Investigation and applications of various analytical controller design methods

Analytical design schemes of proportional integral, proportional derivative and fractional order proportional integral controllers for the stability, robustness and performance of first and second order plus time delay models are presented in this thesis. Presented method gives the generalized equations for mentioned systems. Tuning of the controller parameters are inspired from the characteristics of an ideal system. Throughout the theorems given in the thesis, first, controller parameters are obtained to satisfy desired gain crossover frequency and phase margin for first and second order models. Then, with the proposed method "frequency frame", parameters of the fractional order proportional integral controller are obtained to satisfy gain crossover frequency, phase crossover frequency and phase margin properties simultaneously. Since the proposed method can be used to shape the phase curve of the Bode plot, it is observed that the method improved both the stability and the robustness of the system. All proposed theorems are tested on existing models from the literature and effectiveness of the results obtained from the thesis are shown. KEYWORDS: Analytical, Controller, Design Methods, Stability, Applications