Frequency response analysis and design of the fractional order control systems

A system represented by differential equations where the orders of derivatives can take any real number, can be considered as a fractional order system. The fractional order differential equations are more adequate to describe real world systems than those of integer order models. Fractional calculus also finds great application areas in control engineering. In this thesis, some frequency response analysis and design techniques for fractional order control systems (FOCS) are presented. In this regard, some programs are developed to obtain frequency response plots for FOCS. The extensions of some results developed in the parametric robust control to fractional order interval control systems (FOICS) are presented. Computation of the Bode and Nyquist envelopes of FOICS are studied. Absolute stability of the FOICS are analyzed using Nyquist envelopes in the light of Lur?e, Popov and Circle criterion. These results are used for analysis and design of FOCS in the subsequent chapters of the thesis. This thesis also includes development of some controller design techniques for FOCS, such as; a new tuning method for fractional order PID ( ) controller, a new tuning method for robust controller for first order plus dead time systems, design of robust controllers for control systems with a fractional order interval transfer function using classical design methods, tuning of PID controller based on fractional order reference model using optimization techniques. Extension of some results, which are obtained for classical nonlinear control systems, to fractional order case are also studied in this thesis, such as; limit cycle prediction for nonlinear systems which have fractional order transfer functions, auto-tuning of PID controller for nonlinear control systems which have fractional order transfer functions, stability margin computation for fractional order nonlinear control system with parametric uncertainty structure. A real time application of the controller in a prototype helicopter model is also included in the thesis.