Question #233841

Check the stability of the closed system whose characteristic equation is given by S^4 +4S³ +6S² +2S+3=0,explain with step by step lengthy?

Expert's answer

**Concept:**

The characteristic equation for a given open-loop transfer function G(s) is

1 + G(s) H(s) = 0

According to the Routh tabulation method, the system is said to be stable if there are no sign changes in the first column of the Routh array.

The number of poles lies on the right half of s plane = number of sign changes

**Application:**

By applying Routh tabulation method, we get:

"\\frac{16-2k}{4} > 0"

The system to be stable, there should be no sign changes, i.e.

K < 8

and "K > 0 'or' K < 8"

So"0 < K < 8"

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