# Small Signal Oscillation Mode Parameter using Prony Analysis

Below is a script using matlab m-file to decompose the small signal oscillation mode parameter by using prony analysis. The goal is to achieve the frequency and damping ratio of simulated damped sinusoidal signal. Using this simple script (which prony toolbox is available in matlab) one can utilize for another damped sinusoidal data to get the same parameter.

% Using prony analysis to identify small signal oscillation mode parameter

clear all

close all

fs=56;

ts=1/fs;

t=(0:113)*ts;

y=exp(-0.1.*t).*cos(2*pi*7.*t)+(1/4)*exp(-0.25.*t).*cos(2*pi*70.*t+pi/8);

plot(t,y)

xlabel(‘Time (s)’)

ylabel(‘y(t)’)

% prony

NB=4; NA=4;

[b,a6] = prony(y,NB,NA);         % Prony Analysis

p = roots(a6);

p = log(p);

reig= real(p)/ts;             % imaginer

ieig= imag(p)/ts;             % real

freq=abs(ieig/(2*pi));            % Frequency Oscillation

dr=-reig./(sqrt(reig.^2+ieig.^2));    % Damping Ratio Figure 1. Simulated Damped Sinusoidal Signal, y(t)