Adaptive PI-Based Control for Steering Torque Feedback in Steer-by-Wire Systems: A Physical Modeling Approach
DOI:
https://doi.org/10.15282/ijame.22.3.2025.16.0973Keywords:
Torque Feedback Control, Steer-by-Wire, Physical Model Technique, Adaptive PI Control, Vehicle DynamicAbstract
Steering feel is a crucial factor in Steer-by-Wire (SbW) architecture, where achieving the desired physical feedback is essential for driver experience. This research proposes the application of an adaptive Proportional-Integral (PI)-based controller as a torque tracking algorithm to achieve the targeted steering feel. To support this, a 14-DOF vehicle dynamic model was developed and validated in order to provide the foundation for a torque tracking algorithm to generate steering feel at the steering wheel. In the process of steering feel development, the SbW model was developed using a physical modeling approach based on Newton’s laws, where the steering torque felt by the driver at the wheel corresponds to the torque generated by the rack and pinion assembly. The adaptive tracking torque algorithm is implemented using two methods, which are adaptive PI-based (A-PI) and gain scheduling PI-based (GS-PI) methods. The performance of these controllers was verified by using types of input signals (step and sinusoidal wave) and validated through three vehicle dynamic tests based on the ISO standards, including Double Lane Change, Slalom, and J-Turn tests. The findings showed that the GS-PI controller exhibited significant performance compared to results from the CarSim software, which served as a benchmark. Furthermore, the results indicated that this controller was capable of effectively replicating the desired steering feel with approximately less than 2.5 mean absolute error (MAE). This research study offers a practical control strategy for realistic steering feedback and contributes valuable insight for future SbW development.
References
[1] J. F. Arango, L. M. Bergasa, P. A. Revenga, et al., “Drive-by-wire development process based on ros for an autonomous electric vehicle,” Sensors, vol. 20, no. 21, pp. 6121, 2020.
[2] A. Kırlı, Y. Chen, C. E. Okwudire, and A. G. Ulsoy, “Torque-vectoring-based backup steering strategy for steer-by-wire autonomous vehicles with vehicle stability control,” IEEE Transactions on Vehicular Technology, vol. 68, no. 8, pp. 7319-7328, 2019.
[3] M. Li and L. Eckstein, “Fail-operational steer-by-wire system for autonomous vehicles,” in 2019 IEEE International Conference on Vehicular Electronics and Safety (ICVES), Cairo, Egypt, 2019, pp. 1-6.
[4] K. Chen, X. Pei, D. Sun, Z. Chen, X. Guo, and K. Guo, “Active steering control for autonomous vehicles based on a driver-in-the-loop platform: A case study of collision avoidance,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 233, no. 10, pp. 1422–1437, 2019.
[5] S. A. Mortazavizadeh, A. Ghaderi, M. Ebrahimi, and M. Hajian, “Recent developments in the vehicle steer-by-wire system,” IEEE Transactions on Transportation Electrification, vol. 6, no. 3, pp. 1226-1235, 2020.
[6] G. Perozzi, J.J. Rath, C. Sentouh, J. Floris, and J.C. Popieul, “Lateral shared sliding mode control for lane keeping assist system in steer-by-wire vehicles: Theory and experiments,” IEEE Transactions Intelligent Vehicles, vol. 8, no. 4, pp. 3073–3082, 2023.
[7] H. Muslim, “Design and evaluation of lane-change collision avoidance systems in semi-automated driving,” IEEE Transactions on Vehicular Technology, vol. 72, no. 6, pp. 7082–7094, Jun. 2023.
[8] M. H. Hamdi, F. Ahmad, M. H. Che Hasan, M. H. Harun, and V. Rau Aparow, “Model reference adaptive control of an independent steer-by-wire system: A simulation using a 14-degree-of-freedom vehicle model,” International Journal of Automotive and Mechanical Engineering, vol. 21, no. 4, pp. 11723–11743, 2024.
