Code: D-15 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 best alternative in the following: (2x10)
a. For type one system, the steady-state error due to step input is equal to
(A) zero. (B) finite constant.
(C) infinite. (D) indeterminate.
b. Consider the equation 
. This equation has_________ in the
right half of s-plane.
(A) One root (B) two roots
(C) three roots (D) four roots
c. The transfer function of a phase-lag controller is given by
(A)
. (B)
.
(C) 
. (D)
.
d. The Nyquist plot
of 
of a
system passes through the 
point in the plane, the gain margin of
the system is
(A) greater than zero. (B) zero.
(C) less than zero. (D) infinite.
e. Consider the
function 
where
F(s) is the Laplace transform of f(t). 
is equal to
(A)
zero (B)
(C) 5 (D) infinity
f. For a tachometer
if 
is
the rotor displacement, e (t) is the output voltage and 
is the tachometer
constant, then the transfer function is defined as
(A)
(B)
(C) 
(D)
g. The system matrix
of a continuous time system is given by 
, the characteristic equation is
given by
(A)
. (B)
(C) 
. (D)
h. The root-locus plot is constructed using
(A) the magnitude condition only.
(B) the magnitude and phase angle conditions.
(C) the phase angle condition alone.
(D) The asymptotes.
i. The unit step response of a second order underdamped system exhibits the peak overshoot of 15%. If the magnitude of the input is doubled, the peak overshoot will be
(A) 30% (B) 15%
(C) 7.5% (D) none of these.
j. In a second order system, the damping ratio of unity corresponds to the following condition:
(A) critically damped (B) over damped
(C) under damped (D) undamped
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 Consider
the system shown in Fig.2 below. For 
and 
Obtain (i) rise time 
(ii) peak time 
(iii) maximum
over shoot 
and
settling time ts (for the 2% criterion) when the system is subjected to a unit
step input. (16)
|
Q.3 Consider
that a third-order control system has the characteristic equation 
. Find the
condition on ’K’ for the system to be stable. (16)
Q.4 The
loop transfer function of a unity feedback control system is given by 
. Sketch the
Nyquist plot and using it find out if the closed-loop system is stable. (16)
Q.5 The
characteristic equation of a feedback control system is given by 
. Where K is a
variable parameter. Sketch the root locus diagram of the system when ‘K’ takes
all positive values from zero to infinity. Mark all salient points in the
diagram. (16)
Q.6 a. Derive the Nyquist criterion of stability of a feedback control system whose open-loop transfer function is stable. (8)
b. What is meant by the terms “gain margin” and “phase-margin” of a control system? (8)
Q.7 A
unity-feedback control system has an open-loop transfer function given by 
. Determine the
unit-step and unit-impulse responses for zero initial conditions. (16)
Q.8 Write short notes on any TWO of the following:-
(i) Constant M and N circles.
(ii) Phase-lead compensation.
(iii) Insensitivity and Robustness. (16)
Q.9 A
feedback control system incorporating a dead-time element has the open-loop
transfer function given by 
. Determine the gain and
phase-margins of the system. (16)