scispace - formally typeset
Search or ask a question
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
More filters
Journal ArticleDOI
TL;DR: In this article, the authors describe an application of a recently introduced methodology for modeling of a class of nonlinear systems, Higher-Order Sinusoidal Input Describing Function technique (HOSIDF), to a motion control platform for which a precisely controlled motion at low velocity is required.

17 citations

Journal ArticleDOI
TL;DR: Fundamental results are established for truncation order and its effect in the Volterra class of nonlinear systems, and this work provides a much improved version of the multi-level excitation method for system analysis and identification.

17 citations

Journal ArticleDOI
TL;DR: In this article, a new nonparametric routine is proposed to extend the capability of Volterra analysis in the frequency domain to weakly nonlinear Duffing systems at a much wider range of excitation amplitude range which the current underlying nonlinear differential equation models fail to address.

15 citations

Proceedings ArticleDOI
12 May 2020
TL;DR: In this paper, the authors proposed an optimal sequence of the open loop in which the magnitude of high order harmonics is minimum for a general reset controller, and validated the suggested sequence in the closed-loop system through both simulation and experiments at a Lorentz-actuated precision positioning stage.
Abstract: The PID controller is one of the most used controllers in the industry. However, fundamental limitations due to linearity restrict its performances when higher bandwidth, stability, and precision are required simultaneously in today’s high-tech industry. Reset control is a promising nonlinear control strategy which can overcome these limitations. But it also brings new problems. High order harmonics are introduced into the system because of non-linearity which lead to unwanted dynamics and deterioration of performances. So it is necessary to reduce them as much as possible. It is found that the sequence of different parts of a reset controller has effects on the magnitude of high order harmonics. Through high order sinusoidal input describing functions (HOSIDOFs) tool, the optimal sequence of the open loop in which the magnitude of high order harmonics is minimum is achieved for a general reset controller. The superiority of the suggested sequence in the closed-loop system is validated through both simulation and experiments at a Lorentz-actuated precision positioning stage.

15 citations

Journal ArticleDOI
TL;DR: It is shown in this paper that using the proposed reset element architecture, CgLp gets closer to its ideal behaviour for a range of frequencies, and its performance will be improved accordingly.
Abstract: This paper proposes a fractional-order reset element whose architecture allows for the suppression of nonlinear effects for a range of frequencies. Suppressing the nonlinear effects of a reset element for the desired frequency range while maintaining it for the rest is beneficial, especially when it is used in the framework of a “Constant in gain, Lead in phase” (CgLp) filter. CgLp is a newly introduced nonlinear filter, bound to circumvent the well-known linear control limitation—the waterbed effect. The ideal behaviour of such a filter in the frequency domain is unity gain while providing a phase lead for a broad range of frequencies. However, CgLp’s ideal behaviour is based on the describing function, which is a first-order approximation that neglects the effects of the higher-order harmonics in the output of the filter. Although CgLp is fundamentally a nonlinear filter, its nonlinearity is not required for all frequencies. Thus, it is shown in this paper that using the proposed reset element architecture, CgLp gets closer to its ideal behaviour for a range of frequencies, and its performance will be improved accordingly.

13 citations

References
More filters
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....

    [...]

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]....

    [...]