[9] H. Zhao, B. Wang, G. Zhang, and Y. Feng, “Energy saving design and control of steering wheel system of steering by wire vehicle,” IEEE Access, vol. 7, pp. 44307-44316, 2019.
[10] J. H. Choi, K. Nam, and S. Oh, “Steering feel improvement by mathematical modeling of the electric power steering system,” Mechatronics, vol. 78, no. 102629, 2021.
[11] S. H. Kim and C. N. Chu, “A new manual Steering torque estimation model for steer-by-wire systems,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, vol. 230, issue 7, pp. 993-1008. 2016.
[12] C. Wang, L. Yan, X. Wu, and Z. Kong, “Design of reconfigurable steering feel for steer-by-wire system based on dynamic load observation,” in 2023 7th CAA International Conference on Vehicular Control and Intelligence (CVCI), Changsha, China, 2023, pp. 1-7.
[13] I. Chung, S. Oh, and K. Nam, “Synchronous control of a dual-motor driving rack and pinion module for steer-by-wire system,” IEEE Access, vol. 12, pp. 195358-195369, 2024.
[14] C. Su, H. Li, B. Qiao, et al., “Personalized steering feel design for steer-by-wire systems based on the rack force estimation,” International Journal of Automotive Technology, vol. 24, pp. 1151–1161, 2023.
[15] T. Chugh, F. Bruzelius, M. Klomp, and B. Jacobson, “Steering feedback transparency using rack force observer,” IEEE/ASME Transactions on Mechatronics, vol. 27, no. 5, pp. 3853-3864, 2022.
[16] L. Zhao, X. Zhao, and H. Li, “Rack force fault tolerance estimation of steer-by-wire system under different resolver faults based on sensor flows,” Control Engineering Practice, vol. 147, no. 105941, 2024.
[17] A. Balachandran and J. C. Gerdes, “Designing steering feel for steer-by-wire vehicles using objective measures,” IEEE/ASME Transactions on Mechatronics, vol. 20, no. 1, pp. 373-383, 2015.
[18] Y. Liu, G. Zhang, J. Li, et al., “Steering feedback torque prediction based on sequence-to-sequence network with switcher-assisted training algorithm,” IEEE Transactions on Industrial Informatics, vol. 20, no. 3, pp. 4894-4905, 2024.
[19] K. T. R. Van Ende, D. Schaare, J. Kaste, F. Küçükay, R. Henze, and F. K. Kallmeyer, “Practicability study on the suitability of artificial, neural networks for the approximation of unknown steering torques: Vehicle system dynamics,” Vehicle System Dynamic, vol. 54, no. 10, pp. 1362–1383, 2016.
[20] R. Zhao, W. Deng, B. Ren, and J. Ding, “Modeling on steering feedback torque based on data-driven method,” IEEE/ASME Transactions on Mechatronics, vol. 27, no. 5, pp. 2775-2785, 2022.
[21] S. Abbas, S. Husain, S. Al-Wais, and A. Humaidi, “Adaptive integral sliding mode controller (SMC) design for vehicle steer-by-wire system,” SAE International Journal of Vehicle Dynamic, Stability, and NVH, vol. 8, no. 3, pp. 383-396, 2024.
[22] J. Lee, K. Yi, D. Lee, B. Jang, M. Kim, and S. Hwang, “Haptic control of steer-by-wire systems for tracking of target steering feedback torque,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, vol. 23, no. 5, pp. 1389–1401, 2020.
[23] Y. Liu, X. Wang, G. Zhang, Q. Yuan, Z. Chen, and L. Li, “Road sense construction for steer-by-wire system: data-driven feedback torque design and friction compensated explicit model predictive control,” IEEE Transactions on Transportation Electrification, vol. 10, no. 4, pp. 9918-9930, 2024.
[24] S.-W. Oh, H.-C. Chae, S.-C. Yun, and C.-S. Han, “The design of a controller for the steer-by-wire system,” JSME International Journal Series C Mechanical Systems, Machine Elements and Manufacturing, vol. 47, no. 3, pp. 896–907, 2004.
