Brief paper: Spectral analysis of block structured nonlinear systems and higher order sinusoidal input describing functions
TL;DR: A mapping from the parameters defining the nonlinear and LTI dynamics to the output spectrum is derived, which allows analytic description and analysis of the corresponding higher order sinusoidal input describing functions.
About: This article is published in Automatica.The article was published on 2011-12-01. It has received 29 citations till now. The article focuses on the topics: Describing function & Frequency domain.
Citations
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TL;DR: In this paper, a frequency domain based method for controller design for nonlinear systems is presented, which is applied to optimally design a feed forward friction compensator for an industrial motion stage in a transmission electron microscope.
50 citations
TL;DR: In this article, the effects of nonlinear stiffness and nonlinear damping on the output spectra as well as the output energy spectra over different frequency ranges were examined for the first time using the output frequency response function (OFRF) approach.
40 citations
TL;DR: This paper provides a comparative overview of four classes of frequency domain methods for nonlinear systems: Volterra based models, nonlinear frequency response functions / Bode plots, describing functions and linear approximations in the presence of nonlinearities.
26 citations
TL;DR: It is shown, for the first time, that the output frequency responses of a wide class of nonlinear systems that are described by the NARX (Nonlinear Auto Regressive with eXogenous input) model can be represented by a polynomial function of both the system linear and nonlinear characteristic parameters of interests to the system analysis.
20 citations
Cites background from "Brief paper: Spectral analysis of b..."
...The HOSIDF can be considered to be a special case of the OFRF of a static polynomial nonlinear system (Rijlaarsdam et al, 2011)....
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TL;DR: A new method for reducing harmonic distortion due to element mismatch in digital-to-analog converters is described, achieved by using a large high-frequency periodic dither, which results in more than 10 dB improvement in the signal- to-noise-and-distortion ratio.
Abstract: A new method for reducing harmonic distortion due to element mismatch in digital-to-analog converters is described. This is achieved by using a large high-frequency periodic dither. The reduction in nonlinearity is due to the smoothing effect this dither has on the nonlinearity, which is only dependent on the amplitude distribution function of the dither. Since the high-frequency dither is unwanted in the output of the digital-to-analog converter, the dither is removed by an output filter. The fundamental frequency component of the dither is attenuated by a passive notch filter and the remaining fundamental component and harmonic components are attenuated by the low-pass reconstruction filter. Two methods that further improve performance are also presented. By reproducing the dither on a second channel and subtracting it using a differential amplifier, additional dither attenuation is achieved; and by averaging several channels, the noise-floor of the output is improved. Experimental results demonstrate more than 10 dB improvement in the signal-to-noise-and-distortion ratio.
18 citations
Cites background from "Brief paper: Spectral analysis of b..."
...The number of higher order harmonic components is related to the order of the polynomial [6], [47]–[49]....
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References
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Book•
01 Jan 1943TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Abstract: 0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
27,354 citations
Additional excerpts
...Next, the power series in (3) is rewritten to the sum of one tones using the following relationship (Gradshteyn & Ryzhik, 2000): cos2n−σ (x) = 1 22n−1−σ ⎧⎨ ⎩(1 − σ) ( 2n n ) + n−1∑ m=0 ( 2n − σ m ) cos ((2(n − m) − σ) x) } , (4) with n ∈ N≥1, σ ∈ {0, 1} and the binomial coefficient ( a b ) = a! b!...
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Book•
01 Jan 1945
2,469 citations
"Brief paper: Spectral analysis of b..." refers background or methods in this paper
...The GFRF was first introduced in George (1959) and methods to measure and interpret the GFRF were developed in Billings and Tsang (1989)....
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...Modeling systems in the frequency domain, rather than the time domain, offers important advantages such as easy interpretation of the system dynamics and has led to significant progress in linear controller design (Bode, 1945)....
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Book•
31 Dec 2003TL;DR: Focusing mainly on frequency domain techniques, System Identification: A Frequency Domain Approach, Second Edition also studies in detail the similarities and differences with the classical time domain approach.
