Optimal Control Design of Active Suspension System Based on Quarter Car Model
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Abstract
The optimal control design of the ground-vehicle active suspension system is presented. The active suspension system is to improve the vehicle ride comfort by isolating vibrations induced by the road profile and vehicle velocity. The vehicle suspension system is approached by a quarter car model. Dynamic equations of the system are derived by applying Newton’s second law. The control law of the active suspension system is designed using linear quadratic regulator (LQR) method. Performance evaluation is done by benchmarking the active suspension system to a passive suspension system. Both suspension systems are simulated in computer. The simulation results show that the active suspension system significantly improves the vehicle ride comfort of the passive suspension system by reducing 50.37% RMS of vertical displacement, 45.29% RMS of vertical velocity, and 1.77% RMS of vertical acceleration.
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[1]
N. Uddin, “Optimal Control Design of Active Suspension System Based on Quarter Car Model”, INFOTEL, vol. 11, no. 2, pp. 55-61, Jun. 2019.
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References
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[2] Y. Mohammadi and S. Ganjefar, “Quarter car active suspension system: Minimum time controller design using singular perturbation method,” International Journal of Control, Automation, and Systems, vol. 15, no. 6, pp. 2538–2550, 2017.
[3] H. E. Tseng and D. Hrovat, “State of the art survey: active and semi-active suspension control,” Vehicle System Dynamics, vol. 53, no. 7, pp. 1034–1062, 2015.
[4] A. A. Aly and F. A. Salem, “Vehicle suspension systems control: a review,” International Journal of Control, Automation and Systems, vol. 2, no. 2, pp. 46–54, 2013.
[5] H. Elahi, A. Israr, M. Z. Khan, and S. Ahmad, “Robust vehicle suspension system by converting active and passive control of a vehicle to semi-active control system analytically,” Journal of Automation and Control Engineering, vol. 4, no. 4, 2016.
[6] M. M. ElMadany and Z. S. Abduljabbar, “Linear quadratic Gaussian control of a quarter-car suspen-sion,” Vehicle System Dynamics, vol. 32, no. 6, pp. 479–497, 1999.
[7] I. Youn, R. Tchamna, S. Lee, N. Uddin, S. Lyu, and M. Tomizuka, “Preview suspension control for a full tracked vehicle,” International Journal of Automotive Technology, vol. 15, no. 3, pp. 399–410, 2014.
[8] S. Bououden, M. Chadli, and H. R. Karimi, “A robust predictive control design for nonlinear active suspension systems,” Asian Journal of Control, vol. 18, no. 1, pp. 122–132, 2016.
[9] S.A. Chen, J.C. Wang, M. Yao, and Y.B. Kim, “Improved optimal sliding mode control for a non-linear vehicle active suspension system,” Journal of Sound and Vibration, vol. 395, pp. 1–25, 2017.
[10] D. Ning, S. Sun, H. Li, H. Du, and W. Li, “Active control of an innovative seat suspension system with acceleration measurement based friction estimation,” Journal of Sound and Vibration, vol. 384, pp. 28–44, 2016.
[11] C. Gohrle, A. Schindler, A. Wagner, and O. Sawodny, “Design and vehicle implementation of preview active suspension controllers,” IEEE Transactions on Control Systems Technology, vol. 22, no. 3, pp. 1135–1142, 2014.
[12] G. Wang, C. Chen, and S. Yu, “Robust non-fragile finite-frequency Static output-feedback control for active suspension systems,” Mechanical Systems and Signal Processing, vol. 91, pp. 41–56, 2017.
[13] M. Omar, M. El-Kassaby, and W. Abdelghaffar, “A universal suspension test rig for electro hydraulic active and passive automotive suspension system,” Alexandria Engineering Journal, vol. 56, no. 4, pp. 359–370, 2017.
[14] L. Xiao and Y. Zhu, “Sliding-mode output feedback control for active suspension with nonlinear actuator dynamics,” Journal of Vibration and Control, vol. 21, no. 14, pp. 2721–2738, 2015.
[15] B. Erol and A. Delibasi, “Proportional–integral–derivative type controller for quarter car active suspension system,” Journal of Vibration and Control, vol. 24, no. 10, pp. 1951–1966, 2018.
[16] R. S. Prabakar, C. Sujatha, and S. Narayanan, “Response of a half-car model with optimal magneto rheological damper parameters,” Journal of Vibration and Control, vol. 22, no. 3, pp. 784–798, 2016.
[17] M. Assahubulkahfi, Y. M. Sam, A. Maseleno, and M. Huda, “LQR tuning by particle swarm optimization of full car suspension system,” International Journal of Engineering & Technology (UAE), vol. 7, no.2.13, pp. 328–331, 2018.
[18] Y. Z. Yin, Z. L. Yang, Z. X. Yin, and F. Xu, “Optimal control of LQR for discrete time-varying systems with input delays,” International Journal of Systems Science, vol. 49, no. 5, pp. 1021–1031, 2018.
[19] V. Satyanarayana, B. Sateesh, and N. M. Rao, “Parameters optimization of vehicle suspension system for better ride comfort,” International Journal of Vehicle Performance, vol. 4, no. 2, pp. 186–199,2018.
[20] S. A. Chen, Y. M. Cai, J. Wang, and M. Yao, “A novel LQG controller of active suspension system for vehicle roll safety,” International Journal of Control, Automation and Systems, vol. 16, no. 5, pp. 2203–2213, 2018.
[21] H. Pang, Y. Chen, J. Chen, and X. Liu, “Design of LQG controller for active suspension without considering road input signals,” Shock and Vibration, vol. 2017, 2017.
[22] Q. Zhu, J. J. Ding, and M. L. Yang, “LQG control based lateral active secondary and primary suspensions of high-speed train for ride quality and hunting stability,” IET Control Theory & Applications, vol. 12, no. 10, pp. 1497–1504, 2018.
[23] C. Gohrle, A. Schindler, A. Wagner, and O. Sawodny, “Road profile estimation and preview control for low-bandwidth active suspension systems,” IEEE/ ASME Transactions on Mechatronics, vol. 20, no. 5, pp. 2299–2310, 2015.
[24] Y. M. Sam, J. H. Osman, and M. R. A. Ghani, “A class of proportional-integral sliding mode control with application to active suspension system,” Systems & Control Letters, vol. 51, no. 3-4, pp. 217–223, 2004.
[25] K. Ogata, Modern control engineering. Prentice Hall Upper Saddle River, NJ, 2009.
[26] P. N. Paraskevopoulos, Modern control engineering. CRC Press, 2017.
[27] A. E. Bryson, Applied optimal control: optimization, estimation, and control. Routledge, 2018.
[28] S. S. Rao, Mechanical Vibrations 5th Ed. Pearson, New Jersey, 2011