Ref =
I do not intend to provide an in-depth tutorial on the topic of Integral Transform. The variable s is a complex frequency variable associated with system dynamics, similar to the variable x in a quadratic curve, represented by, a·x² + b·x + c. The Laplace transform of the input is typically used to describe a linear system's input-output relationship by transforming the differential equation (in the time domain) into an algebraic equation (in the frequency domain).
The output in Simulink is, in fact, a rounded figure. Here is how you can compute it:
%% Declare symbolic variables for the complex frequency variable and the time variable
syms s t % s = σ + i·ω
%% Reference input
ref = 3; % reference input value in time domain (as shown in Simulink)
Ref = laplace(ref, t, s) % perform Laplace transform to convert the reference, r(t) into frequency domain, R(s)
%% Dynamic System in transfer function (frequency domain)
Sys = 1/(2*s^2 + s)
%% Perform inverse Laplace transform
Out = Ref*Sys
%% Output in time domain
f = ilaplace(Out, s, t)
f5 = subs(f, t, 5) % substitute t = 5 seconds into the function, f
out = vpa(f5) % output value
