Skip to main content
SpringerLink
Log in

Modeling identification and control of a 6-DOF active vibration isolation system driving by voice coil motors with a Halbach array magnet

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

The sheet current model considering the end effects is applied to design a six-degree-of-freedom (6-DOF) active vibration isolation system (AVIS) driving by the voice coil motors (VCMs). Compared with the charge model, the sheet current method represents higher calculation efficiency. Then, the hybrid functions (HFs) are employed to identify the multi-input and multi-output (MIMO) AVIS, and the identification parameters are used to design the controller. To promote the control performance, the composite nonlinear feedback (CNF) controller is designed based on the identification parameters. Consequently, the simulations and experiments are carried out, compared with PID controller, the CNF controller shows quicker response and smaller overshoot, i.e., the CNF controller achieves the dynamic damping ratio during the control. Thus, the experimental results demonstrate the better performance of the CNF controller.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

B :

Magnetic flux density (T)

μ 0 :

The permeability of the vacuum

M :

Homogeneous magnetization (A/m) r 0

\(\overrightarrow{A}\) :

Magnetic vector potential

I :

Current (A)

L :

The length of wire (m)

K 0 :

Sheet current density (A/m)

S (m) :

M-set sample-hold-functions

T (m) :

M-set triangular functions

ξ :

The damping ratio

ω n :

The natural frequency (Hz)

References

  1. T. Markus, S. Rudolf, S. Andreas, H. Reinhard and S. Georg, Six degree of freedom vibration isolation platform for in-line nano-metrology, IFAC, 49 (21) (2016) 149–156.

    Google Scholar 

  2. E. Csencsics et al., Mechatronic design of an active two-body vibration isolation system, IFAC, 49 (21) (2016) 133–140.

    Google Scholar 

  3. W. Lei, L. Junzhong, Y. Yuanyuan, W. Jing and Y. Jiangbo, Active control of low-frequency vibrations in ultra-precision machining with blended infinite and zero stiffness, International Journal of Machine Tools and Manufacture, 139 (2019) 64–74.

    Article  Google Scholar 

  4. Y. Zhang et al., Dynamic analysis and control application of vibration isolation system with magnetic suspension on satellites, Aerospace Science and Technology, 75 (2018) 99–114.

    Article  Google Scholar 

  5. A. Abbasi, S. Khadem and S. Bab, Vibration control of a continuous rotating shaft employing high-static low-dynamic stiffness isolators, Journal of Vibration and Control, 24 (4) (2018) 760–783.

    Article  MathSciNet  Google Scholar 

  6. S. M. M. Mofidian and H. Bardaweel, Displacement transmissi-bility evaluation of vibration isolation system employing nonlinear-damping and nonlinear-stiffness elements, Journal of Vibration and Control, 24 (18) (2018) 4247–4259.

    Article  MathSciNet  Google Scholar 

  7. X. Wang, F. B. and H. Du, Reduction of low frequency vibration of truck driver and seating system through system parameter identification, sensitivity analysis and active control, Mechanical Systems and Signal Processing, 105 (2018) 16–35.

    Article  Google Scholar 

  8. J. Orivuori, I. Zazas and S. Daley, Active control of frequency varying disturbances in a diesel engine, Control Engineering Practice, 20 (11) (2012) 1206–1219.

    Article  Google Scholar 

  9. G. Shan et al., Experimental characterization, modeling and compensation of rate-independent hysteresis of voice coil motors, Sensors and Actuators A: Physical, 251 (2016) 10–19.

    Article  Google Scholar 

  10. J. H. Lee et al., Control of a hybrid active-passive vibration isolation system, Journal of Mechanical Science and Technology, 31 (12) (2017) 5711–5719.

    Article  Google Scholar 

  11. A. R. Insinga et al., Performance of halbach magnet arrays with finite coercivity, Journal of Magnetism and Magnetic Materials, 407 (2016) 369–376.

    Article  Google Scholar 

  12. B. Shen et al., Optimization study on the magnetic field of superconducting halbach Array magnet, Physica C: Superconductivity and its Applications, 538 (2017) 46–51.

