# GATE Questions & Answers of Root Loci

## What is the Weightage of Root Loci in GATE Exam?

Total 6 Questions have been asked from Root Loci topic of Control Systems subject in previous GATE papers. Average marks 1.83.

The gain at the breakaway point of the root locus of a unity feedback system with open loop transfer function $G\left(s\right)=\frac{Ks}{\left(s-1\right)\left(s-4\right)}$ is

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

$G\left(s\right)=\frac{k\left(s+\frac{2}{3}\right)}{{s}^{2}\left(s+2\right)}$

From the root locus, it can be inferred that when k tends to positive infinity,