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.
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References
Aguirre, L. A., 1995, “Controllability and Observability of Linear System: Some Nonin-variant Aspects,”IEEE Transactions on Education, Vol. 38, No. 1, pp. 33–39.
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.
Chen, C. T., 1979.Linear System Theory and Design, Holt, Reiehart, and Winston, New York.
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.
Hamdan, 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.
Hamdan, 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.
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.
Junkins, J. L. and Kim, Y., 1993,Introduction to Dynamics and Control of Flexible Structures, AIAA Education Series, Washington D. C, American Institute of Aeronautics and Astronautics, Inc.
Kailath, T., 1980,Linear Systems, Prentice-Hall, Englewood Cliffs, N.J.
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.
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.
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.
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.
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.
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.
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Park, U.S., Choi, J.W., Yoo, WS. et al. Optimal placement of sensors and actuators using measures of modal controllability and observability in a balanced coordinate. KSME International Journal 17, 11–22 (2003). https://doi.org/10.1007/BF02984281
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DOI: https://doi.org/10.1007/BF02984281