$H_{\infty}$ norm을 이용한 6 자유도 정밀스테이지의 모델기반 제어기 설계

Design of a Model-based Controller for a 6-DOF Precision Positioning Stage using $H_{\infty}$ norm

  • Moon, Jun-Hee (Dept of Mechatronics, Daelim University College) ;
  • Lee, Bong-Gu (Dept of Mechanical Engineering, Daelim University College)
  • 투고 : 2010.08.02
  • 심사 : 2010.11.10
  • 발행 : 2010.12.01

초록

We developed a model-based controller for 6-DOF micropositioning of a precision stage using $H_{\infty}$ norm, For the design, a state-space system of the mathematical model of the stage is derived In developing the controller, weighting functions are effectively designed in consideration of upper bounds of the sensitivity of the control loop and control input. Step responses in open and closed loop control are provided to verify the micropositioning performance of the stage. By applying the developed controller we prove that the inverse of the weighting function forms the upper bound of the control loop. It is also found that the controller makes the same sensitivity shape with all the DOFs due to the use of $H_{\infty}$ norm. The developed controller is expected to be applied successfully for industrial use.

키워드

참고문헌

  1. Shan, X., Kuo, S., Zhang, J. and Menq, C., "Ultra precision motion control of a multiple degrees of freedom magnetic suspension stage," IEEE/ASME Transactions on Mechatronics, Vol. 7, No. 1, pp. 67-78, 2002. https://doi.org/10.1109/3516.990889
  2. Gordon, C. G.., "Generic Criteria for Vibration-Sensitive Equipment," Proc. of International Society for Optical Engineering(SPIE), Vol. 1619, pp. 71-85, 1991.
  3. Sugihara, K.; Mori, I., Tojo, T., Ito, C., Tabata, M. and Shinozaki, T., "Piezoelectrically driven XY $\{theta}$ table for submicron lithography systems," Rev. of Scientific Instruments, Vol. 60, No. 9, pp. 3024-3029, 1989. https://doi.org/10.1063/1.1140598
  4. Smith, A. R., Gwo, S. and Shih, C. K, "A new high-resolution two-dimensional micropositioning device for scanning probe microscopy applications," Rev. of Scientific Instruments, Vol. 65, No. 10, pp. 3216-3219, 1994. https://doi.org/10.1063/1.1144552
  5. Muthuswamy, J., Salas, D. and Okandan, M., "A chronic micropositioning system for neurophysiology," Proc. the Second Joint EMBS/BMES Conference, pp. 2115-2116, 2002.
  6. Physik Instrumente GmbH & Co, Products webpage, http://www.physikinstrumente.com
  7. Kuo, S.-K. and Meng, C.-H., "Modeling and control of a six-axis precision motion control stage," IEEE/ASME Transactions on Mechatronics, Vol. 10, No. 1, pp. 50-59, 2005. https://doi.org/10.1109/TMECH.2004.842219
  8. Dejima, S., Gao, W., Shimizu, H., Kiyono, S. and Tomita, Y., "Precision positioning of a five degree-of-freedom planar motion stage," Mechatronics, Vol. 15, No. 8, pp. 969-987, 2005. https://doi.org/10.1016/j.mechatronics.2005.03.002
  9. Gao, P. and Swei, S.-M., "A six-degree-of-freedom micro-manipulator based on piezoelectric translators," Nanotechnology, Vol. 10, No. 4, pp. 447-452, 1999. https://doi.org/10.1088/0957-4484/10/4/315
  10. Portman, V. T., Sandler, B.-Z. and Xahavi, E., "Rigid 6-DOF parallel platform for precision 3-D micromanipulation," Int. Journal of Machine Tools and Manufacture, Vol. 41, No. 9, pp. 1229-1250, 2001. https://doi.org/10.1016/S0890-6955(01)00027-X
  11. Chen, S.-C. and Culpepper, M. L., "Design of a six-axis micro-scale nanopositioner - $\{\mu}HexFlex$," Precision Engineering, Vol. 30, No. 3, pp. 314-324, 2006. https://doi.org/10.1016/j.precisioneng.2005.11.002
  12. Kim, H. S., Cho, Y. M. and Moon, J. H. "Active vibration control using a novel three-DOF precision micro-stage," Smart Structures and Materials, Vol. 19, No. 5, Paper No. 055001, 2010. https://doi.org/10.1088/0964-1726/19/5/055001
  13. Yao, Q., Dong, J. and Ferreira, P. M., "Design, analysis, fabrication and testing of a parallel-kinematic micropositioning XY stage," Int. J. of Machine Tools Manufacture, Vol. 47, No. 6, pp. 946-961, 2007. https://doi.org/10.1016/j.ijmachtools.2006.07.007
  14. Moon, J. H., Park, J. H. and Pahk, H. J., "Design and Modeling of a 6-DOF Stage for Ultra-Precision Positioning," Journal of the Korean Society for Precision Engineering, Vol. 26, No. 6, pp. 106-113, 2009.
  15. Ogata, K., "Modem control engineering, 4th ed.," Prentice Hall, 2002.