Identification of Nonlinear Systems in Frequency Domain

Shanmugam, Karthikeyan; Jong, Mark T.

doi:10.1109/taes.1975.308179

Cited by 15 publications

(8 citation statements)

References 8 publications

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“…This is called the “nonlinear AT model MoM Engine.” By dividing the input voltage V g (f) by the input current I g (f) in frequency domain, we derive the input impedance, Z(f). It is shown by Moosavi et al [2009] that so‐called NL‐AT engine, is a system with “mild” nonlinearity, so we can approximate its response by finding the transfer function Z(f), and being careful how we use the results [ Shanmugam and Jong , 1975; Billings and Tsang , 1989]. In step two of the procedure, first we need to assume an excitation current for the channel base, i DH (t), then determine a voltage source for the tower excitation, v DH (t)∣ z = H , which should produce the same current in the channel base.…”

Section: Simulation Resultsmentioning

confidence: 99%

Application of the nonlinear antenna theory model to a tall tower struck by lightning for the evaluation of return stroke channel current and radiated electromagnetic fields

Moosavi¹,

Moini²,

Sadeghi³

et al. 2011

J. Geophys. Res.

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[1] In this paper an improved antenna theory (AT) model with nonlinearly varying resistive loading and fixed inductive loading is used to electromagnetically simulate lightning strikes to tall structures. Measurement data captured from Toronto's CN tower are used to verify the validity of the new model. Both the return stroke channel (RSC) and the tower are modeled by straight thin conducting wires. The wire model of the channel is assumed to have distributed nonlinear resistive elements as a function of current and time, adopted from the numerical models of a spark channel and consequent shockwave from a lightning discharge, yielding a varying value of the channel radius from the base to the cloud along the RSC. Such distributed elements are used to take into account the current attenuation while propagating along the channel and varying propagation speeds lower than the speed of light. RSC current distribution and radiated electromagnetic fields in near, intermediate, and far range distances predicted by the proposed model are compared with those obtained from the measurement data and with those of the original AT model and the AT with fixed inductive loading (ATIL-F) model. Current wave propagation speed profile in RSC and tower is investigated as a function of height as well. The effects of applying different tower geometry models are also studied. It is shown that the new model is able to reproduce one of the characteristic features of the electromagnetic fields radiated by lightning, namely, the far-field inversion of polarity with a zero crossing occurring in the tens of microseconds range. We have also investigated the effect of nonlinearity of the channel assumed in the new model. It is shown that among the electromagnetic models, distributed nonlinear resistance along the channel leads to a zero crossing in the tens of microseconds range even for large values of resistance. It is also shown that decreasing the nonlinearity results in the predictions asymptotically converging to those of the ATIL-F model in which a uniformly distributed resistance along the channel is used. Further, the profile of the return stroke current attenuation and speed and removed charge as a function of height are investigated. Finally, the effect of lossy ground is analyzed using Wait-Cooray convolution formula in the time domain to verify the validity of PEC assumption in the proposed model.

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Section: Simulation Resultsmentioning

confidence: 99%

Application of the nonlinear antenna theory model to a tall tower struck by lightning for the evaluation of return stroke channel current and radiated electromagnetic fields

Moosavi¹,

Moini²,

Sadeghi³

et al. 2011

J. Geophys. Res.

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show abstract

“…Using the results in Shanmugam and Jong [1975] these results are compared to the exact GFRFs, which yields that the results are very close to the true value. This follows from further computations which reveal that the maximum relative error equals 10 −7 when the GFRFs drop below −80 [dB] which is close to the computational precision.…”

Section: Lemma 3 (Polynomial Coefficients and Gfrf)mentioning

confidence: 89%

“…Using results from Shanmugam and Jong [1975], the GFRFs of PWH systems are an explicit function of the LTI dynamics G ± (ξ) and the polynomial coefficients α p . This result is later required for analysis and is summarized in the following lemma.…”

Section: Generalized Frequency Response Functionmentioning

confidence: 99%

New Connections Between Frequency Response Functions for a Class of Nonlinear Systems*

Rijlaarsdam

Oomen

Nuij

et al. 2012

IFAC Proceedings Volumes

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The notion of frequency response functions has been generalized to nonlinear systems in several ways. However, a relation between different approaches has not yet been established. In this paper, frequency domain representations for nonlinear systems are uniquely connected. Specifically, by means of novel analytical results, the generalized frequency response function (GFRF) and the higher order sinusoidal input describing function (HOSIDF) for polynomial Wiener-Hammerstein systems are explicitly related. Necessary and sufficient conditions for this relation to exist and results on uniqueness and equivalence of the HOSIDF and GFRF are provided. Finally, a numerically efficient computational procedure is presented that allows to compute the GFRF from the HOSIDF and vice versa.

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“…Successful identification involves selection of parameters like sampling time and excitation signal and choice of a proper model structure. Several varieties of model structures have been proposed and discussed in the literatures [10][11][12][13][14][15]. Researchers have shown great interests in block oriented models.…”

Section: Glucose-insulin Interaction Processmentioning

confidence: 99%

“…A potential advantage of using nonparametric model is that it can yield nonlinear model predictive control directly from the identified process [13]. The frequency domain analysis gives the nonlinear transfer function from the kernels itself [14,15].…”

Section: Introductionmentioning

confidence: 99%

Frequency domain hammerstein model of glucose-insulin process in IDDM patient

Bhattacharjee

Sutradhar

2010

2010 International Conference on Systems in Medicine and Biology

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This paper deals with a frequency domain kernel estimation problem for modeling a nonlinear dynamic system of multivariable glucose-insulin process in an insulin dependent diabetes mellitus (IDDM) patient. For such a process with uncertainties and parameter variations, the nonparametric models are most useful for closed loop model predictive control. The present work proposes a frequency domain kernel estimation of a Hammerstein model using the harmonic excitation input by taking FFT on the input data sequence from the glucose-insulin process of IDDM patient model. For the multivariable system, the first block is a two-input single output nonlinear block followed by a SISO linear filter. The adaptive recursive least square (ARLS) algorithm is used to solve up to second order kernels of Volterra equations with extended input vector consisting of self and cross components. Twice the length of the extended input vector for the MISO system was considered for finding the kernels and the output in frequency domain. The input-output data taken from the first principle model of nonlinear process, have been used to identify the system with a short filter memory length of M=2 and the validation results have shown good fit both in frequency and time domain responses.

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Identification of Nonlinear Systems in Frequency Domain

Cited by 15 publications

References 8 publications

Application of the nonlinear antenna theory model to a tall tower struck by lightning for the evaluation of return stroke channel current and radiated electromagnetic fields

Application of the nonlinear antenna theory model to a tall tower struck by lightning for the evaluation of return stroke channel current and radiated electromagnetic fields

New Connections Between Frequency Response Functions for a Class of Nonlinear Systems*

Frequency domain hammerstein model of glucose-insulin process in IDDM patient

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