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      • Dept. of Electrical and Electronics Engineering - Ph.D. / Sc.D.
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      • Bilkent Theses
      • Theses - Department of Electrical and Electronics Engineering
      • Dept. of Electrical and Electronics Engineering - Ph.D. / Sc.D.
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      Robustly and strongly stabilizing low order controller design for infinite dimensional systems

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      Author
      Yücesoy, Veysel
      Advisor
      Özbay, Hitay
      Date
      2018-07
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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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 Stabilization
      Strong Stabilization
      Stable Controller
      Finite Dimensional Controller
      In_Nite Dimensional Systems
      Analytic İnterpolation
      Nevanlinna-Pick İnterpolation
      Modi_Ed Nevanlinna-Pick İnterpolation
      Bounded Unit İnterpolation
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      http://hdl.handle.net/11693/47692
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      • Dept. of Electrical and Electronics Engineering - Ph.D. / Sc.D. 136

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