Download VTU BE 2020 Jan ECE Question Paper 17 Scheme 4th Sem 17EC43 Control Systems

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17EC43
?110
Fourth Semester B.E. Degree Examination, Dec.2019/Jan.2020
Control Systems
Time: 3 hrs. Max. Marks: 100

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Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module-1
1 a. Define closed loop control systems and list its advantages and disadvantages with examples.
(04 Marks)
b. For the mechanical system shown in Fig.Q.1(b), write i) The mechanical network ii) the

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equations of motion and iii) the force-current analogous electrical network. (08 Marks)
:-osENt-4-tit)
Fig.Q.1(b)
c. For the system represented by the following equations, find the transfer function X(S)/U(S)
by signal flow graph technique.

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x(t) = x
l
(t) + 0
3
u(t)

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x:(t)=?a
l
x, + x, + f3,u(t)
x'
2

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(t)=?a
2
x, +13,u(t) (08 Marks)
OR
2 a. Define analogous systems. Show that two systems shown in Fig.Q.2(a) are analogous

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systems, by comparing their transfer functions. (08 Marks)

t
C
I

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I 1
I
Va

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b.
Fig.Q.2(a)
For the block diagram shown in Fig.Q.2(b), determine the transfer function C(S)/R(S) using
block diagram reduction technique. (08 Marks)
Fig.Q?2(b)

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1 of 4
C(s)
s)
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C.- ?

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( *
ii
1
? ? '
17EC43

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?110
Fourth Semester B.E. Degree Examination, Dec.2019/Jan.2020
Control Systems
Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.

--- Content provided by⁠ FirstRanker.com ---

Module-1
1 a. Define closed loop control systems and list its advantages and disadvantages with examples.
(04 Marks)
b. For the mechanical system shown in Fig.Q.1(b), write i) The mechanical network ii) the
equations of motion and iii) the force-current analogous electrical network. (08 Marks)

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:-osENt-4-tit)
Fig.Q.1(b)
c. For the system represented by the following equations, find the transfer function X(S)/U(S)
by signal flow graph technique.
x(t) = x

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l
(t) + 0
3
u(t)
x:(t)=?a

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l
x, + x, + f3,u(t)
x'
2
(t)=?a

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2
x, +13,u(t) (08 Marks)
OR
2 a. Define analogous systems. Show that two systems shown in Fig.Q.2(a) are analogous
systems, by comparing their transfer functions. (08 Marks)

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t
C
I
I 1

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I
Va


b.

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Fig.Q.2(a)
For the block diagram shown in Fig.Q.2(b), determine the transfer function C(S)/R(S) using
block diagram reduction technique. (08 Marks)
Fig.Q?2(b)
1 of 4

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C(s)
s)
(04 Marks)
c.
Define the following terms in connection with signal flow graph:

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i) Node
ii) Forward path gain
iii) Feedback loop
iv) Non-touching loops.
Module-2

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3 a. Define the following time response specifications for an underdamped second order system:
i) Rise time, t
r

ii) Peak time, t

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p

iii) Peak-overshoot, M
p

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iv) Settling time, i
s
(04 Marks)
b. A system is given by the differential equation y"(t)+ y
1

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(t) + y(t) = x(t), where y(t) in the
output. Determine all time domain specifications for unit step input. (08 Marks)
c. The open loop transfer function of a unity feedback system is given by G(s) =
OR
4 a. Derive the expressions for i) Rise time, t

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r
and ii) Peak overshoot, M
p
for the
underdamped response of a second order system for a unit step input. (06 Marks)

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b.
For the system shown in Fig.Q.4(b), compute the values of K and T to give an overshoot of
20% and peak time of 2 sec for an unit step excitation. (08 Marks)
c.
Fig.Q.4(b)

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Find the position, velocity and acceleration error constant for a control system having open
loop transfer function G(S)H(S)=
10
. Also find the steady state error for the inpt
S(S +1)

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r(t) = 1 + t. (06 Marks)
Module-3
5 a. State and explain Routh's stability criterion for determining the stability of the system and
mention its limitations. (06 Marks)
b. Determine the number of roots that are

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i) in the right half of s-plane
ii) on the imaginary axis and
iii) in the left half of s-plane
for the system with the characteristic equation s
6

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+ s
5
? 2s
4
? 3s

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3
? 7s
2
? 4s ? 4 = 0.
(06 Marks)

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c.
Sketch the root locus plot of a certain control system, whose characteristic equation is given
by s
3
+ 10s

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2
+ ks + k = 0, comment on the stability. (08 Marks)
2 of 4
le .?
.`"?!

