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In this paper, an optimization method is proposed to design a fractional order system with PID controller by taking Bode’s ideal transfer function as reference model. In the study, PID controllers are preferred because of their simplicity, reliability and robustness. PID controller parameters can be obtained by optimization method. In order to obtain the desired time response, it is sufficient to set two parameters in the Bode’s ideal transfer function. The Bode's ideal transfer function was considered as the reference model and compared with the generated model. The error in the output signal is minimized by the integral performance criteria, and the PID controller parameters are optimized. Integral performance criteria are frequently used in evaluating the performance of control systems. In Simulink model, Matsuda's 4th order integer approximation model is used for fractional order control system. Finally, the success of the optimization method is seen in the given numerical example.

PID Controller Design for a Fractional Order System using Bode’s Ideal Transfer Function