- #1

dontigeh

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Please help.

Thanks

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- Thread starter dontigeh
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- #1

dontigeh

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Please help.

Thanks

- #2

milesyoung

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- 67

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.

- #3

dontigeh

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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.

- #4

milesyoung

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Right, so you could use the general method I described, or if you've had a lecture onYes I want the steady-state error to a step input.

And the value of K used was 0.375.

- #5

timthereaper

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- #6

dontigeh

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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.

- #7

milesyoung

- 818

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I can't decipher what went wrong if you don't show more detail.

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'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.

- #8

FactChecker

Science Advisor

Gold Member

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Since you are going to take the limit of the final formula as s->0, you can do that in each part as the first step. That will simplify things tremendously.

That gives a steady state gain of .375 * 7/0.5 * 100/72 = 7.29166666666667 across the top and a steady state gain of 1 for G_{3} in the feedback loop.

For the entire system I get a steady state gain of 7.29166666666667/(1+7.29166666666667) = 0.879396984924623.

For a unit step input, that would give a steady state error of 1-0.879396984924623 = 0.120603015075377.

I don't know why the MATLAB answer 0.1128 is different. Is it possible that the MATLAB number is from a finite time plot that is an approximation to infinite time?

That gives a steady state gain of .375 * 7/0.5 * 100/72 = 7.29166666666667 across the top and a steady state gain of 1 for G

For the entire system I get a steady state gain of 7.29166666666667/(1+7.29166666666667) = 0.879396984924623.

For a unit step input, that would give a steady state error of 1-0.879396984924623 = 0.120603015075377.

I don't know why the MATLAB answer 0.1128 is different. Is it possible that the MATLAB number is from a finite time plot that is an approximation to infinite time?

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