Describing function

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

Describing Function Analysis in the Presence of Uncertainty

Abstract: A framework is proposed that generalizes describing function (DF) analysis to uncertain systems. By e tting a rational approximation to the DF of nonlinear elements, DF analysis is incorporated into a generalized π framework of robustness analysis. This allows us to consider uncertainty in both the linear and nonlinear components. Information on the size, frequency, and stability of unforced limit cycles is obtained as in the graphical test. The response to sinusoidal driving inputs can also be analyzed in this framework.

A Method for Estimating the Noise Level of Unstable Combustion Based on the Flame Describing Function

Abstract: Practical combustion is often coupled by the system acoustics and under some conditions the process may become unstable giving rise to oscillations of finite amplitude and to discrete tone noise radiation. The objective of this investigation is to model the nonlinear features of unstable combustion to predict limit cycle amplitudes and thus get an estimation of the radiated noise level under such regimes of operation. The present study is based on an analysis derived in a companion paper (Noiray et al. (2008)) which contains a complete nonlinear description of the thermo-acoustic coupling encountered in an unconfined reaction zone layout. Theoretical predictions are successfully compared with a set of measurements. It is shown that nonlinear phenomena such as frequency shifts, triggering or hysteresis may be suitably predicted by an analytical model based on the flame describing function (FDF). The objective of the present paper is to make use of this method to investigate nonlinear acoustic-combustion dy...

General Criterion And Control Strategy Of Collision-free Movement For Manipulators

Abstract: In this paper, we present a general procedure for finding collision-free paths for a polyhedral object moving through space that is cluttered with obstacle polyhedra. The unified criterion of collision- free motion is represented as Conv {H/sub i/)Conv {O/sub j/)=/spl Oslash/ which is suitable for all cases regardless of the space dimensionality. Based on the criterion, we are led to construct the describing function J which stands for minimal distance between the moving object and obstacles. Tha algorithm derived from describing function J can be used to find any path of interest for both the 2-D problem and the 3-D problem. It is shown that the solution method to the find path problem may be reduced to a search technique. Since the describing function J is related to only some extreme points, the strategy for automatically determining safe paths between configurations in presence of obstacles may be effectively sets implemented by a simple programming.

Frequency-domain based feedback control of flow separation using synthetic jets

Abstract: This research aims to facilitate feedback control of flow separation using synthetic jets. The effects of synthetic jets on flow separation are assessed via CFD simulations on a rounded backward-facing step. The NARMAX (Nonlinear Auto Regressive Moving Average with eXogenous inputs) system identification method is applied to develop a nonlinear flow model. Low-pass filtering is introduced as an effective method to facilitate a quasi-linear approximation of the nonlinear fluidic system including synthetic jet actuation in the frequency domain. Employing the describing function method, the approximate frequency response of the system is analyzed and implemented for the synthesis of a linear feedback controller. Finally, a PI controller is demonstrated to achieve tracking of a desired pressure with an improvement in the transient response over the open loop system.