integrated design of control allocation and triple-step control for over-actuated electric ground vehicles with actuator faults, Journal of the Franklin Institute, 357 (2020), 3150-3167.  doi: 10.1016/j.jfranklin.2019.07.035. [39] Z. Y. Wang, U. Montanaro, S. Fallah, A. Sorniotti and B. Lenzo, A gain scheduled robust linear quadratic regulator for vehicle direct yaw moment control, Mechatronics, 51 (2018), 31-45.  doi: 10.1016/j.mechatronics.2018.01.013. [40] S. J. Yim, Unified chassis control with electronic stability control and active front steering for under-steer prevention, International Journal of Automotive Technology, 16 (2015), 775-782.  doi: 10.1007/s12239-015-0078-2. [41] J. H. Yuan, S. H. Ding and K. Q. Mei, Fixed-time SOSM controller design with output constraint, Nonlinear Dynamics, 102 (2020), 1567-1583. [42] D. Zhang, Y. P. Shen, S. Q. Zhou, X. W. Dong and L. Yu, Distributed secure platoon control of connected vehicles subject to DoS attack: Theory and application, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51 (2021), 7269-7278.  doi: 10.1109/TSMC.2020.2968606. [43] H. Zhang and J. Wang, Vehicle lateral dynamics control through AFS/DYC and robust gain-scheduling approach, IEEE Transactions on Vehicular Technology, 65 (2016), 489-494.  doi: 10.1109/TVT.2015.2391184. [44] B. Zheng and S. Anwar, Yaw stability control of a steer-by-wire equipped vehicle via active front wheel steering, Mechatronics, 19 (2009), 799-804.  doi: 10.1016/j.mechatronics.2009.04.005.
2-DOF vehicle model
7-DOF vehicle model
Structure of the integrated control system
Steering wheel angle
The vehicle trajectories under different controllers
Response curves of yaw rate under different controllers
Response curves of sideslip angle under different controllers
The maximum errors between the ideal value and the actual value under different controllers
Side wind disturbance input
The vehicle trajectories under different controllers
Response curves of yaw rate under different controllers
Response curves of sideslip angle under different controllers
The maximum errors between the ideal value and the actual value under different controllers
Controller parameters
 symbol value unit $R$ 0.35 ${m}$ ${C_f}$ 79240 ${N/rad}$ ${C_r}$ 87002 ${N/rad}$ $a$ 1.05 ${m}$ $b$ 1.57 ${m}$ $m$ 1429 ${Kg}$ ${I_z}$ 2400 ${Kg.m}^2$ ${V_x}$ 120 ${{Km/h}}$
 symbol value unit $R$ 0.35 ${m}$ ${C_f}$ 79240 ${N/rad}$ ${C_r}$ 87002 ${N/rad}$ $a$ 1.05 ${m}$ $b$ 1.57 ${m}$ $m$ 1429 ${Kg}$ ${I_z}$ 2400 ${Kg.m}^2$ ${V_x}$ 120 ${{Km/h}}$
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