# Designing of a PID Controller

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.

What I have done so Far: At first:

Then finding $$\ Z_{c} \$$:

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:

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.

• I don't see where you got the $G = 1.806$. – TimWescott Dec 4 '18 at 20:19
• It's actually sigma. And I got by calculating = -5.42*1/3=1.806 – Fazla Rabbi Mashrur Dec 4 '18 at 20:26
• 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. – TimWescott Dec 4 '18 at 20:44
• 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? – TimWescott Dec 4 '18 at 21:05
• $\sigma$, $G$, eh, what's the difference? – TimWescott Dec 4 '18 at 21:05