Analysis of Output Frequencies of Nonlinear Systems

Wu, Xiaofeng; Lang, Zi–Qiang; Billings, S.A.

doi:10.1109/tsp.2007.894387

Cited by 13 publications

(2 citation statements)

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“…The GFRFs have played an important role in nonlinear system analyses [43][44][45][46][47][48][49][50][51]. For example, the output frequency combination characteristics were theoretically explained using GFRFs [43], and algorithms have CHAPTER 1 3 been proposed to determine the nonlinear output frequency components [44][45][46]. The NDE model was reconstructed from a NARX model of a nonlinear system, based on the observation that the GFRFs of the NDE and NARX model of the same system are invariant [47][48][49].…”

Section: (A) the Gfrfs Of Nonlinear Systemsmentioning

confidence: 99%

Analysis and Design of Nonlinear Systems in the Frequency Domain

Zhu

2021

Springer Theses

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Nonlinear system analyses have been widely applied in engineering practice, where the frequency domain approaches have been developed to satisfy the requirement of the analysis and design of nonlinear systems.However, there exist many problems with current techniques including the challenges with the nonlinear system representation using physically meaningful models, and difficulties with the evaluation of the frequency properties of nonlinear systems. In the present work, some new approaches, that have potential to be used to systematically address these problems, are developed based on the NDE (Nonlinear Differential Equation) model and the NARX (Nonlinear Auto Regressive with eXegenous input) model of nonlinear systems.In this thesis, the background of the frequency domain analysis and design of nonlinear systems is introduced in Chapter 1, and the existing approaches are reviewed in Chapter 2. In general, the frequency ABSTRACT II(3) The Output Frequency Response Function (OFRF) in terms of physical parameters of concern is introduced for the NARX Model with parameters of interest for Design (NARX-M-for-D). Moreover, a new concept known as the Associated Output Frequency Response Function (AOFRF) is introduced to facilitate the analysis of the effects of both linear and nonlinear characteristic parameters on the output frequency responses of nonlinear systems.(4) Nonlinear damping can achieve desired isolation performance of a system over both low and high frequency regions and the optimal nonlinear damping force can be realized by closed loop controlled semi-active dampers. Both simulation and laboratory experiments are studied, demonstrating the advantages of the proposed nonlinear damping technologies over both traditional linear damping and more advanced Linear-Quadratic Gaussian (LQG) feedback control which have been used in practice to address building isolation system design and implementation problems. CATALOGUE III AcknowledgementsI would like to thank Prof. Z Q Lang, my supervisor, for his great support and supervision on my PhD study. He has provided a lot of suggestions on my research and writing so that I can complete the project and this PhD thesis.I also want to express my thankfulness to the research and work staffs of the department for their kind help on my study, and also would like to acknowledge the support of Engineering Faculty Scholarship for my PhD study at Sheffield.

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Section: (A) the Gfrfs Of Nonlinear Systemsmentioning

confidence: 99%

Analysis and Design of Nonlinear Systems in the Frequency Domain

Zhu

2021

Springer Theses

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“…The intermodulation components appear at sums and differences of multiples of the input frequencies and can therefore appear below the frequency of the input signal with the lowest frequency. Increasing the order of the polynomial describing the non-linearity or the number of frequency components in the input will generate a higher number of harmonic and intermodulation components 13,48 .…”

Section: Noise and Distortion In Dacsmentioning

confidence: 99%

Existing methods for improving the accuracy of digital-to-analog converters

Eielsen

Fleming

2017

Review of Scientific Instruments

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The performance of digital-to-analog converters is principally limited by errors in the output voltage levels. Such errors are known as element mismatch and are quantified by the integral non-linearity. Element mismatch limits the achievable accuracy and resolution in high-precision applications as it causes gain and offset errors, as well as harmonic distortion. In this article, five existing methods for mitigating the effects of element mismatch are compared: physical level calibration, dynamic element matching, noise-shaping with digital calibration, large periodic high-frequency dithering, and large stochastic high-pass dithering. These methods are suitable for improving accuracy when using digital-to-analog converters that use multiple discrete output levels to reconstruct time-varying signals. The methods improve linearity and therefore reduce harmonic distortion and can be retrofitted to existing systems with minor hardware variations. The performance of each method is compared theoretically and confirmed by simulations and experiments. Experimental results demonstrate that three of the five methods provide significant improvements in the resolution and accuracy when applied to a general-purpose digital-to-analog converter. As such, these methods can directly improve performance in a wide range of applications including nanopositioning, metrology, and optics.

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The Identification and Analysis of Nonlinear Systems in the Frequency Domain

Billings

2013

Nonlinear System Identification

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Analysis of Output Frequencies of Nonlinear Systems

Cited by 13 publications

References 13 publications

Analysis and Design of Nonlinear Systems in the Frequency Domain

Analysis and Design of Nonlinear Systems in the Frequency Domain

Existing methods for improving the accuracy of digital-to-analog converters

The Identification and Analysis of Nonlinear Systems in the Frequency Domain

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