Road-Adaptive Fuzzy-LQR Control for a Quarter-Car Active Suspension System
Corresponding author: Thi Thanh Hoa Lai
Abstract
This study presents an Adaptive Fuzzy–Linear Quadratic Regulator (AF–LQR) controller for a quarter active suspension of a vehicle operating under both stochastic road excitation and ISO 8608. The proposed method integrates a conventional LQR feedback structure with a bounded gain adaptation mechanism to adjust the control intensity according to the suspension deflection and body acceleration levels. Road turbulence was modeled using the ISO 8608 Power Spectral Density (PSD) to reflect the actual driving conditions. The simulation results show that the proposed controller significantly reduces the RMS body acceleration compared with the passive suspension and improves vibration attenuation compared with the classic LQR, while keeping the suspension deflection within safe limits. Compared with the H∞ control, the AF–LQR achieved a more balanced compromise between driving comfort and actuator force requirement, avoiding overly aggressive control actions. Robustness analysis under ±20% parameter variations confirmed stable and consistent performance. The results prove that the AF–LQR is an efficient and computationally lightweight solution for active suspension under real road conditions.
Keywords:
active suspension, adaptive fuzzy control, LQR, H∞ control, ISO 8608, quarter-car modelReferences
K. Arunachalam, P. Jawahar, and P. Tamilporai, "Active Suspension System with Preview Control - A Review," SAE Technical Paper 2003-28-0037.
J. Cao, H. Liu, P. Li and D. J. Brown, " State of the Art in Vehicle Active Suspension Adaptive Control Systems Based on Intelligent Methodologies," IEEE Transactions on Intelligent Transportation Systems, vol. 9, no. 3, pp. 392-405, Sep. 2008.
I. Jiregna and G. Sirata, "A Review of the Vehicle Suspension System," Journal of Mechanical and Energy Engineering, vol. 4, no. 2, pp. 109-114, Jun. 2020.
F. Rana, "Types and application of advance suspension system," International Journal of Automobile Engineering, vol. 5, no. 2, pp. 01-07, Jul. 2024.
A. A. Ferhath and K. Kamalakkannan, "A Review on Various Control Strategies and Algorithms in Vehicle Suspension Systems," International Journal of Automotive and Mechanical Engineering, vol. 20, no. 3, pp. 10720-10735, Oct. 2023.
J. Theunissen, A. T. P. Gruber, M. Dhaens and A. Sorniotti, "Preview-based techniques for vehicle suspension control: a state-of-the-art review," Annual Reviews in Control, vol. 51, pp. 206-235, Jan. 2021.
S. Rozali, M. N. Kamarudin, S. M. Saleh and A. C. Amran, "Linear Quadratic Regulator Design for Vehicle Suspension System," ARPN Journal of Engineering and Applied Sciences, vol. 17, no. 1, Jan. 2022.
K. D. Dandavate and P. R. Kale, "A Review on Controlling Methods for Active Suspension Systems," International Journal for Research in Applied Science and Engineering Technology, vol. 11, no. 11, pp. 1675-1680, Nov. 2023.
W. A. Ashtari, "Enhancing the Performance of Active Suspension Systems Through Adaptive Control," European Journal of Automated Systems, vol. 57, no. 3, pp. 887-897, Jun. 2024.
F. Zhao, S. S. Ge, F. Tu, Y. Qin and M. Dong, "Adaptive neural network control for active suspension system with actuator saturation" IET Control Theory and Applications, vol. 10, no. 14, pp. 1696-1705, Sep. 2016.
S. Chantranuwathana and H. Peng "Adaptive Robust Control for Active Suspension," Proceedings of the American Control Conference, San Diego, CA, USA, Jun. 1999, pp. 1702-1706.
D. Karnopp, "Active damping in road vehicle suspension systems," Vehicle System Dynamics, vol. 12, no. 6, pp. 291-311, Jul. 2007.
G. Li et al., "Research on LPV-H∞ control strategy of magnetorheological semi-active suspension with air spring," Scientific Reports, vol. 15, no. 1, 2025, Art. no. 39206.
K. Yeneneh, M. Walle, T. Mamo and Y. Yalew, "Optimizing active suspension systems with robust h∞ control and adaptive techniques under uncertainties," Applications in Engineering Science, vol. 22, Jun. 2025, Art. no. 100225.
D. Savaresi, F. Favalli, S. Formentin and S. M. Savaresi, "On-line Damping Estimation in Road Vehicle Semi-active Suspension Systems," IFAC PapersOnLine, vol. 52, no. 5, pp. 679-684, Jan. 2019.
Z. Yang, C. Yong, Z. Li and Y. Kangsheng, "Simulation analysis and optimization of ride quality of in-wheel motor electric vehicle," Advances in Mechanical Engineering, vol. 10, no. 5 pp. 01-10, 2018.
L. Zhang , S. Zhang and W. Zhang, "Multi-objective optimization design of in-wheel motors drive electric vehicle suspensions for improving handling stability," Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering, vol. 233, no. 8, pp. 2232-2245, Jun. 2018.
D. T. Tu, "Enhancing Road Holding and Vehicle Comfort for an Active Suspension System Utilizing Model Predictive Control and Deep Learning," Engineering, Technology & Applied Science Research, vol. 14, no. 1, pp. 12931-12936, Feb. 2024.
P. Múčka, "Simulated Road Profiles According to ISO 8608 in Vibration Analysis," Journal of Testing and Evaluation, vol. 46, no. 1, pp. 90-3973, Jan. 2018.
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