Contradiction between Routh's algorithm and checking with some value

I am designing a control system controlled by some microcontroller K:

The open loop gain is $G_{o}(s) = \frac{K}{s(s^{2}+4s+3)}$

and the closed loop gain is obviously $G_{c}(s) = \frac{K}{s(s^{2}+4s+3)+K}$

I tried finding the critical frequency but found something else interesting while trying to find the critical frequency.

I applied Ruth's algorithm to the denominator of the closed loop gain and I get this result:

Obviously for a stable system k doesnt exist but this seemed super odd so I decided to set k = 2 and find all the roots using a calculator and I found that the root is in the left half plane of the Re,Im plane so the system SHOULD be stable. So what am I doing wrong?

posted 11 months ago

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Volpina‭

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