Root Locus Diagram · Control Systems · GATE ECE

Marks 1

Consider the unity-negative-feedback system shown in Figure (i) below, where gain $K \geq 0$. The root locus of this system is shown in Figure (ii) below. For what value(s) of $K$ will the system in Figure (i) have a pole at $-1+j 1$ ?

GATE ECE 2025

The root-locus plot of a closed-loop system with unity negative feedback and transfer function KG(s) in the forward path is shown in the figure. Note that K is varied from 0 to $$\infty$$.

Select the transfer function G(s) that results in the root-locus plot of the closed-loop system as shown in the figure.

GATE ECE 2022

The pole-zero map of a rational function $G(s)$ is shown below. When the closed contour $\Gamma$ is mapped into $G(s)$-plane, then the mapping encircles

GATE ECE 2020

The root locus plot for a system is given below. The open loop transfer function corresponding to this plot is given by

GATE ECE 2011

Which of the following points is NOT on the root locus of a system with the open loop transfer function $$$G\left(s\right)H\left(s\right)=\frac K{s(s+1)(s+3)}$$$

GATE ECE 2002

Given the $$G\left(s\right)H\left(s\right)=\frac K{s\left(s+1\right)\left(s+3\right)}$$, the point of intersection of the asymptotes of the root loci with the real axis is

GATE ECE 2001

The root-locus diagram for a closed loop feedback system is shown in Figure. The system is overdamped.

GATE ECE 2001

If the open loop transfer function is a ratio of a numerator polynomial of degree 'm' and a denominator polynomial of degree 'n', then the integer (n-m) represents the number of

GATE ECE 1994

Marks 2

The characteristic equation of a system is

$$ s^3+3 s^2+(K+2) s+3 K=0 $$

In the root locus plot for the given system, as $K$ varies from 0 to $\infty$, the break-away or break-in point(s) lie within

GATE ECE 2020

A linear time invariant (LTI) system with the transfer function $$$G\left(s\right)=\frac{K\left(s^2+2s+2\right)}{s^2-3s+2}$$$ is connected in unity feedback configuration as shown in the figure.

For the closed loop system shown, the root locus for 0 < K < $$\infty$$ intersects the imaginary axis for K = 1.5. The closed loop system is stable for

GATE ECE 2017 Set 1

The open-loop transfer function of a unity-feedback control system is $$$G\left(s\right)=\frac K{s^2+5s+5}$$$ The value of K at the breakaway point of the feedback control system's root-locus plot is _____________

GATE ECE 2016 Set 1

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as $$G\left(s\right)=\frac{K\left(s+2\right)}{s^2+2s+2}$$ and H(s) = 1 respectively.If the variable parameter K is real positive, then the location of the breakaway point on the root locus diagram of the system is_____________.

GATE ECE 2016 Set 3

For the system shown in the figure, s = –2.75 lies on the root locus if K is_____.

GATE ECE 2015 Set 3

The open-loop transfer function of a plant in a unity feedback configuration is given as $$G\left(s\right)=\frac{K\left(s+4\right)}{\left(s+8\right)\left(s^2-9\right)}$$.The value of the gain K(>0) for which -1 + j2 lies on the root locus is __________________.

GATE ECE 2015 Set 1

The characteristic equation of a unity negative feedback system 1 + KG(s) = 0. The open loop transfer function G(s) has one pole at 0 and two poles at -1. The root locus of the system for varying K is shown in the figure.

The constant damping ratio line, for $$\xi$$ = 0.5 , intersects the root locus at point A. The distance from the origin to point A is given as 0.5. The value of K at point A is ________ .

GATE ECE 2014 Set 4

In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus?

GATE ECE 2014 Set 3

A unity feedback control system has an open-loop transfer function $$$G\left(s\right)=\frac K{s\left(s^2+7s+12\right)}$$$ The gain K for which s = −1 + j1 will lie on the root locus of this system is:

GATE ECE 2007

A unity feedback system is given as,$$$G\left(s\right)=\frac{K\left(1-s\right)}{s\left(s+3\right)}$$$ indicate the correct root locus diagram.

GATE ECE 2005

The root locus of the system $$$G\left(s\right)H\left(s\right)=\frac K{s\left(s+2\right)\left(s+3\right)}$$$ has the break-away point located at

GATE ECE 2003

Consider the points s₁ = −3 + j4 and s₂ = −3 − j2 in the s-plane. Then, for a system with the open loop transfer function $$$G\left(s\right)H\left(s\right)=\frac K{\left(s+1\right)^4}$$$

GATE ECE 1999

Given a unity feedback system with open loop transfer function, $$$G\left(s\right)=\frac K{s\left(s+1\right)\left(s+2\right)}$$$ The root locus plot of the system is of the form.

GATE ECE 1992

The characteristic equation of a feedback control system is given by
s³ +5s² +(K + 6)s + K =0
Where K > 0 is a scalar variable parameter. In the root loci diagram of the system the asymptotes of the root locus for large values of K meet at a point in the s-plane whose coordinates are

GATE ECE 1991

Consider a closed-loop system shown in fig. (a) below. The root locus for it is shown in fig. (b). The closed-loop transfer function for the system is

GATE ECE 1988