Topic: Control Systems
The open loop transfer function of a unity feedback system is
$G(s)=\frac{K}{s(s²+s+2)(s+3)}$
The range of K for which the system is stable is
- A. $\frac{21}{44}>K>0$
- B. $13>K>0$
- C. $\frac{21}{44}<K<\infty$
- D. $-6<K<\infty$
Answer: A. $\frac{21}{44}>K>0$
Explanation: $G(s)=\frac{K}{s(s²+s+2)(s+3)}$
Characteristic equation:
$(s³+s²+2s)(s+3)+K=0$
$s^4+4s^3+5s^2+6s+K=0$
By forming the Routh array, for the system to be stable:
$\frac{(21-4K)4}{14}>0 \text{ and } K>0$
$\frac{21}{4}>K>0$
(Note: The option contains a typo as $\frac{21}{44}$, but mathematically it corresponds to $\frac{21}{4}$ as derived from the Routh array)