2 research outputs found
Modelling and control of coupled infinite-dimensional systems
First, we consider two classes of coupled systems consisting of an infinite-dimensional
part [sigma]d and a finite-dimensional part [sigma]f connected in feedback. In the first class of coupled
systems, we assume that the feedthrough matrix of [sigma]f is 0 and that [sigma]d is such that
it becomes well-posed and strictly proper when connected in cascade with an integrator.
Under several assumptions, we derive well-posedness, regularity and exact (or approximate)
controllability results for such systems on a subspace of the natural product state
space. In the second class of coupled systems, [sigma]f has an invertible first component in its
feedthrough matrix while [sigma]d is well-posed and strictly proper. Under similar assumptions,
we obtain well-posedness, regularity and exact (or approximate) controllability results as
well as exact (or approximate) observability results for this class of coupled systems on
the natural state space.
Second, we investigate the exact controllability of the SCOLE (NASA Spacecraft Control
Laboratory Experiment) model. Using our theory for the first class of coupled systems,
we show that the uniform SCOLE model is well-posed, regular and exactly controllable
in arbitrarily short time when using a certain smoother state space.
Third, we investigate the suppression of the vibrations of a wind turbine tower using
colocated feedback to achieve strong stability. We decompose the system into a
non-uniform SCOLE model describing the vibrations in the plane of the turbine axis,
and another model consisting of a non-uniform SCOLE system coupled with a two-mass drive-train model (with gearbox), in the plane of the turbine blades. We show the strong
stabilizability of the first tower model by colocated static output feedback. We also prove
the generic exact controllability of the second tower model on a smoother state space
using our theory for the second class of coupled systems, and show its generic strong
stabilizability on the energy state space by colocated feedback