Control System 400 Objective Questions From GATE & IES

Objective Questions

Chapter 2

1. For the network shown in Figure P2.43, Vit is the input and i(t) is the output. The transfer functionI(S)=V(S) of the network is

(a)Cs

LCs2 RCs 1 (b)C

LCs2 RCs 1

(c)Cs

RCs2 LCs 1 (d)C

RCs2 LCs 1 IES 1993

2. For the eld-controlled dc servomotor, as shown in Figure P2.44, the transfer function s=Escontains(a) Two times constants, no integration (b) Two times constants, one integration(c) One time constants, one integration (d) One time constants, one integration

IES 1996

3. Amechanical system consists of twomass-spring friction system, as shown in Figure P2.45. The orderof the transfer function X(s)=F(s) is(a) 1 (b) 2(c) 3 (d) 4

IES 1996

R L

j(t) CVi(t)

Figure P2.43 A network (Objective Question 1).

R Ig (Constant)

Singular relationJ1I

L

Figure P2.44 A led-controlled servomotor.

Figure P2.45 Two mass-spring friction system.

4. Consider a multiple gear system, as shown in Figure P2.46. Which one of the following gives theequivalent inertia referred to shaft 1?

(a) J1 J2 N1N2

2 Ja N1N3

N2N4

2(b) J1 J2 N2

N1

2 J3 N2N4

N1N3

2

(c) J1 J2 N1N2

2 J3 N1N2

N3N4

2(d) J1 J2 N2

N1

2 J3 N1N2

N3N4

2

IES 20045. For the mechanical system, shown in Figure P2.47, the system is described as:

(a) Md2y1tdt2

B dy1tdt

K y2t y1t

(c) Md2y1tdt2

B dy1tdt

K y1t y2t

IES 2001

B N

N

BBBN

N

J

J

J

Figure P2.46 A multiple gear system.

B

MK

y2(t) y1(t)

f(t)

Figure P2.47 A mechanical system.

(b) Md2y2tdt2

B dy2tdt

K y2t y1t

(d) Md2y2tdt2

B dy2tdt

K y1t y2t

2 . OBJECTIVE QUESTIONS

Chapter 3

1. Consider a signal ow graph, as in Figure P3.12.

Signal ow graphs, which have the same transfer function, would include:

(a) (i) and (ii) (b) (ii) and (iii)(c) (ii) and (iv) (d) (i) and (iv)

IAS 19992. Consider a signal ow graph shown in Figure P3.13.

1s 2s 3s

1K 2K

3K

(i)1s 2s 3s

1K 2K

3K

(ii)1s 2s 3s1K

2K

3K

(iii)

Figure P3.12 Signal ow graphs for Objective Question 1.

1b

2b

3b

4b

5b 7b

8b 9b 10b

1Z 2Z 6Z


OBJECTIVE QUESTIONS . 3

Consider the following statements regarding the signal ow graph:

(i) There are three forward paths.

(ii) These are three individual loops.

(iii) These are two nontouching loops.

Of these statements:

(a) (i), (ii), and (iii) are correct. (b) (i) and (ii) are correct.(c) (ii) and (iii) are correct. (d) (i) and (iii) are correct.

IES 1998

3. Referring to Figure P3.14, match list I (signal ow graph) with list II (transfer function), and selectthe correct answer using the codes given in the following list:

List I List II

A. Figure (i) 1:P

1 QB. Figure (ii) 2:

Q

1 PQC. Figure (iii) 3:

PQ

1 PQD. Figure (iv) 4:

PQ

1 P2



Codes: A B C D A B C D(a) 2 3 4 1 (b) 2 3 1 4(c) 3 2 1 4 (d) 3 2 4 1

IAS 20004. A system block diagram is shown in Figure P3.15.

The overall transfer function of the system is

C

R G1G2G3

1 G1G2G3H1 G2H2 G3G2H3The value of X in the gure would be equal to(a) H3 (b) G3H3(c) G2H3 (d) G3H3

IAS 20015. The signal ow graph of the system is shown in Figure P3.16.

The transfer function Cs=Ds of the system is(a)

G1sG2s1 G1sHs (b)

G1sG2s1 G1sG2sHs

(c)G2s

1 G1sG2sHs (d)G2s

1 G1sG2sHs IAS 2001

R(s) + + +

1G 2G 3G

1H

2H

C

X




6. The closed loop system shown in Figure P3.17 is subjected to a disturbance Ns.

The transfer function Cs=Ns is given

(a)G1sG2s

1 G1sG2sHs (b)G1s

1 G1sHs

(c)G2s

1 G2sHs (d)G2s

1 G1sG2sHsIES 1997

7. The transfer function of the system shown in Figure P3.18 is

(a)O

R ABC

1 ABC (b)O

R A B C

1 AB AC

(c)O

R AB AC

ABC(d)

O

R AB AC

1 AB AC

IAS 1998


R +

+

A

B

O

C



8. Three blocks G1;G2 and G3 are connected in some fashion such that overall transfer function is

G1 G31 G1G21 G1G2

The blocks are connected in the following manner:

(a) G1;G2 with negative feedback and combination in parallel with G3(b) G1;G3 with negative feedback and G2 in parallel(c) G1;G2 is cascade and combination in parallel with G3(d) G1;G3 in cascade and combination in parallel with G2

IAS 2004

9. In regeneration feedback, the transfer function is given by

(a)GsRs

Gs1 GsHs (b)

GsRs

GsHs1 GsHs

(c)GsRs

GsHs1 GsHs (d)

GsRs

Gs1 GsHs

IAS 199210. The transfer function Cs=Rs of the system, whose block diagram is shown in Figure P3.19, is

(a)G1G2

1 G1H1 G2H2 G1G2H1H2 (b)G1G2

1 G1H1 G2H2 G1G2H1H2

(c)G1G2

1 G1H1 G2H2 (d)G11 G2H2G21 G1H1

1 G1H1 G2H2 G1G2H1H2

IES 1993

R(S) C(S)+ +

1G

1H2H

2G



11. The signal ow graph of a closed loop system is shown in Figure P3.20, wherein TD represents thedisturbance reduces by

(a) Increasing G2s (b) Decreasing G2s(c) Increasing G1s (d) Decreasing G1s

IES 1997

12. The response c(t) of a system to an input r(t) is given by the following different equation:

d2ctdt2

3dctdt

5ct 5rt

The transfer function of the system is given by

(a) Gs 5s2 3s 5 (b) Gs

1

s2 3s 5

(c) Gs 3ss2 3s 5 (d) Gs

s 3s2 3s 5

IES 1996

13. The gain Cs=Rs of the signal ow graph, shown in Figure P3.21, is

(a)G1G2 G2G3

1 G1G2H1 G2G3H1 G4 (b)G1G2 G2G3

1 G1G2H1 G2G3H1 G4

(c)G1G3 G2G3

1 G1G3H1 G2G3H1 G4 (d)G1G3 G2G3

1 G1G3H1 G2G3H1 G4

IES 2003



14. The overall gain Cs=Rs of the block diagram, shown in Figure P3.22, is

(a)G1G2

1 G1G2H1H2 (b)G1G2

1 G2H2 G1G2H1

(c)G1G2

1 G2H2 G1G2H1H2 (d)G1G2

1 G1G2H1 G1G2H2

IES 2003

15. From Figure P3.23, the transfer function of the signal ow graph is

(a)T12

1 T22 (b)T22

1 T12

(c)T12

1 T12 (d)T22

1 T12IES 1992

R(S) + +

+

1G

1H2H

2G


1X 12T

22T

2X




Chapter 4

1. The unit-impulse response of a system is given by ct 0:5et=2. Its transfer function is(a) 1=s 2 (b) 1= 1 2s (c) 2= 1 2s (d) 2= s 2

IAS 1993

2. If the unit-step response of a system is a unit impulse function, then the transfer function of such asystem will be

(a) 1 (b) 1=s

(c) s (d) 1=s2

IAS 1994

3. When a unit-step input is applied, a second-order underdamped system has a peak overshoot of OPoccurring at tmax: If another step input, equal in magnitude to the peak overshoot OP, is applied att tmax, then the system will settle down at(a) 1 OP (b) 1 OP(c) OP (d) 1:0

IAS 1994

4. The system shown in Figure P4.58 is subjected to a unit ramp input on close the switch (s).

(a) Steady-state error will increase and damping coefcient j will decrease.

(b) Both-steady state error and damping coefcient j will increase

(c) Both steady-state error and damping coefcient j will decrease.

