Embed Size (px)
Citation preview
8/20/2019 cs_am05
http://slidepdf.com/reader/full/csam05 1/4
s 391
B.E./B.Tech.
EGREE
EXAMINATION,
APRIIIMAY 2005.
Fifth
Semester
Electronics
and Communication
Engineering
EC 334
-
CONTROL
SYSTEMS
Time
: Three
hours
Maximum:
100 marks
Ordinary
graph
sheet,
semilog
sheet,
polar
graph
sheet will be
provided.
Answer ALL
questions.
PARTA- (10
x2=20 marks )
1. What
is the
mathematical
model of a
system?
2. What
is electrical
analogous
of a
gear?
3.
Write
the transfer
function of the
PID controller.
4.
What are
the standard
test signals
employed
or time domain studies?
5. State the rule for finding out the root loci on the real axis.
6. What
is the
condition
for the system
G(s)
=
* t *:,)
to has a circie
in its root
s(s+ b)
locus?
7.
List
any two
advantagesof
frequency
responseanalysis.
8.
Define
gain
margin of a closed
oop system.
w w w . M a a
n a v a N .
c o m
8/20/2019 cs_am05
http://slidepdf.com/reader/full/csam05 2/4
9.
Draw
the
bode
piot
of a
typical
lead compensator.
10.
write
the transfer
function
of
a typical
iag-lead
compensator.
PARTB- (5x16=80marks )
11.
The
loop transfer
function
of a
feedback
control
system
is
given
by
K(s
+ 6)
G(s),F/(s)
s (s+4 )
(i)
Sketch
the
root
locus
plot
with
K
as
a
variable
parameter and show
that
loci
of
complex
oots
are
part
of
a
circle'
(ii)
Determine
the break-
awayhreak
in
points' if any'
(iii)
Determine
the
range
of K
for which
the system
s under
damped.
(iv)
Determine
the
value
of K
for critical
damping.
(v)
Determine
the
minimum
value
of
damping
ratio'
lZ.
(a) (i)
Derive
the
mathematical
model
of
an armature
controlled
DC
motor.
(ii)
For the
spring,
damper
and
mass
system
shown
in Fig.
12
(a) (ii),
Obtain
the
differential
equations
governing the system
f
is
the
force
applied.
Fig.
12
(a)
(ii)
Or
2
\rr
v
s 391
w w w . M a a
n a v a N .
c o m
8/20/2019 cs_am05
http://slidepdf.com/reader/full/csam05 3/4
(b) (i)
Using block
diagram
from each input to
Fis.
12
(b) (i).
reduction technique
find
the transfer
function
the output
C
for the system
shown
in
Fis. L2 b) i)
(ii)
Draw an equivalent signal
flow
graph
for the system
shown
in
Fig.
12
b) ii).
Fig. 12
(b) (ii)
13.
(a)
(i)
Derive the expression
or
unit impulse
response
of a second
order
under
damped system
G(s)
=
W:
s2+ 2zW,rs
W,?
(ii)
Find
the unit
impulse response
of the second
order
system
rvhose
transfer
function
G(S)
=
-
'
s "
+4s+9
Or
3
s 391
w w w . M a a
n a v a N .
c o m
8/20/2019 cs_am05
http://slidepdf.com/reader/full/csam05 4/4
(b)
(i)
Derive the expression
for steady
state error
of the closed loop
system
n terms of
generalizederror coefficients.
1
(ii)
For a closedoop
system with
G(s)
=;*
and .FI(s) 5,
calculate
generalized rrorcoefficientsnd ind the error series.
14.
(a)
Draw the bode
plot
of the system
G(s)
=
*t#Gtu.
Hence
obtain
the exact
plot
by
doingnecessary
orrections t corner
requencies.
(i)
Find the
gain
margin and,
phase margin
(ii)
The value of
K for
phase
margin
=
20".
Or
(b)
Test the stability
of the unity
feedbacksystem
G(s)
=
--.+
when
(s -1 ) ' ( s+5 )
K
=
10 using Nyquist criterion
and
then find the range of K for stability.
15.
(a)
The open
loop transfer
function of a uncompensated system
is
G(s)
=
.j -
. Design a suitable
lay compensator or the system so that
s(s
+ 2)
the static
velocity error constant
K, is
20
sec-l, the
phase
margin is
atieast 55oand the
gain
margin
is atieast 12 dB.
Or
(b)
Considera
type 1 unit f'eedback ystem
with an OLTF GsG)
=
--K-.11
'
s (s+1 )
is specified hat K,
=
12 sec-1 and.
Qry
=
40" Design
lead
compensator
v
to meet
the specifications.
e--
(
/_ , .__
//
,,
\-
,/-,
J \
) l
r/
/
, / - t
:
s 391
w w w . M a a
n a v a N .
c o m
