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Performance Analysis of Position Estimation in a Quarter-Car Suspension System Using Kalman-Bucy as a State Observer
Corresponding Author(s) : Dian Mursyitah
Kinetik: Game Technology, Information System, Computer Network, Computing, Electronics, and Control,
Vol. 11, No. 1, February 2026
Abstract
This study explores the implementation of the Kalman-Bucy observer for state estimation in a quarter-car suspension system operating under various real-world conditions. The research focuses on evaluating the observer’s performance in the presence of road surface disturbances, such as speed bumps, humps, and potholes, combined with stochastic noise and parameter variations. To test its robustness, the system is subjected to Gaussian white noise with an intensity of 10% in both the process and measurement signals. A sensitivity analysis is also carried out by varying the vehicle mass between 400 kilograms under unloaded conditions and 600 kilograms when fully loaded, thereby simulating different passenger and cargo scenarios. Simulation results demonstrate that the Kalman-Bucy observer consistently provides accurate and stable estimations of vehicle position, even in noisy and dynamically changing environments. The observer achieves a Root Mean Square Error (RMSE) of 3.3885 × 10⁻⁵ m, indicating near-perfect estimation accuracy. When integrated into a PID control framework, the proposed observer significantly improves system performance by reducing rise time from 9.76 s to 0.16 s, decreasing undershoot from −0.22 m to −0.15 m, and maintaining a similar settling time of approximately 25 s. Overall, the Kalman-Bucy observer proves to be a reliable and efficient method for state estimation and control enhancement in active suspension systems, showing strong potential for real-world automotive applications.
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- J. Masri, M. Amer, S. Salman, M. Ismail, and M. Elsisi, "A survey of modern vehicle noise, vibration, and harshness: A state-of-the-art," Ain Shams Engineering Journal, p. 102957, 2024.https://doi.org/10.1016/j.asej.2024.102957
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- M. Ö. Yatak, Ç. Hisar, and F. Şahin, "Fuzzy Logic Controller for Half Vehicle Active Suspension System: An Assessment on Ride Comfort and Road Holding," International Journal of Automotive Science And Technology, vol. 8, no. 2, pp. 179-187, 2024.https://doi.org/10.30939/ijastech..1372001
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- P. Bernard, V. Andrieu, and D. Astolfi, "Observer design for continuous-time dynamical systems," Annual Reviews in Control, vol. 53, pp. 224-248, 2022.https://doi.org/10.1016/j.arcontrol.2021.11.002
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- S. Sunarso, M. P. Bilyastuti, and E. Andayani, "Evaluasi kebijakan larangan pemasangan polisi tidur (Speed bump dan speed hump) di Kabupaten Ponorogo," JIIP-Jurnal Ilmiah Ilmu Pendidikan, vol. 5, no. 12, pp. 5626-5631, 2022.https://doi.org/10.54371/jiip.v5i12.1201
- A. N. Bishop and P. Del Moral, "On the mathematical theory of ensemble (linear-Gaussian) Kalman–Bucy filtering," Mathematics of Control, Signals, and Systems, vol. 35, no. 4, pp. 835-903, 2023.https://doi.org/10.1007/s00498-023-00357-2
- S. W. Ertel and W. Stannat, "Analysis of the ensemble Kalman–Bucy filter for correlated observation noise," The Annals of Applied Probability, vol. 34, no. 1B, pp. 1072-1107, 2024.https://doi.org/10.1214/23-AAP1985
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References
J. Masri, M. Amer, S. Salman, M. Ismail, and M. Elsisi, "A survey of modern vehicle noise, vibration, and harshness: A state-of-the-art," Ain Shams Engineering Journal, p. 102957, 2024.https://doi.org/10.1016/j.asej.2024.102957
S. Yan, C. Liu, and J. Cao, "Comfort-based trajectory and velocity planning for automated vehicles considering road conditions," International journal of automotive technology, vol. 22, pp. 883-893, 2021.https://doi.org/10.1007/s12239-021-0080-9
A. Soliman and M. Kaldas, "Semi-active suspension systems from research to mass-market–A review," Journal of Low Frequency Noise, Vibration and Active Control, vol. 40, no. 2, pp. 1005-1023, 2021.https://doi.org/10.1177/1461348419876392
R. Desai, A. Guha, and P. Seshu, "A comparison of different models of passive seat suspensions," Proceedings of the institution of mechanical engineers, Part D: journal of automobile engineering, vol. 235, no. 9, pp. 2585-2604, 2021.https://doi.org/10.1177/0954407021990922
