The modal analysis approach to modeling of structures and acoustic systems results in infinite-dimensional models. For control design purposes, these models are simplified by removing higher frequency modes which lie out of the bandwidth of interest. Truncation can considerably perturb the in-bandwidth zeros of the truncated model. This paper suggests a method of minimizing the effect of the removed higher order modes on the low frequency dynamics of the truncated model by adding a zero frequency term to the low order model of the system. [S0022-0434(00)01501-X]
Issue Section:
Technical Briefs
1.
Meirovitch, L. 1986, Elements of Vibration Analysis, 2nd Edition, McGraw-Hill, Sydney.
2.
Fraser, A. R., and Daniel, R. W., 1991, Perturbation Techniques for Flexible Manipulators, Kluwer Academic Publishers, MA.
3.
Alberts
, T. E.
, Colvin
, J. A.
, 1991
, “Observations on the Nature of Transfer Functions for Control of Piezoelectric Laminates.
” J. Intell. Mater. Syst. Struct.
, 8
, pp. 605
–611
.4.
Hong
, J.
, Akers
, J. C.
, Venugopal
, R.
, Lee
, M.
, Sparks
, A. G.
, Washabaugh
, P. D.
, and Bernstein
, D.
, 1996
, “Modeling, Identification, and Feedback Control of Noise in an Acoustic Duct
,” IEEE Trans. Control Syst. Technol.
, 4
, No. 3
, pp. 283
–291
.5.
Bisplinghoff, R. L., and Ashley, H., 1962, Principles of Aeroelasticity, Dover Publications, New York.
6.
Clark
, R. L.
, 1997
, “Accounting for Out-of-Bandwidth Modes in the Assumed Modes Approach: Implications on Colocated Output Feedback Control
,” ASME J. Dyn. Syst., Meas., Control
, 119
, pp. 390
–395
.7.
Zhu
, X.
, and Alberts
, T. A.
, 1998
, “Appending a Synthetic Mode to Compensate for Truncated Modes in Coliocated Control
,” Proc. of AIAA GNC, Boston.8.
Pota
, H. R.
, and Alberts
, T. E.
, 1995
, “Multivariable Transfer Functions for a Slewing Piezoelectric Laminate Beam
,” ASME J. Dyn. Syst., Meas., Control
, 117
, pp. 353
–359
.9.
Alberts
, T. E.
, DuBois
, T. V.
, and Pota
, H. R.
, 1995
, “Experimental Verification of Transfer Functions for a Slewing Piezoelectric Laminate Beam
,” Control. Eng.
, 3
, pp. 163
–170
.10.
Pota
, H. R.
, and Alberts
, T. E.
, 1997
, “Vibration Analysis Using Symbolic Computation Software
,” Proc. of the 1997 American Control Conference, Albuquerque, NM, pp. 1400–1401.11.
Moheimani
, S. O. R.
, Petersen
, I. R.
, and Pota
, H. R.
, 1997
, “Broadband Disturbance Attenuation over an Entire Beam
,” Proc. European Control Conference, Brussels, Belgium, to appear in the J. Sound. Vib.12.
Moheimani
, S. O. R.
, Pota
, H. R.
, and Petersen
, I. R.
, 1999
, “Spatial Balanced Model Reduction for Flexible Structures
,” Automatica
, 35
, pp. 269
–277
.13.
Moheimani
, S. O. R.
, Pota
, H. R.
, and Petersen
, I. R.
, 1997
, “Active Vibration Control—A Spatial LQR Approach
,” Proc. Control 97, Sydney, Australia, pp. 622–627.14.
Moheimani
, S. O. R.
, Pota
, H. R.
, and Petersen
, I. R.
, 1998
, “Active Control of Noise and Vibration in Acoustic Ducts and Flexible Structures—A Spatial Control Approach
,” Proc. of the 1998 American Control Conference, Philadelphia, PA, pp. 2601–2605.15.
Lewis, F. L., 1992, Applied Optimal Control and Estimation, Prentice Hall, New Jersey.
Copyright © 2000
by ASME
You do not currently have access to this content.