[25] S. Fankem and S. Müller, “A new model to compute the desired steering torque for steer-by-wire vehicles and driving simulators,” Vehicle System Dynamic, vol. 52, no. 1, pp. 251–271, 2014.
[26] S. Achyuthan and N. K. Prakash, “Modelling of a steer-by-wire system with force feedback and active steering,” in 2017 International Conference on Intelligent Computing and Control Systems (ICICCS), Madurai, India. 2017. pp. 676-680.
[27] J. Wang, H. Wang, C. Jiang, Z. Cao, Z. Man, and L. Chen, “Steering feel design for steer-by-wire system on electric vehicles,” in 2019 Chinese Control Conference (CCC), Guangzhou, China, 2019, pp. 533-538.
[28] G. Zhu, H. Yang, and F. Yu, “Controller design for an automobile steer-by-wire system,” in 2019 IEEE 28th International Symposium on Industrial Electronics (ISIE), Vancouver, BC, Canada. 2019. pp. 1492-1497.
[29] D. Cheon, C. Lee, S. Oh, and K. Nam, “Description of steering feel in steer-by-wire system using series elastic actuator,” in 2019 IEEE Vehicle Power and Propulsion Conference (VPPC), Hanoi, Vietnam, 2019, pp. 1-4.
[30] M. Damian, B. Shyrokau, X. Carrera Akutain, and R. Happee, “Experimental validation of torque-based control for realistic handwheel haptics in driving simulators,” IEEE Transactions on Vehicular Technology, vol. 71, no. 1, pp. 196-209, 2021.
[31] J. Jayachandran and D. Ashok, “Neural network-based approach for the generation of road feel in a steer-by-wire system,” Engineering Journal, vol. 20, no. 5, pp. 49–66, 2016.
[32] J. Lee, S. Chang, K. Kim, et al., “Steering wheel torque control of steer-by-wire system for steering feel,” SAE Technical Paper 2017-01-1567, 2017.
[33] Z. Yang, G. Li, H. He, and G. Li, “Study on road feeling simulation control algorithm for four-wheel independent drive and steering electric vehicle,” in 2017 Chinese Automation Congress (CAC), Jinan, China. 2017, pp. 4872-4875.
[34] R. A. Nikhil, S. Muhammed, and K. Nafeesa, “A new control strategy for improving steering feel of an EPAS system,” in 2020 International Conference on Futuristic Technologies in Control Systems & Renewable Energy (ICFCR). Malappuram, India. 2020, pp. 1-6.
[35] Liuhe, X. Zeng, and L. Shuo, “Design of road feel feedback algorithm for steer-by-wire,” in 2020 4th CAA International Conference on Vehicular Control and Intelligence (CVCI), Hangzhou, China, 2020, pp. 142-146.
[36] S. Woo, C. Heo, M.-O. Jeong, and J.-M. Lee, “Integral analysis of a vehicle and electric power steering logic for improving steering feel performance,” Applied Sciences, vol. 13, no. 20, pp. 11598. 2023.
[37] A. Alex and A. Saleem, “Artificial steering feel in steer by wire systems: a simulation-based evaluation of control strategies,” in 2024 1st International Conference on Trends in Engineering Systems and Technologies (ICTEST), Kochi, India, 2024, pp. 1-8.
[38] A. Alex and A. Saleem, “A lyapunov-based dual controller approach with PSO tuning for steer-by-wire systems with artificial steering feel,” IEEE Access, vol. 12, pp. 188976-188992, 2024.
[39] D. Fu, J. Feng, B. Wang, and Q. Liu, “Research on road sense simulation of steer-by-wire system,” in 2023 5th International Academic Exchange Conference on Science and Technology Innovation (IAECST), Guangzhou, China, 2023, pp. 851-854.
