Code: D-15 Subject: CONTROL ENGINEERING
Time: 3 Hours Max. Marks: 100
NOTE: There are 11 Questions in all.
· Question 1 is compulsory and carries 16 marks. Answer to Q. 1. must be written in the space provided for it in the answer book supplied and nowhere else.
· Answer any THREE Questions each from Part I and Part II. Each of these questions carries 14 marks.
· Any required data not explicitly given, may be suitably assumed and stated.
Q.1 Choose the correct or best alternative in the following: (2x8)
a. The D.C. gain of a system represented by the transfer function
is
(A) 6 (B) 8
(C) 3 (D) 5
b. The 5% settling time of a second order system with a damping ratio of 0.4 and a natural frequency of 5 rad/sec is _______
(A) 2.5 (B) 1.5
(C) 3.0 (D) 4.2
c. If the Laplace transform of f(t) is F(s), then
the Laplace transform of 
will be
(A) 
(B)
(C)
(D)
d. The main assumption that is made in a two-phase a.c. servomotor is that___
(A)
the torque varies linearly w.r.t. the control voltage 
.
(B)
the speed varies inversely w.r.t. the control voltage .
(C) the torque varies linearly w.r.t. the speed.
(D) The torque varies inversely w.r.t. the speed.
e. A high value of bandwidth for the standard second order system is an indication that ______.
(A) the time to reach the first peak is small.
(B) the system is highly damped.
(C) the time to reach the first peak is very large.
(D) the time to reach the first peak is exact equal to zero.
f. The
steady state error with a step input for a unit feedback system with 
will be _______.
(A) 0 (B) 2
(C) 4 (D) 2.5
g. The
asymptotic Bode plot of a system with 
shows that the gain margin for the
system will be______.
(A) 0 (B)
(C) 10 (D) 5
h. The polar plot of
will be of the form _______.
(A) (B)
(C) (D)
PART I
Answer any THREE Questions. Each question carries 14 marks.
Q.2 a. Distinguish between the following pairs:
(i) Static and dynamic systems.
(ii) Closed loop and open loop systems.
(iii) Linear and non-linear system. (6)
b. Draw the schematic-cum-circuit diagram of a field controlled DC servomotor and derive its transfer function. (8)
Q.3 a. Define: state, state trajectory, state space and state transition matrix. (4)
b. Given a transfer function of the form:
Show how it can be converted into a
state variable form. Also comment whether this representation is unique. (10)
Q.4 a. The characteristic equation of a certain system is given as
If the permissible range of K is 
, examine by the
Routh-Hurwitz criterion whether or not the system will have the K in the above
range. (8)
b. Give the schematic of a gyroscope and explain its operation. (6)
Q.5 a. Using force-voltage analogy give the quivalent mechanical network for the electrical network given in Fig.1 (10)
|
b. Explain how root/roots to the left of an axis parallel to the imaginary axis, can be determined as shown in Fig.2, using the Routh-Hurwitz criterion. (4)
|
Q.6 Obtain the transfer function for a system, whose signal flow diagram is shown in Fig 3, using Mason’s Gain formula. (14) (14)
|
PART II
Answer any THREE Questions. Each question carries 14 marks.
Q.7 Sketch the root loci for the system given by 
and determine: (i)
Intersection of the root loci with the imaginary axis. (ii) The range of
values of K for the closed loop system to be stable. (14)
Q.8 Construct the Bode
plots for the open loop frequency response function 
and determine the
phase margin and the phase crossover frequency. (14)
Q.9 For the system shown in Fig 4 find the rise time and maximum overshoot, if the system responds to a unit step input with (i) 2% settling time as 1.4 sec and (ii) time to reach the first peak as 0.58 sec. (14)
|
Q.10 Explain the
Nyquist criterion of stability. Using the Nyquist criterion determine the
stability of the system given by 
(14)
Q.11 Write short notes on any TWO of the following:
(i) Constant N-circles.
(ii) P+I+D Control.
(iii) Synchros. (7+7)