ControlSystem Part B

8/7/2019 ControlSystem Part B

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PART B

Common data for Question 1 and 2 :Disturbance input d(t) is injected into the unity feedback control loop shown in thefigure. Take the reference input r(t) to be unit step.

Q. 1 If the disturbance is measurable, its effect on the output can be minimized significantlyusing a feed forward controller G (s). to eliminate the component of the output due dod(t) = sin, G (j)=1should be(A) 1 3

42 (B) 1

42(C) 2 (D) 2

4

Q. 2 Let G (s) be a PD controller. If d(t) = sin 2t, the amplitude of the frequency componentof y(t) due to d(t) is

(A)5

13(B)

913

(C)1713

(D)2013

Q. 3 A unity feedback system has the transfer function2K(s b)

.

S (s 20)

The value are for which

the loci of all the three roots of the closed loop characteristic equation meet at a singlepoint is

(A)109

(B)209

(C)309

(D)409

Q. 4 A linear time-invariant signal-input single-output system has a state. Pace model given

byfx

dx Gu ; y Hzdy

Where F 0 1 0;G ;H [1 0].4 2 1

Here x is the state vector, u is the input, and y is the output.The damping ratio of the system is(A) 0.25 (B) 0.5 (C) 1 (D) 2

Q. 5 A unity feedback control loop with an open loop transfer function of the formK

s(s a )

has a gain crossover frequency of 1 rad / s and a phase margin of 60. If an element

having a transfer functions 3

s 3is inserted into the loop, the phase margin will

become(A) 0 (B) 30 (C) 45 (D) 60


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Q. 6 A filter is represented by the signal flow graph shown in the figure. Its input is x(t) andoutput is y(t). The transfer function of the filter is

(A) (1 ks)s k

(B)(1 ks)

s k

(C)(1 ks)s k

(D)(1 ks)

s k

Q. 7 A plant with transfer function2

s(s 3)is controlled by a PI controller with K p = 1 and

Ki 0 in a unity feedback configuration. The lowest value of K i that ensures zerosteady state error for a step change in the reference input is

(A) 0 (B)13

(C)12

(D) 1

Statement for Linked Answer Question 8 and 9 :

A unity feedback system has open loop transfer function100

G(s) s(s p) the time atwhich the response to a unit step input reaches its peak is / 8 seconds

Q. 8 The damping coefficient for the closed loop system is(A) 0.4 (B) 0.6 (C) 0.8 (D)1

Q. 9 The value of p is(A) 6 (B) 12 (C) 14 (D) 16

Statement for Linked Answer Question 10 and 11:

Consider a unity feedback system with open loop transfer function

21 6s

G(s)s (1 s)(1 2s)

Q. 10 The phase crossover frequency of the system in radians per second is(A) 0.125 (B) 0.25 (C) 0.5 (D)1

Q. 11 The gain margin of the system is(A) 0.125 (B) 0.25 (C) 0.5 (D)1

Q. 12 A tissue with a refractive index 1.33 is introduced in one of the light paths of aMichelson interferometer operating with a monochromatic coherent light source of wavelength 589 nm. After the introduction of a tissue sample of thickness t, the frin


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pattern is observed to shift by 50 fringes. If the thickness is 2 t, the fringe pattern willshift by(A) 25 fringes (B) 50 fringes (C) 100 fringes (D) 200 fringes

Q. 13 For the closed loop system shown below to be stable, the value of time delay T D (in)Should be less than

(A)4

(B)3

(C) (D)

Q. 14 A closed loop control system is shown below. The range of the controller gain K c which will make the real parts of all the closed loop poles more negative than -1 is

(A) K c > -4 (B) K c > 0 (C) K c > 2 (D) K c < 2

Q. 15 A closed loop control system is shown below. The range of the controller gain K c whichwill make the real parts of all the closed loop poles more negative than -1 is

(A) K c > -4 (B) K c > 0 (C) K c > 2 (D) K c < 2

Q. 16 If a first order system and its time response to a unit step input are as shown below, thegain K is

(A) 0.25 (B) 0.8 (C) 1 (D) 4


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Q. 17 The open loop transfer function of unity feedback system isK(s 2)

