Improved fourier transform to estimate frequency responses

For the automatic tuning of PID controllers, a new identification method is proposed to estimate the frequency responses of the process from the activated process input and output. It can extract many more frequency responses as well as guarantee better accuracy compared with the previous describing function analysis algorithm. Also, the proposed method can be applied to the case that the initial part of the activated process input and output is periodic (cyclic-steady-state), whereas the previous method using the modified Fourier transform cannot incorporate the case.