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Code No: 09A50204
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R09
Set No. 2
III B.Tech I Semester Examinations,May/June 2012
CONTROL SYSTEMS
Common to Electronics And Telematics, Electronics And Communication
Engineering, Electrical And Electronics Engineering
Time: 3 hours
Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. State and explain Nyquist stability criterion. Draw the Nyquist plot for the open
1
loop transfer function G (s) = s(1+0.1s)(1+s)
and discuss the stability of the closed
loop system.
[15]
2. (a) For the system shown in Figure 1, determine K1 , K2 , and ‘a’ such that the system will have a steady state gain of 1.0, a damping ratio & δ = 0 .6, ωn = 5.0.
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(b) A unity feedback control system has the forward transfer function, G(s) =
25
. Find the rise time, peak time and the maximum over shoot for unit
s(s+6)
step input.
[8+7]
Figure 1
3. (a) Find the transfer function of the system shown in Figure 2.
(b) Find the transfer function of a AC servo motor.
4. A unity feedback control system has the transfer function G (s) =
[7+8]
K
s(s+a)
(a) Find the value of ‘K’ and ‘a’ to satisfy the frequency domain specifications of
Mr =1.04 and ω r = 11.55 rad/sec.
(b) Evaluate the settling time and bandwidth of the system for the values of K
and a determined in part (a).
[8+7]
1

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R09
Code No: 09A50204
Set No. 2
Figure 2
5. A unity feedback system has an open loop transfer function G(s) =
Design a Lead-Lag compensator to meet the following specifications:
K
.
s(s+2)(s+60)
(a) Phase margin is at least 400
(b) Steady state error for ramp input is 0.04 rad.
[15]
6. Sketch the root-locus diagram of a control system whose loop transfer function is
K
. Using the diagram or otherwise find the values of gain at
G(s)H(s) = s(s+4)(s+10)
breakaway points and at point of intersection of the loci with the imaginary axis.
[15]
7. Explain the properties of state transition matrix. A linear time invariant system is
described by the state equation:
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X˙ =
0 6
−1 5
X+
0
1
[u] and y =
1 0
X,
X(0) =
0
0
Obtain the state transition matrix. Hence obtain the output response y(t) , t ≥ 0
for a unit step input.
[15]
8. For the geared system shown below in Figure 3, find the transfer function relating
the angular displacement θL to the input torque T1 , where J1 , J2 , J3 refer to
the inertia of the gears and corresponding shafts. N1 , N2 , N3 , and N4 refer to the
number of teeth on each gear wheel.
[15]
2

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R09
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Code No: 09A50204
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Figure 3
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3
Set No. 2

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R09
Set No. 4
Figure 3:
III B.Tech I Semester Examinations,May/June 2012
CONTROL SYSTEMS
Common to Electronics And Telematics, Electronics And Communication
Engineering, Electrical And Electronics Engineering
Time: 3 hours
Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) Explain the Armature voltage controlled DC servomotor and obtain its transfer function.
(b) Obtain the overall transfer function for the block diagram in Figure 4.
[8+7]
2. The characteristic equation of a feedback control system is s3 +4Ks2 +(K+3)s+10=0.
Apply the Nyquist criterion to determine the values of K for a stable closed loop
system. Check the answer by means of the Routh Hurwitz criterion.
[15]
3. Sketch the Bode plot for the following transfer function and determine the system
gain K for the gain cross over frequency ω c to be 5 rad/sec.
Ks2
.
[15]
G(s) = (1+0.2s)(1+0.02s)
4. A unity feedback control system has an open loop transfer function
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G(s) =
K(1+0.2s)(1+0.025s)
s3(1+0.001s)(1+0.004s)
Sketch the complete root locus for −∞ < K < ∞. Indicate the crossing points of
the loci on the jω axis and the corresponding values of K at these points. Also
indicate the range of K for which system closed loop system is stable.
[15]
4

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