Chapter 2
1. For the network shown in Figure P2.43, ViðtÞ is the input and i(t) is the output. The transfer function I(S)=V(S) of the network is
(a) Cs LCs2þ RCs þ 1 (b) C LCs2þ RCs þ 1 (c) Cs RCs2þ LCs þ 1 (d) C RCs2þ LCs þ 1 ½IES 1993
2. For the field-controlled dc servomotor, as shown in Figure P2.44, the transfer function ðsÞ=EðsÞ contains
(a) Two times constants, no integration (b) Two times constants, one integration (c) One time constants, one integration (d) One time constants, one integration
½IES 1996
3. A mechanical system consists of two mass-spring friction system, as shown in Figure P2.45. The order of the transfer function X(s)=F(s) is
(a) 1 (b) 2 (c) 3 (d) 4 ½IES 1996 R L j(t) C Vi(t)
Figure P2.43 A network (Objective Question 1).
R Ig (Constant)
Singular relation
J1I L
Figure P2.44 Afiled-controlled servomotor.
4. Consider a multiple gear system, as shown in Figure P2.46. Which one of the following gives the equivalent inertia referred to shaft 1?
(a) J1þ J2 N1 N2 2 þ Ja N1N3 N2N4 2 (b) J1þ J2 N2 N1 2 þ J3 N2N4 N1N3 2 (c) J1þ J2 N1 N2 2 þ J3 N1N2 N3N4 2 (d) J1þ J2 N2 N1 2 þ J3 N1N2 N3N4 2 ½IES 2004 5. For the mechanical system, shown in Figure P2.47, the system is described as:
(a) Md 2y 1ðtÞ dt2 þ B dy1ðtÞ dt ¼ K y½ 2ðtÞ y1ðtÞ (c) Md 2y 1ðtÞ dt2 þ B dy1ðtÞ dt ¼ K y½ 1ðtÞ y2ðtÞ ½IES 2001 B N N B B B N N J J J
Figure P2.46 A multiple gear system.
B
M
K
y2(t) y1(t)
f(t)
Figure P2.47 A mechanical system.
(b) Md 2y 2ðtÞ dt2 þ B dy2ðtÞ dt ¼ K y½ 2ðtÞ y1ðtÞ (d) Md 2y 2ðtÞ dt2 þ B dy2ðtÞ dt ¼ K y½ 1ðtÞ y2ðtÞ 2 OBJECTIVE QUESTIONS
Chapter 3
1. Consider a signalflow graph, as in Figure P3.12.
Signalflow 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)
½IAS 1999 2. Consider a signalflow graph shown in Figure P3.13.
1 s s2 3 s 1 K K2 3 K (i) 1 s s2 3 s 1 K K2 3 K (ii) 1 s 2 s s3 1 K 2 K 3 K (iii)
Figure P3.12 Signalflow graphs for Objective Question 1.
1 b 2 b 3 b 4 b 5 b b7 8 b b9 b10 1 Z Z2 Z6
Consider the following statements regarding the signalflow 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.
½IES 1998 3. Referring to Figure P3.14, match list I (signalflow graph) with list II (transfer function), and select
the correct answer using the codes given in the following list:
List I List II A. Figure (i) 1: P 1 Q B. Figure (ii) 2: Q 1 PQ C. Figure (iii) 3: PQ 1 PQ D. Figure (iv) 4: PQ 1 P2
Figure P3.14 Signalflow graphs for Objective Question 3.
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
½IAS 2000 4. A system block diagram is shown in Figure P3.15.
The overall transfer function of the system is C
R¼
G1G2G3
1þ G1G2G3H1þ G2H2 G3G2H3 The value of X in thefigure would be equal to
(a) H3 (b) G3H3
(c) G2H3 (d) G3H3
½IAS 2001 5. The signalflow graph of the system is shown in Figure P3.16.
The transfer function CðsÞ=DðsÞ of the system is (a) G1ðsÞG2ðsÞ 1þ G1ðsÞHðsÞ (b) G1ðsÞG2ðsÞ 1 G1ðsÞG2ðsÞHðsÞ (c) G2ðsÞ 1þ G1ðsÞG2ðsÞHðsÞ (d) G2ðsÞ 1 G1ðsÞG2ðsÞHðsÞ ½IAS 2001 R(s) + + + − G1 G2 G3 1 H 2 H C X
Figure P3.15 Signalflow graphs for Objective Question 4.
6. The closed loop system shown in Figure P3.17 is subjected to a disturbance NðsÞ.
The transfer function CðsÞ=NðsÞ is given (a) G1ðsÞG2ðsÞ 1þ G1ðsÞG2ðsÞHðsÞ (b) G1ðsÞ 1þ G1ðsÞHðsÞ (c) G2ðsÞ 1þ G2ðsÞHðsÞ (d) G2ðsÞ 1þ G1ðsÞG2ðsÞHðsÞ ½IES 1997 7. The transfer function of the system shown in Figure P3.18 is
(a) O R¼ ABC 1þ ABC (b) O R¼ Aþ B þ C 1þ AB þ AC (c) O R¼ ABþ AC ABC (d) O R¼ ABþ AC 1þ AB þ AC ½IAS 1998 Figure P3.17 Signalflow graphs for Objective Question 6.
R + + − − A B O C
Figure P3.18 Signalflow graphs for Objective Question 7.