G(s)(s 1 j1)(s 1 ji)

The root locus plot of the system has(A) Two breakaway point located at s = -0.59 and s = -3.41(B) one breakaway point located at s = -0.59(C) one breakaway point located at s = -3.41(D) one breakaway point located at s = -1.41

Q. 18 The bode asymptotic plot of a transfer function is given below. In the frequency rangeshown, the transfer function has

(A) 3 poles and 1 zero (B) 1 pole and 2 zero (C) 2 poles and 1zero (D) 2 poles and 2zero

Statement for Linked Answer Questions 19 and 20

A transfer function with unity Dc gain has three poles at -1, -2, and -3 and no finitezeros. A plant with this transfer function is connected with a proportional controller of

gain K in the forward path, in unity feedback configuration.

Q. 19 The transfer function is

(A)s

(s 1)(s 2)(s 3) (B)

6(s 1)(s 2)(s 3)

(C)s

(s 1)(s 2)(s 3) (D)

6(s 1)(s 2)(s 3)

Q. 20 If the root locus plot of the closed loop system passes through the points j11, themaximum value of K for stability of the unity feedback closed loop system is

(A) 11 (B) 6 (C) 10 (D)6

11 Common Data for Question 21, 22 :

The following figure represents a proportional control scheme of a first order systemwith transportation lag.

Q. 21 The angular frequency in radians /s at which the loop phase lag becomes 180 is(A) 0.408 (B) 0.818 (C) 1.56 (D) 2.023


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Q. 22 The steady state error for a unit step input when the gain K c = 1 is

(A)14

(B)14

(C) 1 (D) 2

Q. 23 A cascade control system with proportional controllers is shown below:

Theoretically, the largest values of the gain K 1 and K 2 that can be set without causing

instability of the closed loop system are(A) 10 and 100 (B) 100 and 10 (C) 10 and 10 (D) and

Q. 24 Consider the following standard state-space description of a linear time-invariant singleinput single output system : x = Ax + Bu = Cx + Du. Which one of the followingstatements about the transfer function CANNOT be true if D 0 ? (A) the system is unstable (B) the system is strictly proper(C) The system is low pass (D) the system is of type zero

Q. 25 A feedback control system with high gain K, is shown in the figure below:

Then the closed loop transfer function is(A) sensitive to perturbations in F(s) and H(s)(B) sensitive to perturbations in G(s) but not to perturbations in H(s)

(C) sensitive to perturbations in H(s) but not to perturbations in G(s)(D) Insensitive to perturbations in G(s) and H(s)

Common Data for Questions 26, 27, 28 :The following figure describes the block diagram of a closed loop process controlsystem. The unit of time is given in minute.


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Q. 26 The digital implementation of the controller with a sampling time of 0.1 minute usingvelocity algorithm is

(A)k

i 1m(k) 0.5 e(k) 0.5 e(k)

(B)

k 1

i 1m(k) 2.0 e(k) 2.0 e(k )

(C) m(k) m(k 1) 0.5[e(k) 0.85e(k 1)] (D)m(k) m(k 1) 0.5[1.05e(k) e(k 1)]

Q. 27 Suppose a disturbance signal d(t) = sin 0.2t unit is applied. The at steady state, theamplitude of the output e(t) due to the effect of disturbance alone is(A) 0.129 unit (B) 0.40 unit (C) 0.528 unit (D) 2.102 unit

Q. 28 The control action recommended for reducing the effect of disturbance at the output(provided that the disturbance signal is measurable is(A) cascade control (B) P-D control(C) ration control (D) feedback-feed forward control

Q. 29 The root locus of a plant is given in the following figure. The root locus crossesimaginary axis at = 4 2 and / s with gain K = 384. It is observed that the point s = -1.5+ j1.5 lies in the root locus. The gain K at s = -1.5 + j 1.5 is computed as

