### Root Locus Technique - Topic wise GATE Questions on Control Systems (from 1987 onwards)

2003
1. The root locus of the system G(s)H(s) = K / [s(s + 2)(s + 3)] has the break away point located at
a) (-0.5, 0)
b) (-2.548, 0)
c) (-4, 0)
d) (-0.748, 0)

2004
2. Given G(s)H(s) = K /[s(s + 1)(s + 3)], the point of intersection of the asymptotes of the root loci with the real axis is
a) - 4
b) 1.33
c) - 1.33
d) 4

2005
3. A unity feedback system is given as G(s) = k(1 – s) / [s(s + 3)]. Indicate the correct root locus diagram.

2007
4. A unity feedback control system has an open loop transfer function G(s) = – K/[s(s2 + 7s + 12)]. The gain k for which s = –1+j1 will lie on the root locus of this system is
a) 4
b) 5.5
c) 6.5
d) 10

2009
5. the feedback configuration and the pole-zero locations of G(s) = (s2 – 2s + 2)/(s2 + 2s +2), are shown below.
The root locus for negative values of k, i.e. for –∞ < k < 0, has break away/break in points and angle of departure at pole P (w.r.t. the positive real axis) equal to
a) ± √2 and 0o
b) ± √2 and 45o
c) ± √3 and 0o
d) ± √3 and 45o

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

2014
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 tranfer functions has this root locus?

8. The characteristic equation of a unity negative feedback system is 1+KG(s) = 0. The open loop transfer function G(s) has one pole at zero 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 ζ = 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 ____________

2015
9. A unity negative feedback system has the open loop transfer function
the value of the gain K (>0) at which the root locus crosses the imaginary axis is __________________

10. The open loop transfer function of a unity feedback configuration is given as
The value of a gain K( >0 ) for which -1+j2 lies on the root locus is _________.

11. A unity negative feedback system has an open loop transfer function G(s) = K / S(S+10), the gain K for the system to have a damping ratio of 0.25 is _____________

12. For the system shown in figure, s = - 2.75 lies on the root locus if K is ____________