(d) Steady-state error will decrease and damping coefcient j will increase.

IAS 19955. The impulse response of a system is given by

ct 12et=2

R(s) K

K1 s

s

s(s + a)C(s)

+

+

Figure P4.58 Figure for Objective Question 4.


which of the following is its unit-step response?

(a) 1 et=2 (b) 1 et(c) 2 et (d) 1 e2t

IAS 1998

6. For the system, shown in Figure P4.59, the damping factor j and undamped natural frequencyvn arerespectively

(a)2KJ

pf

and

J

K

r(b)

K

J

rand

f

2KJ

p

(c)f

2KJ

p andK

J

r(d)

2FKJ

p and KJ

IAS 1999

7. Type of a system depends on the

(a) No. of its poles (b) Difference between the no. of poles and zeros(c) No. of its real poles (d) No. of poles it has at the origin

IAS 20008. A unity feedback system has open loop transfer function as

Gs 16ss 16

The natural frequency of the system is

(a) 16 (b) 8(c) 2 (d) 4

IAS 20029. The system

Gs 0:8s2 s 2

is excited by a unit-step input. The steady-state output is

(a) 0.8 (b) 0.4(c) 0.4 (d) Unbonded

IAS 2003



10. The system shown in Figure P4.60 has a unit-step unit. In order that the steady-state error is 0.1, thevalue of K required is

(a) 0.1 (b) 0.9(c) 1.0 (d) 9.0

IAS (EE) 1994

11. The settling time of a feedback system with the closed-loop transfer function

C s R s

v2ss2 2vns v2n

is

(a) ts 2vn

(b) ts vn2

(c) ts 4vn

(d) ts 4vnIAS (EE) 1998

12. The feedback control system shown in Figure P4.61 is

(a) Type 0 system (b) Type 1 system(c) Type 2 system (d) Type 3 system

IES (EC) 1993


+

2

2( 1)

ss +

2

( 1)

ss s++

2 3

( 3)

ss s

++



13. A typical control system is shown in Figure P4.62. Assuming Rs 1=s; the steady-state error is

(a)1

1K (b) K

(c) Zero (d) 1

IES (EC) 199514. The velocity-error constant Kv of a feedback system of a closed-loop transfer function

CsRs

Gs1 GsHs

is

(a) Kv Lims!0 sG s H s (b) Kv Lims!0 s

G s 1G s H s

(c) Kv Lims!0 sG s (d) Kv Lims!0 s 1 G s H s

IES (EC) 199815. In the derivation of expression for peak percent overshoot

Mp exp 1 2

p !

100%

which one of the following condition is NOT required?

(a) The system is linear and time invariant.

(b) The system transfer function has a pair of complex conjugate poles and no zeros.

(c) There is no transportation delay in the system.

(d) The system has zero initial condition.GATE (EC) 2005

16. For what values of a, does the system shown in Figure P4.63 have a zero steady-state error (timed)for a step input?(a) a 0 (b) a 1(c) a 4 (d) For no value of a

1s + 20

s + 40s(s + 10)

+

R(s)K

C(s)



GATE (EE) 1992

17. A system has the following transfer function

G s 100 s 5 s 50 s4 s 10 s2 3s 10

The type and order of the system are respectively

(a) 4 and 9 (b) 4 and 7(c) 5 and 7 (d) 7 and 5

IES (EE) 199818. For the system shown in Figure P4.64, the state value of the output c(t) is

(a) 0 (b) 1(c) 1 (d) Dependent on the values of K and Kt

IES (EE) 1999

19. Consider the following statements regarding system shown in Figure P4.65, where m mass,B frictional coefcient and K spring constant:1. It represents a conservative system.2. It has a natural frequency of undamped oscillation of

K=m

p:

3. It has a time constant of m/K of these statements.

2

1

5

ss s a

++ +

1

4s +


Ks(s + 2s)

+

C(s)

K

1 + 0.025

Input = Unit step



(a) 1, 2, and 3 are correct (b) 1 and 2 are correct(c) 2 and 3 are correct (d) 1 and 3 are correct

IAS 1997

20. In Figure P4.66, spring constant is K, viscous friction coefcient is B, mass is M and the systemoutput motion is x(t) corresponding to input force F(t). Which of the following parameters relates tothe above system?

Here

1. The constant 1=M2. Damping coefcient B= 2 KMp 3. Natural frequency of oscillation K=Mp

IES (EE) 199521. The step response of a system is ct 1 5et 10e2t 6e3t. The impulse response of the

system is

(a) 5et 20e2t 18e3t (b) 5e t 20e2t 18e3t(c) 5et 20e2t 18e3t (d) 5et 20e2t 18e3t

IAS 2003

22. Given a unity feedback with

G s Ks s 4

B = 0m


M

kF(t)

x(t)



the value of K for damping ratio of 0.5 is

(a) 1 (b) 16(c) 4 (d) 2

IAS 200323. A unity-feedback control system has a forward-path transfer function G(s) is given by

G s 10 1 s s2 s 1 s 5

The steady-state error due to unit parabolic input

rt t2

2Ut

is

(a) Zero (b) 0.5(c) 1.0 (d) Innite

IAS 200324. Damping factor and undamped natural frequency for a position control system is given by

(a) 2KJ

p;

KJ

prespectively (b)

K

2fJ;

K=J

prespectively

(c)f

2KJ

p ;K=J

prespectively (d)

J

2Kf

p ; KJp respectivelyIES (EE) 1992

25. Match List I (TimeDomain Specication) with List II (Equation for Finding Its Value), and select thecorrect answer using the codes given below the lists.

List I (Time Domain Specication) List II (Equation for Finding Its Value)

A. Peak overshoot 1. =vn1 2

p

B. Peak time 2. 4= vn C. Rise time 3. exp=

1 2

p%

D. Settling time (2%) 4. p fcos1=vn1 2

pg

Codes: A B C D A B C D(a) 3 2 4 1 (c) 4 1 3 2(b) 3 1 4 2 (d) 4 2 3 1

IAS 200426. In type I system, a constant output velocity at steady state will be possible, when

(a) There is no error.

(b) There is a constant steady-state error.


(c) There is a variable steady-state error.

(d) There is a uctuating error.IES (EE) 1992

27. If the time response of a system is given by the following equation

y t 5 3 sin vt 1 e3t sin vt 2 e5t

then the steady-state part of the above response is given by

(a) 5 3 sin vt s1 (b) 5 3 sin vt 1 e3t sin vt 2 (c) 5 e5t (d) 5

IES (EE) 199628. The impulse response of a system is 5e10t; its step response is equal to

(a) 0:5e10t (b) 51 e10t(c) 0:51 e10t (d) 101 e10t

IES (EE) 199629. The transfer function of a system is 10/(1 s) when operated as a unity feedback system, the steady-

state error to a unit-step input will be

(a) Zero (b) 1/11(c) 10 (d) Innity

IES (EE) 199630. The unit-impulse response of a second-order system is 1=6e0:8t sin 0:6t . Then the natural

frequency and damping ratio of the system are respectively

(a) 1 and 0.6 (b) 1 and 0.8(c) 2 and 0.4 (d) 2 and 0.3

IES (EE) 200331. A second-order control system has

M jw 100100 v2 10 2p jv

Its Mp (peak magnitude) is

(a) 0.5 (b) 1(c)

2

p(d) 2

IES (EE) 200332. Consider the following system, shown in Figure P4.67, where x(t) sin t.What will be the response

y(t) in the steady state?

x(t) y(t)

1

ss+



(a) sin(t 458)= 2p (b) sin(t 458)= 2p(c)

2

p etsin t (d) sin t cos t

IES (EE) 200433. The damping ratio and natural frequency of a second-order system are 0.6 and 2 rad/s respectively.

Which of the following combinations gives the correct values of peak and settling time, respectively,for the unit-step response of the system?

