Modeling and Robust Control of Large Flexible Space Structures
SCG Report 9609 -- PhD Thesis by Benoit BOULET, 1995
Abstract
In this thesis, we consider the problem of robust control of large flexible space
structures (LFSS). Dynamic models of LFSS are characterized by their high order
and their significant number of highly uncertain, lightly-damped, clustered
low-frequency modes. We propose the use of a left-coprime factorization (LCF) of
LFSS dynamics in modal coordinates for robust control design. The plant
uncertainty is described as stable perturbations of the coprime factors. The
structure of the LCF allows us to transform easily modal parameter uncertainty
into an unstructured description of the uncertainty as stable norm-bounded
perturbations in the factors. The resulting set of perturbed LCFs is guaranteed
to include all perturbed plant models produced by variations in the modal
parameters within their bounds. Uncertainty in the modal factors can also
represent unmodeled modes and actuator dynamics. Closed-loop robustness to
perturbations of the modal parameters within a priori bounds is guaranteed
provided that the infinity-norm of a certain closed-loop sensitivity matrix can be
made less than one with a stabilizing controller. Two multivariable
designs and two mu-synthesis designs for an LFSS experimental testbed are
presented together with simulation and experimental results to illustrate the
technique.
Once a family of perturbed LCF models has been derived from the LFSS model in
modal coordinates, it is often desirable to test if it is consistent with a set of
experimental data obtained on the plant. The objective is to reduce plant model
uncertainty. The model/data consistency problem for coprime factorizations
considered here is this: Given some possibly noisy frequency-response data
obtained by running open or closed-loop experiments on the system, show that these
data are consistent with a given family of perturbed factor models and a noise
model. The results given are applicable to a large class of systems admitting
coprime factorizations in R. A theorem on
boundary interpolation in R is a building block
that allows us to devise computationally simple necessary and sufficient tests to
check if the perturbed coprime factorization is consistent with the data. The
cases of noise-free and noisy open-loop and closed-loop frequency-response data
are treated.
