Control Systems (Set-2)
1. Find the transfer function for the network shown in fig.
(a)
(c)
S2 + 2S + 4 S4 + 2S3 + 3S2 + 3S + 2
(
S S2 + 2S + 4
)
S4 + 2S3 + 3S2 + 3S + 2
(b)
(d)
2. Find the transfer function
(a)
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1 2
S +S+2
(b)
V0 (s ) Vi (s )
S4 + 2S3 + 3S2 + 3S + 2 S2 + 2S + 2 S4 + 2S3 + 3S2 + 3S + 1
for the network shown in Fig.
1 2
S2 + 2S + 2
2S + S + 2
(c)
1 2
S + 2S + 2
(d)
1 2
2S + 2S + 2
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3. For the circuit shown in fig. Find the value of R 2 and C to yield 8% overshoot with a setting time of 1m sec for the voltage a cross the capacitor, with Vi ( f ) as a step input.
(a) R 2 = 1003.7Ω, C = 1.6573 µF
(b) R 2 = 8003.7Ω, C = 1.6573 µF
(c) R 2 = 8003.7Ω, C = 1.6573 × 10−2 µF
(d) R 2 = 1003.7Ω, C = 1.6573 × 10−2 µF
4. If Vi ( t ) is a step voltage in the network shown in fig. Find the value of resistor such that 20% over shoot in voltage will be seen across the capacitor if C = 10−6 F and L = 1H?
(a) 112 Ω
(b) 212 Ω
(c) 612 Ω
(d) 912 Ω
5. Given the circuit of Fig, where C = 10 µ F . Find R and L to yield 15% over shoot with a settling time of 7m sec for the capacitor voltage. The input Vi ( f ) is a unit step input
(a) R = 26.72 Ω, L = 6.7 mH
(b) R = 26.72 kΩ, L = 6.7 H
(c) R = 26.72 MΩ, L = 6.7 mH
(d) R = 26.72 k Ω, L = 6.7 mH
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Consider common Data Q. No: 6, 7 The system shown below 6.
Determine
(a)
7.
8.
C ( S)
?
R ( S)
400 2
S + 16S + 400
(b)
200 2
S + 16S + 200
(c)
500 2
S + 25S + 500
(d)
250 2
S + 25S + 250
Determine percent over shoot, rise time for the above system show? (a) 25.4%, 2.463 sec
(b) 16.3%, 0.171 sec
(c) 16.3%, 0.5 sec
(d) 25.4%, 1.463 sec
Determine
(a)
(c)
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C ( S) R ( S)
for the block diagram shown below
G1 G5 1 + G1 ( G5 G8 + G3 G4 G5 + G2 )
G1 G5 (1 + G2 ) 1 + G1 ( G5G8 + G3G4G5 + G2 + G 3G5G 6G7 )
(b)
(d)
G1 G5 (1 + G2 ) 1 + G1 (G5 G8 + G3G4G5 + G 2 )
G1 G5 1 + G1 ( G5 G8 + G3 G4 G5 + G2 + G3 G5 G6 G7 )
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9.
Find transfer function
(a) (c)
10.
C ( S) R ( S)
G1 G2G3G4 1 + G 2G3G4 + G3G4 + G 4
for the SFG. Shown below?
G1 G2 G3G4 2 + G2G3G 4 + 2G 3G 4 + 2G 4
(b)
(d)
G1 G2G3G4 2 + G2G3G4 + G3G4 + 2G4 G1 G2G3G 4 2 + G2G3G4 + G 3G 4 + 2G 4
For the system of fig, find the values of K1 and K 2 to yield a peak time of 1.5 second and a settling time of 3.2 seconds for the closed loop system’s step response.
11.
(a) K1 = 0.2, K2 = 1.387
(b) K1 = 0.5, K2 = 0.287
(c) K1 = 0.287, K2 = 0.5
(d) K1 = 1.387, K2 = 0.2
The closed loop system is stable when
(i) a < 0, b < 0, k > 0
(ii) a < 0, b > 0, k > b
(iii) a > 0, b > 0, k > 0
(iv) a > 0, b < 0, k > −b
Which of the following statements are correct? (a) i, ii ������
(b) i, ii, iv
(c) ii, iv
(d) i, ii, iii, iv
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12.