(a) 3.33 s and 1.95 s (b) 1.95 s and 3.33 s(c) 1.95 s and 1.5 s (d) 1.5 s and 1.95 s

IES (EE) 200434. Which of the following equations gives the steady-state error for a unity-feedback system excited by

us t tus t t2 us2(a)

1

2 Kp 1

Kv 1

Ka(b)

1

1 Kp 1

Kv 2

Ka

(c)1

Kp 1

Kv 1

Ka(d)

1

1 Kp 1

Kv 1

Ka

IES (EE) 200435. The steady-state error, due to a ramp input for a type-2 system, is equal to

(a) Zero (b) Innite(c) Non-zero number (d) Constant

IES (EE) 200136. Which of the following is the steady-state error of a control system with step-error, ramp-error and

parabolic-error constants Kp; Ku Ka; respectively, for the input 1 t2 3 t ?(a)

3

1 Kp 3

2Ka(b)

3

1 Kp 6

Ka

(c)3

1 Kp 3

Ka(d)

3

1 Kp 6

KaIES (EE) 2005

37. The steady-state error of the type-1 second-order system to unit-ramp input is

(a) 2vn (b) 2=vn(c) 4=vn (d) None of these

38. The unit-step response of a second-order linear system, with zero initial states, is given by

ct 1 1:25e6t sin8t tan11:333; t 0The damping ratio and the undamped natural frequency of oscillation of the system are, respectively

(a) 0.6 and 10 rad/s (b) 0.6 and 12.5 rad/s(c) 0.8 and 10 rad/s (d) 0.8 and 12.5 rad/s

IAS 2000


39. If a second-order systemhas poles at 1 j, then the step response of the systemwill exhibit a peakvalue at(a) 4.5 s (b) 3.5 s(c) 3.14 s (d) 1 s

IAS 200140. In a continuous data system:

(a) Data may be a continuous function of time at all points in the system.(b) Data is necessarily a continuous function of time at all points in the system.(c) Data is continuous at the input and output parts of the system but not necessarily during

intermediate processing of the data.(d) Only the reference signal is a continuous function of time.

41. A control system, having a unit damping factor, will give

(a) A critically damped response (b) An oscillatory response(c) An undamped response (d) No response

IES (EE) 199242. Principles of homogeneity and superposition are applied to

(a) Linear time-variant systems (b) Nonlinear time-variant systems(c) Linear time-invariant system (d) Nonlinear time-invariant systems

IES (EE) 199343. The open-loop transfer function of a unity feedback control system is given by

G s Ks s 1

If the gain K is increased to innity, then the damping ratio will tend to become

(a) 1=2

p(b) 1

(c) 0 (d) 1IES (EE) 1993

44. The transfer system of a control system is given as

T s Kx2 4s K

whereK is the gain of the system in radians/amp. For this system to be critically damped, the value ofK should be

(a) 1 (b) 2(c) 3 (d) 4

IES (EE) 199645. Consider the following statements with reference to a system with velocity-error constant,

Kc 1000:1. The system is stable. 2. The system is of type 1.3. The test signal used is a step input.


Which of these statements are correct?(a) 1 and 2 (b) 1 and 3(c) 2 and 3 (d) 1, 2 and 3

IES (EE) 200346. The response ct to a system is described by the differential equation

d2c t dt2

4 dc t dt

5c t 0

The system response is:

(a) Undamped (b) Underdamped(c) Critically damped (d) Oscillatory

IES (EC) 199947. Consider the following transfer functions:

1:1

s2 s 1 2:4

s2 2s 4

3:2

s2 2s 2 4:1

s2 2s 1

5:3

s2 6s 3

Which of the above transfer functions represents underdamped second-order systems?

(a) 4 and 5 (b) 1, 4 and 5(c) 1, 2 and 3 (d) 1, 3 and 5

IES (EE) 200448. The open-loop transfer function of a unity-feedback control system is given by

G s Ks s 1

If the gain K is increased to innity, then the damping ratio will tend to become

(a) Zero (b) 0.707(c) Unity (d) Innite

IES (EE) 200549. Consider the following statements in connection with the differential equation

4d2y

dt2 36y 36x

1. The natural frequency of the response is 6 rad/sec.2. The response is always oscillatory.3. The percentage overshoot is 10%, and damping ratio of the system is 0.6.4. Both system time constant and settling time are innite.


Which of the statements given above are correct?

(a) 1 and 3 (b) 2 and 4(c) 1, 2 and 3 (d) 2, 3 and 4

IES (EE) 200550. A second-order system exhibits 100% overshoot. Its damping coefcient is:

(a) Equal to 0 (b) Equal to 1(c) Less than 1 (d) Greater than 1

IES (EE) 199851. For a second-order system

2d2y

dt2 4 dy

dt 8y 8x

the damping ratio is

(a) 0.1 (b) 0.25(c) 0.333 (d) 0.5

IES (EC) 199252. In the type-1 system, the velocity error is:

(a) Inversely proportional to the bandwidth of the system

(b) Directly proportional to gain constant

(c) Inversely proportional to gain constant

(d) Independent of gain constantIES (EC) 1992

53. A unity-feedback control system has a forward-path transfer function equal to

42:25

s s 6:5 The unit-step response of this system, starting from rest, will have its maximum value at a timeequal to

(a) 0 sec (b) 0.56 sec(c) 5.6 sec (d) Innity

IES (EC) 199354. Match the system open-loop transfer functions given in List I with the steady-state errors produced

for a unit-ramp input. Select the correct answer using the codes given below the lists:

List I List II

A.30

s2 6s 9 1. Zero

B.30

s2 6s 2. 0.2

C.30

s2 9s 2. 0.3

D.s 1s2

4. Innity



IES (EC) 199355. A plant has the following transfer function

Gs 1s2 0:2s 1

For a step input, it is required that the response settles to within 2% of its nal value. The plantsettling time is

(a) 20 s (b) 40 s(c) 35 s (d) 45 s

IES (EC) 200356. A second-order control system is dened by the following differential equation:

4d2c t dt2

8 dc t dt

16c t 16u t

The damping ratio and natural frequency for this system are respectively

(a) 0.25 and 2 rad/s (b) 0.50 and 2 rad/s(c) 0.25 and 4 rad/s (d) 0.50 and 4 rad/s

IES (EE) 200157. Assuming the transient response of a second-order system to be given by

c t 1 e4t1 2

p sinvn1 2

p

the setting time for the 5% criterion will be

(a) 1/4 s (b) 3/4 s(c) 5/4 s (d) 4 s

IES (EC) 199458. Consider the systems with the following open-loop transfer functions:

1:36

s s 3:6 2:100

s s 5 3:

6:25

s s 4 The correct sequence of these systems in increasing order of the time taken for the unit-stepresponse to settle is

(a) 1, 2, 3 (b) 3, 1, 2(c) 2, 3, 1 (d) 3, 2, 1

IES (EC) 1994


59. Match List I with List II and select the correct answer using the codes given below the lists:

List I (Characteristic equation) List II (Nature of damping)

A. s2 15s 26:25 1. UndampedB. s2 5s 6 2. Under-dampedC. s2 20:25 3. Critically dampedD. s2 4:55s 42:25 4. Overdamped


IES (EC) 199460. For the control system in Figure P4.68 to be critically damped, the value of gain K required is:

(a) 1 (b) 5.125(c) 6.831 (d) 10

IES (EC) 199561. A system has an open-loop transfer function

G s 10s s 1 s 2

What is the steady-state error when it is subjected to the input

r t 1 2t 32t2 ?

(a) Zero (b) 0.4(c) 4 (d) innity

IES (EC) 199562. Consider a unit-feedback control system shown in Figure P4.69. The ratio of the time constants of

the open-loop response to the closed-loop response will be:

2s2 + 7s + 2

+

R(s) C(s)K


R(s) C(s)+

2

4s +



(a) 1:1 (b) 2:1(c) 3:2 (d) 2:3

IES (EC) 199563. Consider the following overall transfer function for a unity feedback system

4

s2 4s 4Which of the following statements regarding this system are correct?

1. Position error constant Kp for the system is 4.2. The system is of type one.3. The velocity-error constant Kv for the system is nite.

Select the correct answer using the codes given below:

(a) 1, 2 and 3 (b) 1 and 2(c) 2 and 3 (d) 1 and 3

IES (EC) 199664. A rst-order system is shown in Figure P4.70. Its time response to a unit-step input is given by

(a) c t 1=T et=T (b) c t T1 et=T(c) c t 1 et=T (d) c t Tet=T

IES (EC) 199665. For a unity-feedback system, the open-loop transfer function is

G s 16 s 2 s2 s 1 s 4

What is the steady-state error if the input is r t 2 3t 4t2 u t ?(a) 0 (b) 1(c) 2 (d) 3 IES (EC) 1996

66. A system has a transfer function

C s R s

4

s2 1:6s 4For the unit-step response, the settling time (in seconds) for 2% tolerance band is

(a) 1.6 (b) 2.5(c) 4 (d) 5

IES (EC) 1996

R(s) C(s)11 sT+



67. A second-order system has the damping ratio and undamped natural frequency of oscillationvn. The settling time at 2% tolerance band of the system is

(a)2

vn(b)

3

vn

(c)4

vn(c) vn

IES (EC) 200068. Which of the following is the steady-state error for a step input applied to a unity-feedback system

with the open-loop transfer function

G s 10s2 14s 50 ?