    Article  Google Scholar 

  13. T. Zhu et al., Vibration isolation using six degree-of-freedom quasi-zero stiffness magnetic levitation, Journal of Sound and Vibration, 358 (2015) 48–73.

    Article  Google Scholar 

  14. N. Alujević et al., Stability and performance limits for active vibration isolation using blended velocity feedback, Journal of Sound & Vibration, 330 (21) (2011) 4981–4997.

    Article  Google Scholar 

  15. N. Alujević et al., Passive and active vibration isolation systems using inerter, Journal of Sound and Vibration, 418 (2018) 163–183.

    Article  Google Scholar 

  16. M. E. Hoque et al., A three-axis vibration isolation system using modified zero-power controller with parallel mechanism technique, Mechatronics, 21 (6) (2011) 1055–1062.

    Article  Google Scholar 

  17. A. Siami et al., Parameter optimization of an inerter-based isolator for passive vibration control of Michelangelo’s Rondanini Pietà, Mechanical Systems and Signal Processing, 98 (2018) 667–683.

    Article  Google Scholar 

  18. M. H. Kim et al., Design and control of a 6-DOF active vibration isolation system using a halbach magnet array, IEEE/ASME Transactions on Mechatronics, 21 (4) (2016) 2185–2196.

    Article  Google Scholar 

  19. Z. Lin, M. Pachter and S. Banda, Toward improvement of tracking performance nonlinear feedback for linear systems, International Journal of Control, 70 (1) (1998) 1–11.

    Article  MathSciNet  Google Scholar 

  20. B. M. Chen et al., Composite nonlinear feedback control for linear systems with input saturation: theory and an application, IEEE Transactions on Automatic Control, 48 (3) (2003) 427–439.

    Article  MathSciNet  Google Scholar 

  21. T. W. Li, Analysis of flat voice coil motor for precision positioning system, International Conference on Electrical Machines & Systems, IEEE (2011).

    Google Scholar 

  22. A. Deb et al., A new set of piecewise constant orthogonal functions for the analysis of linear SISO systems with sample-and-hold, Journal of the Franklin Institute, 335B (2) (1998) 333–358.

    Article  Google Scholar 

  23. A. Deb, A. Dasgupta and G. Sarkar, A new set of orthogonal functions and its application to the analysis of dynamic systems, Journal of the Franklin Institute, 343 (1) (2006) 1–26.

    Article  MathSciNet  Google Scholar 

  24. S. Roychoudhury, A. Deb and G. Sarkar, Analysis and synthesis of homogeneous / non-homogeneous control systems via orthogonal hybrid functions (HF) under state space environment, Journal of Information and Optimization Sciences, 35 (5-6) (2014) 431–482.

    Article  MathSciNet  Google Scholar 

  25. Z. H. Jiang and W. Schaufelberger, Block Pulse Functions and Their Application in Control System, Springer, Berlin (1992).

    Book  Google Scholar 

Download references

Acknowledgments

This work is partially supported by the Science Challenge Project (Grant No. JCKY2016212A506-0105) and the National Natural Science Foundation of China (Grant No. 11802279).

Author information

Authors and Affiliations

  1. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, 200240, China

    Dawei Jiang, Jiasheng Li & Chaodong Deng

  2. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Dawei Jiang, Jiasheng Li, Chaodong Deng & Pinkuan Liu

  3. Institute of Machinery Manufacturing Technology, China Academy of Engineering Physics, Sichuan, 621900, China

    Xingzhan Li

Authors
  1. Dawei Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiasheng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xingzhan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chaodong Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Pinkuan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pinkuan Liu.

Additional information

Recommended by Editor No-cheol Park

Pinkuan Liu is a Professor of School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China. He received his doctoral degree in Mechanical Engineering from Harbin Institute of Technology. His research interests are precision mechatronic engineering and ultra-precision machining.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, D., Li, J., Li, X. et al. Modeling identification and control of a 6-DOF active vibration isolation system driving by voice coil motors with a Halbach array magnet. J Mech Sci Technol 34, 617–630 (2020). https://doi.org/10.1007/s12206-019-1208-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-019-1208-y

Keywords

Search

Navigation