Volume 13, Issue 3 (Journal of Control, V.13, N.3 Fall 2019)                   JoC 2019, 13(3): 71-83 | Back to browse issues page

XML Persian Abstract Print

Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Ramezani Moghadam A, Kebriaei H. Design and stability analysis of optimal controller and observer for Itô stochastic model of active vehicle suspension system. JoC. 2019; 13 (3) :71-83
URL: http://joc.kntu.ac.ir/article-1-541-en.html
1- University of Tehran
Abstract:   (2494 Views)
This paper investigates Itô-type stochastic linear quadratic controller design for uncertain model of vehicle suspension. The Itô stochastic model of quarter-car is constructed considering parametric stochastic perturbations in stiffness and damping characteristics of suspension. To tackle with uncertainties of model, a stochastic optimal control law is obtained applying stochastic Hamilton-Jacobi-Bellman equation. By means of Itô lemma and stochastic extension of Lyapunov method, stochastic stability of the closed-loop system is guaranteed. The stochastic optimal controller is designed for a general form of Itô uncertain model which is comprised multi-dimensional multiplicative perturbations and then it is implemented on perturbed model of vehicle suspension. Furthermore, it is shown that the separation principal does not hold for the system with state multiplicative noise; therefore, the synthesized observer-based controller guarantees the stability of augmented dynamic consists of system and estimation error dynamics. A simulation study is performed to evaluate the effectiveness of stochastic optimal control approach in satisfying objectives of active suspension. To this end, time and frequency responses of ride comfort and road holding characteristics are demonstrated for two specific road cases including sinusoidal bump and ISO random profile.
Full-Text [PDF 1188 kb]   (442 Downloads)    
Type of Article: Research paper | Subject: Special
Received: 2017/11/19 | Accepted: 2018/08/18 | Published: 2019/12/31

