The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?
An open loop transfer function G(s) of a system is
$G\left(s\right)=\frac{K}{s\left(s+1\right)\left(s+2\right)}$
For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,
The root locus of a unity feedback system is shown in the figure
The closed loop transfer function of the system is
The open loop transfer function $G\left(s\right)$ of a unity feedback control system is given as
$G\left(s\right)=\frac{k\left(s+{\displaystyle \frac{2}{3}}\right)}{{s}^{2}\left(s+2\right)}$
From the root locus, it can be inferred that when k tends to positive infinity,
The characteristic equation of a closed-loop system is s(s+1)(s+3)+k(s+2)=0, k>0. Which of the following statements is true?