Topic: Control Systems
Consider the feedback system $G(s) = \frac{K(s+4)}{s(s+1)}$, $H(s) = \frac{1}{s+2}$. The value of gain for which system is marginally stable is
- A. $K = 4$
- B. $K = 6$
- C. $K = 10$
- D. $K = 2$
Answer: B. $K = 6$
Explanation: The characteristic equation is $1 + G(s)H(s) = 0$, which yields $s(s+1)(s+2) + K(s+4) = 0 \Rightarrow s³ + 3s^2 + (K+2)s + 4K = 0$. Using the Routh array, marginal stability occurs when a row of zeros is formed, which happens when the product of the inner terms equals the product of the outer terms. Thus, $3(K+2) = 4K$, giving $3K + 6 = 4K$, so $K = 6$.