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S(ST +1)
i) By what factor should the amplifier gain K be multiplied in order that the dampine
ratio is increased from 0.2 to 0.8?
ii) By what factor should K be multiplied so that the system overshoot for unit step
excitation is reduced from 60% to 20%? (08 Marks)

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C.- ?
( *
ii
1

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? ? '
17EC43
?110
Fourth Semester B.E. Degree Examination, Dec.2019/Jan.2020
Control Systems

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Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module-1
1 a. Define closed loop control systems and list its advantages and disadvantages with examples.
(04 Marks)

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b. For the mechanical system shown in Fig.Q.1(b), write i) The mechanical network ii) the
equations of motion and iii) the force-current analogous electrical network. (08 Marks)
:-osENt-4-tit)
Fig.Q.1(b)
c. For the system represented by the following equations, find the transfer function X(S)/U(S)

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by signal flow graph technique.
x(t) = x
l
(t) + 0
3

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u(t)
x:(t)=?a
l
x, + x, + f3,u(t)
x'

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2
(t)=?a
2
x, +13,u(t) (08 Marks)
OR

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2 a. Define analogous systems. Show that two systems shown in Fig.Q.2(a) are analogous
systems, by comparing their transfer functions. (08 Marks)

t
C

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I
I 1
I
Va

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b.
Fig.Q.2(a)
For the block diagram shown in Fig.Q.2(b), determine the transfer function C(S)/R(S) using
block diagram reduction technique. (08 Marks)

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Fig.Q?2(b)
1 of 4
C(s)
s)
(04 Marks)

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c.
Define the following terms in connection with signal flow graph:
i) Node
ii) Forward path gain
iii) Feedback loop

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iv) Non-touching loops.
Module-2
3 a. Define the following time response specifications for an underdamped second order system:
i) Rise time, t
r

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ii) Peak time, t
p

iii) Peak-overshoot, M

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p

iv) Settling time, i
s
(04 Marks)

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b. A system is given by the differential equation y"(t)+ y
1
(t) + y(t) = x(t), where y(t) in the
output. Determine all time domain specifications for unit step input. (08 Marks)
c. The open loop transfer function of a unity feedback system is given by G(s) =

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OR
4 a. Derive the expressions for i) Rise time, t
r
and ii) Peak overshoot, M
p

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for the
underdamped response of a second order system for a unit step input. (06 Marks)
b.
For the system shown in Fig.Q.4(b), compute the values of K and T to give an overshoot of
20% and peak time of 2 sec for an unit step excitation. (08 Marks)

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c.
Fig.Q.4(b)
Find the position, velocity and acceleration error constant for a control system having open
loop transfer function G(S)H(S)=
10

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. Also find the steady state error for the inpt
S(S +1)
r(t) = 1 + t. (06 Marks)
Module-3
5 a. State and explain Routh's stability criterion for determining the stability of the system and

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mention its limitations. (06 Marks)
b. Determine the number of roots that are
i) in the right half of s-plane
ii) on the imaginary axis and
iii) in the left half of s-plane

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for the system with the characteristic equation s
6
+ s
5
? 2s

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4
? 3s
3
? 7s
2

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? 4s ? 4 = 0.
(06 Marks)
c.
Sketch the root locus plot of a certain control system, whose characteristic equation is given
by s

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3
+ 10s
2
+ ks + k = 0, comment on the stability. (08 Marks)
2 of 4

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le .?
.`"?!
S(ST +1)
i) By what factor should the amplifier gain K be multiplied in order that the dampine
ratio is increased from 0.2 to 0.8?

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ii) By what factor should K be multiplied so that the system overshoot for unit step
excitation is reduced from 60% to 20%? (08 Marks)
Module-4
7 a. Define the following terms in connection with bode plots:
i) Gain cross over frequency

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ii) Phase crossover frequency
iii) Gain margin
iv) Phase margin.
b. A negative feedback control system is characterized by an open loop
G(S)H(S) =

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20
Sketch the polar plot and hence determine w
g
,
S(S +1)(S+ 2)

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Comment on the stability.
(04 Marks)
transfer function
, wpc, G M
and PM.

