how to use Transfer Fcn

Hello!Regarding the use of transfer functions, I don't understand the formulas in the help documentation. What is the meaning of S, and how is 9.493 achieved?

Answer 1

[Sam Chak]

Hi @饕餮王 (Mr. Taotie)

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)

Ref = 

%% Dynamic System in transfer function (frequency domain)
Sys = 1/(2*s^2 + s)

Sys = 

%% Perform inverse Laplace transform
Out = Ref*Sys

Out = 

%% Output in time domain
f   = ilaplace(Out, s, t)

f = 

f5  = subs(f, t, 5)         % substitute t = 5 seconds into the function, f

f5 = 

out = vpa(f5)               % output value

out = 

9.492509991743392771017172046803

[饕餮王]

Wow, I admire it so much, thank you for your help