1100ECT307122103
D
Reg No.:
Pages:4
Name:
APJ ABDUT KALAM TECHNOLOGICAL UNIVERSITY
Fifth Semester B.Tech Degree pxamination December 2021 (201
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Course Code: ECT 307
Course Name: CONTROL SYSTEMS
Max. Marks: 100
PART A
(Answer all questionsl each question carrtes 3
I
z.(
,i
marks)
Marks
both.
What is the criterion on the roots of the characteristic equation for the stability? How
Compare open loop and closed loop control systems. Give one example to
3
3
is it connected to the BIBO stability?
a
J
Draw the signal flow graph for the following set of algebraic equations:
x1:oxs*bxt*cx2
X2
4
= d.X1* ex3
State the angle and magnitude criteria that roots of the characteristic equation
must
3
be satisfied.
5
In a system
represented
by the state vector differential equation, let A is the
coefficient matrix of the state variable vector. Then,
if
A
= [i.
-1r],
nna ,n"
characteristic roots of the system.
Draw the response of an underdamped second order system with complex poles on
the left half of s-plane showing the rise time, peak overshoot, and settling time.
-8
Distinguish between Order of a system and Type of a system.
J
Draw the s-plane contour used for mapping, for stability analysis, to the plane of
J
n
open-loop transfer function.
G(s)H(s):
t 1 ..
' s(s*1)
Explain the choice of the contour
9
Write and explain the transfer function for a first order phase lag compensator.
State
3
the function of a phase lag compensator in a control system.
10
Give nvb advantages for using state variable representation of
Page 1 of 4
systems.
3
1100ECT307122103
PART B
(Answer onefull questiontrom each module, each question canies 14 marks)
11 a)
Find the transfer function of the system shown by the block diagram using direct
block diagram reduction rules.
b) Draw the signal flow graph for the system in question
1l (a) and obtain
the gain
using the Mason's Formula.
'!f
12 a)
Draw the schematic of a second order spring-mass-damper (SMD) system and obtain
its transfer function. Draw the Force current and force voltage analogy circuits of the
SMD system.
b)
Find the differential equation governing the mechanical system shown in fig.
Draw the_ corresponding Force-Voltage analogous circuit
.
13
a)
lvrooure
Module -2
-z
Define position, velocity and acceleration error constants for a unity feedback control
system.
b)
For the second order system with complex poles on the left half of s-plane, derive
the expression for rise time, settling time, and stea{y state error parameters.
L4 a)
Find the response of a system with transfer function
T(s)
b)
:
1
ffi
when subjected to unit step input.
For the system in the block diagram,
G(s)
:
10
s2+14s+50
Page2 of 4
1I00ECT307122103
Find the steady state error
varues for unit step and
unit ramp inputs.
Module -3
. 15a)
A system has characteristic equation,
.K
b)
s3
for the stable system.
* 3s2 + (r + 1)s + 4 = 0. Find the range
of
For a system having open
loop transfer function.
(.
6(s)t1(s) =
(s+
Plot the root locus stating
the steps.
16 a)
1)(s+sxs+6)
Explain the effect of adding
a pole to a second order
system.
b) write the general transfer
functions of P, PI and pID
controllers. Explain their role
in a control system design.
Module _4
using the Nyquist contour,
analyse the following system
to obtain the rimit
the
t7
stab'ity' The system
has the open-loop transfer
function
G(s)Il(s) =
s(r1s *
gain margin of the system.
ofKfor
lxr;;Tt
lt:,"j^::::ta:
18
1.
system from the graph plotted.
I
Determine phase margin
or the
a)
state cauchy's argument
principle with the conditions
to be applied on the contour
ofmapping' State'the Nyquist
criterion of stability on the
open loop transfer function
of a control systern.
b)
Draw the bode prots of
the system with operrroop
transfer function.
G(s)H(s) =
19 a)
s(s + 1)(s +.2)
Explain how the prot can
be used for anarysing the
stability of the system.
Module -5
t€r
1"(s)
- sz + 20s +100is the transfer function
of a system. Draw its signal
flow graph in phase variable
form' Arso represent the
system in the state variable
form.
Page 3
of4
7
7
t4
1l,S€T3gn?'ng3
b)
Find the state trggsition matrix of a systern represented by tr*ro statc
Es
":.
20 a)
iA
having stak coefuient matrix, a
I
jtl
t1
= Lor
A single-inprt single-cnrpW systern has the matix
*= [j,
rarbles.and
'fv
equatiorr 'l
-tul'* [!l"
y=[10
I
0]x
flourm*I.
signd
&te.r-mineth€tresferfirnctiorusingthe
_,
:.,,
b) {.qyst€rh,cbaracterised
by t}€ transfer function
Y(s)
tGt:m
t
2
Find the state and ouput equation in fiiafiix forrr and also test ee
observability of the sYstem
t
'.,=i
Page4of 4
comt*ability and
7