Identification of underdamped process dynamics

This paper presents off-line and on-line identification of underdamped process dynamics in terms of transfer function models. Simple analytical expressions are derived based on the describing function technique. The nonlinear device relay with hysteresis is used to extract process information that help in estimating the unknown process model parameters. Another advantage of relay with hysteresis is that it reduces the effect of measurement noise, which is common in process industries. To further eliminate the ill effects of noise, the Fourier series-based curve fitting technique is employed. Unlike many identification methods that require to solve simultaneously a set of nonlinear equations, the advantage of the proposed method is that the process model parameters are estimated using explicit analytical expressions. The validity and robustness of the proposed method is illustrated with the help of six typical transfer function models from the literature. Results with and without noise are compared using Nyquist's plots.