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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.

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  • \$\begingroup\$ 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. \$\endgroup\$ Mar 8 at 11:16
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    \$\begingroup\$ Are you required to use Ziegler-Nichols? It’s not a particularly good method. \$\endgroup\$
    – Chu
    Mar 8 at 14:04
  • \$\begingroup\$ @Chu I have to use various methods and then compare the results. Z-N is one of those. \$\endgroup\$ Mar 8 at 15:46

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