Computation of the optimal H∞ controller for a fractional order system

Ankara : The Department of Electrical and Electronics Engineering and The Graduate School of Engineering and Science of Bilkent University, 2014.Thesis (Master's) -- Bilkent University, 2014.Includes bibliographical references leaves 49-54.This work investigates the H∞ optimal controller design for a fractional order system with time delay. For illustrative purposes, a magnetic suspension system model, derived by Knospe and Zhu is considered. The transfer function is infinite dimensional including e −hs and a rational function of √ s, where h > 0 represents the delay. Recently in a paper by Ozbay, a formulation is given to design the ¨ H∞ optimal controller for the mixed sensitivity minimization problem for unstable infinite dimensional plants with low order weights. This formulation is used to design the H∞ optimal controller for the fractional order system considered, and it is compared to alternative computation methods for H∞ control of infinite dimensional systems. To implement the controller, approximation methods are also investigated. Furthermore, finite dimensional rational approximation techniques of the fractional order integrator are evaluated for simulation purposes.Karagül, Abidin ErdemM.S