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.

Thanks

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.

Do you mean the steady-state error to a step input?

What value of ##K## did you use? The system is unstable for ##K = 1##.

In general, you could find the transfer function from the input to ##E(s)##, verify it's stable, and use the final value theorem.

timthereaper
Do you mean the steady-state error to a step input?

What value of ##K## did you use? The system is unstable for ##K = 1##.

In general, you could find the transfer function from the input to ##E(s)##, verify it's stable, and use the final value theorem.

Yes I want the steady-state error to a step input.

And the value of K used was 0.375.

Yes I want the steady-state error to a step input.

And the value of K used was 0.375.
Right, so you could use the general method I described, or if you've had a lecture on error constants, you could calculate that instead.

I agree with @milesyoung and say you should compute the closed-loop transfer function and use the final value theorem.

Hi,
Thanks for the help.
I did the following: 1/s(1-(262.5s+262.5)+(700/0.375S^4+7.313s^3+37.313s^2+43.875s+276)), then i did E(infinity) = lim s-> 0 [ 1-700/736]= 0.04891. Which is not correct. The gain is 0.375.

Hi,
Thanks for the help.
I did the following: 1/s(1-(262.5s+262.5)+(700/0.375S^4+7.313s^3+37.313s^2+43.875s+276)), then i did E(infinity) = lim s-> 0 [ 1-700/736]= 0.04891. Which is not correct. The gain is 0.375.
I can't decipher what went wrong if you don't show more detail.

I'd suggest you don't multiply anything out. Just find ##E(s)## symbolically using ##G_1(s),G_2(s),G_3(s)##, and then take the limit.

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