I'm trying to use Ziegler Nichols algorithm to design PID controller for the following transfer function: G=w^2/(2*xws+w^2), w=1 , x=0.2. so since the step response for this function is a second order degree I think I have to use the frequency response method for Ziegler Nichols, which mean I have to determine Kp critical which make the system oscillate in the closed loop, then after that use the table to determine the KI and Kd constants, but the problem is I couldn't determine the Kp which make the system oscillate in the closed loop, so how I can use Ziegler Nichols algorithm here?
1) The ZN works by finding the proportional ultimate gain coefficient Kp which produces a stable oscillation, then using the oscillation characteristics to set the P/I coefficients.
2) You are unable to find Kp.
3) Therefor you are unable to use the ZN method.