Modelling and control applications in fractional order systems

In this thesis, a new integer order approximation method for fractional derivative and integral operators is developed using the stability boundary locus method. Various control applications and design techniques have been studied by using the proposed method based on stability boundary locus fitting. The proposed method is compared with well-known different integer order approximation methods found in the literature in terms of the time response and the frequency response, and acceptable results are obtained. In addition, stability analysis for Smith predictor structures is performed by using the stability boundary locus method, and a model identification technique is presented using stability region. In order to evaluate the disturbance rejection capacity of closed loop control systems, a criterion called reference to disturbance ratio criterion is developed and the PID, PIλDμ and PIλ controller designs are realized as a result of the analysis using this criterion. Furthermore, a design strategy for PIλDμ controller based on the optimization of the integral performance criteria obtained by using the Fourier series method is presented. A PI-PD controller design technique suitable for the standard form structure is proposed by using the stability boundary locus fitting method in fractional order systems. A real-time application of the PIλDμ controller design for the inverted pendulum control system by using the proposed integer order approximation method is given in the last section of the thesis.