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Adaptive Vibration Control of a Vertical Beam under Base Translation Excitation

Jiabao Wang, Baoping Wang
World Scientific Research Journal, (2026), Vol.12, No.9, pp.146-158
Published: September 24, 2026
DOI: 10.6911/WSRJ.202609_12(9).0016
PDF: Download Full Text PDF
Abstract

For a vibration control system of a vertical beam subjected to base excitation, a dynamic model incorporating the excitation term is established based on Euler–Bernoulli beam theory. Experimental results demonstrate the accuracy of the model. An adaptive PID control algorithm based on a Kalman filter is then proposed. The algorithm uses an inclination sensor to simultaneously acquire the beam’s angular position and angular velocity. The Kalman filter provides optimal state estimates to mitigate the effects of measurement noise. Based on the filtered information, the vibration trend is predicted, and adaptive rules are constructed to adjust the PID parameters accordingly. Simulation and experimental results show that, compared with PID control, the proposed method significantly reduces the system settling time and effectively suppresses vibration.

Keywords: Vertical beam; Vibration control; Euler–Bernoulli beam; Kalman filter; PID control.
APA Citation: Jiabao Wang, Baoping Wang (2026). Adaptive Vibration Control of a Vertical Beam under Base Translation Excitation. World Scientific Research Journal, 12(9), 146-158. https://doi.org/10.6911/WSRJ.202609_12(9).0016

References

  1. Zhang, M., Wang, X. Y., & Wen, H. (2024). Reinforcement-learning-based vibration control of a piezoelectric cantilever beam under time-delay effects. Journal of Vibration and Shock, 43(16), 77–83. (In Chinese)
  2. Bian, Y. M., Yin, J. G., Xiong, X. L., et al. (2018). Research on elastic dynamic model of trolley system for anti-sway control system of bridge crane. Procedia CIRP, 78, 285–288. https://doi.org/10.1016/j.procir.2018.08.073
  3. Chen, X., & Fang, Z. C. (2006). Feedback control and numerical simulation of flexible manipulator vibration. Journal of Vibration and Shock, (1), 1–4, 160. (In Chinese)
  4. Du, X., & Cai, G. P. (2009). Active control of a two-link flexible manipulator with a concentrated end mass. Chinese Journal of Applied Mechanics, 26(4), 672–678, 833. (In Chinese)
  5. Lara, L. A., Brito, J. L. V., & Avila, S. M. (2010). Control de vibraciones en una viga Gerber utilizando amortiguadores de masa sintonizados. Dyna, 77(164), 119–129. https://doi.org/10.6036/3650
  6. Burlon, A., Failla, G., & Arena, F. (2016). Exact frequency response analysis of axially loaded beams with viscoelastic dampers. International Journal of Mechanical Sciences, 115, 370–384. https://doi.org/10.1016/j.ijmecsci.2016.07.011
  7. Go, Y. J., Kim, Y. H., & Chang, H. G. (1998). An analysis of the behavior of a simply supported beam with a dry friction damper attached. Applied Acoustics, 55(1), 31–41. https://doi.org/10.1016/s0003-682x(97)00017-1
  8. Soto, M. G., & Adeli, H. (2013). Placement of control devices for passive, semi-active, and active vibration control of structures. Scientia Iranica, 20(6), 1567–1578. https://doi.org/10.1016/j.scient.2013.09.020
  9. Korkmaz, S. (2011). A review of active structural control: Challenges for engineering informatics. Computers & Structures, 89(23–24), 2113–2132. https://doi.org/10.1016/j.compstruc.2011.08.003
  10. Li, K. M., Zhang, K., Liu, Y. B., et al. (2022). Co-simulation and experimental study of a piezoelectric cantilever beam vibration control system. Piezoelectrics & Acoustooptics, 44(6), 917–924. (In Chinese)
  11. Zhang, S. Y., Zhang, S. Q., Li, J., et al. (2017). Shape control and active vibration control of a piezoelectric smart structure based on the PID algorithm. Journal of Northwestern Polytechnical University, 35(1), 74–81. (In Chinese)
  12. Ma, Z. D., Wu, X. X., Wang, W. L., et al. (2025). Design and experimental study of a PID controller based on a mathematical model of a cantilever beam. Mould Manufacturing, 25(8), 19–22. (In Chinese)
  13. Fey, R. H. B., Wouters, R. M. T., & Nijmeijer, H. (2010). Proportional and derivative control for steady-state vibration mitigation in a piecewise-linear beam system. Nonlinear Dynamics, 60(4), 535–549. https://doi.org/10.1007/s11071-009-9614-0
  14. Huang, Z. C., Cheng, Y., Wang, X. G., et al. (2026). Simulation study on vibration control of a partially covered active damping beam. Vibration, Measurement & Diagnosis, 46(2), 366–372, 451–452. (In Chinese)
  15. Ali, M., Khan, M. W., Abid, M., et al. (2020). Variation of fraction in FOPID controller for vibration control of Euler-Bernoulli beam. SN Applied Sciences, 2(12), 1955. https://doi.org/10.1007/s42452-020-03744-0
  16. Sangpet, T., Kuntanapreeda, S., & Schmidt, R. (2018). An adaptive PID-like controller for vibration suppression of piezo-actuated flexible beams. Journal of Vibration and Control, 24(12), 2656–2670. https://doi.org/10.1177/1077546317718421
  17. Zhu, Q., Yue, J. Z., Liu, W. Q., et al. (2017). Active vibration control for a piezoelectric cantilever beam: An adaptive feedforward control method. Smart Materials and Structures, 26(4), 047003. https://doi.org/10.1088/1361-665X/aa5e22
  18. Chen, S. H. (2003). Robust Kalman-filter-based frequency-shaping optimal active vibration control of uncertain flexible mechanical systems with nonlinear actuators. Journal of Vibration and Control, 9(6), 623–644. https://doi.org/10.1177/1077546303009006004
  19. Mohammadi, A., Nayyeri, P., Zakerzadeh, M. R., et al. (2021). Sensor fusion approach for shape estimation of a base-excited cantilever beam. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 235(24), 7870–7879. https://doi.org/10.1177/09544062211010247
  20. Howell, L. L. (2007). Compliant mechanisms (Y. Q. Yu, Trans.). Higher Education Press.
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