AMIETE – ET (NEW SCHEME) – Code: AE61
Subject: CONTROL ENGINEERING
Time: 3 Hours
Max. Marks: 100
NOTE: There are 9 Questions in all.
· Question 1 is compulsory and
carries 20 marks. Answer to Q. 1 must be written in the space provided for it
in the answer book supplied and nowhere else.
· Out of the remaining EIGHT
Questions, answer any FIVE Questions. Each question carries 16 marks.
· Any required data not
explicitly given, may be suitably assumed and stated.
Q.1 Choose the correct or the best alternative in the following: (2
10)
a.
A disc
of inertia J initially at rest acted upon by a torque T(t) as shown in Fig.1, is described by
(A) 
(B) 
(C) 
(D) 
b.
The number of feedback loops present
in
the signal flow graph of Fig.2, is
(A) 1 (B) 2
(C) 3 (D) 4
c. For the
pole-zero plot of Fig.3, the
damping ratio 
is given by
(A) 
(B)
(C) 
(D) 
d. If the root-locus of a system
with
is a circle as shown
in
Fig.4,
then
(A) K is negative
(B) number of asymptotes is 0
(C) plot will not cut the imaginary
axis
(D) all of the above.
e. A system whose characteristic equation is 
will be stable by
Routh-Hurwitz criterion, if
(A) K>0 (B) K>2
(C) 
(D) K>3
f. The
undamped natural frequency 
of a system with 
is
(A)
(B) 
(C) 
(D) 
g. The transfer
function G(s) corresponding
to the polar
plot of Fig.5, is of the form
(A) 
(B) 
(C) 
(D) 
h. The instantaneous rms value of
voltage
proportional to the rotor speed 
developed on a
tachometer with sensitivity 
is given by
(A) 
(B)
(C) 
(D) 
i. A linear
system described by the differential equation
,
with 
as the state variables
has the state model
(A)
(B) 
(C) 
(D) 
j. Consider a
nonlinear system described by
,
, with 
and a possible
Liapunov function 
. The system is
(A) unstable (B) having unstable limit cycles
(C) locally stable or
stable-in-the-small (D) asymptotically stable
Answer any FIVE Questions out
of EIGHT Questions.
Each question carries 16
marks.
Q.2 a. For the mechanical system of Fig.6, draw the
free-body diagram and write the differential equation of the system. Draw the
electrical analogue using force-voltage analogy. (8)
b. For the electrical network as shown in Fig.7,
write the
Q.3 a. Using block-diagram reduction technique,
obtain the overall transfer function for the system as shown in Fig.8. (8)
b. Applying Mason’s gain formula obtain the overall transfer
function for the signal-flow graph as shown in Fig.9. (8)
Q.4 a. Consider
the feedback system shown in Fig.10, with time-constant
and 
. (i) Sketch the
closed-loop system response c(t) for an impulse input 
. (ii) Show that the
effect of feedback is to increase the bandwidth. (4+4)
b. Derive the
transfer function 
of the hydraulic
pump-motor system described by Fig.11, where 
are constants,
p=pressure drop across the motor, 
=coefficient of compressibility, 
= angle through which the motor turns, 
=leakage oil flow rate. (8)
Q.5 a. A second-order unity feedback control system
has an open-loop transfer function 
. By what factor
should the amplifier gain A be multiplied so that
(i) The damping ratio is
increased from a value of 0.2 to 0.6?
(ii) The
overshoot of the unit step response is reduced from 80% to 20%? (4+4)
b.
A signal 
actuates a control system described by 
, where K is a constant and 
. Apply Routh-Hurwitz
criterion to the characteristic equation 1+E(s) = 0 and find the value of K to
keep the system stable. Assume zero
initial conditions. (8)
Q.6 a. Consider
the unity feedback control system with
. Sketch the
root-locus on a graph sheet, and determine the damping factor. Find the
corresponding value of K. (8)
b. Consider
the root 
for nominal gain 
for the system
. Compute the root
sensitivity to K, z and p. (8)
Q.7
a. Construct the Nyquist plot and determine the stability of the system
. (10)
b. Define
gain margin and phase margin. From the
Bode plot diagram drawn in Fig.12, determine the gain margin and phase margin.
State whether the system is stable. (6)
Q.8 a. A
unity feedback type-2 system with 
has its closed-loop
poles always lying on the 
-axis on its root-locus.
It is desired to compensate the system to satisfy that settling time 
and damping factor
. Indicate on the
s-plane the locations for the compensator pole and zero and obtain the
open-loop transfer function
. (8)
b. For each
compensator-lead, lag, lag-lead, write (i)
typical electrical network, (ii) s-plane representation and (iii)
transfer function. Explain the need for compensation networks in control
systems. (6+2)
Q.9 a. Determine the state controllability and
observability of the linear system, described by the equation 
where 
(8)
b. The state
equation of a linear time-invariant system is represented by: 
Write the characteristic
equation and obtain the state transition matrix
. (8)