Free Printable Root locus-GATE

1.

Which of the following points is NOT on the root locus of a system with

the open–loop transfer function G(s)H(s)= $\frac{K}{s\left(s+1\right)\left(s+3\right)}$ [GATE 2002]

a)

$S=-j\sqrt[]{3}$

b)

s=-1.5

c)

s=-3

d)

s=- $\infty$

2.

The root locus of the system G(s)H(s)= $\frac{K}{S\left(S+2\right)\left(S+3\right)}$ has the

break-away point located at [GATE 2003]

a)

(-0.5,0)

b)

(-2.5478,0)

c)

(-4,0)

d)

(-0.784,0)

3.

Given G(s)H(s)= $\frac{K}{S\left(S+1\right)\left(S+3\right)}$ the point of intersection of the

asymptotes of the root loci with the real axis is [GATE 2004]

a)

-4

b)

1.33

c)

-1.33

d)

4

4.

A unity feedback system is given as G(s)= $\frac{K\left(1-s\right)}{s\left(s+3\right)}$ Indicate the correct

root locus diagram [GATE 2005]

a)

b)

c)

d)

5.

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

locus of this system is [GATE 2007]

a)

4

b)

5.5

c)

6.5

d)

10

6.

The root locus plot for a system is given below. The open loop transfer function corresponding to this plot is given by [ GATE 2011 ]

a)

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

b)

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

c)

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

d)

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

7.

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 2014]

a)

$\frac{\left(s+1\right)}{\left(s+2\right)\left(s+4\right)\left(s+7\right)}$

b)

$\frac{\left(s+4\right)}{\left(s+1\right)\left(s+2\right)\left(s+7\right)}$

c)

$\frac{\left(s+7\right)}{\left(s+1\right)\left(s+2\right)\left(s+4\right)}$

d)

$\frac{\left(s+1\right)\left(s+2\right)}{\left(s+4\right)\left(s+7\right)}$

8.

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

system's root-locus plot is [GATE 2016]

(a)

9.

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as G(s)= $\frac{K\left(s+2\right)}{s^2+2s+2}$ 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 (a) .

[GATE-2016]

10.

A unity feedback system has an open loop transfer function G(s)= $\frac{K}{s^2}$ Its root locus plot will be [GATE 2002]

a)

b)

c)

d)

11.

Figure shows the root locus plot (location of poles not given) of a third order system whose open loop transfer function is [GATE 2005]

a)

$\frac{K}{s^3}$

b)

$\frac{K}{s^2\left(s+1\right)}$

c)

$\frac{K}{s\left(s^2+1\right)}$

d)

$\frac{K}{s\left(s^2-1\right)}$

12.

A closed-loop system has the characteristic function $\left(s^2-4\right)\left(s+1\right)+K\left(s-1\right)=0$ Its root locus plot against K is [GATE 2006]

a)

b)

c)

d)

13.

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? [GATE 2010]

a)

Its roots are always real

b)

It cannot have a breakaway

point in the range -1 < Re[s] < 0

c)

Two of its roots tend to infinity

along the asymptotes Re[s] = -1

d)

It may have complex roots in the

right half plane

14.

An open loop transfer function G(s) of system is $\frac{K}{s\left(s+1\right)\left(s+2\right)}$ For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,[GATE 2015]

a)

-0.42

b)

-1.58

c)

-0.42 and -1.58

d)

none of the above.

15.

The gain at the breakaway point of the root locus of a unity feedback

system with open loop transfer function G(s)= $\frac{Ks}{\left(s-1\right)\left(s-4\right)}$ is [GATE 2016]

a)

1

b)

2

c)

5

d)

9

16.

The roots locus of a plant is given in the following figure. The rot locus crosses imaginary at ω = 4 2rad / s with gain K= 384. It is observed that the point

s = −1.5 + j 1.5 lies in the root locus. The gain K at s = −1.5 + j1.5 is computed as [GATE 2006]

a)

11.3

b)

21.2

c)

41.25

d)

61.2

17.

Questions Q.2 & Q.3:

A transfer function with unity DC gain has three poles at -1, -2 and -3 and no finite zeros. A plant with this transfer function is connected with this transfer function is connected with a proportional controller of gain K in the forward path, in a unity

feedback configuration.The transfer function is [GATE 2007]

a)

$\frac{S}{\left(S-1\right)\left(S-2\right)\left(S-3\right)}$

b)

$\frac{6}{\left(S+1\right)\left(S+2\right)\left(S+3\right)}$

c)

$\frac{S}{\left(S+1\right)\left(S+2\right)\left(S+3\right)}$

d)

$\frac{6}{\left(S-1\right)\left(S-2\right)\left(S-3\right)}$

18.

If the root locus plot of the closed loop system passes through the points ± j $\sqrt[]{11}$ , the maximum value of K for stability of the unity feedback closed loop system is [GATE 2007]

a)

$\sqrt[]{11}$

b)

6

c)

10

d)

6 $\sqrt[]{11}$

19.

The open loop transfer function of a unity feedback system is G(s)= $\frac{K\left(s+2\right)}{\left(s+1+j1\right)\left(s+1-j1\right)}$ The root locus plot of the system has [GATE 2008]

a)

Two breakaway points located at

s = -0.59 and s = -3.41

b)

One breakaway point located at

s = -0.59

c)

One breakaway point located at

s = -3.41

d)

One breakaway point located at

s = -1.41

20.

Consider the second- order system with the characteristic equation s(s+3)+K(s+5)=0 Based on the properties of the root loci, it can be shown that the complex portion of the root loci of the given system for 0<k<∞ is described by a circle, and the two breakaway points on the real axis are . [GATE 2011]

a)

$-5\pm\frac{\sqrt[]{5}}{2}$

b)

$-5\pm\sqrt[]{5}$

c)

$-5\pm\sqrt[]{10}$

d)

$-5\pm2\sqrt[]{5}$

21.

A loop transfer function is given by: G(s)H(s)= $\frac{K\left(s+2\right)}{s^2\left(s+10\right)}$ The point of intersection of the asymptotes of G(s)H(s)on the real axis in the s-plane is at (a) .[GATE-2014]

22.

The open loop transfer function of a system G(s)= $\frac{s^2+6s+10}{s^2+2s+2}$ The angle

of arrival of its root loci are [GATE 2015]

a)

$\pm\frac{\pi}{4}$

b)

$\pm\frac{\pi}{3}$

c)

$\pm\frac{\pi}{2}$

d)

$\pm\frac{5\pi}{6}$

23.

The open loop transfer function of a unity gain negative feedback control system is given by G(s)= $\frac{s^2+4s+8}{s\left(s+2\right)\left(s+8\right)}$ The angle θ, at which the root locus approaches the zeros of the system satisfies [GATE 2012]

a)

$\pi-\tan^{-1}\left(\frac{1}{4}\right)$

b)

$3\pi-\tan^{-1}\left(\frac{1}{3}\right)$

c)

$\frac{\pi}{2}-\tan^{-1}\left(\frac{1}{4}\right)$

d)

$\frac{\pi}{4}-\tan^{-1}\left(\frac{1}{3}\right)$

Root locus-GATE

Total questions: 23

Worksheet time: 16mins

Similar Resources on Wayground