Frequency domain based identification of processes using limit cycle information

In this paper, general expressions for the identification of various processes in terms of a stable and unstable first order plus dead time (FOPDT) models are derived. During the identification test, a nonlinear device (relay) is connected to an unknown process through a feedback path which yields sustained oscillations known as limit cycle. The equivalent gain of an asymmetrical relay is approximated by describing function (DF) approach and further used in the deduction of mathematical expressions for process identification. When the process output is subjected to measurement noise, multiple switching at the relay output brings chattering at the output. Therefore, a Fourier series based curve fitting method is utilized in order to retrieve a clean limit cycle output. Further, to show the supremacy of the proposed method comparisons between estimated and actual process models are drawn using frequency response plots.