(A) 11.3

(B) 21.3

(C) 41.25

(D) 61.2

Q. 30 A unity feedback system has the following open lop frequency response :

(rad / sec) 2 3 4 5 6 8 10

G(j ) 7.5 4.8 3. 2.25 1.70 1.00 0.64

G(j ) 118 130 140

150

157 170 180

The gain and phase margin of the system are(A) 0dB, - 180 (B) 3.88dB, - 170 (C) 0dB, 100 (D) 3.88 dB, 10


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Q. 31 The range of the controller gain (K p, K j) that makes the closed loop control system(shown in the following figure) stable is give as

(A) II P KK 0 and K 2012

(B) I PK 0 and K 0

(C) II PK

K 0 and K 2012

(D) II PK

K 0 and K 2012

Q. 32 The signal flow graph representation of a control system is shown below. The transferfunction

Y(s)R(s)

is computed as

(A)1s

(B)2

2s 1

s(s 2)

(C)2

2s(s 1)s 2

(D)1

1s

Q. 33. The transfer function of a position servo system is given as1

G(s)s(s 1)

A first order compensator is designed in a unity feedback configuration so that the polesof the compensated system are placed at -1 j1 and -4. The transfer function of the

compensated system is(A)

s 32(s 5)

(B)2s 3s 5

(C)5(s 1.6)

s 5(D)

3(2s 3)s 4

Q. 34 The state-variable representation of a plant is given byx = A x + Buy = Cx

where x is the state, u is the input and y is the output. Assuming zero initial condition,the impulse response of the plant is given bye(A) exp(At) (B) exp [a (t- )Bu () d ] (C) C exp (At)B (D) C exp [A(t- )Bu ()]

Q. 35 Compared to a conventional two-phase induction motor, a two-phase servomotor has


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(A) a smallerRX

ration and a lighter rotor (B) the sameRX

ration and a heavier

rotor

(C) a largerRX ration and heavier rotor (D) A larger

RX ration and a lighter

rotor

Statement for Linked Answer Question 36 & 37

Given figure shows a closed loop[ unity feedback system. The controller block has atransfer function denoted by G c(s). The controller is cascaded to the plant, which isdenoted by G c(s).

Q. 36 The transfer function G c(s) is

(A)1 0.1s

S(B)

1 0.1ss

(C)s

s 1(D)

ss 1

Q. 37 The peak percentage overshoot of the closed loop system is(A) 5.0% (B) 10.0% (C) 16.3 % (D) 1.63%

Q. 38 Consider a unity feedback control system whose forward path transfer function G(s) =k/s 2. The steady state error, for a step input is(A) 1.0 (B) (C) 0.0 (D) does notexist

Q. 39 The open loop part of a unity feedback control system G(s) is unstable and has twopoles on the right hand side of the s-plane. However, the closed loop system is stable.The number of encirclements made by the Nyquist plot of the (-1, 0) point in the G(s)(A) 2 (B) 0 (C) -3 (D)-1

Q. 40 The transfer function of the open loop system G(s) which is represented by the signalflow graph shown the figure below is

(A) 1 11 1 1 1

G G1 G H G H

(B) 1 21 1 2 2

G G1 G H G H


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(C) 1 21 1 2 2

G G(1 G H )(1 G H )

(D)

1 2

1 1 2 2

G G

1 (G H )(G H )

Q. 41 The Routh-Hurwitz array is given for a third order characteristic equation.

3

3

0

s 1 b 0 0

s a c 0 0(6 k)

03

s k

The coefficients a, b, c and k are such that a = 3, b >0, k > 0, C > 0 and c is a functionof k. the root locus for the corresponding characteristic equation is shown in the givenfigure. The values of k and c for critical stability respectively are(A)6 and 6 (B) 6 and 2 (C) 3 and 2 (D) 3 and 3

Q. 42 The asymptotic magnitude Bode plot of an open loop system G(s) with K > 0 and allpoles and zeros on the left hand side of the s-plane is shown in the figure. It iscompletely symmetric about e. The minimum absolute phase angle contribution byG(s) is given by