Z. Boulaaras, A. Aouiche, and K. Chafaa, "Intelligent FOPID and LQR Control for Adaptive a Quarter Vehicle Suspension System," European Journal of Electrical Engineering, vol. 25, no. 1-6, p. 1, 2023.https://doi.org/10.18280/ejee.251-601
B. Erol and A. Delibaşı, "Proportional–integral–derivative type H∞ controller for quarter car active suspension system," Journal of Vibration and Control, vol. 24, no. 10, pp. 1951-1966, 2018.https://doi.org/10.1177/1077546316672974
V. Provatas and D. Ipsakis, "Design and simulation of a feedback controller for an active suspension system: a simplified approach," Processes, vol. 11, no. 9, p. 2715, 2023.https://doi.org/10.3390/pr11092715
D. N. Nguyen and T. A. Nguyen, "A Novel Hybrid Control Algorithm Sliding Mode‐PID for the Active Suspension System with State Multivariable," Complexity, vol. 2022, no. 1, p. 9527384, 2022.https://doi.org/10.1155/2022/9527384
T. A. Nguyen, "Applying a PID-SMC synthetic control algorithm to the active suspension system to ensure road holding and ride comfort," Plos one, vol. 18, no. 10, p. e0283905, 2023.https://doi.org/10.1371/journal.pone.0283905
V. Dushchenko et al., "Increasing the damping properties of the magnetorheological actuator of the vehicle suspension control system," Electr Eng Electromechanics, vol. 5, pp. 77-86, 2024.https://doi.org/10.20998/2074-272X.2024.5.11
M. Nagarkar, Y. Bhalerao, D. Bhaskar, A. Thakur, V. Hase, and R. Zaware, "Design of passive suspension system to mimic fuzzy logic control active suspension system," Beni-Suef University Journal of Basic and Applied Sciences, vol. 11, no. 1, p. 109, 2022.https://doi.org/10.1186/s43088-022-00291-3
S. Kumar, A. Medhavi, R. Kumar, and P. Mall, "Modeling and analysis of active full vehicle suspension model optimized using the advanced fuzzy logic controller," Int. J. Acoust. Vib, vol. 27, pp. 26-36, 2022.
M. Ö. Yatak, Ç. Hisar, and F. Şahin, "Fuzzy Logic Controller for Half Vehicle Active Suspension System: An Assessment on Ride Comfort and Road Holding," International Journal of Automotive Science And Technology, vol. 8, no. 2, pp. 179-187, 2024.https://doi.org/10.30939/ijastech..1372001
R. Bai and H.-B. Wang, "Robust optimal control for the vehicle suspension system with uncertainties," IEEE transactions on cybernetics, vol. 52, no. 9, pp. 9263-9273, 2021.https://doi.org/10.1109/TCYB.2021.3052816
T. A. Nguyen, "Research on the Sliding Mode–PID control algorithm tuned by fuzzy method for vehicle active suspension," Forces in Mechanics, vol. 11, p. 100206, 2023.https://doi.org/10.1016/j.finmec.2023.100206
E. Balestrieri, P. Daponte, L. De Vito, and F. Lamonaca, "Sensors and measurements for unmanned systems: An overview," Sensors, vol. 21, no. 4, p. 1518, 2021.https://doi.org/10.3390/s21041518
Y. Wang, X. Zhang, K. Li, G. Zhao, and Z. Chen, "Perspectives and challenges for future lithium-ion battery control and management," 2023.https://doi.org/10.1016/j.etran.2023.100260
P. Bernard, V. Andrieu, and D. Astolfi, "Observer design for continuous-time dynamical systems," Annual Reviews in Control, vol. 53, pp. 224-248, 2022.https://doi.org/10.1016/j.arcontrol.2021.11.002
P. Bernard, Observer Design for Nonlinear Systems. Springer International Publishing, 2019.
E. Listijorini, S. Susilo, S. Ula, R. R. Ananda, and H. Haryadi, "Modeling and Dynamic Analysis of Vehincle Suspension Based on State Space Variable " TiMER: Trends in Mechanical Engineering Research, vol. 1, no. 2, pp. 66-70, 2023.https://dx.doi.org/10.62870/timer.v1i2.25765
S. Sunarso, M. P. Bilyastuti, and E. Andayani, "Evaluasi kebijakan larangan pemasangan polisi tidur (Speed bump dan speed hump) di Kabupaten Ponorogo," JIIP-Jurnal Ilmiah Ilmu Pendidikan, vol. 5, no. 12, pp. 5626-5631, 2022.https://doi.org/10.54371/jiip.v5i12.1201
A. N. Bishop and P. Del Moral, "On the mathematical theory of ensemble (linear-Gaussian) Kalman–Bucy filtering," Mathematics of Control, Signals, and Systems, vol. 35, no. 4, pp. 835-903, 2023.https://doi.org/10.1007/s00498-023-00357-2
S. W. Ertel and W. Stannat, "Analysis of the ensemble Kalman–Bucy filter for correlated observation noise," The Annals of Applied Probability, vol. 34, no. 1B, pp. 1072-1107, 2024.https://doi.org/10.1214/23-AAP1985
G. Mohanapriya, S. Muthukumar, S. Santhosh Kumar, and M. Shanmugapriya, "Kalman bucy filtered neuro fuzzy image denoising for medical image processing," Neutrosophic Sets and Systems, vol. 70, pp. 314-330, 2024.
M. S. Mahmood, "A Study of a Quarter-Car Active Suspension System Adaptable to Road Conditions," University of Basrah, 2023.