Robustly and strongly stabilizing low order controller design for infinite dimensional systems
Author
Yücesoy, Veysel
Advisor
Özbay, Hitay
Date
2018-07Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
This thesis deals with the robust stabilization of in nite dimensional systems by
stable and low order controllers. The close relation between the Nevanlinna-Pick
interpolation problem and the robust stabilization is well known in the literature.
In order to utilize this relation, we propose a new optimal solution strategy for
the Nevanlinna-Pick interpolation problem. Di erently from the known suboptimal
solutions, our method includes no mappings or transformations, it directly
solves the problem in the right half plane. We additionally propose a method via
suboptimal solutions of an associated Nevanlinna-Pick interpolation problem to
robustly and strongly stabilize a set of plants which include the linearized models
of two well known under actuated robots around their upright equilibrium
points. In the literature, it is shown that the robust stabilization of an in nite
dimensional system by stable controllers can be reduced to a bounded unit interpolation
problem. In order to use this approach to design a nite dimensional
controller, we propose a predetermined structure for the solution of the bounded
unit interpolation problem. Aforementioned structure reduces the problem to a
classical Nevanlinna-Pick interpolation problem which can be solved by the optimal
solution strategy of this thesis. Finally, by combining the nite dimensional
solutions of the bounded unit interpolation problem with the nite dimensional
approximation techniques, we propose a method to design nite dimensional and
stable controllers to robustly stabilize a given plant. Since time delay systems are
one of the best examples of in nite dimensional systems, we provide numerical
examples of various time delay systems for each proposed method.
Keywords
Robust StabilizationStrong Stabilization
Stable Controller
Finite Dimensional Controller
In_Nite Dimensional Systems
Analytic İnterpolation
Nevanlinna-Pick İnterpolation
Modi_Ed Nevanlinna-Pick İnterpolation
Bounded Unit İnterpolation