Frequency domain identification of FIR models from noisy input – output data (original) (raw)
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The least-squares identification of FIR systems subject to worst-case noise
Systems & Control Letters, 1994
The least-squares identification of FIR systems is analyzed assum.ing that the noise is a bounded signal and the input signal is a pseudo random binary sequence. A lower bowid on the worst-case transfer fWiction error shows that the least-square estimate of the transfer function diverges as the order of the FIR system is increased. Tlus implies that, in the presence of the worst-case noise, the trade-off between the estimation error due to the disturbance and the bias error (due to wunodeled dynanucs) is sigiuficantly different from the corresponding trade-off in the random error case: with a worst-case fonnulation, the model complexity should not increase indefuutely as the size of the data set increases.
IEEE Transactions on Automatic Control, 1999
Presents a generalized frequency domain identification method to identify single-input/single-output (SISO) systems combining two previously published extensions in one method: arbitrary but persistent excitations are allowed and a nonparametric noise model is extracted from the same data that are used to identify the system. The method is directly applicable to identification in feedback if an external persistently exciting reference signal
FIR System Identification Using Feedback
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This paper describes a new approach to finite-impulse (FIR) system identification. The method differs from the traditional stochastic approximation method as used in the traditional least-mean squares (LMS) family of algorithms, in which we use deconvolution as a means of separating the impulse-response from the system input data. The technique can be used as a substitute for ordinary LMS but it has the added advantages that can be used for constant input data (i.e. data which are not persistently exciting) and the stability limit is far simpler to calculate. Furthermore, the convergence properties are much faster than LMS under certain types of noise input.
Proceedings of 1994 33rd IEEE Conference on Decision and Control
In this paper we present a n o vel non-iterative algorithm for identifying linear time-invariant discrete time state-space models from frequency response data. We show that the algorithm recover the true system of order n if n +2 noise-free frequency response measurements are given at uniformly spaced frequencies. The algorithm is demonstrated to be related to the recent timedomain subspace identi cation algorithms formulated in the frequency domain. The algorithm is applied to real frequency data, originating from a exible mechanical structure, with promising results. In a companion paper robustness and stochastic analysis is performed.
IFAC Proceedings Volumes, 2006
System identification often means the determination of linear models from input-output data. The behaviour of many systems can be described by an s-domain or z-domain transfer function model, at least for a given excitation amplitude range. The quality of the fit can be assessed by the analysis of the residuals, that is, of the difference between the measured data and the model. However, even slight nonlinearities can be misleading, by causing part of the residuals non-explicable by the linear model. We cannot simply tell if the excess residual error is due to undermodelling or to nonlinear system behaviour. This can lead to erroneous overmodelling. Therefore, characterisation of the nonlinear system behaviour is essential in the verification of linear models. The Frequency Domain System Identification Toolbox has been extended with analysis tools of nonlinear system behaviour. Specially designed excitation signals allow the description of nonlinearity levels. By this, model verification becomes possible even if nonlinear error terms excess linear additive noise.
A new frequency domain system identification method
Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2011
A new frequency domain system identification method based on a multi-frequency input signal is proposed. Frequency contents of the oscillating signal are estimated using a modified Kaczmarz algorithm proposed in this paper. Lyapunov stability analysis is performed for this new Kaczmarz algorithm and transient bounds for estimation error are established. Moreover, a new method for estimation of the variance of the measurement noise in Kaczmarz algorithms is also described. A comparison of a transient performance of modified Kaczmarz algorithm and a recursive least-squares algorithm is presented. The results are applied to a frequency domain identification of a DC motor.
Blind identification of two-channel FIR systems: a frequency domain approach
IFAC-PapersOnLine
This paper describes a new approach for the blind identification of a two-channel FIR system from a finite number of output measurements, in the presence of additive and uncorrelated white noise. The proposed approach is based on frequency domain data and, as a major novelty, it enables the estimation to be frequency selective. The features of the proposed method are analyzed by means of Monte Carlo simulations. The benefits of filtering the data and using only part of the frequency domain are highlighted by means of a numerical example.
Closed-loop identification of unstable systems using noncausal FIR models
2013 American Control Conference, 2013
Noncausal finite impulse response (FIR) models are used for closed-loop identification of unstable multi-input, multi-output plants. These models are shown to approximate the Laurent series inside the annulus between the asymptotically stable pole of the largest modulus and the unstable pole of the smallest modulus. By delaying the measured output relative to the measured input, the identified FIR model is a noncausal approximation of the unstable plant. We present examples to compare the accuracy of the identified model obtained using least squares, instrumental variables methods, and prediction error methods for both infinite impulse response (IIR) and noncausal FIR models under arbitrary noise that is fed back into the loop. Finally, we reconstruct an IIR model of the system from its stable and unstable parts using the eigensystem realisation algorithm.
Frequency-domain identification of linear time-invariant systems under nonstandard conditions
IEEE Transactions on Instrumentation and Measurement, 1997
This paper presents a frequency-domain identification method for parametric transfer function models of linear time invariant systems that takes into account the nonzero initial condition and/or the transient effects in the response of the system when excited by periodic or time-limited signals. The method is useful for systems with large settling times where it takes too much time for the system to reach a steady state so that measurements can begin. In the special case of free decay experiments the presented technique is a frequency-domain version of fitting exponentially damped sinusoids embedded in noise. The theory is illustrated by simulations and a real measurement example.
Identification of linear systems using polynomial kernels in the frequency domain
Journal of Process Control, 2002
In prior work we presented an identification algorithm using polynomials in the time domain. In this article, we extend this algorithm to include polynomials in the frequency domain. A polynomial is used to represent the imaginary part of the Fourier transform of the impulse response. The Hilbert transform relationship is used to compute the real part of the frequency response and hence the complete process model. The polynomial parameters are computed based on the computationally efficient linear least square method. The order of the polynomial is estimated based on residue decrement. Simulated and experimental results show the effectiveness of this method, particularly for short input/output data sequence with high signal to noise ratio. The frequency domain polynomial model complements the time domain methods since it can provide a good estimate of the time to steady state for time domain FIR (finite impulse response) models. Confidence limits in time or frequency domain can be computed using this approach. Noise rejection properties of the algorithm are illustrated using data from both simulated and real processes. #