Code: A-11 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) infinite. (B) zero.
(C) Finite constant. (D) indeterminate.
b. Consider the equation 
. This equation has___
roots in the right half of s-plane.
(A) one (B) two
(C) three (D) four
c. The transfer
function of a phase-lead compensator is given as 
. The maximum phase-shift provided
by this compensator is
(A)
. (B)
.
(C) 
. (D)
.
d. The transfer function of a P-D controller is
(A)
. (B)
.
(C) 
. (D)
.
e. The Nyquist plot
of 
of a
system encloses the 
point in the GH-plane, the gain
margin of the system in dB is
(A) greater than zero (B) zero
(C) less than zero (D) infinite
f. Consider the
function 
where
F (s) is the Laplace transform of f (t). 
is equal to
(A) 5 (B) 2.5
(C) zero (D) infinity
g. For a type-2 system, the steady-state error due to ramp input is equal to
(A) zero. (B) finite constant.
(C) infinite. (D) indeterminate.
h. 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)
.
i. The system
matrix of a l.t.i (linear time-invariant) continuous time system is given by 
, the
characteristic equation of the system is given by
(A)
. (B)
.
(C) 
. (D) 
.
j. Given a unity
feedback control system with 
the value of K for a damping ratio
of 0.5 is
(A) 1. (B) 16.
(C) 4. (D) 8.
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 a. Explain
(i) The steady-state error.
(ii) The type of a control system. (4)
b. Determine
the steady-state error for a unit-step, unit ramp and parabolic input 
for the
unity-feedback control system whose open-loop transfer function is given as 
. (12)
Q.3 Obtain the unit-impulse and the unit-step responses of a unity feedback control system whose open-loop transfer function is
. What are the steady-state values
of the outputs? (16)
Q.4 a. Define the terms
(i) gain margin (ii) phase margin. (4)
b. Consider the
unity-feedback control system whose open-loop transfer function is 
. Determine the
value of ‘a’ so that the phase margin is . (12)
Q.5 a. Explain in brief
the effect of adding a pole or a zero in the left half of s-plane in the
open-loop transfer function 
of a control system on the
root-locus diagram. (4)
b. Determine
the range of ‘K’ for the stability of a unity-feedback control system whose
open-loop transfer function is 
. (12)
Q.6 a. Discuss the effects of P, I and P+I controllers on a second order system. (4)
b. Consider the
closed-loop control system whose open-loop transfer function is 
. Find the
maximum value of ‘K’ for which the system is stable. (12)
Q.7 A
unity feedback system has an open-loop transfer function of 
.
(i)
Determine
the magnitude of 
in dB at an angular frequency of 
rad/sec.
(ii) Determine the phase-margin in degrees.
(iii) Determine the gain margin in dB. Is the system stable? (5+5+6)
Q.8 A
unity-feedback system has the plant transfer function 
.
(i)
Determine
the frequency at which the plant has a phase-lag of .
(ii)
An
integral controller with transfer function 
is placed in the feed forward path
of this system. Find the value of K such that the compensated system has an
open-loop gain margin of 2.5. (8
+ 8)
Q.9 a. Using block diagram reduction rules, convert the block diagram of Fig.1 to a single loop. (12)
|
b. Determine
for the
system in Fig.1. (4)