Simulink Control Design™ - MathWorks

Describing Function Analysis of Nonlinear Simulink

Models

This example shows how to use the frequency response estimation to perform a

sinusoidal-input describing function analysis, for a model with a saturation nonlinearity.

Background on Describing Function Analysis

Describing function analysis is a widely known technique to study frequency response of

nonlinear systems. It is an extension of linear frequency response analysis. In linear

systems, transfer functions depend only on the frequency of the input signal. In nonlinear

systems, when a specific class of input signal such as a sinusoidal is applied to a nonlinear

element, you can represent the nonlinear element by a function that depend not only on

frequency, but also on input amplitude. This function is referred to as a describing

function. Describing function analysis has a wide area of applications from frequency

response analysis to prediction of limit cycles.

To use sinusoidal-input describing function analysis, which is the most common type of

describing function analysis, your model should satisfy these conditions:

(^1) Nonlinearity is time-invariant.
(^2) Nonlinearity does not generate any subharmonic as a response to the input
sinusoidal.
(^3) The system filters out the super-harmonics generated by the nonlinearity (this
assumption is often referred to as filtering hypothesis).
In this example, you perform describing function analysis on a model with saturation
nonlinearity that satisfies all the assumptions above.
Step 1: Opening the Model
Open the Simulink model with a saturation nonlinearity.
scdsaturationDF
mdl = 'scdsaturationDF';
Describing Function Analysis of Nonlinear Simulink Models