Question

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:

• A. 17.5
• B. 4
• C. 13.5
• D. 3.5

Hint:

The Routh-Hurwitz criterion helps analyze the stability of dynamic systems based on the characteristic equation.

Answer 1

The Correct Option is C

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.