Control-Oriented Order Reduction of Finite Element Model

[+] Author and Article Information
K. Harold Yae

Department of Mechanical Engineering, Center for Simulation and Design Optimization, The University of Iowa, Iowa City, IA 52242

Daniel J. Inman

Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

J. Dyn. Sys., Meas., Control 115(4), 708-711 (Dec 01, 1993) (4 pages) doi:10.1115/1.2899200 History: Received October 02, 1990; Revised December 29, 1992; Online March 17, 2008


In the dynamics modeling of a structure, finite element analysis employs reduction techniques, such as Guyan’s reduction, that remove some of the “insignificant” physical coordinates, that is, degrees of freedom at a node point. Despite such reduction, the resultant model is still too large for control design. This warrants further reduction as is frequently done in control design by approximating a large dynamical system with a fewer number of state variables. A problem, however, arises because a model usually undergoes, before being reduced, some form of coordinate transformations that destroy the physical meanings of the states. To correct such a problem, we developed a method that expresses a reduced model in terms of a subset of the original states. The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. The model is then converted to a state-space form, and reduced further by the internal balancing method. At this stage, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transformation that is developed in this paper, however, this reduced model is expressed by a subset of the original states, so that the states in the reduced model can be related to the degrees of freedom of the nodes in the original finite element model.

Copyright © 1993 by The American Society of Mechanical Engineers
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