I have the block diagram in the picture where L = 0 and τ = 0.02. New parameters kP and kI must be determined to make the cross-over frequency 100 rad/sec. As I understand it, one must solve the task by finding a kp and ki that gives an amplitude of 1 at 100 rad/sec. Should I count on an open loop or a closed loop? If you count on an open loop, what do you do with the gain of 20 in the feedback loop? What are the differences between open and closed loops in this case?

 

The gain of 20 in the feedback path affects the closed-loop behavior but does not contribute to the open-loop transfer function since it appears after summation and feedback subtraction. For an open-loop analysis feedback blocks are ignored when computing the open-loop transfer function. I think you can use MATLAB or Simulink to calculate KP and Ki.