Optimal Fuzzy Robust PID Controller for Active Suspension Systems
Keywords:
Suspension system, Robust control, Optimization, Fuzzy robust PID
Abstract
The suspension systems are responsible for neutralizing the vibrations caused by the roughness of the road surface imposed on the car. In this paper, a quarter car model (with two degrees of freedom) is employed to investigate the exerted vibrations on the suspension system. After developing the equation of motion, a combination of two fuzzy and robust PID (FRPID) controllers is applied to the system to suppress the vibrations. The coefficients of these controllers are parameters that are optimized by the Whale Optimization Algorithm (WOA). It is observed that the proposed approach is successful to control the car suspension system properly with a very low error. Finally, the proposed controller is compared with a recently published method in the literature. As the results show, the proposed control method in this paper provides better outcomes.
References
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[32] Pang, H., Y. Wang, X. Zhang, and Z. Xu. 2019. “Robust State-feedback Control Design for Active Suspension System with Time-varying Input Delay and Wheelbase Preview Information.” Journal of the Franklin Institute 356 (4): 1899–1923.
[33] Alvarez-Sánchez, E. 2013. “A Quarter-car Suspension System: Car Body Mass Estimator and Sliding Mode Control.” Procedia Technology 7: 208–214.
[34] Mirjalili, S. and A. Lewis, The whale optimization algorithm. Advances in engineering software, 2016. 95: p. 51-67.
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[2] Félix-Herrán, L., et al. Control of a semi-active suspension with a magnetorheological damper modeled via Takagi-Sugeno. in 18th Mediterranean Conference on Control and Automation, MED'10. 2010. IEEE.
[3] Nagarkar, M.P., G.J.V. Patil, and R.N.Z. Patil, Optimization of nonlinear quarter car suspension–seat–driver model. Journal of advanced research, 2016. 7(6): p. 991-1007.
[4] Mahmoodabadi, M. and N. Nejadkourki, Optimal fuzzy adaptive robust PID control for an active suspension system. Australian Journal of Mechanical Engineering, 2020: p. 1-11.
[5] Yao, G., et al., MR damper and its application for semi-active control of vehicle suspension system. Mechatronics, 2002. 12(7): p. 963-973.
[6] Bagheri, A., et al., Pareto optimization of a two-degree of freedom passive linear suspension using a new multi-objective genetic algorithm. 2011.
[7] Shelke, G.D., A.C. Mitra, and V.R. Varude, Validation of simulation and analytical model of nonlinear passive vehicle suspension system for quarter car. Materials Today: Proceedings, 2018. 5(9): p. 19294-19302.
[8] Pang, H., F. Liu, and Z. Xu, Variable universe fuzzy control for vehicle semi-active suspension system with MR damper combining fuzzy neural network and particle swarm optimization. Neurocomputing, 2018. 306: p. 130-140.
[9] Rao, L.G. and S. Narayanan, Sky-hook control of nonlinear quarter car model traversing rough road matching performance of LQR control. Journal of Sound and Vibration, 2009. 323(3-5): p. 515-529.
[10] Yıldız, A.S., et al., Nonlinear adaptive control of semi-active MR damper suspension with uncertainties in model parameters. Nonlinear Dynamics, 2015. 79(4): p.2753-2766.
[11] Paksoy, M. and M. Metin, Nonlinear semi-active adaptive vibration control of a half vehicle model under unmeasured road input. Journal of Vibration and Control, 2019. 25(18): p. 2453-2472.
[12] Wu, J., et al., A load-dependent PWA-H∞ controller for semi-active suspensions to exploit the performance of MR dampers. Mechanical Systems and Signal Processing, 2019. 127: p. 441-462.
[13] Al-Rawashdeh, Y.M., S. El Ferik, and M.A. Abido. Robust Full-Car Active Suspension System. in 2019 10th International Conference on Information and Communication Systems (ICICS). 2019. IEEE.
[14] Eski, I. and Ş. Yıldırım, Vibration control of vehicle active suspension system using a new robust neural network control system. Simulation Modelling Practice and Theory, 2009.17(5): p. 778-793.
[15] Mustafa, G.I., H. Wang, and Y. Tian, Vibration control of an active vehicle suspension systems using optimized model-free fuzzy logic controller based on time delay estimation. Advances in Engineering Software, 2019. 127: p141-149.
[16] L.A. Zadeh, Fuzzy algorithms, Inform. Contr. 12 (1968) 94–102.
