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
Dissertation•
01 Jan 2012
2 citations
Cites methods from "Higher-order sinusoidal input descr..."
...The description of the hysteretic systems in harmonic domain is also a typical method [50],[55],[1],[86],[51]....
[...]
TL;DR: The research proves that the proposed 2-DOF design structure is suitable to be implemented into the systems involving nonlinearities such as actuator saturation and is taken into consideration in the controller design and implementation process for disturbance attenuation problem.
Abstract: In order to deal with disturbance attenuation problem in the presence of norm bounded uncertainties, different techniques involving H2/H∞ and linear quadratic regulator (LQR) designs exist in liter...
2 citations
Cites methods from "Higher-order sinusoidal input descr..."
...Moreover, a model-free 2-DOF controller is introduced in order to compensate the process nonlinearities and uncertainties (Radac and Precup, 2015)....
[...]
12 Jul 2021
TL;DR: In this paper, a fractional-order augmented state analogue of the reset integrator is investigated, which is composed of a series of augmented states that each possesses unique reset values, providing the same first order harmonic behavior but reduced higher order harmonics magnitude compared to the traditional reset-integrator.
Abstract: Linear control such as PID possesses fundamental limitations, seen through the Waterbed effect. Reset control has been found to be able to overcome these limitations, while still maintaining the simplicity and ease of use of PID control due to its compatibility with the loop shaping method. However, the resetting action also gives rise to higher order harmonics that hinders consistent realization of the aforementioned expected improvement. In this paper, a fractional-order augmented state analogue of the reset integrator is investigated. This analogue is composed of a series of augmented states that each possesses unique reset values, providing the same first order harmonic behavior but reduced higher order harmonics magnitude compared to the reset integrator. The optimal number of augmented states along with the corresponding tuning values are investigated. To validate the improvement, the reset integrator and the optimal fractional order analogue are tuned to equally improve disturbance rejection of a high precision 1 DOF positioning stage while maintaining the stability level, with both designed to overcome linear control. From simulation and experimental results, it was found that the novel fractional-order augmented state analogue gives rise to disturbance rejection performance that is closer to the desired and expected improvement, compared to using the traditional reset integrator.
2 citations
08 Mar 2020
TL;DR: An optical second-order Volterra filter is demonstrated using wave mixing and delays to measure the frequency response and perform the compensation of a nonlinearly distorted 20Gbaud 4-APSK signal with BER reduction.
Abstract: We demonstrate an optical second-order Volterra filter using wave mixing and delays. We measure the frequency response and perform the compensation of a nonlinearly distorted 20Gbaud 4-APSK signal with BER reduction from 8.2×10-3 to 3.2×10-3.
2 citations
TL;DR: In this article , a pulse-based model for analyzing general reset control systems both in open-loop and closed-loop is developed, for the rst time enabling loop-shaping implemented into the analysis of reset controller systems accurately.
Abstract: In the precision motion industry, the demand for machines with higher speed, accuracy, and stability is rapidly increasing. Traditional linear controllers struggle to meet these requirements due to fundamental limitations such as Bode’s gain-phase relationship and waterbed effects. Hence, non-linear controllers that can address these constraints are needed. Reset controllers are potential alternatives with the advantage of phase lead in comparison to their linear counterparts. However, reset controllers are incompatible with the loop-shaping analysis technique, since loop-shaping relies on the simple first-order element, whereas reset controllers include complex higher-order harmonics. Thus, the analysis and design of reset controllers remain bottle-necks in their way of widespread application. In this paper, a new analytical technique for reset controllers is proposed to break the limitations. A novel pulse-based model for analyzing general reset control systems both in open-loop and closed-loop is developed, for the first time enabling loop-shaping implemented into the analysis of reset control systems accurately. Corresponding sensitivity functions are subsequently illustrated. Finally, through intuitive examples, the accuracy of the proposed model is evaluated.
1 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
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....
[...]
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]....
[...]