Describing function

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

Describing functions, limit cycles and reduced models in nonlinear systems

Abstract: A criterion for the absence of limit cycles in nonlinear multivariable systems is proposed. It is very flexible and can give less conservative results. Comparison is made with existing criteria, and it is also shown that the criterion has great attractions when reduced models are used.

Describing function applied to HVDC systems harmonic instability

Abstract: The adoption of voltage-controlled oscillator based firing systems has almost completely eliminated the harmonic instabilities experienced in early HVDC systems. However, the basic feature of such systems (equidistant firing) is adversely affected by the feedback action of the current control loop, since the direct current may contain uncharacteristic harmonics which are not filtered out by the controller. Under certain circumstances (such as an imbalance and/or a distortion in the alternating voltage, DC-or AC-side resonances near DC or AC harmonic frequencies, respectively) instabilities may occur which are characterised by oscillations synchronised with the alternating voltage, i.e. harmonic instabilities. Nonlinear control-system theory, namely the describing-function method, was used to show that these oscillations are limit cycles whose conditions of occurrence can be predicted. A detailed computer model for an hvdc link was developed which allows the calculation of both the DC and the AC harmonics in the steady state and the describing function for subharmonics of the firing frequency of the convertor. Limit cycles can be predicted by the Nichols chart technique.

A New Perspective on the Flame Describing Function of a Matrix Flame

Abstract: This paper considers a fundamental thermoacoustic test rig developed by Noiray (“Linear and nonlinear analysis of combustion instabilities, application to multipoint injection systems and control strategies”, PhD thesis, Ecole Centrale Paris, 2007) and models it with an entirely analytical approach. The test rig is treated as a system of two coupled elements: an acoustic resonator and a flame with oscillating rate of heat release. We describe the acoustics of the combustion rig in terms of modes, and derive a governing equation for one such mode. This turns out to be the equation for a damped harmonic oscillator, forced by the heat release rate from the flame. In order to model the heat release rate, and in particular its nonlinear aspects, we develop a generalised nτ-law with amplitude-dependent coefficients and multiple time-lag. The coefficients are determined from Noiray’s measured flame describing function. Stability predictions are made by evaluating the sign of the damping coefficient in the govern...

Comparison of experimental identification techniques for a nonlinear SDOF system

Abstract: Several experimental nonlinear identification techniques have been presented in the literature. In this paper, several of these techniques are applied to a single degree of freedom system and the results are compared. We apply a time-domain technique and two frequency-domain techniques to the second mode of a cantilevered beam. The frequency-domain techniques include a backbone curve-fitting technique based on the describing function method and an amplitude and frequency sweep technique based on the method of multiple-scales. The equation of motion is derived from a Lagrangian using the assumed-modes method. Based on the form of the equation of motion, we note that the restoring-force-surface method cannot be used to determine the equation of motion. Differences in the parameter estimates are discussed. We conclude by discussing the limitations we encountered for each technique. These include the inability to separate nonlinear curvature and inertia effects and problems with estimating the coefficients of small terms with the time-domain technique.