Question

The polar diagram of a conditionally stable system for open loop gain $K=1$ is shown in the figure. Theopen loop transfer function of the system is known to be stable. The closed loop system is stable for

• A. $K<5and\frac{1}{2}<K<\frac{1}{8}$
• B. $K<\frac{1}{8}and\frac{1}{2}<K<5$
• C. $K<\frac{1}{8}and5<K$
• D. $K<\frac{1}{8}andK<5$

Answer 1

The correct option is B $K<\frac{1}{8}and\frac{1}{2}<K<5$


System is stable in region $-0.2$ to $-2$ & on the left side of $-8$ as number of encirclement there is zero.

$0.2K<1\Rightarrow K<5$
$2K>1\Leftarrow K>0.5$
$\therefore 0.5<K<5$
$1>8K$
$K<\frac{1}{8}$
(Negative sign only shows that it is on negative axis)