# Ziegler Nichols for second order transfer function

I have a second order overdamped transfer function as follows - $$\frac{1}{(70s+1)(50s+1)}$$ and now I want to use a PID controller and tune it using Ziegler-Nichols. I have worked with Ziegler Nichols only for higher order systems so used to think it's not feasible for second order systems. But recently I read somewhere it's possible if the system is overdamped which my system is (damping coefficient came out to be 1.69). But while making Routh array, I am getting just one condition which is K > -1. I am not able to get any K (= Kcr) to have sustained oscillations.

P.S. I have used L-T method and found the answer but want to know what's missing in the above method.

• For a second order system a pahse angle in Nyqvist plot ends (for high frequency) at the -180 deg. So it is impossible that there is no such gain, that would make the system oscillating. – Marko Buršič Mar 8 at 11:16
• Are you required to use Ziegler-Nichols? It’s not a particularly good method. – Chu Mar 8 at 14:04
• @Chu I have to use various methods and then compare the results. Z-N is one of those. – Surbhi Goel Mar 8 at 15:46