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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TL;DR: Two non-parametric estimation techniques are considered: radial basis function neural network (RBF-NN)-based estimation and support vector machine (SVM)-based estimation for nonlinear frequency response function (FRF) estimation for a class of nonlinear systems.
Abstract: In this paper, we perform the nonlinear frequency response function (FRF) estimation for a class of nonlinear systems. Two non-parametric estimation techniques are considered: radial basis function neural network (RBF-NN)-based estimation and support vector machine (SVM)-based estimation. Based on the system's available observations, the proposed estimation models are used to predict its frequency response. Simulation results are provided to demonstrate the model implementation. Finally, a comparative study is carried out to evaluate the effectiveness of the RBF-NN and SVM schemes, which has demonstrated that the SVM outperformed RBF-NN in the FRF estimation.
4 citations
TL;DR: In this article, the mass flow rate characteristic of a pneumatic valve set in the frequency domain is analyzed and the describing function of nonlinearity can be determined analytically.
4 citations
TL;DR: In this paper, a simple method that corrects distorted output signal of the excitation device by means of predistortion of its input signal is presented and this output signal, applied to the system under test, is cleaned from the undesirable components produced by theexcitation device.
3 citations
Cites methods from "Higher-order sinusoidal input descr..."
...If no predistortion is applied and if the excitation signal is distorted due to the excitation device, complex nonlinear models and techniques that are used to describe the nonlinear behaviour of nonlinear systems under test using different approaches (parametric [31] or nonparametric [32]), based on different models such as Generalized Hammerstein model [33, 34], Volterra model [35, 36], or describing functions [37], can lead to erroneous results....
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18 Aug 2011
TL;DR: A frequency domain method is introduced that allows fast and high accuracy tuning of controller parameters when the closed loop system is subject to nonlinear influences and this methodology is applied to optimally compensate friction in a high precision motion stage of a transmission electron microscope.
Abstract: Friction is a performance limiting factor in many industrial motion systems. Correct compensation or control of friction and other nonlinearities is generally difficult. Apart from the complex nature of friction, compensation of even the most basic type of friction, Coulomb friction, is non trivial.Most available tuning methods rely on time domain data and are often unable to distinguish between nonlinear effects of friction and that of for example linear viscous damping. Furthermore, the sensitivity of time domain data to the influence of friction is too low for correct tuning in many of the high precision motion applications currently used in industry. In this paper a frequency domain method is introduced that allows fast and high accuracy tuning of controller parameters when the closed loop system is subject to nonlinear influences. This methodology is applied to optimally compensate friction in a high precision motion stage of a transmission electron microscope. Theoretical and experimental results are presented and related to time domain performance to illustrate the advantage of frequency domain tuning over time domain tuning.
3 citations
Cites background or methods from "Higher-order sinusoidal input descr..."
...This definition of the HOSIDF is slightly different from the one used in [3] and is formalized below....
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...This representation of nonlinear effects in the frequency domain is captured by the higher order sinusoidal input describing functions [2], [3], [4], [8], [10], which describe the systems response (gain and phase) at harmonics of the base frequency of a sinusoidal input signal....
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01 Jan 2023
TL;DR: In this paper , a phase shaping method was proposed to suppress nonlinearity of a single-state reset element in a desired range of frequencies and allow the non-linearity to provide its phase benefit.
Abstract: This paper addresses nonlinearity in reset elements and their effects. Reset elements are known for having less phase lag compared to their linear counterparts; however, they are nonlinear elements and produce higher-order harmonics. This paper investigates the higher-order harmonics for reset elements with one resetting state and proposes an architecture and a method of design which allows for band-passing the nonlinearity and its effects, namely, higher-order harmonics and phase advantage. The nonlinearity of reset elements is not entirely useful for all frequencies, e.g., they are useful for reducing phase lag at cross-over frequency region; however, higher-order harmonics can compromise tracking and disturbance rejection performance at lower frequencies. Using proposed "phase shaping" method, one can selectively suppress nonlinearity of a single-state reset element in a desired range of frequencies and allow the nonlinearity to provide its phase benefit in a different desired range of frequencies. This can be especially useful for the reset elements in the framework of "Constant in gain, Lead in phase" (CgLp) filter, which is a newly introduced nonlinear filter, bound to circumvent the well-known linear control limitation -- the waterbed effect.
3 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
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 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
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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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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