SEMINAR: ROBUSTLY AND STRONGLY STABILIZING LOW ORDER CONTROLLER DESIGN FOR INFINITE DIMENSIONAL SYSTEMS
Ph.D. Defence in Electrical and Electronics Engineering
Supervisor: PROF. DR. HİTAY ÖZBAY
The seminar will be on Tuesday, July 3, 2018 at 14:30, @EE-314
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. We provide numerical examples for each proposed method to show the e_ectiveness and the conservatism of each method.
Keywords: Robust stabilization, Strong stabilization, Stable controller, Finite dimensional controller, In_nite dimensional systems, Analytic interpolation, Nevanlinna-Pick interpolation, Modi_ed Nevanlinna-Pick interpolation, Bounded unit interpolation.