(a) ess 0 (b) ess 0:83(c) ess 1 (d) ess 1

IES (EC) 200169. In the system shown in Figure P4.71, where

r t 1 2t t 0 the steady-state value of the error et is equal to(a) Zero (b) 2/10(c) 10/2 (d) Innity

IES (EE) 200170. Consider the unity-feedback system as shown in Figure P4.72. The sensitivity of the steady-state

error to change in parameter K and parameter a with ramp inputs are respectively(a) 1, 1 (b) 1, 1(c) 1, 0 (d) 0, 1

IES (EC) 200271. When the time period of an observation is large, the type of error is:

(a) Transient error (b) Steady-state error(c) Half-power error (d) Position-error constant

IES (EC) 2003

r(t) e(t) C(t)+

210( 1)

( 2)

ss s

++


r(t) e(t) C(t)+2

10( 1)

( 2)

ss s

++



72. What is the unit-step response of a unity-feedback control system having forward-path transferfunction

G s 80s s 18 ?

(a) Overdamped (b) Critically damped(c) Underdamped (d) Undamped oscillatory

IES (EC) 200473. What is the steady-state error for a unity-feedback control system having

G s 1s s 1

due to unit-ramp input?(a) 1 (b) 0.5

(c) 0.25 (d)0:5

pIES (EC) 2005

74. Given a unity-feedback system with

G s Ks s 4

what is the value of K for a damping ratio of 0.5?

(a) 1 (b) 16(c) 4 (d) 2

IES (EC) 200575. Match List I (System G(s)) with List II (Nature of response), and select the correct answer using the

codes given.

List I (System G(s)) List II (Nature of response)

A.400

s2 12s 400 1. Undamped

B.900

s2 90s 400 2. Critically damped

C.225

s2 30s 225 3. Underdamped

D.625

s2 0s 225 4. Overdamped


IES (EC) 200576. An underdamped second-order system with negative damping will have the two roots:

(a) On the negative real axis as real roots

(b) On the left-hand side of the complex plane as complex roots


(c) On the right-hand side of the complex plane as complex conjugates

(d) On the positive real axis as real rootsIES (EC) 2005

77. Which of the following expresses the time at which second peak in step response occurs for a second-order system?

(a)

vn1 2

p (b) 2vn

1 2

p(c)

3

vn1 2

p (d) 1 2

pIES (EC) 2005

78. The steady-state error of a stable of type 0 unity-feedback system for a unit-step function is

(a) 0 (b) 1=1 Kp(c) 1 (d) 1=Kp

GATE (EC) 199079. A second-order system has a transfer function given by

G s 25s2 8s 25

If the system, initially at rest, is subjected to a unit-step input at t 0, the second peak in theresponse will occur at(a) s (b) =3 s(c) 2=3 s (d) =2 s

GATE (EC) 199180. A unity-feedback control system has an open-loop transfer function

G s 4 1 2s s2 s 2

If the input to the system is a unit ramp, the steady-state error will be

(a) 0 (b) 0.5(c) 2 (d) Innity

GATE (EC) 199181. The step-error coefcient of a system

G s 1s 6 s 1

with unity feedback is

(a) 1=6 (b) 1(c) 0 (d) 1

GATE (EC) 199582. Consider a unity-feedback control system with open-loop transfer function

G s Ks s 1


The steady-state error of the system due to a unit-step input is

(a) Zero (b) K(c) 1/K (d) Innite

GATE (EC) 199883. For a second-order system with the closed-loop transfer function

T s 9s2 4s 9

the settling time for 2% band, in seconds, is:

(a) 1.5 (b) 2.0(c) 3.0 (d) 4.0

GATE (EC) 199984. If the characteristic equation of a closed-loop system is s2 2s 2 0, then the system is

(a) Overdamped (b) Critically damped(c) Underdamped (d) Undamped

GATE (EC) 200185. Consider a system with a transfer function

G s s 6Ks2 s 6

Its damping ratio will be 0.5 when the value of K is

(a) 2/6 (b) 3(c) 1/6 (d) 6

GATE (EC) 200286. The transfer function of a system is

G s 100s 1 s 100

For a unit-step input to the system, the approximate setting time for 2% criterion is:

(a) 100 s (b) 4 s(c) 1 s (d) 0.1 s

GATE (EE) 200287. For a feedback-control system of type 2, the steady-state error for a ramp input is:

(a) Innite (b) Constant(c) Zero (d) Interminate

GATE (EE) 199688. A unit-feedback system has an open-loop transfer function G(s). The steady-state error is zero for

(a) Step input and type-1 G(s) (b) Ramp input and type-1 G(s)(c) Step input and type-0 G(s) (d) Ramp input and type-0 G(s)

GATE (EE) 200089. A unity-feedback system has an open-loop transfer function

Gs 25ss 6


The peak overshoot in the step-input response of the system is approximately equal to:

(a) 5% (b) 10%(c) 15% (d) 20%

GATE (EE) 200090. If the ramp input is applied to a type-2 system, the steady-state error is:

(a) Positive constant (b) Negative constant(c) Zero (d) Positive innity

GATE (EE) 200091. Consider the unit-step response of a unity-feedback control system, whose open-loop transfer

functions is

Gs 1ss 1

The maximum overshoot is equal to

(a) 0.143 (b) 0.153(c) 0.163 (d) 0.173

GATE (EE) 199692. An open-loop transfer function of a unity-feedback system is given by

K

s s 1 If the value of gain K is such that the system is critically damped, the closed-loop poles of the systemwill lie at:

(a) 0.5 and 0.5 (b) j0:5(c) 0 and 1 (d) 0.5 j0:5

GATE (EE) 200293. The block diagram shown in Figure P4.73 gives a unity-feedback closed-loop control system. The

steady-state error in the response of the above system to the unit-step input is:

(a) 25% (b) 0.75%(c) 6% (d) 33%

IES (EE) 200194. A block diagram of a closed-loop control system is given in Figure P4.74. The values of K and P are

respectively (such that the system has a damping ratio of 0.7 and an undamped natural frequency,vn,of 5 rad/sec):

(a) 20 and 0.3 (b) 20 and 0.2(c) 25 and 0.3 (d) 25 and 0.2

u(t) + v(t)

3

15s +15

1s +



IES (EC) 199795. The unit-impulse response of a second-order underdamped system, starting from rest, is given by

ct 12:5e6t sin 8t; t 0The steady-state value of the unit-step response of the system is equal to:

(a) 0 (b) 0.25(c) 0.5 (d) 1.0

GATE (EE) 200496. In the case of a second-order system described by a differential equation

Jd20dt2

F d0dt

k0 kiwhere i and 0 are the input and output shaft angles, the natural frequency is given by:

(a)K=J

p(b)

J=K

p(c)

KJ

p(d)

K Jp

IES (EC) 199797. Assuming unit-ramp input match List I (System type) with List II (Steady-state error), and select the

correct answer using the codes given below the lists:

List I (system type) List II (steady-state error)

A. 0 1. KB. 1 2. 1C. 2 3. 0D. 3 4. 1=4


IES (EC) 200398. A unity-feedback second-order control system is characterized by

G s Ks Js B

s( s + 2)K

+ C(s)R(s)

1 + sP



where J moment of inertia, K system gain and B viscous damping coefcient. The transientresponse specication, which is not affected by variation of system gain, is the:

(a) Peak overshoot (b) Rise time(c) Settling time (d) Damped frequency of oscillation

IES (EE) 199799. A linear second-order system with the transfer function

G s 49s2 16s 49

is initially at rest and is subjected to a step-input signal. The response of the system will exhibit apeak overshoot of:

(a) 16% (b) 9%(c) 2% (d) Zero

IES (EE) 1998100. The unit-impulse response of a linear time-invariant second-order system is

gt 10e8t sin 6t t 0The natural frequency and the damping factor of the system are respectively

(a) 10 rad/s and 0.6 (b) 10 rad/s and 0.8(c) 6 rad/s and 0.6 (d) 6 rad/s and 0.8

IES (EE) 1999101. If a jb are the complex conjugate roots of a characteristic equation of a second-order system,

then its damping coefcient and natural frequency will be respectively:

