Topic
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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01 Jul 1974
TL;DR: In this article, the authors investigated the stability of limit cycles in nonlinear feedback systems with several describing function (d.f.) predicted limit cycle solutions and showed that for a single-frequency limit cycle the necessary conditions for stability of Loeb and Gelb could be satisfied yet the limit cycle was unstable.
Abstract: This paper investigates the stability of limit cycles in nonlinear feedback systems with several describing function (d.f.) predicted limit cycle solutions. The investigations showed that for a single-frequency limit cycle the necessary conditions for stability of Loeb and Gelb could be satisfied yet the limit cycle was unstable. Also the simple and often used graphical criterion was found to be incorrect. On the other hand, the incremental-describing function (i.d.f.) method used for both asynchronous and synchronous perturbations gave sufficient conditions, within the expected d.f. accuracy, for all the situations. It is further shown that the synchronous i.d.f. and the Loeb criterion are normally identical. The combined mode limit cycle oscillations were also satisfactorily predicted by a twoinput d.f. and i.d.f.
24 citations
TL;DR: In this article, the Fourier series for the exciting current was derived for a single-phase transformer by describing function methods, and a simple mathematical model characterized by simple calculation and with high precision was presented for the harmonics of exciting current.
Abstract: In a transformer, the harmonic model is essential for the filter design and analysis of harmonic power flow. Among all of the harmonic analyses of nonlinear devices, the core nonlinearity caused by the transformer hysteresis has received the most interest. Although many harmonic models have been proposed to interpret the nonlinearity of the transformer core, most of them require complex calculations. In this study, we derive the mathematical formulas of the exciting current for a single-phase transformer by the describing function methods. The mathematical expression allows us to obtain the Fourier series for the exciting current; and, then, it provides the various order harmonic magnitudes and phase angles of the exciting current. This work also presents a mathematical model characterized by simple calculation and with high precision for the harmonics of exciting current. The transformer is under no load condition. Actual measuring verifies the effectiveness of the proposed model.
24 citations
TL;DR: A sliding mode control based on fuzzy logic is proposed as an alternative to reduce chattering where DF method is used to demonstrate its attenuation level at the output of the plant.
24 citations
TL;DR: In this article, the existence of limit cycle oscillations of prototypical aeroelastic wing sections with structural nonlinearity using the describing function method has been investigated using a dynamic model that includes an asymmetric structural non-linearity in the pitch degree-of-freedom.
Abstract: The paper treats the question of the existence of limit cycleoscillations of prototypical aeroelastic wing sections with structuralnonlinearity using the describing function method. The chosen dynamicmodel describes the nonlinear plunge and pitch motion of a wing. Themodel includes an asymmetric structural nonlinearity in the pitchdegree-of-freedom. The dual-input describing functions of thenonlinearity are derived for the limit cycle analysis. Analyticalexpressions for the average value, and the amplitude and frequency ofoscillation of pitch and plunge responses are obtained. Based on ananalytical approach as well as the Nyquist criterion, stability of thelimit cycles is examined. Numerical results are presented for a set ofvalues of the flow velocities and the locations of the elastic axiswhich show that the predicted limit cycle oscillation amplitude andfrequency as well as the mean value are quite close to the actualvalues. Furthermore, for the chosen model with linear aerodynamics, itis seen that the amplitude of the pitch limit cycle oscillation does notalways increase with the flow velocity for certain elastic axislocations.
24 citations
TL;DR: The results demonstrate that the proposed approach describes the diode impedance using a limited number of parameters, while highlighting relevant dynamic characteristics that are overlooked by classical models.
24 citations