3,129 research outputs found
Application of Lanczos vectors to control design of flexible structures
This report covers research conducted during the first year of the two-year grant. The research, entitled 'Application of Lanczos Vectors to Control Design of Flexible Structures' concerns various ways to obtain reduced-order mathematical models for use in dynamic response analyses and in control design studies. This report summarizes research described in several reports and papers that were written under this contract. Extended abstracts are presented for technical papers covering the following topics: controller reduction by preserving impulse response energy; substructuring decomposition and controller synthesis; model reduction methods for structural control design; and recent literature on structural modeling, identification, and analysis
A Lanczos Method for Approximating Composite Functions
We seek to approximate a composite function h(x) = g(f(x)) with a global
polynomial. The standard approach chooses points x in the domain of f and
computes h(x) at each point, which requires an evaluation of f and an
evaluation of g. We present a Lanczos-based procedure that implicitly
approximates g with a polynomial of f. By constructing a quadrature rule for
the density function of f, we can approximate h(x) using many fewer evaluations
of g. The savings is particularly dramatic when g is much more expensive than f
or the dimension of x is large. We demonstrate this procedure with two
numerical examples: (i) an exponential function composed with a rational
function and (ii) a Navier-Stokes model of fluid flow with a scalar input
parameter that depends on multiple physical quantities
Unsymmetric Lanczos model reduction and linear state function observer for flexible structures
This report summarizes part of the research work accomplished during the second year of a two-year grant. The research, entitled 'Application of Lanczos Vectors to Control Design of Flexible Structures' concerns various ways to use Lanczos vectors and Krylov vectors to obtain reduced-order mathematical models for use in the dynamic response analyses and in control design studies. This report presents a one-sided, unsymmetric block Lanczos algorithm for model reduction of structural dynamics systems with unsymmetric damping matrix, and a control design procedure based on the theory of linear state function observers to design low-order controllers for flexible structures
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