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(06Marks)
17EC43
6
OR
a. For a system with characteristic equation s

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4
+ ks
3
+ s
2

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+ s + 1 = 0, determine the range of K
for stability. (04 Marks)
b. Determine the values of 'V and 'a' for the open loop transfer function of a unity feedback
K(s +1)
system is given by G(s) =

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3
, so that the system oscillates at a frequency of
s +as
-
+3s+1

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2rad/sec. (06 Marks)
c. Draw the root locus diagram for the system shown in Fig.Q.6(c), show all the steps involved
in drawing the root locus. Determine:
i) The least damped complex conjugate closed loop poles and the value of `le
corresponding to these roots

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ii) Minimum damping ratio. (10 Marks)
Fig.Q.6(c)
c. A unity feedback control system has G(s) =
100(1+0.1s)
s(s + (o.o is +

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. Draw the Bode plots and
hence determine W
ee
., W
c

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, GM and PM. Comment on the stability. (10 Marks)
OR
8
a.
A unity feedback control system has G(s)?

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200(s + 2)
, . Draw the bode plots and
s(s
-
+ lOs + 100)

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hence determine stability of the system. (10 Marks)
b. Using Nyquist stability criterion, find the range of K for closed loop stability for the
negative feedback control system having the open loop transfer function
G(S)H(S) =
K

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(lo Marks)
S(S
-
+ 2S +2)
3 of 4

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C.- ?
( *
ii
1

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? ? '
17EC43
?110
Fourth Semester B.E. Degree Examination, Dec.2019/Jan.2020
Control Systems

--- Content provided by‌ FirstRanker.com ---

Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module-1
1 a. Define closed loop control systems and list its advantages and disadvantages with examples.
(04 Marks)

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b. For the mechanical system shown in Fig.Q.1(b), write i) The mechanical network ii) the
equations of motion and iii) the force-current analogous electrical network. (08 Marks)
:-osENt-4-tit)
Fig.Q.1(b)
c. For the system represented by the following equations, find the transfer function X(S)/U(S)

--- Content provided by‌ FirstRanker.com ---

by signal flow graph technique.
x(t) = x
l
(t) + 0
3

--- Content provided by​ FirstRanker.com ---

u(t)
x:(t)=?a
l
x, + x, + f3,u(t)
x'

--- Content provided by‌ FirstRanker.com ---

2
(t)=?a
2
x, +13,u(t) (08 Marks)
OR

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2 a. Define analogous systems. Show that two systems shown in Fig.Q.2(a) are analogous
systems, by comparing their transfer functions. (08 Marks)

t
C

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I
I 1
I
Va

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b.
Fig.Q.2(a)
For the block diagram shown in Fig.Q.2(b), determine the transfer function C(S)/R(S) using
block diagram reduction technique. (08 Marks)

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Fig.Q?2(b)
1 of 4
C(s)
s)
(04 Marks)

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c.
Define the following terms in connection with signal flow graph:
i) Node
ii) Forward path gain
iii) Feedback loop

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iv) Non-touching loops.
Module-2
3 a. Define the following time response specifications for an underdamped second order system:
i) Rise time, t
r

--- Content provided by​ FirstRanker.com ---

ii) Peak time, t
p

iii) Peak-overshoot, M

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p

iv) Settling time, i
s
(04 Marks)

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b. A system is given by the differential equation y"(t)+ y
1
(t) + y(t) = x(t), where y(t) in the
output. Determine all time domain specifications for unit step input. (08 Marks)
c. The open loop transfer function of a unity feedback system is given by G(s) =

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OR
4 a. Derive the expressions for i) Rise time, t
r
and ii) Peak overshoot, M
p

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for the
underdamped response of a second order system for a unit step input. (06 Marks)
b.
For the system shown in Fig.Q.4(b), compute the values of K and T to give an overshoot of
20% and peak time of 2 sec for an unit step excitation. (08 Marks)

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c.
Fig.Q.4(b)
Find the position, velocity and acceleration error constant for a control system having open
loop transfer function G(S)H(S)=
10