[17] L.A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Syst. Man Cybern. 3 (1) (1973) 28–44.
[18] H. Nasser, E.H. Kiefer-Kamal, H. Hu, S. Belouettar, E. Barkanov, Active vibration damping of composite tructures using a nonlinear fuzzy controller, Compos. Struct. 94 (4) (2012) 1385–1390.
[19] P. Li, F.J. Jin, Adaptive fuzzy control for unknown nonlinear systems with perturbed dead-zone inputs, Acta Automat. Sinica 36 (4) (2010) 573–579.
[20] M. Marinaki, Y. Marinakis, G.E. Stavroulakis, Fuzzy control optimized by PSO for vibration suppression of beams, Control Eng. Pract. 18 (6) (2010) 618–629.
[21] D. Wang, X. Lin, Y. Zhang, Fuzzy logic control for a parallel hybrid hydraulic excavator using genetic algorithm, Automat. Constr. 20 (5) (2011) 581–587.
[22] R.E. Precup, M.B. Ra˘dac, M.L. Tomescu, E.M. Petriu, S. Preitl, Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems, Expert Syst. Appl. 40 (1) (2013) 188–199.
[23] S.W. Tong, G.P. Liu, Real-time simplified variable domain fuzzy control of PEM fuel cell flow systems, Eur. J. Control 14 (3) (2008) 223–233.
[24] J.N. Lygouras, P.N. Botsaris, J. Vourvoulakis, V. Kodogiannis, Fuzzy logic controller implementation for a solar air-conditioning system, Appl. Energy 84 (12) (2007) 1305–1318.
[25] U. Zuperl, F. Cus, M. Milfelner, Fuzzy control strategy for an adaptive force control in end-milling, J. Mater. Process. Technol. 164–165 (2005) 1472–1478.
[26] X.G. Duan, H.X. Li, H. Deng, Robustness of fuzzy PID controller due to its inherent saturation, J. Process Contr. 22 (2) (2012) 470–476.
[27] O. Karasakal, M. Guzelkaya, I. Eksin, Online tuning of fuzzy PID controllers via rule weighing based on normalized acceleration, Eng. Appl. Artif. Intell. 26 (1), (2013) 184–197.
[28] H. Boubertakh, M. Tadjine, P.Y. Glorennec, Tuning fuzzy PD and PI controllers using reinforcement learning, ISA Trans. 49 (4) (2010) 543–551.
[29] R.E. Precup, R.C. David, E.M. Petriu, M.-B. Ra˘dac, S. Preitl, J. Fodor, Evolutionary optimization-based tuning of low-cost fuzzy controllers for servo systems, Knowl.-Based Syst. 38 (2013) 74–84.
[30] E. Sanchez, T. Shibata, L.A. Zadeh, Genetic lgorithms and Fuzzy Logic Systems, World Scientific, River Edge, NJ, 1997.
[31] J. Kennedy, R.C. Eberhart, Particle swarm ptimization, in: Proceedings of the IEEE International Conference on Neural Networks, vol. 4, Perth, Australia, 1995, pp. 1942–1948.
[32] Pang, H., Y. Wang, X. Zhang, and Z. Xu. 2019. “Robust State-feedback Control Design for Active Suspension System with Time-varying Input Delay and Wheelbase Preview Information.” Journal of the Franklin Institute 356 (4): 1899–1923.
[33] Alvarez-Sánchez, E. 2013. “A Quarter-car Suspension System: Car Body Mass Estimator and Sliding Mode Control.” Procedia Technology 7: 208–214.
[34] Mirjalili, S. and A. Lewis, The whale optimization algorithm. Advances in engineering software, 2016. 95: p. 51-67.
[35] Pedrycz, W., Fuzzy control and fuzzy systems. 1993: Research Studies Press Ltd.
[36] Hájek, P., Metamathematics of fuzzy logic. Vol. 4. 2013: Springer Science & Business Media.
[37] Araki, M., PID control. Control Systems, Robotics and Automation: System Analysis and Control: Classical Approaches II, 2009: p. 58-79.
Published
2021-09-01
How to Cite
Salari Bardsiri, M., Sotoodeh Bahraini, M., & Shafiee Sarvestany, A. (2021). Optimal Fuzzy Robust PID Controller for Active Suspension Systems. Majlesi Journal of Mechatronic Systems, 10(3), 27-34. Retrieved from https://ms.majlesi.info/index.php/ms/article/view/497
Section
Articles
