**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)

**Solution :**https://www.youtube.com/watch?v=f_IljSih2eU

**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

**Solution :**https://www.youtube.com/watch?v=1eQ1YNdEF_4

**2005**

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

**Solution :**https://www.youtube.com/watch?v=cCAfe9ydiU8

**2007**

4. A unity feedback control system has an open loop transfer function G(s) = – K

**/**[s(s

^{2}+ 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

**Solution :**https://www.youtube.com/watch?v=ppJqQhOp_xk

**2009**

5. the feedback configuration and the pole-zero locations of G(s) = (s

^{2}– 2s + 2)/(s

^{2}+ 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 0

^{o}

b) ± √2 and 45

^{o}

c) ± √3 and 0

^{o}

d) ± √3 and 45

^{o}

**Solution :**https://www.youtube.com/watch?v=uagcsFAoEB0

**2011**

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

**Solution :**https://www.youtube.com/watch?v=ARZuGJ_JqBo

**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?

**Solution :**https://www.youtube.com/watch?v=3X9gdDGti0Q

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 ____________

**Solution :**https://www.youtube.com/watch?v=hEIZpN9XAPM

**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 __________________

**Solution :**https://www.youtube.com/watch?v=taFVjNfxJ_Q

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 _________.

**Solution :**https://www.youtube.com/watch?v=IhF_FZ9IJvI

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 _____________

**Solution :**https://www.youtube.com/watch?v=LCcmOh0C1rY

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

**Solution :**https://www.youtube.com/watch?v=mhCsqV9Gd2g

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