How to plot a step response of symbolic laplace and inverse laplace function

Hello

I have a problem with drawing the esponse from the Laplace transform nad inverse laplace transform.

I want to determine the response of the system to the given signal, the response to the inverse transform and compare these responses in one graph

For example i have G(s) = 1/(s+1) nad step U = 1/s,

My code:

G = tf(1,[1 1])

[y t] = step(G) % i want to get t out of step first

syms s; clear G;

G = 1/(s+1)

U = 1/s

Gstep = G*U

Gistep = matlabFunction(ilaplace(Gstep))

ezplot(Gistep,t)

hold on

ezplot(Gstep,t)

ylim([0 2])

But I dont think thats correct

Answer 1

[Sam Chak]

Hi @Ralph Sparrow

Here is the MATLAB script:

clear all; clc

% Define symbolic variables
syms s t y(t) Y(s) 

D1y = diff(y);
% Dynamical system
Eqn = D1y + y == heaviside(t)

% Perform Laplace Transform of Eqn
LEqn = laplace(Eqn);

% Substitute Laplace transform of y(t) for Y(s), and y(0) for the initial condition
LEqn = subs(LEqn, {laplace(y(t), t, s), y(0)}, {Y(s), 0});

% Isolate Y(s) in LEqn
LEqn = isolate(LEqn, Y(s))

% Perform inverse Laplace transform on the right-hand side of LEqn
y(t) = ilaplace(rhs(LEqn))

% Plot the solution
fplot(@(t) y(t), [0 10])
grid on
xlabel('Time, t')
ylabel('y(t)')

Result:

You can compare the above result with the step response of your transfer function:

G = tf(1, [1 1])
step(G, 10)

[Sam Chak]

Note that after isolating , you get

because

.

Also, since you are going to make a comparison with the step response step() and the function assumes the initial condition by default, then you need to make the substitution of this initial value.