Book ChapterDOI
Principal component analysis of flexible systems--Open-loop case
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In this paper, a generic class of flexible systems, characterized by finitely many lightly damped harmonic oscillators, is analyzed by means of the "open-loop principal component analysis", that is, singular value analysis and Gramian balancing.Abstract:
A generic class of flexible systems, characterized by finitely many lightly damped harmonic oscillators, is analyzed by means of the "open-loop principal component analysis," that is, singular value analysis and Gramian balancing. As the main result, it is shown that, as the damping ratio goes to zero, the balanced state coordinates are decoupled and coincide with the modal coordinates. Further, simple formulas expressing the "asymptotic singular values" as functions of the modal parameters are derived.read more
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Book ChapterDOI
Model reduction for flexible structures
Wodek Gawronski,Jer-Nan Juang +1 more
TL;DR: In this article, a robust model reduction technique was developed to study the sensitivity of modeling error to variations in the damping of a structure and new concepts of grammians defined over a finite time and/or a frequency interval were proposed.
Journal ArticleDOI
Mechanical and Control-Oriented Design of a Monolithic Piezoelectric Microgripper Using a New Topological Optimization Method
TL;DR: In this paper, an evolutionary approach is used to optimize a truss-like planar structure made of passive and active building blocks, made of piezoelectric material.
Journal ArticleDOI
Model reduction for flexible space structures
Wodek Gawronski,Trevor Williams +1 more
TL;DR: In this article, the conditions under which modal truncation yields a near-optimal reduced-order model for a flexible structure are presented, and a robust model reduction technique to cope with the damping uncertainties typical of flexible space structure is developed.
Journal ArticleDOI
Selection of component modes for flexible multibody simulation
John T. Spanos,Walter S. Tsuha +1 more
TL;DR: In this article, a mode selection procedure is outlined whereby component modes are selected from the Craig-Bampton (fixed interface plus constraint), MacNeal-Rubin (free interface plus residual), or Benfield-Hruda (loaded interface) mode sets in accordance with a modal ordering scheme derived from balanced realization theory.
Journal ArticleDOI
Balanced actuator and sensor placement for flexible structures
W. Gawronski,K. B. Lim +1 more
TL;DR: In this article, the root-mean-square law of the Hankel singular values is derived for flexible structures in modal and balanced coordinates, and the properties of flexible structures are derived from these properties.
References
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Journal ArticleDOI
Principal component analysis in linear systems: Controllability, observability, and model reduction
TL;DR: In this paper, it is shown that principal component analysis (PCA) is a powerful tool for coping with structural instability in dynamic systems, and it is proposed that the first step in model reduction is to apply the mechanics of minimal realization using these working subspaces.
Journal ArticleDOI
Linear Operators. Part I: General Theory.
TL;DR: Dunford and Schwartz as discussed by the authors provided a comprehensive survey of the general theory of linear operations, together with applications to the diverse fields of more classical analysis, and emphasized the significance of the relationships between the abstract theory and its applications.
Book
Infinite dimensional linear systems theory
TL;DR: In this paper, a mathematical framework in terms of semigroups is developed which enables the generalisation of the finite-dimensional results to infinite dimensions, and which includes partial differential equations and delay equations as special cases.
Journal ArticleDOI
Feedback control of flexible systems
TL;DR: In this paper, a feedback controller is developed for a finite number of modes of the flexible system and the controllability and observability conditions necessary for successful operation are displayed, and the combined effect of control and observation spillover is shown to lead to potential instabilities in the closed-loop system.