# designing PID controller using Ziegler Nichols algorithm

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?

• The Transfer function is difficult to decipher, can you tidy it up? But if it's a 'normal' 2nd order system then it will only produce continuous oscillations when the damping coefficient, $\zeta =0$
– Chu
Jan 23 '16 at 19:21
• @chu so I can't find the PID coefficient by using Ziegler Nichols methods Jan 23 '16 at 20:30
• In what kind of form is your transfer function? ZN is not an algortithm, it's a method of turning the right knobs on PID controller when you don't have a known transfer function. Jan 23 '16 at 23:12
• Give a properly formatted transfer function and there may be a chance of answering. What is xsiws for example?
– Chu
Jan 23 '16 at 23:39

## 1 Answer

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.