Cover
Vol. 24 No. 2 (2024)

Published: August 31, 2024

Pages: 34-42

Original Article

Mechanical Vibration Reduction of a Nonlinear Half-Car Model using Integral-Proportional Derivative (I-PD) Controller

Mustafa Mohammed Matrood 1 Ameen Ahmed Nassar 2
1 Department of Seawater, Basrah Oil Company, Basrah, Iraq
2 Department of Mechanical Engineering, College of Engineering, University of Basrah, Basrah, Iraq
History
  • Received: June 6, 2024
  • Revised: July 2, 2024
  • Accepted: July 9, 2024
  • Available Online: August 17, 2024
DOI

https://doi.org/10.33971/bjes.24.2.5

Abstract

Vehicles usually consist of several essential systems. The performance of the vehicle is evaluated through the efficiency of these systems to perform their duties. The suspension system is one of these systems dedicated to absorbing shocks arising from vehicles passing over road bumps, thus reducing vibrations and achieving passenger comfort while driving. This paper presents a study on enhancing ride comfort in a nonlinear half-car model using a modified Proportional-Integral-Derivative (PID) controller. In this study a half-car model is developed considering the nonlinearities in the suspension system components. A nonlinear half-car model was adopted to increase accuracy and make the overall system closer to reality. Instead of the feed-forward conventional PID controller gains, the proposed controller gains are formed by putting the proportional and derivative gains in the feedback path while keeping the integral gain in the feed-forward path to act as an I- PD controller. The proposed controller is integrated into the model to deal with these nonlinearities effectively and to achieve the optimal performance of the vehicle body. The overall system has been developed and simulated in the Matlab Simulink environment to show the dynamic response. Simulation results demonstrate the effectiveness of the I-PD controller in improving the ride comfort and handling stability of the nonlinear half-car model by reducing body acceleration and suspension deflection. A comparison with other study has been conducted to verify the effectiveness of the proposed controller.

