State of the art in linear system identification: time and frequency domain methods

Abstract

Identi cation of time-invariant linear dynamic systems is a mature subject. In this contribution we focus on the interplay between methods that use time and frequency domain data, respectively. The frequency domain data could be either input/output Fourier transforms or frequency functions. We explain how these di erent kinds of data types are used to t models, and how closely related the methods are. Of special interest is how transients (initial conditions and deviations from periodic signals) are handled. Direct estimation of time-continuous models is also discussed, as well as software aspects.Keywords: identi cation State of the Art in Linear System Identification: Time and Frequency Domain Methods Lennart LjungAbstract-Identification of time-invariant linear dynamic systems is a mature subject. In this contribution we focus on the interplay between methods that use time and frequency domain data, respectively. The frequency domain data could be either input/output Fourier transforms or frequency functions. We explain how these different kinds of data types are used to fit models, and how closely related the methods are. Of special interest is how transients (initial conditions and deviations from periodic signals) are handled. Direct estimation of timecontinuous models is also discussed, as well as software aspects.

System identification of Active Magnetic Bearing for commissioning

“…Time and frequency domain data are equivalent and the duality between them have emerged recently [25]. The primary issue with frequency domain methods, and the reason it got a bad name, is spectral leakage while transforming time-domain data into frequency domain (Discrete Fourier Transform or DFT) [23].…”

Estimating the “effective period” of bilinear systems with linearization methods, wavelet and time-domain analyses: From inelastic displacements to modal identification

“…Perhaps, the most well known and powerful method in the system identification community is the Prediction Error Method (PEM). It initially emerged from the maximum likelihood framework of Aström and Bohlin [19] and subsequently was widely accepted via the corresponding MATLAB [20] identification toolbox developed following the theory advanced by Ljung [21], [22], [23]. Figure 4(center-left) plots with a heavy dark line the signal generated with the prediction error method (PEM) that best identifies the acceleration response history of bilinear system with strength / 0.155 Q m g  , first period 1 0.…”

“…One of the most well known and powerful methods for linear systems in the system identification community is the Prediction Error Method (PEM). It initially emerged from the maximum likelihood framework of Aström and Bohlin [19] and subsequently was widely accepted via the corresponding MATLAB [20] identification toolbox developed following the theory advanced by Ljung [21], [22], [23]. In this work the prediction error method is also employed to extract the dominant effective period of the response of bilinear hysteretic systems and the results obtained from this time domain method are compared with the results obtained with the abovementioned time-frequency analysis (wavelet transform) and the equivalent linearization methods also introduced in this section.…”

Learning Non-linear Multivariate Dynamics of Motion in Robotic Manipulators

“…Building a local approximation of the dynamics has been first reviewed within the time series analysis [Priestley, 1980, Chamroukhi et al, 2009, Ljung, 2004. These works consider solely uni-dimensional data with a major motivation of predicting time series.…”