I would like to take the inverse laplace transform of a transfer function.

I got a transfer function using MATLAB's tf command.

I need to take the inverse laplace transform of said transfer function but I can't seem to get it.

My code looks like this

%-Element values

R(1) = 100000;

R(2) = R(1);

L = 4.7*10^-3;

C = 0.001*10^-9;

for i = 1:2

G(i) = 1/R1;

end

%-Define constants

a = G(i)*G(i)/C;

b = (G(i)+G(i));

e = L*C;

c = (G(i)*G(i)*L+C)/(e);

d = G(i)/e;

f = 0

numerator = [a f];

denominator = [b c d];

transfer_function = tf(numerator, denominator)

transfer_function= F;

syms s t

g = ilaplace(F)

[response , time] = step(transfer_function);

plot(time, response)

xlabel('Time(s)');

ylabel('Magnitude(V)');

axis([time(1) time(end) min(response) 1.05*max(response)]);

grid;

grid minor;

I get the following error "Check for incorrect argument data type or missing argument in call to function 'ilaplace'.

Error in ME330Assignment2 (line 27)

g = ilaplace(F)"

Any guidance is appreciated. Thank you!

[Andres Cardenas]

Thank you!

[Star Strider]

As always, my pleasure!

Answer 1

[Star Strider]

The Control System Toolbox tf objects cannot directly be used as symbolic objects. So it has to be re-defined as a symbolic fraction.

There were a few other problems that I corrected.

%-Element values
R(1) = 100000;
R(2) = R(1);
L = 4.7E-3;
C = 0.001E-9;
for i = 1:2 
    G(i) = 1/R(i);
end
%-Define constants
a = G(i)*G(i)/C;
b = (G(i)+G(i));
e = L*C;
c = (G(i)*G(i)*L+C)/(e);
d = G(i)/e;
f = 0

f = 0

numerator = [a f];
denominator = [b c d];
transfer_function = tf(numerator, denominator)

transfer_function =
 
              100 s
  ------------------------------
  2e-05 s^2 + 312.8 s + 2.128e09
 
Continuous-time transfer function.

% F = transfer_function;
syms s t
F = poly2sym([a f],s) / poly2sym([b c d],s)

F = 

F = simplifyFraction(F)

F = 

g = ilaplace(F)

g = 

g = simplifyFraction(g)

g = 

gstep = ilaplace(F * laplace(heaviside(t)))                                     % Provide An Input

gstep = 

gstep = simplifyFraction(gstep)                                                 

gstep = 

figure
fplot(gstep, [0 1E-6])
grid

[response , time] = step(transfer_function);

figure
plot(time, response)
xlabel('Time(s)');
ylabel('Magnitude(V)');
axis([time(1) time(end) min(response) 1.05*max(response)]);
grid;
grid minor;

.