I have a second order overdamped transfer function as follows -
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.