(a)b

a2 b2p anda2 b2

p(b)

ba2 b2p

(c)a

a2 b2p anda2 b2

p(d)

aa2 b2p and a

2 b2IES (EE) 2000

102. A unity-feedback control system has a forward-path transfer function

G s 10 1 4s s2 1 s

If the system is subjected to an input

rt 1 t t2

2t 0

then the steady-state error of the system will be:

(a) Zero (b) 0.1(c) 10 (d) Innity

IES (EE) 2000103. The effect of error-rate damping is:

(a) To reduce steady-state error (b) Delay the response(c) To provide larger settling time (d) None of the above


Chapter 5

1. If the characteristic equation of a system is s3 14s2 56s k 0 then it will be stable only if:

(a) 0 < K < 784 (c) 10 > K > 600(b) 1 < K < 64 (d) 4 < K < 784

IAS 19942. The rst two rows of Rouths tabulation of a fourth-order system are:

s4 1 10 5s3 2 20

The number of roots of the system lying on the right half of the s-plane is:

(a) Zero (b) 2(c) 3 (d) 4

IAS 19963. The rst stability test showed the sign as follows:Rows I II III IV V VI VIISigns + + + + +The number of roots of the system lying the right half of the s-plane is:

(a) 2 (b) 3(c) 4 (d) 5

IAS 1998

4. For the block diagram shown in Figure P5.21, the limiting values of K for the stability of inner loopis found to be x < K < y, the overall system will be stable if and only if:

(a) 4x < K < 4y (b) 2x < K < 2y(c) x < K < y (d) x=2 < K < y=2

IES (EE) 2000



5. A system with the characteristic equation s4 2s3 11s2 18s 18 0 will have a closed-looppoles such that:

(a) All poles lie in the left half of the s-plane.(b) All poles lie in the right half of the s-plane.(c) Two poles lie symmetrically on the imaginary axis of the s-plane.(d) No pole lies on the imaginary axis of the s-plane.

IAS 1993

6. By properly choosing the value of K, the output c(t) of the system (as shown in Figure P5.22) can bemade to oscillate sinusoidally at a frequency (in rad/s) of:

(a) 1 (b) 2(c) 3 (d) 4

IAS 19937. Which one of the following statements is true for the system shown in Figure P5.23?

(a) Open-loop system is unstable but closed-loop system is stable.(b) Open-loop system is stable but closed-loop system is unstable.(c) Both open-loop and closed-loop system are stable.(d) Both open-loop and closed-loop systems are unstable.

IAS 1993

Ks(s+1)(s+4)

c(t)




8. Match List I with List II and select the correct answer using the codes given below the lists:

List I (Roots in the s-plane) List II (Corresponding impulse response)


Codes: A B C D A B C D

(a) 5 1 2 4 (b) 3 4 2 1(c) 5 2 1 4 (d) 4 3 1 5

IAS 1995

9. Consider the following statements regarding the stability analysis by RouthHurwitz criterion.

1. For a system to be stable, all the coefcients of the characteristic equation must be present and ofthe same sign.

2. If a system is to be stable, there should not be any sign change in the rst column of the Routhsarray.

3. The order of the auxillary equation obtained from the elements of the Rouths table is alwaysodd.


(a) 1 and 2 are correct.(b) 2 and 3 are correct.(c) 1 and 3 are correct.(d) 1, 2 and 3 are correct.

IAS 1999

10. A closed-loop system is shown in Figure P5.24. The largest possible value of for which the systemwould be stable is:

(a) 1 (b) 1.1(c) 1.2 (d) 2.3

IES (EC) 1998

11. The number of roots in the left-half of s-plane for the equation s3 4s2 s 6 0 would be(a) 1 (b) 2(c) 3 (d) 4

IAS 2001



12. The characteristic equation of a feedback-control system is s3 Ks2 5s 10 0 for the system tobe critically stable, the values of K should be

(a) 1 (b) 2(c) 3 (d) 4

IES (EE) 199913. A closed-loop system is stable when all its poles in the s-plane lie

(a) On the positive real axis (b) On the imaginary axis(c) In the left half (d) In the right half IAS 2002

14. Consider the equation 2s4 s3 3s2 5s 10 0. The number of roots this equation has in theright half of the s-plane is:

(a) One (b) Two(c) Three (d) Four

IAS 200315. The feedback system shown in Figure P5.25 is stable for all values of K is given by:

(a) K > 0 (b) K < 0(c) 0 < K < 42 (d) 0 < K < 60

IAS 200316. For making an unstable system stable:

(a) Gain of the system should be increased.(b) Gain of the system should be decreased.(c) The number of zeros to the loop transfer function should be increased.(d) The number of poles to the loop-transfer function should be increased.

IES (EE) 199217. While forming a Rouths array, the situation of a row zeros indicates that the system:

(a) Has symmetrically located roots (b) Is not sensitive to variations in gain(c) Is stable (d) Is Unstable

IES (EC) 199718. The characteristic equation of a closed-loop system is given by s4 6s3 11s2 6s k 0: Stable

closed-loop behavior can be ensured when the gain K is such that:

(a) 0 < K < 10 (b) K > 10(c) 1 K < 1 (d) 0 < K 20

IES (EE) 1993



19. By a suitable choice of the scalar parameter K, the system shown in Figure P5.26 can be made tooscillate continuously at a frequency of:

(a) 1 rad/s (b) 2 rad/s(c) 4 rad/s (d) 8 rad/s

IES (EE) 1993

20. The open-loop transfer functions with unity feedback are given below for different systems:

1. G s 2s 2 2. G s

2

s s 2

3. Gs 2s2s 2 4. G s

2 s 1 s s 2

Among these systems, the unstable system is

(a) 1 (b) 2(c) 3 (d) 4

IES (EE) 1993

21. The open-loop transfer function of a control system is given by

K s 10 s s 2 s a

The smallest possible value of a for which this system is stable in a closed loop for all positive valuesof K is:

(a) 0 (b) 8(c) 10 (d) 12

IES (EE) 1994

22. The open-loop transfer function of a unity-feedback control system is given by

G s K s 2 s 1 s 7 For K > 6, the stability characteristic of the open-loop and closed-loop conguration of the systemare, respectively:

(a) Stable and stable (b) Unstable and stable(c) Stable and unstable (d) Unstable and unstable

IES (EE) 1994



23. The open-loop transfer function of a system is given by

G s Ks s 2 s 4

The value of K which will cause sustained oscillations in the closed-loop unity feedback, is:

(a) 16 (b) 32(c) 48 (d) 64

IES (EE) 1996

24. The characteristic equation 1 G(s)H(s) 0 of a system is given by s4 6s3 11s2 6s K 0. For the system to be stable, the value of the gain K should be:(a) Zero (b) Greater than zero but less than 10(c) Greater than 10 but less than 20 (d) Greater than 20 but less than 30

IES (EE) 1996]

25. The characteristic equation for a third-order is q(s) a0s3 a1s2 a2s a3 0: For the third-order system to be stable, besides that all the coefcients have to be positive, which one of thefollowing has to be satised as a necessary and sufcient condition?

(a) a0a1 a2a3 (b) a1a2 a0a3(c) a2a3 a1a0 (d) a0a3 a1a2 IES (EE) 2004

26. For which of the following values of K, the feedback, shown in Figure P5.27, is stable?

(a) K > 0 (b) K < 0(c) 0 < K < 42 (d) 0 < K < 6 0

IES (EE) 2005

27. Consider the equation 2s4 s3 3s2 5s 10 0: How many roots does this equation have inthe right half of the s-plane?

(a) One (b) Two(c) Three (d) Four

IES (EE) 2005



28. When all the roots of the characteristic equation are found in the left of an s-plane, the responsedue to the initial condition will:(a) Increase to innity as time approaches innity(b) Decrease to zero as time approaches innity(c) Remain constant for all time(d) Be oscillating

IES (EC) 199229. Match List I with List II and select the correct answer by using the codes given below the lists:

List I (characteristic root location) List II (system characteristic)

A. (1 j), (1j) 1. Marginally stableB. (2 j), (2j), (2j), (2j) 2. UnstableC. j, j, 1, 1 3. StableCodes: A B C A B C(a) 1 2 3 (b) 3 1 2(c) 2 3 1 (d) 1 3 2 IES (EC) 1992

30. Match List I with List II and select the correct answer by using the codes given below the list:

List I (Roots in the s-plane) List II (Impulse response)

