Title page for ETD etd-10242005-124120
|Type of Document
||Compensator design for a system of two connected beams
|Burns, John A.
|Cliff, Eugene M.
|Gunzburger, Max D.
|Hannsgen, Kenneth B.
|Herdman, Terry L.
- Approximation theory
- Flexible structures Automatic control
- Control theory
|Date of Defense
The goal of this paper is to study the LQG problem for a class of infinite dimensional systems.
We investigate the convergence of compensator gains for such systems when standard
finite element schemes are used to discretize the problem. We are particularly interested
in the analysis of the uniformly exponential stability of the corresponding closed - loop
systems resulting from the finite dimensional compensators. A specific multiple component
flexible structure is used to focus the analysis and to test problem in numerical simulations.
An abstract framework for analysis and approximation of the corresponding dynamics
system is developed and used to design finite - dimensional compensators. Linear semigroup
theory is used to establish that the systems are well posed and to prove the convergence
of generic approximation schemes. Approximate solutions of the optimal regulator and
optimal observer are constructed via Galerkin - type approximations. Convergence of the
scheme is established and numerical results are presented to illustrate the method
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