How to tackle noise with PI controller
Bode plot will show lack of phase margin at unit gain. So the solution is to add phase lead compensation  (s/T + 1) near the unity gain T=1/ωo  for ωo being the unity loop gain frequency and adding 45 deg phase margin, so that the 2nd order system becomes a 1st order slope during the unity gain region. The frequency response should then have have more gain margin, less overshoot to a step input and less peaking in LPF breakpoint.