Describing function

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

Scaled relative graphs for system analysis.

Abstract: Scaled relative graphs were recently introduced to analyze the convergence of optimization algorithms using two dimensional Euclidean geometry. In this paper, we connect scaled relative graphs to the classical theory of input/output systems. It is shown that the Nyquist diagram of an LTI system on $L_2$ is the convex hull of its scaled relative graph under a particular change of coordinates. The SRG may be used to visualize approximations of static nonlinearities such as the describing function and quadratic constraints, allowing system properties to be verified or disproved. Interconnections of systems correspond to graphical manipulations of their SRGs. This is used to provide a simple, graphical proof of the classical incremental passivity theorem.

Susceptibility of 3-phase power systems to ferro-nonlinear oscillations

Abstract: A numerical method is described for predicting the possibility of jump resonance or subharmonic oscillations being sustained by a given 3-phase circuit, based on the describing function and dual-input describing function concepts of control theory The method can be applied to predict asymmetrical jump modes which have no equivalent in single-phase circuits Results predicted by this method are compared with results obtained from laboratory experiments

An algorithm for generating real describing functions

Abstract: A classical method of dealing with the non-linear elements in a transfer function is to assume that they can be separated from the linear section and can then be represented by describing functions The standard method of calculating these describing functions has been to use a graphical method which breaks the non-linear characteristic into a series of linear sections and super-imposes their effects onto a sinusoidal input The output is assumed to be a Fourier series and the Fourier transform for the first coefficient of this series is calculated in a piecemeal fashion The process is not difficult but there is a considerable amount of calculation involved In this paper an algorithm is presented which enables the describing functions of real non-linearities, with any number of linearized sections, to be simply written down without the usual onerous calculations Additionally, a method of quickly sketching the general shape of describing functions is outlined

Non-uniform error-sampled control system

Abstract: A nonuniform ADC (analog-to-digital converter) is shown to be a viable option for a system designed for zero or small steady state errors. The choice of quantization levels is based on the ease of hardware implementation, speed of response, and the idea that, in control systems designed for zero steady state error, it should be sufficient to know the error with certain precision around zero, but that away from zero the same precision need not be necessary. A describing function analysis of the effect of the nonlinearity due to nonuniform quantization is presented. Some simulation results are also included. >