The characteristic equation for the system is
\[
s^3 + 9s^2 + 26s + 12(2 + K_c) = 0
\]
Using Routh test, the value of Kc that will keep the system stable is:
Show Hint
- 17.5
- 4
- 13.5
- 3.5
The Correct Option is C
Solution and Explanation
Step 1: Apply the Routh-Hurwitz criterion.
The Routh-Hurwitz criterion is applied to determine the stability of the system. We form the Routh array using the coefficients of the characteristic equation. For stability, the number of sign changes in the first column determines the value of \(K_c\) that will keep the system stable.
Step 2: Conclusion.
Using the Routh test, we find that the correct value of \(K_c\) that keeps the system stable is (C) 13.5.
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