Showing papers by "Johan Schoukens published in 2013"

FRF Measurement of Nonlinear Systems Operating in Closed Loop

Abstract: To prevent unstable behavior or saturation, a frequency response function (FRF) measurement is often performed under closed-loop conditions (e.g., open-loop gain measurements of an operational amplifier). The difficulty of such FRF measurements is that the nonlinear (NL) distortions also perturb the input via the feedback loop. The latter introduces a bias in the estimate of the best linear approximation (BLA) and jeopardizes the interpretation of the output NL distortions. In this paper, we solve these problems via a generalized definition of the BLA that is valid for NL systems operating in feedback. The classical definition for open-loop systems follows as a special case.

Design of Quasi-Logarithmic Multisine Excitations for Robust Broad Frequency Band Measurements

Abstract: The logarithmic distribution of spectral lines in excitation signals is widely used to measure the transfer functions of dynamic systems over a wide frequency band, covering several decades. Periodic signals are very popular in many advanced dynamic signal analyzers. Generating multitone periodic signals requires an equidistant frequency grid which conflicts with the logarithmic distribution, particularly at the low frequencies. In this paper, we offer an elegant solution to get around this problem using an improved choice for the amplitude spectrum of the multitone. We also offer a simple way to tune the frequency spacing of such a signal to allow for robust identification of the system under test.

Bounding the Polynomial Approximation Errors of Frequency Response Functions

Abstract: Frequency response function (FRF) measurements take a central place in the instrumentation and measurement field because many measurement problems boil down to the characterization of a linear dynamic behavior. The major problems to be faced are leakage and noise errors. The local polynomial method (LPM) was recently presented as a superior method to reduce the leakage errors with several orders of magnitude while the noise sensitivity remained the same as that of the classical windowing methods. The kernel idea of the LPM is a local polynomial approximation of the FRF and the leakage errors in a small-frequency band around the frequency where the FRF is estimated. Polynomial approximation of FRFs is also present in other measurement and design problems. For that reason, it is important to have a good understanding of the factors that influence the polynomial approximation errors. This article presents a full analysis of this problem and delivers a rule of thumb that can be easily applied in practice to deliver an upper bound on the approximation error of FRFs. It is shown that the approximation error for lowly damped systems is bounded by $(B_{LPM}/B_{3dB})^{R + 2}$ with $B_{LPM}$ the local bandwidth of the LPM, $R$ the degree of the local polynomial that is selected to be even (user choices), and $B_{3dB}$ the 3 dB bandwidth of the resonance, which is a system property.

Data for benchmarking in nonlinear system identification

Abstract: System identification is a fundamentally experimental field of science in that it deals with modeling of system dynamics using measured data. Despite this fact many algorithms and theoretical results are only tested with simulations at the time of publication. One reason for this may be a lack of easily available live data. This paper therefore presents three sets of data, suitable for development, testing and benchmarking of system identification algorithms for nonlinear systems. The data sets are collected from laboratory processes that can be described by block – oriented dynamic models, and by more general nonlinear difference and differential equation models. All data sets are available for free download.

Structured non-linear noise behaviour and the use of median averaging in non-linear systems with m-sequence inputs

Abstract: In non-linear system identification, results from traditional non-parametric identification techniques contain both linear and non-linear contributions. When Gaussian excitation signals (including random-phased multisines) are used, the non-linear contributions are noise-like and therefore not easy to distinguish from environment noise and measurement noise. In contrast, when excitation signals based on binary maximum-length sequences (m-sequences) are used, a particular property of the sequences results in the non-linear contributions being structured. It is shown in this study that it is possible to take advantage of this structure by using a median-based averaging technique, rather than the more traditional arithmetic mean-based averaging, to obtain better identification performance.