Step Response and Root Locus are give me different answers

Question

Nélio Dias 2021-5-15

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回答： Paul 2021-5-15

HI, thanks for reading my question. I have this transfer function

ans =
 
               (s+4)
  -------------------------------
  (s+73.34) (s+10) (s^2 + 4s + 8)

And I want the overshoot, so I used the rlocus function and got this

*

So the gain, pole, damping, overshoot and frequency are all ok. But if I use the step response with gain of 6880, I will have this

the overshoot go to 32.6%. Then, I dont understand why this have different answers. What Im doing wrong?

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Answer 1

Paul 2021-5-15

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https://ww2.mathworks.cn/matlabcentral/answers/830468-step-response-and-root-locus-are-give-me-different-answers#answer_700188

在 MATLAB Online 中打开

The information in the datatip on the root locus plot is only applicable for a response defined by that pole location (and its conjugate if complex), not all of the closed loop poles. So in this case the data tip is giving the information for the step response of only those second order poles:

step(tf(9.88^2,[1 2*0.405*9.88 9.88^2]))

The overshoot is 25%.