Control of active suspension system in the presence of nonlinear spring and damper

Document Type : Article

Author

Department of Mechanical Engineering, Faculty of Engineering, Gazi University, 06570 Maltepe, Ankara, Turkey

Abstract

Two methods which are computationally simple and easy to apply are developed by using state dependent Riccati equation (SDRE) approach and approximating sequence of Riccati equation (ASRE) approach to control active suspension system in the presence of nonlinear spring and damper. Additionally, effectivenesses of the both control methods developed by utilizing two recently introduced SDRE and ASRE techniques are compared. First, methodologies of both approaches are presented. After that, nonlinear dynamics of the vehicle suspension system is described in terms of conveniently selected state variables for better control performance. Then, a cost function is written by using suspension and tire deflections, sprung mass velocity and acceleration, and unsprung mass velocity variables to improve ride quality, suspension deflection, and tire deflection. Additionally, a convenient representation of this cost function in terms of state variables is obtained to realize better control. A bump expressed as sinusoidal function and roughness of the road expressed as white noise are taken into consideration as the disturbances from the road. Finally, quarter vehicle suspension system equivalent model of Ford Fiesta Mk2 is used as an example and simulations obtained by using the developed control methods are checked against the performance requirements and corresponding passive suspension system.

Keywords

References

References:
[1] Marzbanrad, J., Hojjat, Y., Zohoor, H. and Nikravesh, S.K. “Optimal preview control design of an active suspension based on a full car model”, Scientia Iranica, 10(1), pp. 23-36 (2003).
[2] Sayyaadi, H. and Shokouhi, N. “New dynamics model for rail vehicles and optimizing air suspension parameters using GA”, Scientia Iranica B, 16(6), pp. 496-512 (2009).
[3] Soleymani, M., Montazeri-Gh, M. and Amiryan, R. “Adaptive fuzzy controller for vehicle active suspension system based on traffic conditions”, Scientia Iranica B, 19(3), pp. 443-453 (2012).
[4] Fakhraei, J., Khanlo, H.M. and Ghayour, M. “Chaotic behaviors of a ground vehicle oscillating system with passengers”, Scientia Iranica B, 24(3), pp. 1051-1068 (2017).
[5] Dumitriu, M. “Numerical study of the influence of suspended equipment on ride comfort in high-speed railway vehicles”, Scientia Iranica B, 27(4), pp. 1897-1915 (2020).
[6] Rezazadeh, A. and Moradi, H. “Design of optimum vibration absorbers for a bus vehicle to suppress unwanted vibrations against harmonic and random road excitations”, Scientia Iranica B, 28(1), pp. 241-254 (2021).
[7] Malekshahi, A., Mirzaei, M., and Aghasizade, S. “Non-linear predictive control of multi-input multi-output vehicle suspension system”, Journal of Low Frequency Noise, Vibration and Active Control, 34(1), pp. 87-106 (2015).
[8] Liang, Y.-J., Li, N., Gao, D.-X. and Wang, Z.-S. “Optimal vibration control for nonlinear systems of tracked vehicle half-car suspensions”, International Journal of Control, Automation and Systems, 15(4), pp. 1675-1683 (2017).
[9] Abdalla, M.O., Al Shabatat, N., and Al Qaisi, M. “Linear matrix inequality based control of vehicle active suspension system”, Vehicle System Dynamics, 47(1), pp. 121-134 (2009).
[10] Pusadkar, U.S., Chaudhari, S.D., Shendge, P.D. and Phadke, S.B. “Linear disturbance observer based sliding mode control for active suspension systems with non-ideal actuator”, Journal of Sound and Vibration, 442, pp. 428-444 (2019).
