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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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Posted ContentDOI
17 Oct 2022
TL;DR: In this paper , the authors focused on the voltage source converter (VSC) control systems in wind farms and tried to detect the nonlinear behavior caused by the bilateral or unilateral saturation hard limits based on higher-order statistics analysis.
Abstract: In recent years, the sub-synchronous oscillation (SSO) accidents caused by wind power have received extensive attention. A method is needed to distinguish if nonlinear behavior exists in the recorded equal-amplitude accident waveforms, so that different methods can be adopted to analyze the mechanism of the oscillation. The theory of higher-order statistics (HOS) has become a powerful tool for detection of nonlinear behavior (DNB) in production quality control since 1960s. However, HOS analysis has been applied in mechanical condition monitoring and fault diagnosis, even after being introduced into the power system and wind farms. This paper focuses on the voltage source converter (VSC) control systems in wind farms and tries to detect the nonlinear behavior caused by the bilateral or unilateral saturation hard limits based on HOS analysis. First, the traditional describing function is extended to obtain more frequency domain information, and hereby the harmonic characteristics of bilateral and the unilateral saturation hard limit are studied. Then the bispectrum and trispectrum are introduced as HOS, which are extended into bicoherence and tricoherence spectrums to eliminate the effects from linear parts in the VSC control system. The effectiveness of DNB and classification based on HOS is strictly proved and its detailed calculation and estimation process is illustrated. Finally, the proposed method is demonstrated and further discussed through simulation results.
Journal ArticleDOI
TL;DR: In this article, a method for computing the sine wave equivalent gain or describing function of a, double-valued nonlinearity is presented, illustrated by considering four common types of such a non-linearity and t.he gains for each of these characteristics as obtained by following the present procedure and the conventional procedure.
Abstract: A method for computing the sine wave equivalent gain or describing function of a, double-valued non-linearity is presented. The method is illustrated by considering four common types of such a non-linearity and t.he gains for each of these characteristics as obtained by following the present procedure and the conventional procedure are compared. It is also pointed out that the present procedure can have advantage over the conventional procedure in that the stability analysis can be simplified raid the design of an optimum compensation schema can be facilitated.
Proceedings ArticleDOI
03 Aug 1994
TL;DR: In this article, the authors treat relatively new oscillators in the class of parallel resonant switching mode oscillators and present flexible methods of triggering their MOSFET switches through ring transformers.
Abstract: Switching-mode-oscillators constitute a unique class in the field of oscillators and also in the field of switching-mode-invertors. The paper treats relatively new oscillators in the class. They can be entitled as parallel resonant switching mode oscillators. Furthermore, flexible methods of triggering their MOSFET switches through ring transformers are discussed. Analysis of the system's useful limit cycle dynamics is helped by resorting to the describing function method.
Book ChapterDOI
01 Jan 1991
TL;DR: In this paper, the authors describe software written for the investigation of the stability of, and limit cycles in nonlinear sampled-data systems using a new approach based on the z-transform describing function and includes two sections, a numerical section which consists of solving numerically the system characteristic equation and a graphical section which plots the ZDF of the nonlinearity and the Nyquist locus of the linear plant on a z-or a w-plane.
Abstract: Publisher Summary The paper describes software written for the investigation of the stability of, and limit cycles in, nonlinear sampled-data systems. The software uses a new approach based on the z-transform describing function and includes two sections, A numerical section which consists of solving numerically the system characteristic equation and a graphical section which plots the ZDF of the nonlinearity and the Nyquist locus of the linear plant on a z-or a w-plane. Both methods investigate automatically the different limit cycles that may occur at the same frequency but with different waveshapes at the output of a two segment nonlinearity.
Proceedings ArticleDOI
09 Jul 2007
TL;DR: Simulation and experimental results are presented to illustrate the performance and demonstrate the feasibility in practical applications of the proposed plasma ignition system with self-oscillating resonance tracking capability.
Abstract: Reducing emissions and increasing efficiency of modern spark ignited internal combustion engines are crucial for the future of the environment and the global economy. This paper presents a plasma ignition system with self-oscillating resonance tracking capability to promote these objectives. The proposed ignition system is composed of a high quality factor series RLC circuit driven by a radio frequency (RF) generator to start and sustain a plasma torch for a prescribed duration inside the combustion chamber. Resonant frequency tracking is achieved using an integrated self-oscillating feedback topology. A phase-lead compensator is used to compensate for the propagation delay in the RF generator and a signum type nonlinearity is used to achieve the amplitude limitation for sustained oscillation. The describing function method is employed for analysis and design of the self-oscillating resonance tracking system. Simulation and experimental results are presented to illustrate the performance of the proposed ignition system and to demonstrate its feasibility in practical applications.

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