A. Two imaginary roots

B. Two complex roots in the right half plane

C. A single root on the negative real axis

D. A single root at the origin

Codes: A B C D

(a) 2 3 1 4(b) 1 2 3 4(c) 4 3 2 1(d) 3 2 4 1

IES (EC) 1992


31. Howmany roots of the characteristic equation s5 s4 2s3 2s2 3s 15 0 lie in the left halfof the s-plane?

(a) 1 (b) 2(c) 3 (d) 5

IES (EC) 199332. Acontrol system is shown in Figure P5.28. Themaximumvalue of the gainK for which the system is

stable is:

(a)3

p(b) 3

(c) 4 (d) 5 IES(EC) 1993

33. Consider the following statements regarding the number of sign change in the rst column of Routhin respect of the characteristic equation s2 2as 4 :1. If a ", where " is near to zero, number of sign changes will be equal to zero.2. If a 0, the number of sign change will be equal to one.3. If a "; where " near zero, the number of sign changes will be equal to two.Of these statements:

(a) 1, 2 and 3 are correct (b) 1 and 2 are correct(c) 2 and 3 are correct (d) 1 and 3 are correct

IES (EC) 199434. The value of K for which the unity-feedback system

G s Ks s 2 s 4

crosses the imaginary axis is

(a) 2 (b) 4(c) 6 (d) 48

IES (EC) 199735. The rst column of a Routh array is:

s5 1s4 2s3 3=2s2 1=3s1 10s0 2



How many roots of the corresponding equation are there in the left of the s-plane?

(a) 2 (b) 3(c) 4 (d) 5

IES (EC) 199636. The characteristic equation of a system is given by 3s4 10s3 5s2 2 0. This system is:

(a) Stable (b) Marginally stable(c) Unstable (d) None of (a), (b) or (c)

IES (EE) 200237. The loop transfer function of Q closed-loop system is given by

G s H s ks2 s2 2s 2

The angle of departure of the root locus at s 1 j is(a) Zero (b) 90(c) 90 (d) 180

IES (EC) 199838. The RouthHurwitz criterion cannot be applied when the characteristic equation of the system

contains any coefcients which is:

(a) Negative real and exponential functions of s(b) Negative real, both exponential and sinusoidal functions of s(c) Both exponential and sinusoidal functions of s(d) Complex, both exponential and sinusoidal functions of s

IES (EC) 200039. Which one of the following characteristics equations can result in a stable operation of the feedback

system?

(a) s3 4s2 s 6 0 (b) s3 s2 5s 6 0(c) s3 4s2 10s 11 0 (d) s4 s3 2s2 4s 6 0

IES (EC) 200040. Consider the following statements: RouthHurwitz criterion gives

1. Absolute stability2. The number of roots lying on the right half of the s-plane.3. The gain margin and phase margin

Which of the statements are correct?


IES (EC) 200041. The given characteristic polynomial s4 s3 2s 3 0 has:

(a) Zero root in the RHS of the s-plane (b) One root in the RHS of the s-plane(c) Two roots in the RHS of the s-plane (d) Three roots in the RHS of the s-plane

IES (EC) 2001


42. A system has a single pole at the origin. Its impulse response will be:

(a) Constant (b) Ramp(d) Decaying exponential (d) Oscillatory

IES (EC) 2002

43. Match List I (Polezero plot of linear control system) with List II (Response of the system), and selectthe correct answer using the codes given below the lists:

List I (Polezero plot of linear control system) List II (Response of the system)

1.

2.

4.

3.


Codes: A B C D

(a) 4 3 1 2(b) 4 3 2 1(c) 3 4 2 1(d) 3 4 1 2

IES (EC) 2002

44. The characteristic equation of a control system is given by

s6 2s5 8s4 12s3 20s2 16s 16s 0

The number of the roots of the equation, which lie on the imaginary axis of the s-plane, is:

(a) Zero (b) 2(c) 4 (d) 6

IES (EC) 2003

45. The closed-loop system shown in Figure P5.29 becomes marginally stable, if the constant K ischosen to be:

(a) 10 (b) 20(c) 30 (d) 40

IES (EE) 2002

46. An open loop system has a transfer function

1

s3 1:5s2 s 1It is converted into a closed-loop system by providing negative feedback having transfer function20(s 1). Which one of the following is correct?The open loop and closed loop system are respectively:

(a) Stable and stable (b) Stable and unstable(c) Unstable and stable (d) Unstable and unstable

IES (EC) 2004



47. An electromechanical closed-loop control system has the characteristic equation s3 6Ks2 K 2 s 8 0; where K is the forward gain of the system. The condition for the closed-loopstability is:

(a) K 0.528 (b) K 2(c) K 0 (d) K 2528

GATE (EC) 199048. The characteristic equation of a feedback control system is given by s3 5s2 K 6 s K 0;

where K > 0 is a scalar variable parameter. In the rootloci diagram of the system, the asymptotesof the rootlocus for large values of K meet at a point in the s-plane, whose coordinates are:

(a) (3, 0) (b) (2, 0)(c) (1, 0) (d) (2, 0)

GATE (EC) 199149. For a second-order system, damping ratio, ; is 0 < < 1, then the roots of the characteristic

polynomial are:

(a) Real but not equal (b) Real and equal(c) Complex conjugates (d) Imaginary

GATE (EC) 1995

50. The number of roots of s3 5s2 7s 3 0 in the left half of the s-plane is:(a) Zero (b) One(c) Two (d) Three

GATE (EC) 1998

51. The transfer function of a system is

2s2 6s 5s 1 2 s 2

The characteristic equation of the system is:

(a) 2s2 6s 5 0 (b) s 1 2 s 2 0(c) 2s2 6s 5 s 1 2 s 2 0 (d) 2s2 6s 5 s 1 2 s 2 0

GATE (EC) 199852. A system described by the transfer function

H s 1s3 s2 Ks 3

is stable. The constraints on a and K are:

(a) > 0; K < 3 (b) > 0; K > 3(c) < 0; K > 0 (d) > 0; K < 0

GATE (EC) 2000


53. The characteristic polynomial of a system is q s 2s5 s4 4s3 2s2 2s 1. The system is:(a) Stable (b) Marginally stable(c) Unstable (d) Oscillatory

GATE (EC) 200254. The open-loop transfer function of a unity feedback system is

G s Ks s2 s 2 s 3

The range of K for which the system is stable is:

(a) 21/44 > K > 0 (b) 13 > K > 0(c) 21/4 < K < 1 (d) 6 < K < 1

GATE (EC) 200455. For the polynomial P s s5 s4 2s3 2s2 3s 15; the number of roots that lie in the right

half of the s-plane is:

(a) 4 (b) 2(c) 3 (d) 1

GATE (EC) 2004

56. A feedback system is shown in Figure P5.30. The system is stable for all positive values of K, if:

(a) T 0 (b) T < 0(c) T > 1 (d) 0 < T < 1

IES (EE) 200057. The open-loop transfer function of a unity-feedback control system is

G s K s 10 s 20 s2 s 2

The closed-loop system will be stable, if the value of K is:

(a) 2 (b) 3(c) 4 (d) 5

IES (EE) 1998



58. The number of roots of the equation 2s4 s3 3s2 5s 7 0 that lie in the right half of thes-plane is:

(a) Zero (b) One(c) Two (d) Three

GATE (EE) 1998

59. The characteristic equation of a feedback control system is 2s4 s3 3s2 5s 10 0. Thenumber of roots in the right half of the s-plane are:

(a) Zero (b) 1(c) 2 (d) 3

GATE (EE) 2003

60. First column elements of the Rouths tabulation are 3, 5, 3/4, 1/2 and 2. It means that thereis/are:

(a) One root in the left half of the s-plane (b) Two roots in the half of the s-plane(c) Two root in the right half of the s-plane (d) One root in the right half of the s-plane

IES (EC) 1999

61. The loop gain GH of a closed-loop system is given by

K

s s 2 s 4

The value of K for which the system just becomes unstable, is:

(a) K 6 (b) K 8(c) K 48 (d) K 96

GATE (EE) 2003

62. A unity-feedback system having an open-loop gain

G s H s K 1 s 1 s

becomes stable when:

(a) | K | > 1 (b) K > 1(c) | K | < 1 (d) K

(c) One negative real root, two imaginary roots and two roots with positive real parts(d) One positive real root, two imaginary roots and two roots with negative real parts

GATE (EE) 2006

64. The characteristic equation of a control system is given by ss 4s2 2s 2 Ks 1 0.What are the angles of the asymptotes for the root loci for K 0?(a) 608, 1808, 3008 (b) 08, 1808, 3008(c) 1208, 1808, 2408 (d) 08, 1208, 2408

IES (EE) 2005

65. Figure P5.64 shows the Nyquist plot of the open-loop transfer function G(s)H(s) of a system. IfG(s)H(s) has one right-hand pole, the closed-loop system is:

(a) Always stable(b) Unstable with one closed-loop right-hand poles(c) Unstable with two closed-loop right-hand poles(d) Unstable with three closed-loop right-hand poles

GATE (EC) 2003

66. For the equation s3 4s2 s 6 0; the number of roots in the left half of the s-plane will be:(a) Zero (b) One(c) Two (d) Three

GATE (EE) 2004

Figure P5.64


Chapter 6

1. Which one of the following application software is used to obtain an accurate root locus plot?

(a) LISP (b) MATLAB(c) dBASE (d) Oracle

IES (EC) 2003

2. Despite the presence of a negative feedback, control systems still have problems of instabilitybecause the:

(a) Components used have nonlinearities.(b) Dynamic equations of the subsystems are not known exactly.(c) Mathematical analysis involves approximations.(d) The system has a large negative phase angle at high frequencies.

