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First of all, I am new to this Q/A site. If I am doing anything wrong, please forgive me. I am having some trouble solving this problem:
Given the system of Figure(1), design a PID controller so that the system can operate with a peak time that is third(3 times) that of the uncompensated system at 20% overshoot and with zero steady-state error for a step input.

Figure(1):Uncompensated feedback control system

What I have done so Far: At first: enter image description here

Then finding \$ Z_{c} \$: enter image description here

Now I have to find PD compensated System using this matlab code:

clear all
close all
clc
Gs=zpk([-8 -0.85],[-3 -6 -10],1)
rlocus(Gs)

But the result is frustrating as I am not getting any kind of result here: enter image description here

Am I missing something here?? What's wrong with my solution up to the point. I have solved it with for 2/3 times and 1/3 times. Both times I was successful but in case of 3 times not getting any result.

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  • \$\begingroup\$ I don't see where you got the \$G = 1.806\$. \$\endgroup\$ – TimWescott Dec 4 '18 at 20:19
  • \$\begingroup\$ It's actually sigma. And I got by calculating = -5.42*1/3=1.806 \$\endgroup\$ – Fazla Rabbi Mashrur Dec 4 '18 at 20:26
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    \$\begingroup\$ First, the root locus has a point on the real line if that point is to the left of an odd number of poles - zeros. So when poles and zeros alternate, your root locus will be entirely on the real line. That's a good sign that you've got a calculation wrong. \$\endgroup\$ – TimWescott Dec 4 '18 at 20:44
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    \$\begingroup\$ You're scaling your \$t_p\$ down by a factor of three; shouldn't you be scaling both parts of your dominant pole frequency up by a factor of three? \$\endgroup\$ – TimWescott Dec 4 '18 at 21:05
  • \$\begingroup\$ \$\sigma\$, \$G\$, eh, what's the difference? \$\endgroup\$ – TimWescott Dec 4 '18 at 21:05

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