Root Locus Quiz

 $G(s)H(s)=K/(s+1)(s^2+4s+5)$  

Consider the loop transfer function 

 In the root locus diagram the centroid will be located at:

• -2.1
  

• -1.78

• -1.66

• -1.06
  

Which one of the following is not the property of root loci?

• The root locus is symmetrical about imaginary axis

• They start from the open loop poles and terminate at the open loop zeroes

• The breakaway points are determined from dK/ds = 0

• Segments of the real axis are the part of the root locus if and only is the total number of real poles and zeroes to their right is odd.

The characteristic equation of a control system is given as $1+K(s+4)/s(s+7)(s^2+2s+2)=0$ . The real axis intercept for root locus asymptote is:

• -2.25

• -1

• -1.67

• 0

If the gain of the system is reduced to a zero value, the roots of the system in the s-plane,

• Coincide with zero

• Move away from zero

• Move away from poles

• Coincide with the poles

The addition of open loop zero pulls the root loci towards:

• The left and therefore system becomes more stable

• The right and therefore system becomes unstable

• Imaginary axis and therefore system becomes marginally stable

• The left and therefore system becomes unstable

Number of roots of characteristic equation is equal to the number of ______________

• Branches

• Root

• Stem

• Poles

The open loop transfer function of the feedback control system is given by $G(s)=K(s+3)/s(s+4)^2(s+5)(s+6)$  

The number of asymptotes and the centroid of asymptotes of the root loci of closed loop system is

• 4 and (-4,0)

• 3 and (-12,0)

• -4 and (-4,0)

• -3 and (-12,0)

When the number of poles is equal to the number of zeroes, how many branches of root locus tends towards infinity?

• 1

• 2

• 0

• Equal to number of zeroes

If root loci plots of a particular control system do not intersect the imaginary axis at any point, then the gain margin of the system will be:

• 0

• 0.707

• 1

• Infinite

If a feedback control system has its open loop transfer function G(s)H(s) = K/(s-2)(s2+3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will be

• -5

• 10

• 5

• -10