GATE (EC) 2005

3. The open-loop transfer function of unity-feedback control system is

G s Ks s a s b ; 0 < a b

The system is stable if:

(a) 0 < K 0?

IES (EE) 199623. The open-loop transfer function of a feedback-control system is given by

G s H s K s 2 s s 4 s2 4s 8

In the root-locus diagram of the system, the asymptotes of the root-loci for large values ofK meet at apoint in the s-plane. Which one of the following is the set of coordinates of that point?

(a) (1, 0) (b) (2, 0)(c) (10/3, 0) (d) (2, 0)

IES (EE) 1996


24. Consider the following statements with reference to the root loci of the characteristic equation ofunity-feedback control system with an open-loop transfer function of

G s K s 1 s 3 s 5 s s 2 s 4

1. Reach locus starts at an open-loop pole and ends either at an open-loop zero or innity.2. Reach locus starts at an open-loop pole or innity and ends at an open-loop zero.3. There are three separate root loci.4. There are ve separate root loci.

Which of these statements are correct?


IES (EE) 2003

25. The loop transfer function of a system is given by

G s H s K s 10 s 100 s s 25 2

The number of loci terminating at innity is:

(a) 0 (b) 1(c) 2 (d) 3

IES (EE) 200326. A control system has

G s H s Ks s 4 s2 4s 20 ; 0 < K <

What is the number of breakaway points in the root locus diagram?

(a) One (b) Two(c) Three (d) Zero

IES (EE) 200427. An open-loop transfer function of a feedback system has m poles and n zeros (m > n). Consider the

following statements:

1. The number of separate root loci is m.2. The number of separate root loci is n.3. The number of root loci approaching innity is (m n).4. The number of root loci approaching innity is (m n).Which of the statements given above are correct?


IES (EE) 200528. Consider the root-locus diagram (Figure P6.28) of a system and the following statements:

1. The open-loop system is a second-order system.2. The system is overdamped for K > 1.3. The system is absolutely stable for all values of K.


Which of these statements are correct?


IES (EC) 199229. A transfer function G(s) has type pole-zero plot, as shown in Figure P6.29. Given that the steady-

state gain is 2, the transfer function G(s) will be given by:

(a)2 s 1

s2 4s 5 (b)5 s 1

s2 4s 4(c)

10 s 1 s2 4s 5 (d)

10 s 1 s 2 2

IES (EC) 199330. In the root locus for open-loop transfer function

G s H s K s 6 s 3 s 5

the breakaway and break-in points are located respectively at:

(a) 2 and 1 (b) 2.47 and 3.77(c) 4.27 and 7.73 (d) 7.73 and 4.27

IES (EC) 199431. If the open-loop transfer function of the system is

G s H s K s 10 s s 8 s 16 s 72

then a closed-loop pole will be located at s 12 when the value of K is:(a) 4355 (b) 5760(c) 9600 (d) 9862

IES (EC) 1994




32. A unity-feedback system has

G s Ks s 1 s 2

In the root locus, the breakaway point occurs between:

(a) s 0 and 1 (b) s 1 and 1(c) s 1 and 2 (d) s 2 and 1

IES (EC) 199533. The loop-transfer function of a feedback control system is given by

GsHs Kss 2s2 2s 2

The number of asymptotes of its root loci is:

(a) 1 (b) 2(c) 3 (d) 4

IES (EC) 199634. Which of the following effects are correct in respect of addition of a pole to the system loop transfer

function?

1. The root locus is pulled to the right.2. The system response becomes slower.3. The steady state error increases.


(a) 1 and 2 are correct. (b) 1, 2 and 3 are correct.(c) 2 and 3 are correct. (d) 1 and 3 are correct.

IES (EC) 199835. The intersection of asymptotes of root-loci of a system with the open-loop transfer function

G s H s Ks s 1 s 3

is

(a) 1.44 (b) 1.33(c) 1.44 (d) 1.33

IES (EC) 200036. The root-locus plot of the system having the loop-transfer function

G s H s Ks s 4 s2 4s 5

has(a) No breakaway point (b) Three real breakaway points(c) Only one breakaway point (d) One real and two complex breakaway points

IES (EC) 2001


37. An open-loop transfer function is given by

G s H s K s 1 s s 2 s2 2s 2

It has:

(a) One zero at innity (b) Two zeros at innity(c) Three zeros at innity (d) Four zeros at innity

IES (EC) 200138. Which of the following is the open-loop transfer function of the root loci shown in

Figure P6.30?

(a)K

s s T1 2(b)

K

s T1 s T2 2

(c)K

s T 3 (d)K

s2 sT1 1 IES (EC) 2002

39. The instrument used for plotting the root locus is called:

(a) Slide rule (b) Spirule(c) Synchro (d) Selsyn

IES (EC) 200240. A control system has

G s H s K s 1 s s 3 s 4

Root locus of the system can lie on the real axis:

(a) Between s 1 and s 3 (b) Between s 0 and s 4(c) Between s 3 and s 4 (d) Towards left of s 4

IES (EC) 2002

j

r1

r2

r3



41. Figure P6.31 shows the root locus of a unity-feedback system. The open-loop transfer function of thesystem is:

(a)K

s s 1 s 2 (b)Ks

s 1 s 2 (c)

K s 1 s s 2 (d)

K s 2 s s 1 IES (EC) 2003

42. The root loci of a feedback control system for large values of s are asymptotic to the straight lineswith angles u to the real axis given by the equation:

(a)p z 2K 1 (b)

2K 1 p z

(c) 2K(p z) (d) 2Kpz

IES (EC) 200443. Consider the following statements: In root-locus plot, the breakaway points:

1. Need not always be on the real axis alone2. Must lie on the root loci3. Must lie between 0 and1Which of these statements are correct?


IES (EC) 199944. Which of the following is not the property of root loci?

(a) The root locus is symmetrical about jv axis.(b) They start from the open-loop poles and terminate at the open-loop zeros.(c) The breakaway points are determined from dK/ds = 0.(d) Segments of the real axis are part of the root locus, if and only if the total number of real poles

and zeros to their right is odd.

IES (EC) 1995



45. An open-loop transfer function is given by

K s 3 s 5

Its root-loci will be as in

IES (EC) 199746. Given a unity-feedback system with open-loop transfer function

Gs Ks s 1 s 2

The root locus plot of the system is of the form:

GATE (EC) 1992


47. If the open-loop transfer function is a ratio of a numerator polynomial of degreem and a denominatorpolynomial of degree n, then the integer (n m) represents the number of:(a) Break-away points (b) Unstable poles(c) Separate root loci (d) Asymptotes

GATE (EC) 199448. Consider the loop-transfer function

G s H s K s 6 s 3 s 5

In the root-locus diagram, the centroid will be located at:

(a) 4 (b) 1(c) 2 (d) 3

IES (EC) 199949. Consider the points s1 3 j4 and s2 3 j2 in the s-plane. Then, for a system with the

open-loop transfer function

G s H s Ks 1 4

(a) s1 is on the root locus, but not s2: (b) s2 is on the root locus, but not s1:(c) Both s1 and s2 are on the root locus. (d) Neither s1 nor s2 is on the root locus.

