time domain specifications calculations from graph

from the step() inbuilt function to plot second order system response, form the graph how to mark various time domain specifications in MATLAB2022b.

Answer 1

[Epsilon]

Hi Pranav,

The step() function can be used to plot the second order system response. Here is a documentation link to Step response plot of dynamic system; step response data - MATLAB step (mathworks.com).

Also the stepinfo() function can be used to compute step-response characteristics which can then be used to update the plot of the step response. Here is a documentation link to Rise time, settling time, and other step-response characteristics - MATLAB stepinfo (mathworks.com).

Here is an attached exemplar code for your reference, hope it helps!

% Define system parameters
wn = 5;  % Natural frequency (rad/s)
zeta = 0.5;  % Damping ratio

% Define an exemplar transfer function 
num = [wn^2];  % Numerator coefficients
den = [1, 2*zeta*wn, wn^2];  % Denominator coefficients
sys = tf(num, den);

% Plot the step response
step(sys);
hold on;

% Calculate time-domain specifications
info = stepinfo(sys);

% Mark Rise Time
plot([info.RiseTime info.RiseTime], [0 1], 'r--', 'DisplayName', 'Rise Time');

% Mark Peak Time
plot([info.PeakTime info.PeakTime], [0 info.Peak], 'g--', 'DisplayName', 'Peak Time');

% Mark Settling Time
plot([info.SettlingTime info.SettlingTime], [0 1], 'b--', 'DisplayName', 'Settling Time');

% Mark Overshoot
plot(info.PeakTime, info.Peak, 'ro', 'DisplayName', 'Overshoot');

% Add labels and legend
xlabel('Time (seconds)');
ylabel('Response');
title('Step Response with Time Domain Specifications');
legend('show');
hold off;