[40] G. Shi, T. Liu, S. Wang, C. Guo, and Y. Liu, “High authenticity steering feel control strategy for Steer-by-Wire system based on terminal sliding mode rack force observer,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, vol. 0, no. 0, 2024.
[41] H. Zhou, A. Pang, J. Yang, and Z. He, “Structured H∞ control of an electric power steering system,” Complexity, vol. 2020, no. 1, 2020.
[42] F. Heinrich, J. Kaste, S.G. Kabil, et al., “Methods for modeling the steering wheel torque of a steer-by-wire vehicle,” Automotive and Engine Technology, vol. 7, no. 1–2, pp. 53–64, 2022.
[43] S. C. Zou and W. Z. Zhao, “Synchronization and stability control of dual-motor intelligent steer-by-wire vehicle,” Mechanical Systems and Signal Processing, vol. 145, pp. 106925, 2020.
[44] J. Tian, G. Tan, X. Pan, M. Cai, C. Huang, and Y. Yan, “Research on road sense simulation and stability control of SBW system,” in 2021 China Automation Congress (CAC) 2021, Beijing, China, 2021, pp. 4065–4070.
[45] H. Hwang, H. Choi, and K. Nam, “Practical synchronous steering angle control of a dual-motor driving steer-by-wire system,” IEEE Access, vol. 7, pp. 133100–133110, 2019.
[46] L. De Novellis, A. Sorniotti, P. Gruber, and A. Pennycott, “Comparison of feedback control techniques for torque-vectoring control of fully electric vehicles,” IEEE Transactions on Vehicular Technology, vol. 63, no. 8, pp. 3612–3623, 2014.
[47] S. S. Husain, M. Q. Kadhim, A. S. M. Al-Obaidi, A. F. Hasan, A. J. Humaidi, and D. N. Al Husaeni, “Design of robust control for vehicle steer-by-wire system,” Indonesian Journal of Science and Technology, vol. 8, no. 2, pp. 197–216, 2023.
[48] D. Cheon, K. Nam, and S. Oh, “Design and robust control of a precise torque controllable steering module for steer-by-wire systems,” IEEE Transactions on Industrial Electronics, vol. 69, no. 12, pp. 13245–13254, 2022.
[49] R. P. Borase, D. K. Maghade, S. Y. Sondkar, et al., “A review of PID control, tuning methods and applications,” International Journal of Dynamic Control, vol. 9, pp. 818–827, 2021.
[50] S. B. Joseph, E. G. Dada, A. Abidemi, D. O. Oyewola, and B. M. Khammas, “Metaheuristic algorithms for PID controller parameters tuning: review, approaches and open problems,” Heliyon, vol. 8, no. 5, p. e09399, 2022.
[51] H. Khodadadi and H. Ghadiri, “Self-tuning PID controller design using fuzzy logic for half car active suspension system,” International Journal of Dynamic and Control, vol. 6, pp. 224–232, 2018.
[52] B. Kristiansson and B. Lennartson, “Robust and optimal tuning of PI and PID controllers,” IEE Proceedings Control Theory Application, vol. 149, no. 1, pp. 17–25, 2002.
[53] K. Ranjbaran and M. Tabatabaei, “Fractional order [PI], [PD] and [PI][PD] controller design using Bode’s integrals,” International Journal of Dynamics and Control, vol. 6, no. 1, pp. 200–212, 2018.
[54] M. R. Bongulwar and B. M. Patre, “Design of FOPID controller for fractional-order plants with experimental verification,” International Journal of Dynamics and Control, vol. 6, no. 1, pp. 213–223, 2018.
[55] M. Lazar and W. Heemels, “Predictive control of hybrid systems: input-to-state stability results for sub-optimal solutions,” Automatica, vol. 45, pp. 180–185, 2009.
[56] A. Cruz-Bernal, “Meta-heuristic optimization techniques and its applications in robotics,” Recent Advances on Meta-Heuristics and Their Application to Real Scenarios, InTech, p. 53, 2013.
