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Roll No.
Time: 3 Hours B. TECH. (SEM VI) THEORY EXAMINATION 2018-19 CONTROL SYSTEM I Total Marks: 70
Note: 1. Attempt all Sections. If require any missing data; then choose suitably.
SECTION A
1. Attempt all questions in brief. 2 x 7 = 14
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- Write the condition for the system to be controllable.
- Compare an open loop control system with a close loop control system.
- What do mean by type and order of the system?
- State the effect of adding a zero to the forward path transfer function of the system.
- Differentiate between transient response and steady state response of a system.
- What will be the steady state error of the type 1 system, when subjected to unit parabolic input?
- State the relation between unit step and unit ramp signal.
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SECTION B
2. Attempt any three of the following: 7 x 3 = 21
- (i) Establish the correlation between time domain response and frequency domain response of a system (5+2)
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(ii) Define the terms: Settling time and Phase Margin - Draw the block diagram of a standard second order control system in closed loop form and derive the relation for its time response when subjected to unit step input.
- (1) Construct state model for the system characterized by the following differential equation: (3+4)
+6+11+6=4 dt3 dt2 dt
(ii)Check controllability and observability of the following system:--- Content provided by FirstRanker.com ---
0 1 0
A = 0 0 1 B = 0 C=[10 5 1]
-6 -11 -6 4 - (i) The open loop transfer function of a control system is given below
2(s² + 3s + 20)--- Content provided by FirstRanker.com ---
G(s)H(s) =
s(s + 2)(s² + 4s +10)
Determine static error coefficient and steady state error for the input given as
(1) 5 (2) 4t (3) 4t2/2
(ii) Using Routh- Hurwitz criterion, discuss the stability of the following characteristic equation--- Content provided by FirstRanker.com ---
F(s) = s6 + 3s5 +6s4 + 12s3 + 12s² + 12s + 8 (3+4) - The open loop transfer function of a unity feedback system is
25
G(s) =
s(s + 5)--- Content provided by FirstRanker.com ---
Find i) Natural frequency of oscillation ii) Damped frequency of oscillation
iii) Damping ratio iv) Maximum over shoot of unit step input.
SECTION C
3. Attempt any one part of the following: 7x1=7
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- (a) Using Bode Plot, comment on the stability of the following unity feedback open loop transfer function
G(s) = 50
(s+1)(s+2) - (b) Use Bode Plot to determine the gain K for the open loop transfer function given below so that gain margin is 15 dB
K--- Content provided by FirstRanker.com ---
G(jo)H(jo) =
jo(0.10+1)(jo+2)
4. Attempt any one part of the following: 7x1=7
- (a) Using Nyquist plot determine (a) Phase crossover frequency (b) Gain crossover frequency for
2.5K--- Content provided by FirstRanker.com ---
G(s)H(s) =
s(0.4s+1)(0.2s+1) - (b) Draw the analogous electrical circuit for the system shown below. Use F-V and F-I analogy. All the symbols have usual meaning.
Ka
M3--- Content provided by FirstRanker.com ---
?x3(t).
K?
Ba
Ma
BI--- Content provided by FirstRanker.com ---
?
?
?
?
fer)
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5. Attempt any one part of the following: 7x1=7
- (a) Elaborate the step wise procedure for plotting the root locus of a given open loop transfer function.
- (b) Sketch the root locus for the open loop transfer function of a unity feedback control system given below
K
G(s) =--- Content provided by FirstRanker.com ---
s(s+1)(s+3)
6. Attempt any one part of the following: 7x1=7
- (a) For the following block diagram, determine over all transfer function using block diagram reduction technique
R(s) S1--- Content provided by FirstRanker.com ---
+
G1
G2
S2
H1--- Content provided by FirstRanker.com ---
T1
H3
+
C(s)
S3--- Content provided by FirstRanker.com ---
G3
G4
T2
H2 - (b) Find overall transfer function using signal flow graph:
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H
C(s)
R(s)
G
G2--- Content provided by FirstRanker.com ---
G3
H2
H3
7. Attempt any one part of the following: 7x1=7
- (a) Using Mason's Gain Formula, find over all transfer function for the following system
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H2
A
G2
TG3
H3--- Content provided by FirstRanker.com ---
GI
GS
96
H
6--- Content provided by FirstRanker.com ---
G4
CCS)
Gg
Gy
Ha - (b) Using block diagram reduction technique, find over all transfer function for the following system
X(s)
G4
R(s)
C(s)--- Content provided by FirstRanker.com ---
Gi
G2
G3
Gs
FirstRanker.com--- Content provided by FirstRanker.com ---
H5
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