Vibration Suppression Using a Constrained Rate-Feedback-Threshold Control Strategy

[+] Author and Article Information
D. C. Zimmerman

Department of Aerospace Engineering, Mechanics & Engineering Science, University of Florida, Gainesville, FL 32611

D. J. Inman

Department of Mechanical & Aerospace Engineering, State University of New York at Buffalo, Buffalo, NY 14260

J.-N. Juang

Spacecraft Dynamics Branch, NASA Langley Research Center, Hampton, VA 23665

J. Vib. Acoust 113(3), 345-353 (Jul 01, 1991) (9 pages) doi:10.1115/1.2930191 History: Received January 01, 1990; Revised September 01, 1990; Online June 17, 2008


A finite time, minimum force rate-feedback-threshold controller is developed to bring a system with or without known external disturbances back into an “allowable” state bound in finite time. The disturbances are assumed to be expandable in terms of Fourier series. The optimal control is defined by a two-point boundary value problem coupled to a set of definite integral constraints. Quasi-closed form solutions are derived which replace the solution of the two-point boundary value problem and definite integral constraints with the solution of algebraic equations and the calculation of matrix exponentials. Examples are provided which demonstrate the threshold control technique and compare the quasi-closed form solutions with numerical and MACSYMA generated exact solutions.

Copyright © 1991 by The American Society of Mechanical Engineers
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