(A) 78.6 (B) 90 (C) 101.4 (D) 180

Q. 43 A controller loop structure is shown in the figure with FC, FT, TC and TT denotingFlote Controller, flow Transmitter, Temperature Controller and TemperatureTransmitter respectively. This loop is an example of

(A)Ration Control (B) Feed forward Control(C) Split Range control (D) Cascade control

Q. 44 A single input single output linear system is described by the equations


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dx

Ax bu and y cx du,dt

where a is an n n matrix and x and b are n 1 rectors. The transfer function is given by(A) c[sI -A] -1b (B) c[sI -A] -1b+d (C) c[sI -A]b (D) c[sI -A]b+d

Q. 45 Identify the transfer function corresponding to an all-pas filter from the following :

(A)1 s1 s

(B)2

1 s1 s

(C)1

1 s (D)

s1 s

Q. 46 Fig Q. 80 shows the polar plot of a system. The transfer function of the system is

(A) 5(1 + 0.1s)

(B) (1 + 0.5s)

(C) 5(1 + 10s)

(D) 5(1+ s)

Q. 47 Fig. Q. 79 shows the bode magnitude plot of a system. The minimum phase transferfunction of the system I s given by

(A)

880 1

28

80 12

(B)

s20 1

2s

20 12

(C)8(s 2)

s(s 20)

(D)8(s 2)s(s 20)

Q. 48 A certain closed loop system with unity feedback has the forward path transfer function

given byK

G(s)s(s 1)(s 5)

. With the gain set at the ultimate value, the system will

oscillate at an angular frequency of (A) 6 rad/s (B) 5 rad/s (C) 2rad/s (D) 3 rad/s

Q. 49 The torque-speed curve of a constant field armature controlled DC servomotor is shown


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in fig. Q.77. The armature resistance in and torque constant in Nm/A of the motorespectively are

(A) (1.76, 0.68)

(B) (1.76, 0.85)

(C) (2.00, 0.25)

(D) (0.01, 0.81)

Q. 50 A certain system exhibited an over shoot of 16% when subjected to an input of 2u(t),where u(t) is a step input. The damping ration and decay ratio respectively are(A) (0.8, 0.0810) (B) 0.5, 0.0256 (C) (1.0, 0.1626) (D) (1.1, 0.0089)

Q. 51 A casual, analog system has transfer function 2 2a

H(s) .s a

Assuming a sampling

time of t seconds, the poles of the transfer function H(z) for an equivalent digital systemobtained using impulse invariance method are at

(A) et at(e ,e ) (B)a a

j , jt t

(C) jaT juT(e , e ) (D)

aT/ 2 aT/ 2(e ,e )

Q. 52 The proportional band of a PI controller is 50% and the reset time is 0.2s. The transferfunction of the controller is given by

(A)1

50 10.2s

(B)1

50 15s

(C)1

2 15s

(D)1

2 1s

Q. 53 The steady state error due to a unit-step disturbance input D(s) in fig. Q.24 is

(A) 0

(B) 0.012

(C) 0.021

(D) 0.025

Q. 54 For a first order instrument a 5% settling time is equal to(A) three times the time constant(B) two t imes the time constant(C) the time constant(D) time required for the output signal to reaches 5% of the final value

Data given below should be used for answering question. Q.55 and Q.56


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The root locus plot for a system, with transfer function2

,s(s 1)(s 2)

is shown in Fig.

Q.55. unity feedback proportional control system is built using this system.

