Design of a Constrained Nonlinear Controller using Firefly Algorithm for Active Suspension System
Authors
Abstract
Active vehicle suspension system is designed to increase the ride comfort and road holding of vehicles. Due to limitations in the external force produced by actuator, the design problem encounters the constraint on the control input. In this paper, a novel nonlinear controller with the input constraint is designed for the active suspension system. In the proposed method, at first, a constrained multi-objective optimization problem is defined. In this problem, a performance index is defined as a weighted combination of the predicted responses of the nonlinear suspension system and control input. Then, this problem is solved by the modified firefly optimization algorithm to find the constrained optimal control input. To evaluate the performance of the proposed method, the results of the unconstrained and constrained controllers are provided and discussed for various road excitations. The results show a remarkable increase in the ride comfort with the limited force, while other suspension outputs including the suspension travel and tire deflection being in the acceptable ranges. In addition, these controllers are compared with Sliding Mode Control (SMC) and Nonlinear Model Predictive Control (NMPC) in the presence of model uncertainty.
Keywords
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20. Chen, W. H., Ballance, D. J., Gawthrop, P. J., “Optimal Control of Nonlinear Systems: A Predictive Control Approach”, Automatica, Vol. 39, No. 4, pp. 633-641, 2003.
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23. Wong, JY., “Theory of Ground Vehicles”, Canada: John Wiley and Sons, 2008.
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25. Yang, X. S., “Nature-Inspired Metaheuristic Algorithms”, Luniver Press, 2010.
26. Gupta, A. and Padhy, P. K., “Modified Firefly Algorithm Based Controller Design for Integrating and Unstable Delay Processes”, Engineering Science and Technology, an International Journal, Vol. 19, No. 1, pp. 548-558, 2016.
27. Yin, J., “Asymptotic Stability in Probability and Stabilization for a Class of Discrete‐Time Stochastic Systems”, International Journal of Robust and Nonlinear Control, Vol. 25, No. 15, pp. 2803-2815, 2015.
28. Keighobadi, J., Faraji, J., and Rafatnia, S., “Chaos Control of Atomic Force Microscope System using Nonlinear Model Predictive Control”, Journal of Mechanics, Vol. 33, No. 3, pp. 405-415, 2017.
2. Khiavi, A. M., Mirzaei, M., and Hajimohammadi, S., “A New Optimal Control Law for the Semi-Active Suspension System Considering the Nonlinear Magneto-Rheological Damper Model”, Journal of Vibration and Control, Vol. 20, No. 14, pp. 2221-2233, 2014.
3. Arslan, Y. Z., Sezgin, A. and Yagiz, N., “Improving the Ride Comfort of Vehicle Passenger Using Fuzzy Sliding Mode Controller”, Journal of Vibration and Control, Vol. 21, No. 9, pp.1667-1679, 2015.
4. Lin, J. S., and Kanellakopoulos, I., “Nonlinear Design of Active Suspensions”, IEEE Control Systems, Vol. 17, No. 3, pp. 45-59, 1997.
5. Huang, Y., Na, J., Wu, X., Liu, X., and Guo, Y., “Adaptive Control of Nonlinear Uncertain Active Suspension Systems with Prescribed Performance”, ISA Transactions, Vol. 54, pp. 145-155, 2015.
6. Rubió-Massegú, J., Rossell, J. M., Karimi, H. R., and Palacios-Quinonero, F., “Static Output-Feedback Control under Information Structure Constraints”, Automatica, Vol. 49, No. 1, pp. 313-316, 2013.
7. 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, Vol. 333, No.11, pp. 2281-2296, 2014.
8. Wang, W., Song, Y., Xue, Y., Jin, H., Hou, J., and Zhao, M., “An Optimal Vibration Control Strategy for a Vehicle's Active Suspension Based on Improved Cultural Algorithm”, Applied Soft Computing,Vol. 28, pp. 167-174, 2015.
9. Malekshahi, A. and Mirzaei, M., “Designing a Non-Linear Tracking Controller for Vehicle Active Suspension Systems Using an Optimization Process”, International Journal of Automotive Technology, Vol. 13, No. 2, pp. 263-271, 2012.
10. Mirzaei, M. and Mirzaeinejad, H. “Fuzzy Scheduled Optimal Control of Integrated Vehicle Braking and Steering Systems”, IEEE/ASME Transactions on Mechatronics, Vol. 22, No. 5, pp. 2369-79, 2017.
