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Journal ArticleDOI

Higher-order sinusoidal input describing functions for the analysis of non-linear systems with harmonic responses

01 Nov 2006-Mechanical Systems and Signal Processing (Academic Press Inc.)-Vol. 20, Iss: 8, pp 1883-1904
TL;DR: In this paper, an extension to higher-order describing functions is realized by introducing the concept of the harmonics generator, which relates the magnitude and phase of the higher harmonics of the periodic response of the system to the magnitude of a sinusoidal excitation.
About: This article is published in Mechanical Systems and Signal Processing.The article was published on 2006-11-01. It has received 100 citations till now. The article focuses on the topics: Describing function & Harmonic (mathematics).
Citations
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Journal ArticleDOI
01 Jan 2019
TL;DR: In this paper, the authors proposed an efficient way to include higher harmonics of the flame response by an extended FDF, which includes additional transfer functions that relate higher harmonic of the heat release rate to the forcing velocity.
Abstract: The Flame Describing Function (FDF) is widely used to model non-linear thermo-acoustic phenomena, e.g. limit cycle oscillations in a combustor. The FDF is a weakly non-linear approach, because it accounts for the amplitude dependence of the flame response, but besides that relies on quasi-linear assumptions. In particular, it neglects the excitation of higher harmonics – a typical non-linear feature, which may play a major role in certain thermo-acoustic systems. Consequently, the FDF may provide inaccurate or incomplete results in such cases. In this study, we propose an efficient way to include higher harmonics of the flame response by an extended FDF, which includes additional transfer functions that relate higher harmonics of the heat release rate to the forcing velocity. The extended FDF is also a weakly non-linear approach, and requires the same effort for determination as the standard FDF. This paper shows how to determine the extended FDF and how to employ it for the prediction of limit cycle oscillations. The proposed concept is applied to predict and analyse the limit cycle of a laminar premixed burner for which the standard FDF delivered inaccurate results. Results obtained with the extended FDF show good agreement with fully compressible numerical simulation of the same configuration. Thus, the extended FDF proves its ability to provide accurate predictions in situations where higher harmonics play an important role in thermo-acoustic limit cycles.

37 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed an approach to detect, localize, and parametric identification of nonlinear elements by using incomplete FRF data, which can be used for detection, localization, characterization, and parameterization.

30 citations

Journal ArticleDOI
TL;DR: A general procedure for the design of the physical parameters of the NARX-M-for-D in the frequency domain is proposed, which has the potential to be applied to design a wide range of engineering systems and structures.
Abstract: In this paper, a nonlinear auto regressive with eXegenous input (NARX) model of nonlinear systems, where the physical parameters of interest for the system design appear explicitly as coefficients in the model, is introduced. The model is referred to as the NARX model with parameters of interest for design (NARX-M-for-D). The output frequency response function (OFRF) in terms of these physical parameters is then introduced for the NARX-M-for-D, and an efficient algorithm is derived to determine the OFRF so as to facilitate the design of nonlinear systems in the frequency domain. Moreover, a general procedure for the design of the physical parameters of the NARX-M-for-D in the frequency domain is proposed, which has the potential to be applied to design a wide range of engineering systems and structures. Finally, two case studies are provided to demonstrate the new OFRF-based nonlinear system design and its significance in engineering applications.

30 citations


Cites background from "Higher-order sinusoidal input descr..."

  • ...The HOSIDF can be considered as a special case of the OFRF [20]....

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  • ...To address this issue, many new concepts such as nonlinear output FRF [15], OFRF [16], and higherorder sinusoidal input describing functions (HOSIDF) [17] have been proposed....

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Journal ArticleDOI
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.

29 citations


Cites background from "Higher-order sinusoidal input descr..."

  • ...Open and closed loop identification of the HOSIDFs are discussed in Nuij et al. (2006) and Nuij, Steinbuch, and Bosgra (2008a)....

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  • ...The Higher Order Sinusoidal Input Describing Functions (HOSIDFs) are introduced in Nuij et al. (2006)....

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  • ...Definition and analysis In Nuij et al. (2006) the output of a class of nonlinear systems, subject to (2) is considered....

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Journal ArticleDOI
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

References
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Book
01 Jan 1991
TL;DR: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
Abstract: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).

15,545 citations

Journal ArticleDOI
TL;DR: This survey is the first to bring to the attention of the controls community the important contributions from the tribology, lubrication and physics literatures, and provides a set of models and tools for friction compensation which will be of value to both research and application engineers.

2,658 citations

Book
31 Dec 2003
TL;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

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


Additional excerpts

  • ...Some approaches addressed the describing function analysis [5,6] to replace a non-linear element with a quasi-linear descriptor which gain is a function of input amplitude....

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Journal ArticleDOI
TL;DR: In this article, an iterative method is proposed for the identification of nonlinear systems from samples of inputs and outputs in the presence of noise, which consists of a no-memory gain (of an assumed polynomial form) followed by a linear discrete system.
Abstract: An iterative method is proposed for the identification of nonlinear systems from samples of inputs and outputs in the presence of noise. The model used for the identification consists of a no-memory gain (of an assumed polynomial form) followed by a linear discrete system. The parameters of the pulse transfer function of the linear system and the coefficients of the polynomial non-linearity are alternately adjusted to minimize a mean square error criterion. Digital computer simulations are included to demonstrate the feasibility of the technique.

707 citations


"Higher-order sinusoidal input descr..." refers background in this paper

  • ...This structure, however, is not a Hammerstein model since the second block is not necessarily linear [14]....

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