Consider the following Routh table. Notice that the S5 row was originally all zero’s. Tell how many roots of the original polynomial were in the right half–plane, in the left half– plane and on the jw–axis. S7
1
2
–1
–2
S6
1
2
–1
–2
S5
3
4
–1
0
S4
1
–1
–3
0
S3
7
8
0
0
S2
–15
–21
0
0
S1
–9
0
0
0
S0
–21
0
0
0
(a) 2, 1, 4 13.
(b) 3, 2, 2
(c) 1, 2, 4
(d) 1, 4, 2
For the characteristic equation given, find the constraints on K1 and K 2 such that only two jω poles in the s–plane? S4 + K1S3 + S2 + K 2S + 1 = 0 (a) There is no relationship between K1 and K 2 that will yield just two jω poles (b) K1 = K 2 − 1 , K 2 = K1 + 1 (c)
K1K 2 = K1 − K 2
(d) K12 + K 22 = K1K 2
14.
If a seventh order system has a row of zeros at S3 row and two sign change below the S4 row, how many jω poles does the system have?
(a) 0 15.
(b) 2
(c) 4
(d) None of these
A system is shown in Fig(a). The response to a unit step, when K = 1 is shown in Fig(b). Determine the value of ‘K’ so that steady state error is equal to zero.
Fig (a) (a) 0.25 ������
Fig (b) (b) 0.5
(c) 0.75
(d) 1.25
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16.
Consider the block diagram shown in Fig. Select the value of K that will result in zero over shoot to a step Input. Provide the most rapid response that is attainable.
(a) K = 0.2 17.
(b) K = 0.1
(c) K = 0.05
(d) K = 0.01
Consider the following signal loop feed back structure illustrating the return difference. The return difference FA is
(a) A β
18.
(b) 1 + Aβ
(c)
Aβ 1 + Aβ
(d)
Aβ 1 − Aβ
The control loop configuration of a process is shown in fig For a nominal value of system parameter K equal to 1, the sensitivity of over all transfer function T(s) to Variations in Parameter K of fig. at a particular frequency ω = 5r/sec is
(a) 1
19.
(b) 1.414
(c) 0.414
(d) 0.5
The characteristic equation of a control system is given by 2S5 + S4 + 4S3 + 2S2 + 2S +1 = 0 . The system is (a) Stable
20.
(b) Marginally stable
(c) Unstable
(d) Oscillatory
The characteristic equation of a control system is given by S6 + 2S5 + 8S4 + 12S3 + 20S2 + 16S + 16 = 0 .
The number of the roots of the equation which lie on the imaginary axis of s–plane is (a) Zero ������
(b) 2
(c) 4
(d) 6
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21.
22.
23.
A system has a transfer function
C (S) R ( S)
=
50 . Find rise time and settling time? S + 50
(a) 0.44 sec, 0.8 sec
(b) 0.044 sec, 0.08 sec
(c) 4.4 sec, 8 sec
(d) 0.044 sec, 0.8sec
The general form of the capacitor voltage for the electrical network shown in fig is
(a) 1 + Ae−10t cos ( 20 t + φ )
(b) 0.02 + A e −10t cos (20t + φ )
(c) 0.02 + A e −20t cos (10t + φ )
(d) 1 + A e −20t cos (10t + φ )
The second order system poles locating in the s–plane are shown in shaded region. The range of % M p of the system is
24.
(a) 0.43 %< Mp < 16.3%
(b) 25.4 %< % Mp < 40%
(c) 16.3 %< % Mp < 25.4%
(d) 40% < % Mp < 60%
The open loop transfer function of a unity feed back system is G ( s ) =
K ( S + 2)
(S2 + 1) (S + 4 ) (S − 1)
.
