Describing function

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

Nonlinear oscillation via Volterra series

Abstract: Using a novel approach, the amplitude and frequency of nearly sinusoidal nonlinear oscillators can be calculated by solving two algebraic nonlinear equations. These determining equations can be generated to within any desired accuracy using a recursive algorithm based on Volterra series. Our method inherits many desirable features of the harmonic balance method, the describing function method, and the averaging method. Our technique is analogous to, but is much simpler than, the classic approach due to Krylov, Bogoliubov, and Mitropolsky. Unlike conventional techniques, however, our approach imposes no severe restriction on either the degree of nonlinearity, or the amplitude of oscillation. Moreover, the accuracy of the solution can be determined by a constructive algorithm.

Nonlinear Servoanalysis of Human Lens Accommodation

Abstract: A servoanalysis of the feedback control system for lens accommodation has been based upon experimental evidence designed to explore the nonlinear properties. Because these nonlinearities are essential to the functioning of the system, a describing function approach was employed. Computation served to obtain open-loop characteristics. The transfer function of the linear part is F( s) = 4 ( 1 + 0.15s) e-0." s ( 1 + 2 [ 0.3( 0.08)] + ( 0.08s) 2) ( 4) and some assignments of portions of this equation to the physical elements of the lens system are suggested. The no-memory nonlinearity has general saturation characteristics; two related models, one with quite unusual aspects, are presented, and independent evidence for these adduced. The combined model accounts for large and small signal responses, stability characteristics, predicts certain noise spectral features of the openand closed-loop lens system. Phase discrepancies, possible sampled data properties, and the even-error-signal operator put forward crucial new experiments.

Nonlinear damping and quasi-linear modelling.

Abstract: The mechanism of energy dissipation in mechanical systems is often nonlinear. Even though there may be other forms of nonlinearity in the dynamics, nonlinear damping is the dominant source of nonlinearity in a number of practical systems. The analysis of such systems is simplified by the fact that they show no jump or bifurcation behaviour, and indeed can often be well represented by an equivalent linear system, whose damping parameters depend on the form and amplitude of the excitation, in a 'quasi-linear' model. The diverse sources of nonlinear damping are first reviewed in this paper, before some example systems are analysed, initially for sinusoidal and then for random excitation. For simplicity, it is assumed that the system is stable and that the nonlinear damping force depends on the nth power of the velocity. For sinusoidal excitation, it is shown that the response is often also almost sinusoidal, and methods for calculating the amplitude are described based on the harmonic balance method, which is closely related to the describing function method used in control engineering. For random excitation, several methods of analysis are shown to be equivalent. In general, iterative methods need to be used to calculate the equivalent linear damper, since its value depends on the system's response, which itself depends on the value of the equivalent linear damper. The power dissipation of the equivalent linear damper, for both sinusoidal and random cases, matches that dissipated by the nonlinear damper, providing both a firm theoretical basis for this modelling approach and clear physical insight. Finally, practical examples of nonlinear damping are discussed: in microspeakers, vibration isolation, energy harvesting and the mechanical response of the cochlea.

Analysis of CLL Voltage-Output ResonantConverters Using Describing Functions

Abstract: A new AC equivalent circuit for the CLL voltage-output resonant converter is presented, that offers improved accuracy compared with traditional FMA-based techniques. By employing describing function techniques, the nonlinear interaction of the parallel inductor, rectifier and load is replaced by a complex impedance, thereby facilitating the use of AC equivalent circuit analysis methodologies. Moreover, both continuous and discontinuous rectifier-current operating conditions are addressed. A generic normalized analysis of the converter is also presented. To further aid the designer, error maps are used to demonstrate the boundaries for providing accurate behavioral predictions. A comparison of theoretical results with those from simulation studies and experimental measurements from a prototype converter, are also included as a means of clarifying the benefits of the proposed techniques.

A continuous model for the tapped-inductor boost converter

Abstract: A continuous, low-frequency, small-signal averaged model for the tapped-inductor boost converter with input filter is developed and experimentally verified, from which the dc transfer function and the small-signal line input and duty ratio input describing functions can easily be derived. A new effect due to storage-time modulation in the transistor switch is shown to explain observed excess filter damping resistance without associated loss in conversion efficiency. The presence of an input filter can cause a severe disturbance, even a null, in the control duty ratio describing function, with consequent potential performance difficulties in a converter regulator.