Implementation of Fractional Order PID Controller Tuning Methods Based on Control System Frequency Response

Functions with fractional order (FO) diffintegrals do not have general analytical solutions in time domain and precise numerical methods are expensive. Control system tuning methods are iterative and especially in case of FO the function value computations can be time consuming. Time domain based numerical methods for calculating step and impulse response can have a static error while the frequency domain method is claimed to be exact. This thesis analyzes step response in frequency domain using Fourier series of a low frequency square wave (FSM) method for fractional order PID controller tuning. The thesis has found that the method is promising, but sensitive to optimized function and frequency range choice and in case of unstable functions does not always give precise results. Some methods are created to improve the precision.