Break Points

Q. The root locus of the feedback control system having the characteristic equation,
$s^2+6Ks+2s+5=0$

Where K>0, enters into the real axis at

1. $s=-1$
2. $s=-\sqrt{5}$
3. $s=-5$
4. $s=\sqrt{5}$

Q.

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system, are given as $G\left(s\right)=\frac{K(s+2)}{s^2+2s+2}andH\left(s\right)=1$, 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

1. -3.41

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

1. 
2. 
3. 
4. 

Q. Consider the points $s_1=-3+j4$ and $s_2=-3-j2$ in the s-plane. Then, for a system with the open-loop transfer function
$G\left(s\right)H\left(s\right)=\frac{K}{(s+1{)}^4}$

1. $s_1$ is on the root locus, but not $s_2$
2. $s_2$ is on the root locus, but not $s_1$
3. both $s_1$ and $s_2$ are on the root locus
4. neither $s_1$ nor $s_2$ is on the root locus

Q. Consider open loop transfer function of unity negative feedback system as $G\left(s\right)=\frac{K(s^2+16)}{s(s+4)}$breakaway point is /are :

1. -9.65
2. -1.66
3. -166 : -9.65
4. 9.65

Q. The loop transfer function of a feedback control system is given by,
$G\left(s\right)H\left(s\right)=\frac{K(s+6)}{s(s+4)}$
The range of value of K for underdamped system will be

1. $-4<K<1.07$
2. $1.07<K<14.93$
3. $K>14.93$
4. $K<-4$

Q. The open loop transfer fucntion of a unity feedback system is
$G\left(s\right)=\frac{k(s+2)}{(s+1+j1)(s+1-j1)}.$
The root locus plot of the system has

1. two breakaway points located at s = -0.59
2. one breakaway point located at s =-0.59
3. one breakaway point located at s =-3.41
4. one breakaway point located at s =-1.41

Q. 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?

1. Its roots are always real.
2. It cannot have a breakway point in the range -1 <Re[s] < 0.
3. Two of its roots tend to infinity along the asymptotes Re[s] = -1.
4. It may have complex roots in the right half plane.

Q. An open loop transfer funtion G(s) of a system is $G\left(s\right)=\frac{K}{s(s+1)(s+2)}.$ For a unity feedback system, the breakway point of the root loci on the real axis occurs at,

1. -0.42
2. -1.58
3. -0.42 and -1.58
4. None of the above

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

1. $(-0.5,0)$
2. $(-2.548,0)$
3. $(-4,0)$
4. $(-0.784,0)$