[57] J. Annisa, I. Z. M. Darus, M. O. Tokhi, and S. Mohamaddan, “Implementation of PID based controller tuned by evolutionary algorithm for double link flexible robotic manipulator,” in 2018 International Conference on Computational Approach in Smart Systems Design and Applications (ICASSDA), Sarawak, Malaysia, 2018, pp. 1–5.
[58] M. A. Şen and M. Kalyoncu, “Optimal tuning of PID controller using Grey Wolf Optimizer algorithm for quadruped robot,” Balkan Journal of Electrical and Computer Engineering, vol. 6, no. 1, pp. 29–35, 2018.
[59] D. Sandoval, I. Soto, and P. Adasme, “Control of direct current motor using ant colony optimization,” in 2015 CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies (CHILECON), Santiago, Chile, 2015, pp. 79–82.
[60] M. A. Azizul, F. Ahmad, J. Karjanto, M. H. Che Hasan, and S. Sulaiman, “Modelling, simulation and testing of steer-by-wire system with variable steering ratio control strategy in 14-DOF full vehicle model,” International Journal of Automotive and Mechanical Engineering, vol. 21, no. 4, pp. 11784-11808, 2024.
[61] Y. Shengbing, D. Chunan, J. Xuewu, and C. Kuiyuan, “Research on road feeling control strategy of steer-by-wire,” SAE Technical Paper, no. 2007-01-3652, 2007.
[62] H. Zheng, C. Zong, and L. Yu, “Road feel feedback design for vehicle steer-by-wire via electric power steering,” SAE Technical Paper, no. 2013-01-2898, 2013.
[63] W. Liang, W. Zhao, C. Wang, and S. Zou, “Harmonic suppression and road feeling control of steer-by-wire system with permanent magnet synchronous motor,” Mechanical Systems and Signal Processing, vol. 172, no. 108983, 2022.
[64] A. Kirli and M. S. Arslan, “Online optimized hysteresis-based steering feel model for steer-by-wire systems,” Advances in Mechanical Engineering, vol. 8, no. 7, 2016.
[65] N. Bajçinca, R. Cortesão, and M. Hauschild, “Robust control for steer-by-wire vehicles,” Autonomous Robot, vol. 19, pp. 193–214, 2005.
[66] H. Wang, H. Kong, Z. Man, D. M. Tuan, Z. Cao, and W. Shen, “Sliding mode control for steer-by-wire systems with AC motors in road vehicles,” IEEE Transactions on Industrial Electronics, vol. 61, no. 3, pp. 1596-1611, 2014.
[67] Z. Sun, J. Zheng, Z. Man, and H. Wang, “Robust control of a vehicle steer-by-wire system using adaptive sliding mode,” IEEE Transactions on Industrial Electronics, vol. 63, no. 4, pp. 2251-2262, 2016.
[68] D. Lee, K.-s. Kim and M. Han, “Model-based analysis of the hysteresis curve of an electric power steering system,” in 2020 20th International Conference on Control, Automation and Systems (ICCAS), Busan, Korea (South), 2020, pp. 490-495.
[69] M. Selçuk Arslan, “A hysteresis-based steering feel model for steer-by-wire systems,” Mathematical Problems in Engineering, vol. 2017, no. 2313529, 2017.
[70] M. Irmer, R. Degen, A. Nüßgen, K. Thomas, H. Henrichfreise, and M. Ruschitzka, “Development and analysis of a detail model for steer-by-wire systems,” IEEE Access, vol. 11, pp. 7229-7236, 2023.
[71] A. Verl and T. Engelberth, “Adaptive preloading for rack-and-pinion drive systems,” CIRP Annals, vol. 67, no. 1, pp. 369–372, 2018.
[72] D. E. Williams, “Synthetic torque feedback to improve heavy vehicle drivability,” Proc. Inst. Mech. Eng., Part D: J. Automobile Eng., vol. 223, no. 12, pp. 1517–1527, 2009.
