Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
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Optimal Placement of Sensors and Actuators Using Measures of Modal Controllability and Observability in a Balanced Coordinate

  • Park, Un-Sik (Department of Computer-Controlled Mechanical Systems, Graduate School of Engineering Osaka University) ;
  • Choi, Jae-Weon (School of Mechanical Engineering and Research Institute of Mechanical Technology Pusan National University) ;
  • Yoo, Wan-Suk (School of Mechanical Engineering and Research Institute of Mechanical Technology Pusan National University) ;
  • Lee, Man-Hyung (School of Mechanical Engineering and Research Institute of Mechanical Technology Pusan National University) ;
  • Son, Kwon (School of Mechanical Engineering and Research Institute of Mechanical Technology Pusan National University) ;
  • Lee, Jang-Myung (School of Mechanical Engineering and Research Institute of Mechanical Technology Pusan National University) ;
  • Lee, Min-Cheol (School of Mechanical Engineering and Research Institute of Mechanical Technology Pusan National University) ;
  • Han, Sung-Hyun (Department of Mechanical Engineering Kyungnam University)
  • Published : 2003.01.01
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Abstract

In this paper, a method for optimal placement of sensors and actuators is presented by using new measures of modal controllability and observability defined in a balanced coordinate system. The proposed new measures are shown to have a great advantage in practical use when they are used as criteria for selecting the locations of sensors and actuators, since the most controllable and observable locations can be obtained to be identical. In addition, they are more accurate than the measures of Hamdan and Nayfeh in that the effects of the eigenvector norm are considered into the magnitude of measures. In simulations, to verify the effectiveness of the proposed measures and optimal placement method, the closed-loop response of a simply supported flexible beam, in which the number and locations of actuators are determined by using the proposed measures and optimal placement method, has been examined and compared with the case of Hamdan and Nayfeh’s measures.

Keywords

References

  1. Aguirre, L. A., 1995, 'Controllability and Observability of Linear System: Some Noninvariant Aspects,' IEEE Transactions on Education, Vol. 38, No. 1, pp. 33-39 https://doi.org/10.1109/13.35021810.1109/13.350218
  2. Balas, M. J., 1982, 'Trends in Large Space Structure Control Theory : Fondest Hopes, Wildest Dreams,' IEEE Transactions on Automatic Control, Vol. 27, No. 3, pp. 522-535 https://doi.org/10.1109/TAC.1982.1102953
  3. Chen, C. T., 1979, Linear System Theory and Design, Holt, Reiehart, and Winston, New York
  4. Choi, J. W., Lee, J. G., Kim, Y. and Kang, T., 1995, 'Design of an Effective Controller via Disturbance Accommodating Left Eigenstructure Assignment,' Journal of Guidance, Control, and Dynamics, Vol. 18, No. 2, pp. 347-354 https://doi.org/10.2514/3.21390
  5. Hnmdan, A. M. A., and Nayfeh, A. H., 1989a, 'Measures of Modal Controllability and Observability for First - and Second - Order Linear Systems,' Journal of Guidance, Control. and Dynamics, Vol. 12, No. 3, pp. 421-428 https://doi.org/10.2514/3.20424
  6. Hamdam, A. M. A. and Nayfeh, A. H., 1989b, 'Eigenstructure of the State Matrix of Balanced Realization,' Journal of Guidance, Control, and Dynamics, Vol. 12, No. 4, pp. 605-607 https://doi.org/10.2514/3.56494
  7. Hyland, D. C., Junkins, J. L. and Longman, R. W., 1993, 'Active Control Technology for Large Space Structures,' Journal of Guidance, Control. and Dynamics, Vol. 16, No. 5, pp. 801-821 https://doi.org/10.2514/3.21087
  8. Junkins, J. L. and Kim, Y., 1993, Introduction to Dynamics and Control of Flexible Sturctures, AIAA Education Series, Washington D. C., American Institute of Aeronautics and Astronautics, Inc
  9. Kailath, T., 1980, Linear Systems, Prentice-Hall, Englewood Cliffs, N. J.
  10. Linder, D. K., Babendreier, J. and Hamdan, A. M. A., 1989, 'Measures of Controllability and Observability and Residue,' IEEE Transactions on Automatic Control, Vol. 34, No. 6, pp. 648-650 https://doi.org/10.1109/9.24240
  11. Longman, R. W., Sirlin, S. W., Li, T. and Sevaston, G., 1982, 'The Fundamental Structure of Degree of Controllability and Degree of Observability,' AIAA/AAS Paper 82-1434, San Diego, CA
  12. IEEE Transactions on Aerospace and Electronic Systems v.29 no.2 Sensor/Actuator Placement for Flexible Space Structure Maghami, P. G.;Joshi, S. M. https://doi.org/10.1109/7.210073
  13. Maghami, P. G. and Joshi, S. M., 1993, 'Sensor/Actuator Placement for Flexible Space Structure,' IEEE Transactions on Aerospace and Electronic Systems, Vol. 29, No. 2, pp. 345-351 https://doi.org/10.1109/7.21007310.1109/7.210073
  14. Moore, B. C., 1981, 'Principal component analysis in linear systems: Controllability, observability and model reduction,' IEEE Transactions on Automatic Control, Vol. 26, No. 1, pp. 17-32 https://doi.org/10.1109/TAC.1981.1102568
  15. Nurre, G. S., Ryan, R. S., Scofield, H. N. and Sims, J. L., 1984, 'Dynamics and Control of Large Space Structures,' Journal of Guidance, Control, and Dynamics, Vol. 7, No. 5, pp. 514-526 https://doi.org/10.2514/3.19890
  16. Yam, Y., Johnson, T. L., and Lang, J. H., 1987, 'Flexible System Model Reduction and Control System Design Based upon Actuator and Sensor Influence Functions,' IEEE Transactions on Automatic Control, Vol. 32, No. 7, pp. 573-582 https://doi.org/10.1109/TAC.1987.1104681