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Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.


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Journal ArticleDOI
TL;DR: The paper presents a technique of linearization of a memory-type nonlinearity with a Gaussian input by applying the concept of "complex describing function" and the quasi-linearized transfer function for the non linearity with the statistical input is termed "complex equivalent gain".
Abstract: The paper presents a technique of linearization of a memory-type nonlinearity with a Gaussian input by applying the concept of "complex describing function." The quasi-linearized transfer function for the nonlinearity with the statistical input is termed "complex equivalent gain." The magnitude of the complex equivalent gain is defined as the ratio of the rms value of the output correlated component to the rms value of the input of the nonlinearity while the phase is assumed to be frequency independent. Furthermore, it is pointed out that the complex describing function for a memory-type nonlinearity is a limiting case of complex equivalent gain where the input to the nonlinearity is a simple sine wave. Finally, a closed-loop control system incorporating a memory-type nonlinearity and impressed by a Gaussian input is analyzed by using the proposed quasi-linearization technique. The results obtained from an analog computer study of the system which agree closely with the results of analysis are also presented.

3 citations

Journal ArticleDOI
TL;DR: A new global stability analysis method dedicated to fuzzy control systems containing Mamdani fuzzy controllers with dynamics to control SISO linear / linearized plants is proposed.

3 citations

Proceedings ArticleDOI
08 Mar 1992
TL;DR: The exponential-input describing function technique is utilized to investigate the transient response of a fuzzy controller and the accuracy of the approximate solution is determined.
Abstract: The exponential-input describing function technique is utilized to investigate the transient response of a fuzzy controller. The symmetric features that fuzzy addition introduces in the decision table of a fuzzy control algorithm made possible the decoupling of the effects of the output error time sequences and, consequently, the representation of the algorithm by multilevel relays. Computer simulations were carried out on a second-order system to assess the performance of the controller, and determine the accuracy of the approximate solution. >

3 citations

Journal ArticleDOI
01 Jan 1993
TL;DR: In this paper, the frequency response characteristics for an analog PWM high-speed on-off valve at the points that the periods of the input signal are certain times of the carrier ones can be calculated based on its switching behaviors.
Abstract: High-speed on-off valves are widely used in PWM electropneumatic servo systems and their characteristics are generallly described by their on and off delay time. This paper focuses on establishing the relationships between their on-off switching behaviors and their frequency response characteristics. A method is proposed by which the frequency response characteristics for an analog PWM high-speed on-off valve at the points that the periods of the input signal are certain times of the carrier ones can be calculated based on its switching behaviors. Then a simple and direct describing function for a PWM high-speed on-off valve is established based on the simulation.

3 citations

DissertationDOI
25 Feb 2017
TL;DR: Low-order nonlinear models for the prediction of the nonlinear behaviour of thermoacoustic systems are developed, in which linear acoustics is combined with a nonlinear heat release model to enable analysis both in the frequency and time domains.
Abstract: Thermoacoustic oscillations may arise in combustion chambers when unsteady heat release and acoustic fluctuations constructively interfere. These oscillations generally lead to undesired consequences, and need to be avoided. Linear stability analysis can be used to investigate the linear stability of a thermoacoustic system, by calculating the frequencies and growth rates of thermoacoustic modes. Adjoint methods can then be used to understand what parameters in the configuration under investigation have to be changed to make it less susceptible to thermoacoustic oscillations. Linear stability is, however, not sufficient in general to ensure safe operability conditions. This is because nonlinear and non-normal effects may trigger finite amplitude oscillations when the system is subject to finite amplitude perturbations. A thorough fully nonlinear investigation of thermoacoustic systems is prohibitively expensive both experimentally and numerically, and one needs to approximate the nonlinear response of the system. In this thesis, low-order nonlinear models for the prediction of the nonlinear behaviour of thermoacoustic systems are developed. These models are based on thermoacoustic networks, in which linear acoustics is combined with a nonlinear heat release model. The acoustic networks considered in this thesis can take into account mean flow and non-trivial acoustic reflection coefficients, and are cast in state-space form to enable analysis both in the frequency and time domains. Starting from linear analysis, the stability of thermoacoustic networks is investigated, and the use of adjoint methods for understanding the role of the system’s parameters on its stability is demonstrated. Then, a fully nonlinear analysis using various state-of-the-art methods is performed, to highlight the strengths and weaknesses of each method. Two novel frameworks that fill some gaps in the available methods are developed: the first, called Flame Double Input Describing Function (FDIDF), is an extension of the Flame Describing Function (FDF). The FDIDF approximates the flame nonlinear response when it is forced simultaneously with two frequencies, whereas the FDF is limited to one frequency. Although more expensive to obtain, the FDIDF contains more nonlinear information than the FDF, and can predict periodic and quasiperiodic oscillations. It is shown how, in some cases, it corrects the prediction of the FDF about the stability of thermoacoustic oscillations. The

3 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202312
202230
202142
202057
201953
201847