# How can I design a PI controller for a closed loop system, which requires a bandwidth equal to the natural frequency and a set Phase Margin?

For a school project I have to hand in a small report on a this problem. I've been studying so much for it but right now I'm just mixing up everything I've seen and just don't know where to start. I'd really appreciate it if somebody could point me in the right direction.

For a system with transfer function $$G(s) = 4/(s²+s+4),$$ I have to design a PI controller. The required bandwidth for the closed loop system is the size of the natural frequency. I need to design the PI controller in such way that the phase margin is 50 degrees.

• What have you done so far? Has your prof suggested a method? Direct pole placement? Bode design? Trial and error? – Ben Jun 28 '18 at 19:20