Steady State Error of controlled loop system

Question

I am trying to calculate the steady state error of the following system but unable to do it. I have used MATLAB and calculated the steady state error to be 0.1128 but don't understand the steps that I need to do to calculate this.

Please help.

Thanks

Answer 1

Here is how you proceed :

1. Reduce the system to either unity feedback system or a Single block representing the closed loop transfer function. In your case, reducing to a single block should be easy.

2. For a unity feedback system , as shown

   

Then from the diagram

E(s) = R(s) - Y(s) = R(s) - G(s)E(S)

Or

E(s) = R(s) / [ 1 + G(s)]

If you reduce it to a single block, Then

E(s) = R(s) - R(s)G(s) = R(s)[ 1 - G(s)]

If you have non unity feedback system, then

G'(s) = G(s) / [ 1 + G(s)H(s) - G(s)]

will reduce it to the form in figure.

3. For steady state error, you need to specify the input. 3 inputs are used :

   • Step with Laplace transform 1/s
   • Ramp with Laplace transform 1/s^2
   • Parabolic with Laplace transform 2/s^3

4. Substitute the transform of input into the equation for your error obtained in step 2.

5. Use the final value theorem acc to which

E(infinity) = lim s-> 0 [ s.E(s)]