Anna University Coimbatore 2009 B.E Electrical and Electronics Engineering Control system - Question Paper

Asymptotes are straight lines which are parallel to root locus going to infinity an meet the root locus at infinity. Angle--+or - 180(2q+1)/n-m, q------0,1,2,----(n-m)
23.) What is centroid ,How it is calculated?
The meeting point of asymptotes with real axis is called centroid.CENTROID=sum of poles-sum of zeros /n-m
24.) What is breakaway point and breakin point?
At breakaway point the root locus breaks from the real axis to enter into the complex plane.At breakin point the root locus enters the real axis from complex plane
25.) What is dominant pole?
The dominant point is a pair of complex conjugate pole which decides transient response of the system.In higher order systems the
dominant poles are very close to origin and all other poles of the system are widely separated and so they have less effect on
transient response of the system.
26.) How do you obtain the crossing point of root locus in imaginary axis?
By Routh Hurwitz method.

16 Marks
1. Using routh criterion determine the location of the roots of the subsequent characteristic formula and comment on the stability of the system.
a) 2s5+2s4+5s3+5s2+3s+5=0
b) 2s6+4s5+s4-32s3+51s2+3s+15=0

2. The characteristic equations for certain feedback control system are provided
below. In every case, determine the range of values of K for which the system
is stable.
a)s4+3s3+3s2+s+K=0
b)s4+s3+3Ks2+(K+2)s+4=0

3. The open loop transfer function certain unity feed back systems is provided by
G(s) = K(s+13)/s(s-2)(s2+5s+16). Determine the value of K which will reason
sustained oscillations in the closed loop system what is the corresponding
oscillation frequencies?

4. A unity feedback system has an open-loop transfer function, G(s)=K/s(s2+8s+32). Sketch the root locus and determine the dominant closed loop poles with ? = 0.5. Determine the value of K at this point.

5. The open loop transfer function of an unity feedback control system is provided beneath. In every case, sketch the Nyquist plot and determine the stability of the system.
a) G(s) = K(s+3)/s(s-1)
b) G(s) = K / (s+1) (s+1.5)(s+2)
6..Given the open loop transfer function a system with unity feed
back,G(s)H(s)=K/s(s+2)(s+10).Determine the range of K for which closed
loop system is stable.
7..Write the rules for constructing the root locus.
. Locate poles & Zeros
. obtain centroid & asymptotes
. obtain Break away or Break in points
. obtain crossing point in imaginary axis

Earning:   Approval pending.