Question

A unity feedback system has the open loop transfer function,
$G\left(s\right)=\frac{1}{(s-1)(s+2)(s+3)}$
The Nyquist plot of G(s) encircle the origin.

• A. Never
• B. Once
• C. Twice
• D. Thrice

Answer 1

The correct option is B Once

$G\left(s\right)=\frac{1}{(s-1)(s+2)(s+3)}$

Number of encirclements for (0,0) = no. of open loop poles on right hand plane - no. of open loop zeros on right hand plane

number of open loop poles on right hand plane = 1

number of open loop zeros on right hand plane = 0

$\therefore$ N = 1-0 = 1

$\therefore$ number of encirclements about origin = 1