Accounting for Out-of-Bandwidth Modes in the Assumed Modes Approach: Implications on Colocated Output Feedback Control

[+] Author and Article Information
R. L. Clark

Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300

J. Dyn. Sys., Meas., Control 119(3), 390-395 (Sep 01, 1997) (6 pages) doi:10.1115/1.2801270 History: Received September 01, 1995; Online December 03, 2007


Colocated, output feedback is commonly used in the control of reverberant systems. More often than not, the system to be controlled displays high modal density at a moderate frequency, and thus the compliance of the out-of-bandwidth modes significantly influences the performance of the closed-loop system at low frequencies. In the assumed modes approach, the inclusion principle is used to demonstrate that the poles of the dynamic system converge from above when additional admissible functions are used to expand the solution. However, one can also interpret the convergence of the poles in terms of the zeros of the open-loop system. Since colocated inputs and outputs are known to have interlaced poles and zeros, the effect of a modification to the structural impedance locally serves to couple the modes of the system through feedback. The poles of the modified system follow loci defined by the relative location of the open-loop poles and zeros. Thus, as the number of admissible functions used in the series expansion is increased, the interlaced zeros of the colocated plant tend toward the open-loop poles, causing the closed-loop poles to converge from above as predicted by the inclusion principle. The analysis and results presented in this work indicate that the cumulative compliance of the out-of-bandwidth modes and not the modes themselves is required to converge the zeros of the open-loop system and the poles of the closed-loop system.

Copyright © 1997 by The American Society of Mechanical Engineers
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