Robust analysis and design of fractional order control systems

The notion of fractional order derivative and integral has been known since the development of conventional calculus. Generally, however, due to its complexity, it has been studied by the mathematicians for a long time. The most important property of the fractional order representation is that it is more accurate to describe real world systems than those of integer order models. In this thesis, the robust analysis and design of the fractional order control systems has been studied. The results obtained can be summarized as follows: Integer order approximations of s^? for ?=0.1,0.2,?,0.9 by using continued fraction expansion method have been calculated and each of them is given in a table. Equivalent integer order transfer functions of fractional order derivative (s^([??,¯?])) having interval order uncertainty are computed. The design of PI, PD and PID controllers for fractional order systems with time delay has been done using stability boundary locus method. Integer order approximations are used to show the effects of the order of approximation and original system on the stability region. Then, the extension of the stability boundary locus method for computation of all stabilizing fractional order PI^? D^?, PI^? and PD^? controllers to the fractional order systems with time delay is given. To investigate time domain analysis of fractional order controllers, MATLAB Simulink block diagrams are constructed. Design of PI^? controller for the fractional order systems with time delay using weighted geometrical center method is presented. Stability of fractional order polynomials having parametric uncertainty (Fractional Order Interval Polynomials-FOIP) is studied. It has been shown that the Kharitonov theorem is not sufficient for testing robust stability of the FOIP. A method based on the edge theorem for construction of the value set and robust stability results of the FOIP family are presented. Besides, robust stability of the fractional order system having interval order uncertainty has been studied. Some results related to real time control of inverted pendulum system by using fractional order PI^? D^? controller are presented. KEY WORDS: Fractional order control systems, fractional order controllers, PID, parametric uncertainty, robust stability, integer order approximations, inverted pendulum.