Q. 55 The maximum possible controller gain, for which the unity feedback system is stable, isapproximately

(A) 6.0

(B) 3.0

(C) 0.4

(D) 0.2

Q. 56 The maximum possible controller gain, for which the unity feedback system exhibits anon-oscillatory response to a unit step input, is(A) 6.0 (B) 3.0 (C) 0.4 (D) 0.2

Q. 57 The transfer function of a second order band-pas filter, having a centre frequency of 1000rad./s, selectivity of 100 and a gain of 0 dB at the centre frequency, is

(A) 2 210s

s 10s 10 (B) 2 6

s

s s 10 (C) 2 7

100s

s 100s 10 (D)

2 6100s

s 10s 10

Q. 58 The transfer function of a system is given by0.1sY(s) e

X(s) 1 s. If x(t) is 0.5 sin t, then The

phase angle between the output and the input will be(A) -39.27 (B) -45 (C) -50.73 (D) -90

Q. 59 For a dynamic system, various matrices for a state space model are given by0 1 0

A = -2 -3 , B = 1 and C = [1 0]. The system poles are located at(A) -2, -1 (B) -2, -3 (C) -3, -1 (D) -1, 0

Q. 60 A PID controller has the transfer function0.4

2s

with the unit of time expressed in

minutes.. The parameters proportional band and reset time for the above controller arerespectively


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(A) 200% and 0.4 min (B) 50 % abd 0.4 min(C) 200 % and 5 min (D) 50 % and 5 min .

Q. 61 The response of a system to a unit impulse is y(t) = e -5(t-1) . Which one of the followingis the correct statement about the system ?

(A) The system is nonlinear(B) The system is unstable in open loop(C) The steady-state gain of the system for a unit step input is 0.2(D) The steady-state gain of the system for a unit step input is 1.0

Q. 62 In fig. K 1 are proportional controllers. For the control system to remain stable, theupper limits of K 1 and K 2 are

(A) , (B) 1, (C) , 10 (D) 10, 1

Q. 63 The closed loop control system shown in Fig. Q. 77 has 1 > 0. The system will remainstable for all 1 in the range

(A) 1 0.5 (B) 10.5 1.0 (C) 1 1.0 (D) 1 1.0 Q. 64 The transfer function of a system is A. The steady-state gain of the system to a unit-step

input is

(A) 2A

(B) 0

(C) (D) not possible to be determined

Q. 65 In the feedback scheme shown in Fig. Q. 27, the time-constant of the closed loop systemwill be


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Q. 66 A three- stack variable reluctance stepper motor has 12 numbers of rotor and stator teeth

on each stack. The resolution of angular rotation for the stepper motor, assuming no.two stacks are excited simultaneously, is(A) 10 (B) 15 (C) 20 (D) 30

Q. 67 The steady state error for the feedback control system shown in Fig. Q.25 whensubjected to a unit step input is

(A) Zero (B) p

1(1 KK ) (C)

p

p

KK

(1 KK ) (D) infinite

Q. 68 In a synchro pair, the control transmitter excites the three stator windings of the controltransformer. The stator winding voltages will have(A) equal magnitudes but different phase(B) different magnitudes and different phase(C) equal magnitudes and phases(D) Different magnitudes but equal phases

Q. 69 A unity feedback system has on open loop transfer functionk

G(s) s(s 3) . The valueof k that yields damping ration of 0.5 for the closed loop system is(A) 1 (B) 3 (C) 5 (D) 9

Q. 70 A unit ramp input is applied to the system shown in the adjoining figure. The steadystate error in its output is

(A) 0 (B) 0.5 (C) 1 (D) 2

Q. 71 The asymptotic Bode magnitude plot of a lead network with its pole and zero on the lefthalf of the s- plane is shown in the adjoining figure. The frequency at which the phaseangle of the network is maximum (in rad/s) is


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(A)3

10

(B)1

20

(C)1

20

(D)1

30

Q. 72 The rotor of the control transformer of a synchro-pair gives a maximum voltage of 1.0 vat a particular position of the rotor of the control transmitter. The transmitter rotor isnow rotated by 30 anticlockwise keeping the transformer rotor stationary. Thetransformer rotor voltage for this position is(A) 1.0 V (B) 0.866 V (C) 0.5 V (D) 0 V

Q. 73 The open loop transfer function of a unity gain feedback system is given by:k(s 3)

G(s)(s 1)(s 2)

The range of positive values of k for which the closed loop system will remain stable is(A) 1< k

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ControlSystem Part B