[11] Deshpande, V.S., Mohan, B., Shendge, P.D. and Phadke, S.B. “Disturbance observer based sliding mode control of active suspension systems”, Journal of Sound and Vibration, 333, pp. 2281-2296 (2014).
[12] Wang, D., Zhao, D., Gong, M. and Yang, B. “Nonlinear predictive sliding mode control for active suspension system”, Shock and Vibration, 2018, pp. 1-10 (2018).
[13] Rath, J.J., Veluvolu, K.C. and Defoort, M. “Active control of nonlinear suspension system using modified adaptive supertwisting controller”, Discrete Dynamics in Nature and Society, 2015, pp. 1-10 (2015).
[14] Wang, H., Lu, Y., Tian, Y. and Christov, N. “Fuzzy sliding mode based active disturbance rejection control for active suspension system”, Proc IMechE Part D: J Automobile Engineering, 234(2-3), pp. 449-457 (2020).
[15] Rui, B “Nonlinear adaptive sliding-mode control of the electronically controlled air suspension system”, International Journal of Advanced Robotic Systems, 16(5), pp. 1-6 (2019).
[16] Zhang, Y., Liu, Y. and Liu, L. “Minimal learning parameters-based adaptive neural control for vehicle active suspensions with input saturation”, Neurocomputing, 396, pp. 153-161 (2020).
[17] Huang, Y., Na, J., Wu, X., Liu, X., and Guo, Y. “Adaptive control of nonlinear uncertain active suspension systems with prescribed performance”, ISA Transactions, 54, pp. 145-155 (2015).
[18] Zhu, Y. and Zhu, S. “Nonlinear time-delay suspension adaptive neural network active control”, Abstract and Applied Analysis, 2014, pp. 1-6 (2014).
[19] Pan, H. Sun, W. Jing, X. Gao, H. and Yao, J. “Adaptive tracking control for active suspension systems with non-ideal actuators”, Journal of Sound and Vibration, 399, pp. 2-20 (2017).
[20] H. Pang, X. Zhang, and Z. Xu, “Adaptive backstepping-based tracking control design for nonlinear active suspension system with parameter uncertainties and safety constraints”, ISA Transactions, 88, pp. 23-36 (2019).
[21] Na, J., Huang, Y., Wu, X., Gao, G., Herrmann, G. and Jiang, J.Z. “Active adaptive estimation and control for vehicle active suspensions with prescribed performance”, IEEE Transactions on Control Systems Technology, 26(6), pp. 2063-2077 (2018).
[22] Yao, J., Zhang, J.Q., Zhao, M.M. and Li, X. “Active control of a nonlinear suspension with output constraints and variable-adaptive-law control”, Journal of Vibroengineering, 20(7), pp. 2690-2704 (2018).
[23] Yao, J., Zhang, J.Q., Zhao, M.M. and Li, X. “Adaptive control of a nonlinear suspension with time delay compensation”, Journal of Vibroengineering, 21(3), pp. 684-695 (2019).
[24] Qin, W., Ge, P., Liu, F. and Long, S. “Adaptive robust control for active suspension systems: targeting nonholonomic reference trajectory and large mismatched uncertainty”, Nonlinear Dyn, 104, pp. 3861–3880 (2021).
[25] Qin, W., Liu, F., Yin, H. and Huang, J. “Constraint-based adaptive robust control for active suspension systems under sky-hook model”, IEEE Transactions on Industrial Electronics, published online (2021).
[26] Pan, H., Sun, W., Gao, H., Hayat, T. and Alsaadi, F. “Constrained robust adaptive control for vehicle active suspension systems”, Int. J. Vehicle Design, 68(1/2/3), pp. 5-21 (2015).
[27] Zhang, J., Ding, F., Zhang, B., Jiang, C., Du, H. and Li, B “An effective projection-based nonlinear adaptive control strategy for heavy vehicle suspension with hysteretic leaf spring”, Nonlinear Dyn, 100, pp. 451-473 (2020).