GATE (EC) 199950. Which of the following points is NOT on the root locus of a system with the open-loop transfer

function

G s H s Ks s 1 s 3

(a) s j 3p (b) s 1.5(c) s 3 (d) s 1

GATE (EC) 200251. The root locus of the system

G s H s Ks s 2 s 3

has the break-away point located at:

(a) (0.5, 0) (b) (2.548, 0)(c) (4,0) (d) (0.784, 0)

GATE (EC) 200352. Given

G s H s Ks s 1 s 3

the point of intersection of the asymptotes of the root loci with the real axis is:

(a) 4 (b) 1.33(c) 1.33 (d) 4

GATE (EC) 2004


53. A unity-feedback system has an open-loop transfer function, G s K=s2: The root loci plot is:

GATE (EE) 200254. Figure P6.32 shows the root-locus plot (location of poles not given) of a third-order system whose

open-loop transfer function is:

(a)K

s3(b)

K

s2 s 1 (c)

K

s s2 1 (d)K

s s2 1

GATE (EE) 200555. The root-locus plot for an uncompensated unstable system is shown in Figure P6.33. The system is to

be compensated by a compensated zero. The most desirable of the compensating zero would be thepoint marked:

(a) A (b) B(c) C (d) D



IES (EE) 199756. The loop-transfer function GH of a control system is given by

GH Ks s 1 s 2 s 3

Which of the following statements regarding the conditions of the system root loci diagram is/are correct?1. There will be four asymptotes.2. There will be three separate root loci.3. Asymptotes will intersect at real axis at A 2=3.Which of the follwing is the correct answer?

(a) 1 alone (b) 2 alone(c) 3 alone (d) 1, 2 and 3

IES (EE) 199857. Match List-I with List-II in respect of the open-loop transfer function

G s H s K s 10 s2 20s 500

s s 20 s 50 s2 4s 5 and select the correct answer using the codes given below the lists:

List I (Types of loci) List II (Numbers)

A. Separate loci 1. oneB. Loci on the real axis 2. twoC. Asymptotes 3. threeD. Break-away points 4. ve

Codes: A B C D A B C D

(a) 3 4 2 1 (b) 3 4 1 2(c) 4 3 1 2 (d) 4 3 2 1

IES (EE) 199958. If the characteristic equation of a closed-loop system is

1 Ks s 1 s 2 0



the centroid of the asymptotes in root-locus will be:(a) Zero (b) 2(c) 1 (d) 2

IES (EE) 199959. The characteristic equation of a linear control system is s2 5Ks 10 0: The root-loci of the

system for 0 < K < 1 is:

IES (EE) 200060. The characteristic equation of a feedback control system is given by s3 5s2 K 6 s K 0:

In a root-loci diagram, the asymptotes of the root loci for large K meet at a point in the s-plane,whose coordinates are:

(a) (2, 0) (b) (1, 0)(c) (2, 0) (d) (3, 0)

IES (EE) 200161. Which of the following are the characteristics of the root locus of

G s H s K s 5 s 1 s 3

1. It has one asymptote. 2. It has intersection with jv-axis.3. It has two real axis intersection. 4. It has two zeros at innity.

Select the correct answer using the codes given below:(a) 1 and 2 (b) 2 and 3(c) 3 and 4 (d) 1 and 3

IES (EE) 2002

(a)

j

Re

K = 0

K = 0

K = K =

(b)

j

ReK = 0K = 0

K =

K =

(c) (d)

j

Re

K = 0

K = 0K = K =

j

Re

K = 0 K = 0

K =

K =


Chapter 7

1. A system is described by

X 0 12 3

x 01

u and Y 1 0x

The transfer function is:

(a)1

s2 2s 3 (b)1

2s2 3s 1(c)

1

s2 3s 2 (d)1

3s2 2s 1[IAS 1995]

2. Consider the single-input system described by the vector-matrix state equation A t But;and the output equation Yt Ct, where t is the state vector, u(t) is the control input and

A 0 11 2

; B 01

; C 1 1

The system is:

(a) Controllable and observable (b) Controllable but unobservable(c) Uncontrollable but observable (d) Uncontrollable and unobservable

[IAS 1995]

3. Which of the following systems is completely state controllable?

(a)X1X2

1 0

0 2

x1x2

2

1

u (b)

X1X2

1 0

0 2

x1x2

2

0

u

(c)X1X2

1 0

0 1

x1x2

1

0

u (d)

X1X2

0 0

2 2

x1x2

2

2

u

[IAS 1996]

4. A control system is represented as x AX BU, y CX. Consider the following statements inthis regard:

1. The pair (AB) is controllable implies that the pair (ATBT) is observable.

2. The condition of controllability depends on the matrices A and B of the system.

3. The pair (AC) is observable implies that the pair (ATCT) is controllable.



[IAS 1997]

5. The state representation for a second-order system is given by X1 x1 u, X2 x1 2x2 u.Consider the following statements regarding the above systems:

1. The system is completely state-controllable.

2. If x1 is the output, then the system is output controllable.

3. If x2 is the output, then the system is output controllable.


Of these statement:


[IAS 1997]

6. Given a system represented by equation

X 0 12 3

x 01

u; Y 1 0 x

The equivalent transfer function representation G(s) of the system is:

(a) Gs 1s2 5s 2 (b) Gs

1

s2 3s 2(c) Gs 3

s2 3s 2 (d) Gs 2

s2 2s 2 [IES 1993]7. A nonlinear system cannot be analyzed by Laplace transform because:

(a) It has no zero initial conditions.

(b) The superpositions law cannot be applied.

(c) Nonlinearity is generally not well dened.

(d) All of the above. [IES 1992]

8. Which of the following statements regarding the state transition matrix is correct?

(a) f0 0 (b) f0 0 f 1=t (c) f t1 t2 ft1 ft2 (d) f t1 t2 ft1 t0 ft2 t0

[IAS 2000]

9. A system G(s) is expressed in the state variable form as x JX Bu, y CXDu. Consider thefollowing statements with regard to the properties of Jordan canonical matrix J.

1. The diagonal elements of J are poles of G(s).

2. All the elements below the principal diagonal are zeros.

3. All the elements above the principal diagonal are zeros.

Among these statements:

(a) 1 and 3 are correct (b) 1 and 2 are correct(c) 2 alone is correct (d) 3 alone is correct

[IAS 1999]

10. For

fs s 6

s2 6s 51

s2 6s 55

s2 6s 5s

s2 6s 5

2664

3775


the coefcient matrix A is:

(a)6 5

6 0

(b)5 50 6

(c)6 0

5 6

(d)0 1

5 6

[IAS 1998]

11. A linear second-order single-input continuous time system is described by the following set ofdifferential equations:

X1 2x1 4x2, X2 2x1 x2 u(t)where x1 and x2 are state variables and u(t) is the input. The system is:

(a) Controllable and stable (b) Controllable but unstable(b) Uncontrollable and unstable (d) Uncontrollable but stable

[IAS 1998]

12. The second-order system X AX has

A 1 11 0

The values of its damping factor x and natural frequency on are respectively:

(a) 1 and 1 (b) 0.5 and 1(c) 0.707 and 2 (d) 1 and 2

[IES 1996]

13. Which of the following properties are associated with the state transition matrix (t)?

1. ft f1t2. ft1=t2 ft1 f1t23. f t1 t2 ft2 ft1Select the correct answer using the codes given below:


[IES 1996]

14. The state variable description of a single-input single-output linear system is given by: Xt AXt but and yt CXt; where

A 1 12 0

; B 0

1

; C 1 1

The system is:

(a) Controllable and observable (b) Controllable but on observable(c) Uncontrollable but observable (d) Uncontrollable and unobservable

[IES 1996]


15. A system is described by state equation

X1X2

2 0

0 2

x1x2

1

1

u

The state transition matrix of the system is:

(a)e2t 10 e2t

(b)

e2t 00 et

(c)e2t 10 e2t

(d)

e2t 10 e2t

[IES 1994]

16. The state equation of a system is

X 0 120 9

X 01

u

The poles of this system are located at:

(a) 1, 9 (b) 1, 20(c) 4, 5 (d) 9, 20

[IES 1995]

17. The system matrix of a continuous-time system, described in the state variable form, is

A x 0 00 y 10 1 2

24

35

The system is stable for all values of x and y satisfying:

(a) x

1

2(b) x >

1

2; y > 0

(c) x < 0; y < 2 (d) x < 0; y /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False

/CreateJDFFile false /Description > /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ > /FormElements false /GenerateStructure false /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles false /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /DocumentCMYK /PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged /UntaggedRGBHandling /UseDocumentProfile /UseDocumentBleed false >> ]>> setdistillerparams> setpagedevice

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