[73] D. Williams and K. Sherwin, “Artificial steering feel,” SAE International Journal of Passenger Cars – Mechanical System, vol. 2, no. 1, pp. 229–238, 2009.
[74] Y. Jiang, W. Deng, S. Zhang, et al., “Studies on influencing factors of driver steering torque feedback,” SAE Technical Paper 2015-01-1498, 2015.
[75] I. Kushiro and K. Suzuki, “Analysis for vehicle dynamics and steering system parameters effect on steering characteristics of steering feel (Fundamental study for performance design of objective target on steering feel),” Transition JSME, vol. 83, 2017.
[76] B.-H. Nguyen and J.-H. Ryu, “Direct current measurement-based steer-by-wire systems for realistic driving feeling,” in 2009 IEEE International Symposium on Industrial Electronics, Seoul, Korea (South), 2009, pp. 1023-1028.
[77] T. Dogruer and N. Tan, “Design of PI controller using optimization method in fractional order control systems,” IFAC-PapersOnLine, vol. 51, no. 4, pp. 841–846, 2018.
[78] O. A. Somefun, K. Akingbade, and F. Dahunsi, “The dilemma of PID tuning,” Annual Reviews in Control, vol. 52, pp. 65-74, 2021.
[79] A. R. Kumar and P. J. Ramadge, “DiffLoop: Tuning PID controllers by differentiating through the feedback loop,” in 2021 55th Annual Conference on Information Sciences and Systems (CISS), Baltimore, MD, USA, 2021, pp. 1-6.
[80] D. W. Clarke, “Pretuning and adaptation of PI controllers,” IEE Proceedings - Control Theory and Applications, vol. 150, no. 6, 2003.
[81] J. -W. Jung, V. Q. Leu, T. D. Do, E.-K. Kim and H. H. Choi, “Adaptive PID speed control design for permanent magnet synchronous motor drives,” IEEE Transactions on Power Electronics, vol. 30, no. 2, pp. 900-908, 2015.
[82] J. Viola, L. Angel and J. M. Sebastian, “Design and robust performance evaluation of a fractional order PID controller applied to a DC motor,” IEEE/CAA Journal of Automatica Sinica, vol. 4, no. 2, pp. 304-314, 2017.
[83] J. Qiao, Z. Liu, and Y. Zhang, “Gain scheduling based PID control approaches for path tracking and fault tolerant control of a quad-rotor UAV,” International Journal of Mechanical Engineering and Robotics Research, vol. 7, no. 4, pp. 401–408, 2018.
[84] L. He, F. Li, C. Guo, B. Gao, J. Lu, and Q. Shi, “An adaptive PI controller by particle swarm optimization for angle tracking of steer-by-wire,” IEEE/ASME Transactions on Mechatronics, vol. 27, no. 5, pp. 3830-3840, 2022.
[85] H. Choi and S. Choi, “Design of the steering feedback controller of a steer-by-wire system using admittance model,” International Journal of Automotive Technology, vol. 25, pp. 565–574, 2024.
[86] H. Zhang, W. Jiang, W. Zhao, et al., “Tracking and fault-tolerant controller design for uncertain steer-by-wire systems using model predictive control,” Chinese Journal of Mechanical Engineering, vol. 37, p. 141, 2024.
[87] Y. Han, L. He, X. Wang, and C. Zong, “Research on torque ratio based on the steering wheel torque characteristic for steer-by-wire system,” Journal of Applied Mathematics, vol. 2014, no. 929164, 2014.
[88] D. Karimi and D. Mann, “Torque feedback on the steering wheel of agricultural vehicles,” Computers and Electronics in Agriculture, vol. 65, no. 1, pp. 77-84, 2009.
[89] R. C. Chabaan, “Torque estimation in electrical power steering systems,” in 2009 IEEE Vehicle Power and Propulsion Conference, Dearborn, MI, USA, 2009, pp. 790-797.
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