Keywords

References

  1. R. Rajamani, Vehicle dynamics and control, Second edition, Springer, New York Dordrecht Heidelberg, 2012.
  2. J. E. D. Ekoru, O. A. Dahunsi and J. O. Pedro, “PID control of a nonlinear half-car active suspension system via force feedback,” IEEE Africon 11, Victoria Falls, Zambia, pp. 16, 2011. https://doi.org/10.1109/AFRCON.2011.6071979
  3. S. Kumar and A. Medhavi, “Modeling and analysis of active full vehicle suspension model optimized using the advanced Fuzzy Logic controller,” International Journal of Acoustics and Vibration, Vol. 27, No.1, pp. 26-36, 2022.
  4. P. S. Kumar, K. Sivakumar, R. Kanagarajan and S. Kuberan, “Adaptive Neuro Fuzzy inference system control of active suspension system with actuator dynamics,” Journal of Vibroengineering, Vol. 20, No. 1, pp. 541-549, 2018. https://doi.org/10.21595/jve.2017.18379
  5. G. I. Y. Mustafa, H. Wang, and Y. Tian, “Optimized fast terminal sliding mode control for a half-car active suspension systems,” International Journal of Automotive Technology, Vol. 21, pp. 805-812, 2020.
  6. P. Gandhi, S. Adarsh and K. I. Ramachandran, “Performance analysis of half car suspension model with 4 DOF using PID, LQR, Fuzzy and ANFIS controllers,” Procedia Computer Science, Vol. 115, pp. 2-13, 2017.
  7. H. Khodadadi and H. Ghadiri, “Self - tuning PID controller design using Fuzzy logic for half car active suspension system,” International Journal of Dynamics and Control, Vol. 6, No. 3, pp. 224-232, 2018.
  8. J. O. Pedro, M. Dangor, O. A. Dahunsi, and M. M. Ali, “Differential evolution-based PID control of nonlinear full-car electrohydraulic suspensions,” Mathematical Problems in Engineering, Vol. 2013, pp. 1-13, 2013.
  9. Y. J. Liang, N. Li, D. X. Gao and Z. S. Wang, “Optimal vibration control for nonlinear systems of tracked vehicle half-car suspension,” International Journal of Control, Automation and Systems, Vol. 15, No. 4, pp. 1675-1683, 2017. https://doi.org/10.1007/s12555-015-0447-7
  10. A. Yildiz, “Optimum suspension design for non-linear half vehicle model using particle swarm optimization (PSO) algorithm,” Vibroengineering Procedia, Vol. 27, pp. 43-48, 2019. https://doi.org/10.21595/vp.2019.21012
  11. M. A. Khan, M. Abid, N. Ahmed, A. Wadood and H. Park, “Nonlinear control design of a half-car model using feedback linearization and an LQR controller,” Applied Sciences, Vol. 10, No. 9, pp. 1-17, 2020.
  12. M. Dangor, O. A. Dahunsi, J. O. Pedro, and M. M. Ali, “Evolutionary algorithm-based PID controller tuning for nonlinear quarter-car electrohydraulic vehicle suspensions,” Nonlinear Dynamics, Vol. 78, pp. 27952810, 2014. https://doi.org/10.1007/s11071-014-1626-4
  13. A. H. Mohamed, D. Abidou and S. A. Maged, “LQR and PID Controllers Performance on a Half Car Active Suspension System,” International Mobile, Intelligent, and Ubiquitous Computing Conference (MIUCC), Cairo, Egypt, pp. 48-53, 2021.
  14. V. Barethiye, G. Pohit, and A. Mitra, “Modeling and analysis of passive suspension system using half car model based on hybrid shock absorber model,” Proceedings of the 14th International Conference on Vibration Problems, pp. 1225-1237, 2021.
  15. D. Tan, C. Lu and X. Zhang, “Dual-loop PID control with PSO algorithm for the active suspension of the electric vehicle driven by in-wheel motor,” Journal of vibroengineering, Vol. 18, Issue 6, pp. 3915-3929, 2016.
  16. Z. Yang, L. Wang, Y. Yu, Z. Mou and M. Ou, “Analysis and control of nonlinear vibration of autonomous vehicle passing through hybrid consecutive speed control humps,” Bulletin of the Polish Academy of Sciences Technical Sciences, Vol. 70, No. 6, pp. 1-9, 2022.
  17. A. Pati, S. Singh and R. Negi, “Sliding mode controller design using PID sliding surface for half car suspension system,” 2014 Students Conference on Engineering and Systems, Allahabad, India, pp. 1-6, 2014.
  18. Y. Nan, W. Shi and P. Fang, “Improvement of ride performance with an active suspension based on fuzzy logic control,” Journal of vibroengineering, Vol. 18, No. 6, pp. 3941-3955, 2016.
  19. M. P. Nagarkar, Y. J. Bhalerao, G. J. V. Patil and R. N. Z. Patil, “GA-based multi-objective optimization of active nonlinear quarter car suspension system-PID and fuzzy logic control,” International Journal of Mechanical and Materials Engineering, Vol. 13, No. 10, pp. 1-20, 2018.
  20. O. A. Dahunsi, M. Dangor, J. O. Pedro and M. M. Ali, “Proportional + integral + derivative control of nonlinear full-car electrohydraulic suspensions using global and evolutionary optimization techniques,” Journal of low frequency noise, vibration and active control, Vol. 39, No. 2, pp. 393-415, 2020.
  21. L. C. Félix-Herrán, D. Mehdi, J. d. J. Rodriguez-Ortiz, V. H. Benitez, R. A. Ramirez-Mendoza and R. Soto, “Disturbance rejection in a one-half semi active vehicle suspension by means of a Fuzzy - H∞ controller,” Shock and Vibration, pp. 1-14, 2019.
  22. S. Zhu, H. Du and N. Zhang, “Development and implementation of Fuzzy, Fuzzy PID and LQR controllers for an roll-plane active hydraulically interconnected suspension,” 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Beijing, China, pp. 20172024, 2014.
  23. J. O. Pedro and N. Baloyi, “Design of direct adaptive controller for a half-car suspension system,” 2017 IEEE AFRICON, Cape Town, South Africa, pp. 467-472, 2017.
  24. W. K. Lan and E. D. Ni, “Design of Fuzzy-PID controller for ride comfort enhancement of a half-car vehicle with active suspension system,” Applied Mechanics and Materials, Volumes 313-314, pp. 382-386, 2013.
  25. D. Rodriguez-Guevara, A. Favela-Contreras, F. BeltranCarbajal, C. Sotelo and D. Sotelo, “An MPC-LQR-LPV controller with quadratic stability conditions for a nonlinear half-car active suspension system with electrohydraulic actuators,” Machines, Vol. 10, No. 2, pp. 1-18, 2022. https://doi.org/10.3390/machines10020137
  26. J. D. Ekoru and J. O. Pedro, “Proportional-integralderivative control of nonlinear half-car electro-hydraulic suspension system,” Journal of Zhejiang University SCIENCE A, Vol. 14, No. 6, pp. 401-416, 2013.
  27. F. Hasbullah and W. F. Faris, “Simulation of disturbance rejection control of active half-car active suspension system using active disturbance rejection control with decoupling transformation,” 4th International Conference on Mathematical Applications in Engineering, Vol. 949, pp.1-20, 2017.
  28. S. Kumar and A. Medhavi, “Optimization of nonlinear passive suspension system to minimize road damage for heavy goods vehicle,” International Journal of Acoustics and Vibration, Vol. 26, No. 1, pp. 56-63, 2021.
  29. J. Wu and Z. Liu, “Piecewise affine H∞ control of halfcar magneto-rheological suspension systems,” Int. federation of automatic control hosting, Vol. 51, No. 31, pp. 967-972, 2018.
  30. K. Ogata, Modern control engineering, Fifth edition, Prentice Hall, New Jersey 07458, 2010.
  31. S. J. S. Prasad, D. Selvakarthi and C. Aravind, “Set Point Tracking and Load Disturbance Rejection with PID and IPD Controllers in Different Zones of Barrel Heating System,” International Journal of ChemTech Research, Vol. 12, No. 3, pp. 109-113, 2019.
  32. V. Kumar and K. S. Rana, “Some investigations on hybrid fuzzy IPD controllers for proportional and derivative kick suppression,” International Journal of Automation and Computing, Vol. 13, No. 5, pp. 516-528, 2016. https://doi.org/10.1007/s11633-016-1009-z
  33. V. T. Diep, P. D. Hung and N. T. Su, “I-PD Controller Design based on Robust Viewpoint,” 2019 2nd International Conference of Intelligent Robotic and Control Engineering (IRCE), Singapore, pp. 27-31, 2019.
  34. A. Abdulameer, M. Sulaiman, M. S. M. Aras and D. Saleem, “GUI based system analysis using PID controller for education,” Indonesian Journal of Electrical Engineering and Computer Science, Vol. 3, No. 1, pp. 91101, 2016. http://doi.org/10.11591/ijeecs.v3.i1.pp91-101