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I would like to know what I am doing wrong for this PID controller design problem. I have all the parameters calculated ($\zeta$,$\omega_n$,$\sigma$...) and I have my target point set up. But now I need to find the zeros for the PID controller. I am have the equation

$$\sum \text{angles from zeros} - \sum \text{angles from poles} = (2k-1)\times 180 $$
where k = #poles - # zeros of the open loop system....I think.

In my case with the PID controller and the Plant function I have 4 poles and 2 zeros (unknown).

So using geometry I find the angles of all the the open loop transfer function and then I am given the the hint "either set both zeros at the same location or set one close to the origin and calculate the location of the other I chose the latter. So I picked a point close to the origin found its angle and then found the angle of the new zero by subtracting the angle of the poles from the angle of the zero and then subtract that from 180 to get the angle for the new zero. The root locus for this doesn't even come close to my desired point so I assume I am doing this completely wrong.

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    $\begingroup$ @ Motorscooter, would you consider posting on here your root locus? What you have for a system? $\endgroup$ – willpower2727 Dec 2 '15 at 1:01

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