Hi, I have some difficulties with PI controller design, please, take a look.

Transfer function of the system is

Denumerator from the closed-loop transfer function (considering PI controller, where K is proportional gain, and T is integral gain) is

after simplifying

I've tried Graham-Lathrop Method, but I got 2 equations with 3 parametres:

I've tried Naslin method and manual tuning as well without any success. Then I've tried to design P controller only, but got negative proportional gain...

What am I doing wrong?

Any advice would be greatly appreciated! Thanks for your time.

Liptak

NOTE: sorry for the external images, but latex compilator isn't working right now.