Compensator for a 6th Order System

[trojsi]

Homework Statement

I have a sixth order system with two complex dominant poles shown in the root locus plot attached. This is done using sisotool. I have requirements of 5% overshot and 1.5sec settling time which I have to satisfy. These are shown as border lines with yello shading on the root locus plots.

To satisfy the requirements, a compensator is needed to twist the locus out of the border while varying the proportional gain. I managed to get the two dominant poles out of the border by placing 2 complex zeros close to the origin but could not get near to the requirements.The pole closest to the origin is real and negative but it is inside the border with a zero very close to it. Will this pole effect me since it is real? If yes what is the best way to move it out of the border?

Homework Equations

The Attempt at a Solution

 

[Valkarie]

Yes, the pole closest to the origin will effect you. It is difficult to move this pole out of the border without changing the other poles as they are all linked. To move the pole out of the border, you can try adding another zero close to the pole or use a combination of zeros and poles to twist the locus. You can also adjust the proportional gain to shift the real pole outside the border.