Embarrassing Laplace question using ilaplace

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

Answer 1

[Jyotish Robin]

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!

Answer 2

[Star Strider]

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