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Precision Position Controller Design for a 6-DOF Stage with Piezoelectric Actuators and Lever Linkages Based on Nonlinearity Estimation

압전 구동기와 레버 링키지를 이용한 6 자유도 스테이지의 비선형성 평가에 기초한 정밀 위치 제어기의 설계

  • Published : 2009.10.01

Abstract

Precision stages for 6-DOF positioning, actuated by PZT stacks, which are fed back by gap sensors and guided by flexure hinges, have enlarged their application territory in micro/nano manufacturing and measurement area. The precision stages inherently have such limitations as the nonlinearity between input and output in piezoelectric stacks, feedback signal noise in precision capacitive gap sensors and low material damping in precision kinematic linkages of mechanical flexures. To surmount these limitations, the precision stage is modeled with physics-based variables, which are identified by transient response correspondence, and a gain margin calculation algorithm using the Prandtl-Ishlinskii model and describing function is newly developed to assess system performance more precisely than linear controller design schemes. Based on such analyses, a precision positioning controller is designed. Excellent positioning accuracy with rapid settlement accomplished by the controller is shown in step responses of the closed-loop system.

Keywords

Precision Position Control;Flexure Hinge;6-DOF Stage;Describing Function;Piezoelectric Actuator;Gain Margin

References

  1. Gordon, C. G., 1991, 'Generic Criteria for Vibration - Sensitive Equipment,' Proceedings of International Society for Optical Engineering (SPIE), San Jose, CA, November 4-6, Vol. 1619, pp. 71-85 https://doi.org/10.1117/12.56826
  2. Physik Instrumente (PI) GmbH homepage, 2009, www.physikinstrumente.com, accessed March 23, 2009
  3. Yao, Q., Dong, J. and Ferreira, P. M., 2007, 'Design, Analysis, Fabrication and Testing of a Parallel- Kinematic Micropositioning XY Stage,' International Journal of Machine Tools & Manufacture, Vol. 47, pp. 946-961 https://doi.org/10.1016/j.ijmachtools.2006.07.007
  4. Kang, D., Kim, K., Choi, Y., Gweon, D., Lee, S. and Lee, M., 2005, 'Design and Control of Flexure Based X Y ${\theta}_Z$ Stage,' Journal of Mechanical Science and Technology, Vol. 19, No. 11, pp. 2157-2164 https://doi.org/10.1007/BF02916513
  5. Park, J. H., 2003, 'Development of the 6 DOF Ultra Precision Positioning System using the PZT Actuators and Elastic Hinges' , Ph.D Thesis for mechanical engineering, Seoul National University.
  6. Piezomechanik GmbH catalog, 2009, www. piezomechanik.com, accessed March 23, 2009
  7. Kuhnen, K. and Janocha, H., 2001, 'Inverse Feedforward Controller for Complex Hysteretic Nonlinearities in Smart-Material Systems,' Control Intell. Syst., vol. 29, pp. 74-83
  8. Kuhnen, K. and Janocha, H., 2002, 'Complex Hysteresis Modeling of a Broad Class of Hysteretic Nonlinearities,' Proc. 8th Int. Conf. New Actuators, pp. 688-691
  9. Slotine, J. E. and Li, W., 1991, Applied Nonlinear Control, Prentice-Hall, pp. 157-187
  10. Bergen, A. R., Chua, L. O., Mees, A. I. and Szeto, E. W., 1982, 'Error Bounds for General Describing Function Problems,' IEEE Transactions on Circuits and Systems, Vol. CAS-29, No. 6, pp. 345-354 https://doi.org/10.1109/TCS.1982.1085166
  11. Cavallo, A., Natale, C., Pirozzi, S. and Visone, C., 2005, 'Limit Cycles in Control Systems Employing Smart Actuators with Hysteresis,' IEEE/ASME Trans. on Mechatronics, Vol. 10, No. 2, pp. 172-180 https://doi.org/10.1109/TMECH.2005.844711
  12. Shan, X., Kuo, S., Zhang, J. and Menq, C., 2002, '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 https://doi.org/10.1109/3516.990889
  13. Paros, J. M. and Weisbord, L., 1965, 'How to Design Flexure Hinges,' Machine Design, Vol. 37, pp. 151-156
  14. Bashash, S. and Jalili N., 2007, 'Robust Multiple Frequency Trajectory Tracking Control of Piezoelectrically Driven Micro/Nanopositioning Systems,' IEEE Trans. on Control Systems Technology, Vol. 15, No. 5, pp. 867-878 https://doi.org/10.1109/TCST.2007.902949