[28] Ding, F., Li, Q., Jiang, C., Han, X., Liu, J., Du, H. and Lei, F. “Event-triggered control for nonlinear leaf spring hydraulic actuator suspension system with valve predictive management”, Information Sciences, 551, pp. 184-204 (2021).
[29] Wu, Y., Li, B., Du, H., Zhang, N. and Zhang, B. “Fault-tolerant prescribed performance control of active suspension based on approximation-free method”, Vehicle System Dynamics, published online (2021).
[30] Lu, Y., Wang, H. and Tian, Y. “Active disturbance rejection control for active suspension system of nonlinear full car”, 2018 IEEE 7th Data Driven Control and Learning Systems Conference, Enshi, Hubei Province, China, pp. 724-729 (2018).
[31] Nourisola, H. and Ahmadi, B. “Robust adaptive Hinfinity controller based on GA-Wavelet-SVM for nonlinear vehicle suspension with time delay actuator”, Journal of Vibration and Control, 22(20), pp. 4111-4120 (2016).
[32] Zhang, M. and Jing, X. “Switching logic-based saturated tracking control for active suspension systems based on disturbance observer and bioinspired X-dynamics”, Mechanical Systems and Signal Processing, 155, pp. 107611 (18 pages) (2021).
[33] Demir, O., Keskin, I., and Cetin, S. “Modeling and control of a nonlinear half-vehicle suspension system: A hybrid fuzzy logic approach”, Nonlinear Dyn, 67(3), pp. 2139-2151 (2012).
[34] Aldair, A.A. and Wang, W.J. “A Neurofuzzy controller for full vehicle active suspension systems”, Journal of Vibration and Control, 18(12), pp. 1837-1854 (2011).
[35] Cimen, T. ‘‘Systematic and effective design of nonlinear feedback controllers via the state-dependent Riccati equation (SDRE) method’’, Annual Reviews in Control, 34(1), pp. 32-51 (2010).
[36] Kilicaslan, S. “Tracking control of elastic joint parallel robots via state-dependent Riccati equation”, Turk J Elec Eng & Comp Sci, 23(2), pp. 522-538 (2015).
[37] Banks, S.P. and Dinesh, K. “Approximate optimal control and stability of nonlinear finite and infinite-dimensional systems”, Annals of Operations Research, 98(1-4), pp. 19-44 (2000).
[38] Kilicaslan, S. and Banks, S.P. “A separation theorem for nonlinear systems”, Automatica, 45(4), pp. 928-935 (2009).
[39] Kilicaslan, S. and Banks, S.P. ‘‘Existence of solutions of Riccati differential equations’’, ASME Journal of Dynamic Systems, Measurement, and Control, 134(3), pp. 031001 (11 pages) (2012).
[40] Beltran-Carbajal, F., Chavez-Conde, E., Favela-Contreras, A., and Chavez-Bracamontes, R. “Active nonlinear vehicle suspension based on real time estimation of perturbation signals”, Proceedings of the 2011 IEEE International Conference on Industrial Technology (ICIT), Auburn, AL, USA, pp. 437-442 (2011).
[41] Giua, A., Melas, M., Seatzu, C., and Usai, G. ‘‘Design of a predictive semiactive suspension system’’, Vehicle System Dynamics, 41(4), pp. 277-300 (2004).
[42] Pedro, J.O., Dangor, M., Dahunsi, O.A., and Ali, M.M. “Intelligent feedback linearization control of nonlinear electrohydraulic suspension systems using particle swarm optimization”, Applied Soft Computing, 24, pp. 50-62 (November 2014).
[43] ISO 2631, ‘‘Mechanical vibration and shock-evaluation of human exposure to whole-body vibration-Part 1: General requirements, International Organization for Standardization’’, Geneva, Switzerland, (2003).
[44] Rajamani, R. ‘‘Active automotive suspensions’’, In Vehicle Dynamics and Control, pp. 341-347, Springer, NY, USA (2006).
Scientia Iranica
Volume 29, Issue 3
Transactions on Mechanical Engineering (B)
May and June 2022
Pages 1221-1235

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