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A new process 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 and guarantees better accuracy than the previous describing function analysis algorithm. In addition, the proposed method can be applied to the case that the initial part of the activated process data is periodic (cyclic-steady-state), which is not possible with any previous nonparametric identification methods using the modified Fourier transform or Fourier analysis. Furthermore, it can incorporate all the cases in which either the initial part is steady-state and the final part is cyclicsteady-state or both the initial and final parts are steady-state. V

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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.