1. [1] W. Sun, H. Gao, and O. Kaynak, "Finite Frequency H∞ Control for Vehicle Active Suspension Systems," IEEE Transactions on Control Systems Technology, vol. 19, pp. 416-422, 2011. [DOI:10.1109/TCST.2010.2042296]
2. [2] H. Du, K. Y. Sze, and J. Lam, "Semi-active H∞ control of vehicle suspension with magneto-rheological dampers," Journal of Sound and Vibration, vol. 283, pp. 981-996, 2005. [DOI:10.1016/j.jsv.2004.05.030]
3. [3] S. Chantranuwathana and H. Peng, "Force tracking control for active suspensions-theory and experiments," in Control Applications, 1999. Proceedings of the 1999 IEEE International Conference on, 1999, pp. 442-447.
4. [4] 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, pp. 217-223, 2004. [DOI:10.1016/j.sysconle.2003.08.007]
5. [5] W. Sun, H. Pan, Y. Zhang, and H. Gao, "Multi-objective control for uncertain nonlinear active suspension systems," Mechatronics, vol. 24, pp. 318-327, 2014. [DOI:10.1016/j.mechatronics.2013.09.009]
6. [6] H. Li, X. Jing, H.-K. Lam, and P. Shi, "Fuzzy sampled-data control for uncertain vehicle suspension systems," IEEE Transactions on Cybernetics, vol. 44, pp. 1111-1126, 2014. [DOI:10.1109/TCYB.2013.2279534]
7. [7] M. S. Fallah, R. B. Bhat, and W. F. Xie, "Optimized Control of Semiactive Suspension Systems Using H $ _ infty $ Robust Control Theory and Current Signal Estimation," IEEE/ASME Transactions on Mechatronics, vol. 17, pp. 767-778, 2012. [DOI:10.1109/TMECH.2011.2126590]
8. [8] Y. Huang, J. Na, X. Wu, X. Liu, and Y. Guo, "Adaptive control of nonlinear uncertain active suspension systems with prescribed performance," ISA transactions, vol. 54, pp. 145-155, 2015. [DOI:10.1016/j.isatra.2014.05.025]
9. [9] R. A. Ibrahim, Parametric random vibration: Courier Dover Publications, 2008.
10. [10] C. W. To, Nonlinear random vibration: Swets & Zeitlinger, 2000.
11. [11] V. Capasso and D. Bakstein, "An introduction to continuous-time stochastic processes," Birkhax user Boston, p. 1, 2005.
12. [12] J. L. Speyer and W. H. Chung, Stochastic processes, estimation, and control: SIAM, 2008. [DOI:10.1137/1.9780898718591]
13. [13] H. Schioler, M. Simonsen, and J. Leth, "Stochastic stability of systems with semi-Markovian switching," Automatica, vol. 50, pp. 2961-2964, 2014. [DOI:10.1016/j.automatica.2014.09.008]
14. [14] F. Li and Y. Liu, "Global stability and stabilization of more general stochastic nonlinear systems," Journal of Mathematical Analysis and Applications, vol. 413, pp. 841-855, 2014. [DOI:10.1016/j.jmaa.2013.12.021]
15. [15] Q. Wang and C. Wei, "Decentralized robust adaptive output feedback control of stochastic nonlinear interconnected systems with dynamic interactions," Automatica, vol. 54, pp. 124-134, 2015. [DOI:10.1016/j.automatica.2015.01.017]
16. [16] A. Mesbah, S. Streif, R. Findeisen, and R. D. Braatz, "Stochastic nonlinear model predictive control with probabilistic constraints," in American Control Conference (ACC), 2014, 2014, pp. 2413-2419. [DOI:10.1109/ACC.2014.6858851]
17. [17] J. Hu, Z. Wang, H. Gao, and L. K. Stergioulas, "Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties, and randomly occurring nonlinearities," IEEE Transactions on Industrial Electronics, vol. 59, pp. 3008-3015, 2012. [DOI:10.1109/TIE.2011.2168791]
18. [18] K. D. Rao and S. Kumar, "Modeling and simulation of quarter car semi active suspension system using LQR controller," in Proceedings of the 3rd International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA) 2014, 2015, pp. 441-448. [DOI:10.1007/978-3-319-11933-5_48]
19. [19] J.-l. Yao, W.-k. Shi, J.-q. Zheng, and H.-p. Zhou, "Development of a sliding mode controller for semi-active vehicle suspensions," Journal of Vibration and Control, vol. 19, pp. 1152-1160, 2013. [DOI:10.1177/1077546312441045]
20. [20] A. Ulsoy, D. Hrovat, and T. Tseng, "Stability robustness of LQ and LQG active suspensions," Journal of dynamic systems, measurement, and control, vol. 116, pp. 123-131, 1994. [DOI:10.1115/1.2900666]
21. [21] H.-C. Sohn, K.-T. Hong, K.-S. Hong, and W.-S. Yoo, "An adaptive LQG control for semi-active suspension systems," International Journal of Vehicle Design, vol. 34, pp. 309-326, 2004. [DOI:10.1504/IJVD.2004.004060]
22. [22] B. Assadsangabi, M. Eghtesad, F. Daneshmand, and N. Vahdati, "Hybrid sliding mode control of semi-active suspension systems," Smart Materials and Structures, vol. 18, p. 125027, 2009. [DOI:10.1088/0964-1726/18/12/125027]
23. [23] M. A. R. Ramezaney, E. Fathi, and M. M. Ansarey, "Optimum synthesis of sensory layout in active suspension based on linear observer," in Electrical Engineering (ICEE), 2013 21st Iranian Conference on, 2013, pp. 1-6. [DOI:10.1109/IranianCEE.2013.6599616]
24. [24] L. Xiao and Y. Zhu, "Sliding-mode output feedback control for active suspension with nonlinear actuator dynamics," Journal of Vibration and Control, vol. 21, pp. 2721-2738, 2015. [DOI:10.1177/1077546313514760]
25. [25] J.-Q. Sun, Stochastic dynamics and control vol. 4: Elsevier, 2006. [DOI:10.1016/S1574-6917(06)04001-3]
26. [26] J. Yong and X. Y. Zhou, Stochastic controls: Hamiltonian systems and HJB equations vol. 43: Springer Science & Business Media, 1999.
27. [27] M. A. Rami and X. Y. Zhou, "Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls," IEEE Transactions on Automatic Control, vol. 45, pp. 1131-1143, 2000. [DOI:10.1109/9.863597]
28. [28] X. Mao, Stochastic differential equations and applications: Elsevier, 2007. [DOI:10.1533/9780857099402]
29. [29] F. Lin, Robust control design: an optimal control approach vol. 18: John Wiley & Sons, 2007. [DOI:10.1002/9780470059579]
30. [30] E. Platen, "An introduction to numerical methods for stochastic differential equations," Acta numerica, vol. 8, pp. 197-246, 1999. [DOI:10.1017/S0962492900002920]
31. [31] J. C. Dixon, Suspension geometry and computation: Wiley Online Library, 2009. [DOI:10.1002/9780470682906]

Add your comments about this article : Your username or Email:

Send email to the article author

© 2021 CC BY-NC 4.0 | Journal of Control

Designed & Developed by : Yektaweb