# Embarrassing Laplace question using ilaplace

3 views (last 30 days)
Robert on 16 Jan 2017
Answered: Star Strider on 20 Jan 2017
I always get stuck using ilaplace And then 6 months goes by and i get stuck again because i don't use it often enough
Im just trying to plot the step response of a first order system using the step command which works fine as always. Just for kicks i want to take the same function take the inverse laplace function and plot it against t manually They should yield the EXACT same answer but yet it doesn't.
Can anyone see my mistake?
clear all
clc
syms R C S
R = linspace(1,10000,5);
C = .0001;
for r = 1:5
Vout_in_t = ilaplace(5/(R(r)*C*S+1))
ezplot(Vout_in_t,[0,2])
hold on
my = tf([1], [1 1/(R(r)*C)])
figure
opt = stepDataOptions
opt.StepAmplitude = 5
step(my,opt)
hold on
end

Jyotish Robin on 20 Jan 2017
Edited: Jyotish Robin on 20 Jan 2017
Hi Robert,
From the given code , what I understood is that the transfer function you are trying to use is the one below:
S/(1+RCS)
In that case , you have to rewrite the line which defines your transfer function as:
>>my = tf([1 0], [(R(r)*C) 1])
Hope this helps!

Star Strider on 20 Jan 2017
If you want to see the response to the step input, you need to convolve it with the Laplace transform of the unit step, (1/s).
See if this does what you want:
syms R C s
R = linspace(1,10000,5);
C = .0001;
for r = 1:5
Vout_in_t = ilaplace(5/(R(r)*C*s+1) * 1/s)
ezplot(Vout_in_t,[0,2])
hold on
my = tf([1], [1 1/(R(r)*C)])
figure
opt = stepDataOptions
opt.StepAmplitude = 5
step(my,opt)
end
hold off

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