Improved Fourier transform for processes with initial cyclic‐steady‐state

Abstract

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

Improved frequency response model identification method for processes with initial cyclic‐steady‐state

“…The proposed algorithm provides accurate frequency responses data sets for all desired frequencies and can be applied to various process conditions. It need not have to store the process input and output data, while the most advanced previous method10 requires a significant amount of memory for a data preprocessing step. Furthermore, the proposed method completely removes the effects of static disturbances and shows good robustness to measurement noises.…”

“…Also, it need not have to store the process input and output data. Meanwhile, the most advanced previous method requires a significant amount of memory for the data preprocessing step 10…”

“…They cannot incorporate the case in which both the initial part and the final part are cyclic‐steady‐state. So, Cheon et al10 proposed a new method which can be applied to a greater variety of situations (initial/final steady‐state, initial steady‐state/final cyclic‐steady‐state, and initial/final cyclic‐steady‐state). It also provides exact frequency responses for all desired frequencies.…”

“…It has the ability to provide exact frequency responses for all desired frequencies as well as it is applicable to various conditions of processes (both initial/final steady‐state, initial steady‐state/final cyclic‐steady‐state and both initial/final cyclic‐steady‐state). Also, it requires a smaller amount of memory than the previous method10 because it does not require any data preprocessing step. Furthermore, it provides the exact models even in the presence of a static disturbance and shows an acceptable robustness to measurement noises.…”

Asymmetric delayed relay feedback identification based on the n -shifting approach

“…However, as the describing function (DF) based methods give points in the Nyquist map whose accuracy depends on the filtering capacity of the process, other methods have been proposed based on different modifications of the Fourier transform (Cheon et al, 2010;Cheon et al, 2011;Ma & Zhu, 2006;Sung & Lee, 2000;Wang et al, 1997;. All these algorithms have in common that they use all the process data from the initial transient region to the final cyclic steady-state part of the experiment.…”