11. Aghasizade, S. and Mirzaei ,M., “An Integrated Strategy for Vehicle Active Suspension and Antilock Braking Systems”, Journal of Theoretical and Applied Vibration and Acoustics, Vol. 3, No. 1, pp. 97-110, 2017.
12. Malekshahi, A., Mirzaei, M., and Aghasizadeh, S., “Non-Linear Predictive Control of Multi Input Multi-Output Vehicle Suspension System”, Journal of Low Frequency Noise, Vibration and Active Control, Vol. 34, No. 1, pp. 87-106, 2015.
13. Wang, G., Chen, C. and Yu, S., “Yu, Optimization and Static Output-Feedback Control for Half-Car Active Suspensions with Constrained Information”, Journal of Sound and Vibration, Vol. 378, pp. 1-13, 2016.
14. Sun, W., Gao H. and Kaynak, O., “Vibration Isolation for Active Suspensions with Performance Constraints and Actuator Saturation”, IEEE/ASME Transactions on Mechatronics, Vol. 20, No. 2, pp. 675-683, 2015.
15. Drehmer, LR., Paucar Casas, WJ., and Gomes, H. “Parameters Optimisation of a Vehicle Suspension System Using a Particle Swarm Optimisation Algorithm”, Vehicle System Dynamics, Vol. 53, No. 4, pp. 449-474, 2015.
16. Kanarachos, S., Dizqah, AM., Chrysakis, G., and Fitzpatrick, M. E., “Optimal Design of a Quadratic Parameter Varying Vehicle Suspension System Using Contrast-Based Fruit Fly Optimisation”, Applied Soft Computing, Vol. 62, pp. 463-477, 2018.
17. Mahmoodabadi, MJ., Farhadi, F., and Sampour, S., “Firefly Algorithm Based Optimum Design of Vehicle Suspension Systems”, International Journal of Dynamics and Control, pp. 1-13, 2018. DOI: 10.1007/s40435-018-0453-8.
18. Pedro, J.O., Dangor, M., Dahunsi, O. A. and Ali, M. M., “Dynamic Neural Network-Based Feedback Linearization Control of Full-Car Suspensions using PSO”, Applied Soft Computing, 2018. DOI: 10.1016/j.asoc.2018.06.002.
19. Talib, MH. Ab., and MatDarus, I. Z., “Intelligent Fuzzy Logic with Firefly Algorithm and Particle Swarm Optimization for Semi-Active Suspension System Using Magneto-Rheological Damper”, Journal of Vibration and Control, Vol. 23, No. 3, pp. 501-514, 2017.
20. Chen, W. H., Ballance, D. J., Gawthrop, P. J., “Optimal Control of Nonlinear Systems: A Predictive Control Approach”, Automatica, Vol. 39, No. 4, pp. 633-641, 2003.
21. Chen, H. and Guo, K. H., “Constrained H∞ Control of Active Suspensions, an LMI Approach”, IEEE Transactions on Control Systems Technology, Vol. 13, No. 3, pp. 412-421, 2005.
22. Du, H., Li, W. and Zhang, N., “Integrated Seat and Suspension Control for a Quarter Car with Driver Model”, IEEE Transactions on Vehicular Technology. Vol. 61, No. 9, pp. 3893-3908, 2012.
23. Wong, JY., “Theory of Ground Vehicles”, Canada: John Wiley and Sons, 2008.
24. ISO, Mechanical Vibration and Shock-Evaluation Of Human Exposure to Whole-Body Vibration-Part 1: General Requirements, in, International Organization for Standardization, 1997.
25. Yang, X. S., “Nature-Inspired Metaheuristic Algorithms”, Luniver Press, 2010.
26. Gupta, A. and Padhy, P. K., “Modified Firefly Algorithm Based Controller Design for Integrating and Unstable Delay Processes”, Engineering Science and Technology, an International Journal, Vol. 19, No. 1, pp. 548-558, 2016.
27. Yin, J., “Asymptotic Stability in Probability and Stabilization for a Class of Discrete‐Time Stochastic Systems”, International Journal of Robust and Nonlinear Control, Vol. 25, No. 15, pp. 2803-2815, 2015.
28. Keighobadi, J., Faraji, J., and Rafatnia, S., “Chaos Control of Atomic Force Microscope System using Nonlinear Model Predictive Control”, Journal of Mechanics, Vol. 33, No. 3, pp. 405-415, 2017.
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