lnertia Weight-free Particle Swarm Optimization in Optimal Control Design for Vehicle Active Suspension Systems

Abstract

Vehicle active suspension systems play an important role in ride comfort and driving safety. This study considers the problem of an efficient control scheme design for vehicle active suspension systems. The active suspension systems aim to get more comfortable riding and good handling for random road disturbances. The purpose of this work is to reduce the driver’s entire body acceleration and thereby improve ride comfort. The inertial weight-free particle swarm optimization (PSO) method is utilized to obtain weighting matrices of the optimal control namely linear quadratic regulator (LQR) for the active suspension systems. The designed state-feedback controller is applied to the quarter-car suspension system under different road profiles. Simulation results of the inertia weight-free PSO-tuned LQR are compared with the results of the classical-tuned controller and standard PSO-tuned LQR controller to show the effectiveness.

Keywords

• Active suspension system
• Standard PSO
• Inertia-weight-free PSO
• LQR
• Road disturbance.

References

1. [1] V. S. Deshpande, B. Mohan, P. D. Shendge, and S. B. Phadke, “Disturbance observer based sliding mode control of active suspension systems,” J. Sound Vib., vol. 333, no. 11, pp. 2281–2296, 2014.
2. [2] I. Fialho and G. J. Balas, “Road adaptive active suspension design using linear parameter-varying gain-scheduling,” IEEE Trans. Control Syst. Technol., vol. 10, no. 1, pp. 43–54, 2002.
3. [3] X. Shao, F. Naghdy, and H. Du, “Reliable fuzzy H∞ control for active suspension of in-wheel motor driven electric vehicles with dynamic damping,” Mech. Syst. Signal Process., vol. 87, pp. 365–383, 2017.
4. [4] J. Cao, P. Li, and H. Liu, “An interval fuzzy controller for vehicle active suspension systems,” IEEE Trans. Intell. Transp. Syst., vol. 11, no. 4, pp. 885–895, 2010.
5. [5] A. R. Kaleli̇ and H. İ. Akolaş, “Aktif araç süspansiyon sistemi İçin makine Öğrenimi tabanlı kontrol sisteminin geliştirilmesi,” Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 11, no. 2, pp. 421–428, 2022.
6. [6] M. P. Nagarkar, Y. J. Bhalerao, G. J. Vikhe Patil, and R. N. Zaware Patil, “GA-based multi-objective optimization of active nonlinear quarter car suspension system—PID and fuzzy logic control,” Int. J. Mech. Mater. Eng., vol. 13, no. 1, 2018.
7. [7] A. Unger, F. Schimmack, B. Lohmann, and R. Schwarz, “Application of LQ-based semi-active suspension control in a vehicle,” Control Eng. Pract., vol. 21, no. 12, pp. 1841–1850, 2013.
8. [8] S. Manna et al., “Ant colony optimization tuned closed-loop optimal control intended for vehicle active suspension system,” IEEE Access, vol. 10, pp. 53735–53745, 2022.

9. [9] J. S. David Reddipogu and V. K. Elumalai, “Hardware in the loop testing of adaptive inertia weight PSO-tuned LQR applied to vehicle suspension control,” J. Control Sci. Eng., vol. 2020, pp. 1–16, 2020.
10. [10] A. E. Bryson, “Control of spacecraft and aircraft (Vol. 41)”. Princeton: Princeton university press, 1993.
11. [11] H. Maghfiroh, M. Nizam, M. Anwar, and A. Ma’Arif, “Improved LQR control using PSO optimization and Kalman filter estimator,” IEEE Access, vol. 10, pp. 18330–18337, 2022.
12. [12] K. Hassani and W.-S. Lee, “Multi-objective design of state feedback controllers using reinforced quantum-behaved particle swarm optimization,” Appl. Soft Comput., vol. 41, pp. 66–76, 2016.
13. [13] E. Vinodh Kumar, G. S. Raaja, and J. Jerome, “Adaptive PSO for optimal LQR tracking control of 2 DoF laboratory helicopter,” Appl. Soft Comput., vol. 41, pp. 77–90, 2016.
14. [14] S. B. Karanki, M. K. Mishra, and B. K. Kumar, “Particle swarm optimization-based feedback controller for unified power-quality conditioner,” IEEE Trans. Power Deliv., vol. 25, no. 4, pp. 2814–2824, 2010.
15. [15] X. Shao, J. Zhang, and X. Zhang, “Takagi-Sugeno fuzzy modeling and PSO-based robust LQR anti-swing control for overhead crane,” Mathematical Problems in Engineering, vol. 2019, p. 14, 2019.
16. [16] T. Yuvapriya, P. Lakshmi, and V. K. Elumalai, “Experimental validation of LQR weight optimization using bat algorithm applied to vibration control of vehicle suspension system,” IETE J. Res., pp. 1–11, 2022.
17. [17] R. R. Das, V. K. Elumalai, R. Ganapathy Subramanian, and K. V. Ashok Kumar, “Adaptive predator–prey optimization for tuning of infinite horizon LQR applied to vehicle suspension system,” Appl. Soft Comput., vol. 72, pp. 518–526, 2018.
18. [18] Quanser, Active Suspension System: User Manual, Quanser Corporation, Ontario, Canada, 2009.
19. [19] Q. Chen, B. Liu, Q. Zhang, J. J. Liang, P. N. Suganthan, and B. Y. Qu, “Problem definitions and evaluation criteria for CEC 2015 special session on bound constrained single-objective computationally expensive numerical optimization,” Al-roomi.org. [Online]. Available:https://alroomi.org/multimedia/CEC_Database/CEC2015/RealParameterOptimization/ExpensiveOptimization/CEC2015_ExpensiveOptimization_TechnicalReport.pdf. [Accessed: 05-Apr-2023].
20. [20] M. R. Tanweer, S. Suresh, and N. Sundararajan, “Improved SRPSO algorithm for solving CEC 2015 computationally expensive numerical optimization problems,” in 2015 IEEE Congress on Evolutionary Computation (CEC), 2015.
21. [21] J. L. Rueda and I. Erlich, “MVMO for bound constrained single-objective computationally expensive numerical optimization,” in 2015 IEEE Congress on Evolutionary Computation (CEC), 2015
22. [22] E. O. Wilson, Sociobiology: The New Synthesis, 25th ed. London, England: Harvard University Press, 2000.
23. [23] W. Zhang, Selforganizology: The science of self-organization. WORLD SCIENTIFIC, 2016.
24. [24] C. W. Reynolds, “Flocks, herds and schools: A distributed behavioral model,” Comput. Graph. (ACM), vol. 21, no. 4, pp. 25–34, 1987.
25. [25] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of ICNN’95 - International Conference on Neural Networks, 2002.
26. [26] W. J. Zhang, “Particle swarm optimization: A Matlab algorithm,” Iaees.org. [Online]. Available:http://www.iaees.org/publications/journals/selforganizology/articles/2022-9(3-4)/particle-swarm-optimization-Matlab-algorithm.pdf. [Accessed: 05-Apr-2023].
27. [27] C. Blum, M. J. B. Aguilera, A. Roli, and M. Sampels, Eds., Hybrid metaheuristics: An emerging approach to optimization. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008.
28. [28] I. H. Osman and G. Laporte, “Metaheuristics: A bibliography,” Ann. Oper. Res., vol. 63, no. 5, pp. 511–623, 1996.
29. [29] M. Jaberipour, E. Khorram, and B. Karimi, “Particle swarm algorithm for solving systems of nonlinear equations,” Comput. Math. Appl., vol. 62, no. 2, pp. 566–576, 2011.