Find the range of ‘K’ for which there will be only two closed loop right half plane poles? (a) No value of ‘K’ exists
(b) K > 2
(c) K < 12
(d) K > 12
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Statement for Linked Answer Questions 25, 26 Consider a plant with transfer function G ( s ) =
1 . Let K u and T u be the S ( S + 1) ( S + 2)
ultimate gain and ultimate period corresponding to the frequency response based closed Ziegler – Nichols cycling method respectively. The Ziegler – Nichols tuning rule for a P– controller is given as K = 0.5 K u 25.
The values of K u and T u respectively are
(a) 8 and π / 2 sec 26.
(b) 6 and π / 2 sec
(c) 6 and
2 π sec
(d) 8 and
2 π sec
The gain of the transfer function between the plant output and an additive load disturbance input of frequency
2π in closed loop with a P–controller designed according T u
to the Ziegler Nichols tuning rule as given above is (a) –1
27.
(b) 0.5
(c) 1
(d) 2
The open loop transfer function of a unity feed back. Control system is given by G ( S) =
S2 + 4S + 8 . The angle θ , at which the root locus approaches the Zeros of the S ( S + 2 ) (S + 8 )
system, satisfies: (a) θ = π − tan−1 (1/4) (c) θ =
28.
π 1 − tan−1 2 4
(b) θ =
3π − tan−1 (1/3) 4
(d) θ =
π 1 − tan−1 4 3
The open loop transfer function of a unity feed back control system is given by G (s ) =
K
(S + P )
3
;P>0
The value of ‘K’ for the damping ratio to be 0.5 corresponding to the dominant closed loop complex conjugate pair is (a) P 4
29.
(b) P 3
(c) P 2
(d) P
The unit step response of a linear time invariant system is y ( t ) = 5e−10 u ( t ) , Where u ( t ) is the unit step function. If the out put of the system corresponding to an unit impulse input δ ( t ) is h ( t ) , then h ( t ) is
(a) −50 e −10t u ( t )
(b) 5u ( t ) − 50 e−10t δ ( t )
(c) 5e−10t δ ( t )
(d) 5δ ( t ) − 50 e−10t u ( t )
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Statement for linked answer question 30 and 31 A disturbance input d ( t ) is injected in to the unity feedback control shown in the Fig. Take unity feedback control loop shown in the Fig. Take the reference input to be a unit step
30.
If the disturbance is measurable, its effect on the output can be minimized significantly using a feed forward controller Gff (s ) . To eliminate the component of the output due to d ( t ) = sin t , Gff ( jω )|ω=1 should be
(a) 31.
Let
1
−3π /4
2
Gff ( s ) be
y ( t ) due
1
−π /4
2
a PD controller. If
d (t)
(c)
2 π
(d)
2 −π /4
= sin 2t, the amplitude of the frequency component of
d ( t ) is
5 13
(a)
32.
to
(b)
(b)
9 13
(c)
17 13
(d)
20 13
A closed loop control system with PI controller is shown below. Determine the minimum value of integral gain ‘K’ such that they steady state error of the closed loop control system is zero for unit step input?
(a) 0 33.
(b) 0.1
(c) 0.2
(d) 0.3
For the closed loop system shown below, determine the values of K P and K d such that the steady state error for unit step input is 0.05 and settling time for 2% criterion is 0.4 sec?
(a)
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KP
= 20, K d = 1
(b)
KP
= 10, K d = 2
(c)
KP
= 19, K d = 2
(d)
KP
= 19, K d = 1
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34.
A PI controller is used to improve the steady state error for unit parabolic input as shown in fig. Determine the PI controller Transfer function
Gc
( s ) such that the steady state error
for unit parabolic input is 0.01?
(a)
35.
10 +
100 S
(b)
50 +
100 S
(c)
75 +
100 S
(d)
150 +
100 S
The block diagram of a control system is shown in figure. The value of ‘a’ is adjusted such that %M pis 1.5% for the above system. Determine the steady state error for unit ramp input with and with out ‘a’?
(a) 0.25, 0.4
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(b) 0.25, 0.5
(c) 0.25, 0.25
(d) 0.25, 0.6
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