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. Also find the steady state error for the inpt
S(S +1)
r(t) = 1 + t. (06 Marks)
Module-3
5 a. State and explain Routh's stability criterion for determining the stability of the system and

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mention its limitations. (06 Marks)
b. Determine the number of roots that are
i) in the right half of s-plane
ii) on the imaginary axis and
iii) in the left half of s-plane

--- Content provided by‌ FirstRanker.com ---

for the system with the characteristic equation s
6
+ s
5
? 2s

--- Content provided by‍ FirstRanker.com ---

4
? 3s
3
? 7s
2

--- Content provided by​ FirstRanker.com ---

? 4s ? 4 = 0.
(06 Marks)
c.
Sketch the root locus plot of a certain control system, whose characteristic equation is given
by s

--- Content provided by‌ FirstRanker.com ---

3
+ 10s
2
+ ks + k = 0, comment on the stability. (08 Marks)
2 of 4

--- Content provided by⁠ FirstRanker.com ---

le .?
.`"?!
S(ST +1)
i) By what factor should the amplifier gain K be multiplied in order that the dampine
ratio is increased from 0.2 to 0.8?

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ii) By what factor should K be multiplied so that the system overshoot for unit step
excitation is reduced from 60% to 20%? (08 Marks)
Module-4
7 a. Define the following terms in connection with bode plots:
i) Gain cross over frequency

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ii) Phase crossover frequency
iii) Gain margin
iv) Phase margin.
b. A negative feedback control system is characterized by an open loop
G(S)H(S) =

--- Content provided by‌ FirstRanker.com ---

20
Sketch the polar plot and hence determine w
g
,
S(S +1)(S+ 2)

--- Content provided by‍ FirstRanker.com ---

Comment on the stability.
(04 Marks)
transfer function
, wpc, G M
and PM.

--- Content provided by FirstRanker.com ---

(06Marks)
17EC43
6
OR
a. For a system with characteristic equation s

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4
+ ks
3
+ s
2

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+ s + 1 = 0, determine the range of K
for stability. (04 Marks)
b. Determine the values of 'V and 'a' for the open loop transfer function of a unity feedback
K(s +1)
system is given by G(s) =

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3
, so that the system oscillates at a frequency of
s +as
-
+3s+1

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2rad/sec. (06 Marks)
c. Draw the root locus diagram for the system shown in Fig.Q.6(c), show all the steps involved
in drawing the root locus. Determine:
i) The least damped complex conjugate closed loop poles and the value of `le
corresponding to these roots

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ii) Minimum damping ratio. (10 Marks)
Fig.Q.6(c)
c. A unity feedback control system has G(s) =
100(1+0.1s)
s(s + (o.o is +

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. Draw the Bode plots and
hence determine W
ee
., W
c

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, GM and PM. Comment on the stability. (10 Marks)
OR
8
a.
A unity feedback control system has G(s)?

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200(s + 2)
, . Draw the bode plots and
s(s
-
+ lOs + 100)

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hence determine stability of the system. (10 Marks)
b. Using Nyquist stability criterion, find the range of K for closed loop stability for the
negative feedback control system having the open loop transfer function
G(S)H(S) =
K

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(lo Marks)
S(S
-
+ 2S +2)
3 of 4

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1?
Fig.Q.9(b)
1h\
Module-5
9 a. State the advantages of state variable analysis.

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(04 Marks
b. Obtain the state model for the electrical system shown in Fig.Q.9(b). Take i
o
(t) as output.
(06 Marks)

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For a system represented by the state model
[x; (t) = 1 [001
+
01 x (t)1
u(t) and y(t) = 11 0

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(t)_ L-3 ?4 x2(t)]
x2(t)
Determine:
i) The state transition matrix, 0) and
ii) The transfer function of the system. (10 Marks

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,

OR
10 a. Define state transition matrix and list its properties. (04 Marks)
0 1 0

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b. Consider a state model with matrix A = 3 0 2 . Determine the model matrix M.
?12 ?7 ?6
(06 Marks)
c.
Obtain the time response of the following non homogeneous state equation:

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1
-
x;(t)1 [1 01 rx,(0
-
1

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+
1
-
1
x

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1
2
(t)] Ll li Lx 2
(t)
]

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1 u(t)
i
where u(t) is a unit step function, when x(0).
0

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I
[ (10 Marks)
c.
4 of 4
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