Abstract: Preface to the First Edition Preface to the Second Edition Acknowledgments List of Operators and Notational Conventions List of Symbols List of Abbreviations Chapter 1 An Introduction to Identification Chapter 2 Measurement of Frequency Response Functions Standard Solutions Chapter 3 Frequency Response Function Measurements in the Presence of Nonlinear Distortions Chapter 4 Detection, Quantification, and Qualification of Nonlinear Distortions in FRF Measurements Chapter 5 Design of Excitation Signals Chapter 6 Models of Linear Time-Invariant Systems Chapter 7 Measurement of Frequency Response Functions The Local Polynomial Approach Chapter 8 An Intuitive Introduction to Frequency Domain Identification Chapter 9 Estimation with Know Noise Model Chapter 10 Estimation with Unknown Noise Model Standard Solutions Chapter 11 Model Selection and Validation Chapter 12 Estimation with Unknown Noise Model The Local Polynomial Approach Chapter 13 Basic Choices in System Identification Chapter 14 Guidelines for the User Chapter 15 Some Linear Algebra Fundamentals Chapter 16 Some Probability and Stochastic Convergence Fundamentals Chapter 17 Properties of Least Squares Estimators with Deterministic Weighting Chapter 18 Properties of Least Squares Estimators with Stochastic Weighting Chapter 19 Identification of Semilinear Models Chapter 20 Identification of Invariants of (Over) Parameterized Models References Subject Index Author Index About the Authors
2,379 citations
"Brief paper: Spectral analysis of b..." refers methods in this paper
...In Pintelon and Schoukens (2001) frequency domain identification methods are discussed which provide a quantitativemeasure for the level and type of nonlinear influences....
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Book•
01 Jan 1968
TL;DR: The theory of automatic control has been advanced in important ways during recent years, particularly with respect to stability and optimal control, but these theories do not, however, lay to rest all questions of importance to the control engineer.
Abstract: ABRAMSON Information theory and coding BATTIN Astronautical guidance BLACHMAN Noise and its effect on communication BREMER Superconductive devices BROXMEYER Inertial navigation systems GELB AND VANDER VELDE Multiple-input describing functions and nonlinear system design GILL Introduction to the theory of finite-state machines HANCOCK AND WINTZ Signal detection theory HUELSMAN Circuits, matrices, and linear vector spaces KELSO Radio ray propagation in the ionosphere MERRIAM Optimization theory and the design of feedback control systems MUUM Biological control systems analysis NEWCOMB Linear multiport synthesis PAPOULIS The fourier integral and its applications R. N. BRACEWELL) STEINBERG AND LEQUEUX (TRANSLATOR Radio astronomy WEEKS Antenna engineering PREFACE The theory of automatic control has been advanced in important ways during recent years, particularly with respect to stability and optimal control. These are significant contributions which appeal to many workers, including the writers, because they answer important questions and are both theoretically elegant and practically useful. These theories do not, however, lay to rest all questions of importance to the control engineer. The designer of the attitude control system for a space vehicle booster which, for simplicity, utilizes a rate-switched engine gimbal drive, must know the characteristics of the limit cycle oscillation that the system will sustain and must have some idea of how the system will respond to attitude commands while continuing to limit-cycle. The designer of a chemical process control system must be able to predict the transient oscillations the process may experience during start-up due to the limited magnitudes of important variables in the system. The designer of a radar antenna pointing system with limited torque capability must be able to predict the rms pointing error due to random wind disturbances on the antenna, and must understand how these random disturbances will influence the behavior of the system in its response to command inputs. But more important than just being able to evaluate how a given system will behave in a postulated situation is the fact that these control engineers must design their systems to meet specifications on important characteristics. Thus a complicated exact analytical tool, if one existed, would be of less value to the designer than an approximate tool which is simple enough in application to give insight into the trends in system behavior as a function of system parameter values or possible compensations, hence providing the basis for system design. As an analytical tool to answer questions such as these in a way …
1,244 citations
Journal Article•
634 citations