8. Three blocks G1; G2and G3are connected in some fashion such that overall transfer function is G1þ G3ð1 þ G1G2Þ
1þ G1G2 The blocks are connected in the following manner:
(a) G1; G2with negative feedback and combination in parallel with G3 (b) G1; G3with negative feedback and G2in parallel
(c) G1; G2is cascade and combination in parallel with G3 (d) G1; G3in cascade and combination in parallel with G2
½IAS 2004 9. In regeneration feedback, the transfer function is given by
(a) GðsÞ RðsÞ¼ GðsÞ 1þ GðsÞHðsÞ (b) GðsÞ RðsÞ ¼ GðsÞHðsÞ 1 GðsÞHðsÞ (c) GðsÞ RðsÞ¼ GðsÞHðsÞ 1þ GðsÞHðsÞ (d) GðsÞ RðsÞ ¼ GðsÞ 1 GðsÞHðsÞ ½IAS 1992 10. The transfer function CðsÞ=RðsÞ of the system, whose block diagram is shown in Figure P3.19, is
(a) G1G2 1þ G1H1þ G2H2 G1G2H1H2 (b) G1G2 1þ G1H1þ G2H2þ G1G2H1H2 (c) G1G2 1þ G1H1þ G2H2 (d) G1ð1 þ G2H2ÞG2ð1 þ G1H1Þ 1þ G1H1þ G2H2þ G1G2H1H2 ½IES 1993 R(S) + + C(S) − G1 − 1 H H2 2 G
11. The signalflow graph of a closed loop system is shown in Figure P3.20, wherein TDrepresents the disturbance reduces by
(a) Increasing G2ðsÞ (b) Decreasing G2ðsÞ (c) Increasing G1ðsÞ (d) Decreasing G1ðsÞ
½IES 1997 12. The response c(t) of a system to an input r(t) is given by the following different equation:
d
2cðtÞ
dt
2þ
3dcðtÞ
dt
þ 5cðtÞ ¼ 5rðtÞ
The transfer function of the system is given by(a) GðsÞ ¼ 5 s2þ 3s þ 5 (b) GðsÞ ¼ 1 s2þ 3s þ 5 (c) GðsÞ ¼ 3s s2þ 3s þ 5 (d) GðsÞ ¼ sþ 3 s2þ 3s þ 5 ½IES 1996 13. The gain CðsÞ=RðsÞ of the signal flow graph, shown in Figure P3.21, is
(a) G1G2þ G2G3 1þ G1G2H1þ G2G3H1þ G4 (b) G1G2þ G2G3 1þ G1G2H1þ G2G3H1 G4 (c) G1G3þ G2G3 1þ G1G3H1þ G2G3H1þ G4 (d) G1G3þ G2G3 1þ G1G3H1þ G2G3H1 G4 ½IES 2003 Figure P3.20 Signalflow graphs for Objective Question 11.
14. The overall gain CðsÞ=RðsÞ 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 ½IES 2003 15. From Figure P3.23, the transfer function of the signalflow graph is
(a) T12 1 T22 (b) T22 1 T12 (c) T12 1þ T12 (d) T22 1þ T12 ½IES 1992 R(S) + + + 1 G 1 H H2 2 G
Figure P3.22 Signalflow graphs for Objective Question 14.
1 X T12 22 T 2 X
Figure P3.23 Signalflow graphs for Objective Question 15. Figure P3.21 Signalflow graphs for Objective Question 13.
Chapter 4
1. The unit-impulse response of a system is given by cðtÞ ¼ 0:5et=2. Its transfer function is
(a) 1=ðs þ 2Þ (b) 1= 1 þ 2sð Þ
(c) 2= 1 þ 2sÞð (d) 2= s þ 2ð Þ
½IAS 1993 2. If the unit-step response of a system is a unit impulse function, then the transfer function of such a
system will be
(a) 1 (b) 1=s
(c) s (d) 1=s2
½IAS 1994 3. When a unit-step input is applied, a second-order underdamped system has a peak overshoot of OP occurring at tmax: If another step input, equal in magnitude to the peak overshoot OP, is applied at t¼ tmax, then the system will settle down at
(a) 1þ OP (b) 1 OP
(c) OP (d) 1:0
½IAS 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 coefficient j will decrease. (b) Both-steady state error and damping coefficient j will increase
(c) Both steady-state error and damping coefficient j will decrease. (d) Steady-state error will decrease and damping coefficient j will increase.
½IAS 1995 5. The impulse response of a system is given by
cðtÞ ¼
1
2
e
t=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
½IAS 1998 6. For the system, shown in Figure P4.59, the damping factorj and undamped natural frequency vnare
respectively (a) 2 ffiffiffiffiffi KJ p f and ffiffiffiffi J K r (b) ffiffiffiffi K J r and f 2pffiffiffiffiffiKJ (c) f 2pffiffiffiffiffiKJ and ffiffiffiffi K J r (d) 2Fffiffiffiffiffi KJ p and K J ½IAS 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
½IAS 2000 8. A unity feedback system has open loop transfer function as
GðsÞ ¼ 16 sðs þ 16Þ The natural frequency of the system is
(a) 16 (b) 8 (c) 2 (d) 4 ½IAS 2002 9. The system GðsÞ ¼ 0:8 s2þ 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
½IAS 2003 Figure P4.59 Figure for Objective Question 4.
10. The system shown in Figure P4.60 has a unit-step unit. In order that the steady-state error is 0.1, the value of K required is
(a) 0.1 (b) 0.9
(c) 1.0 (d) 9.0
½IAS (EE) 1994 11. The settling time of a feedback system with the closed-loop transfer function
C sð Þ R sð Þ¼ v2 s s2þ 2v nsþ v2n is (a) ts¼ 2 vn (b) ts¼ vn 2 (c) ts¼ 4 vn (d) ts¼ 4vn ½IAS (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
½IES (EC) 1993 Figure P4.60 Figure for Objective Question 10.
+ − 2 2 ( 1) s s + 2 ( 1) s s s++ 2 3 ( 3) s s s + +
Figure P4.61 Figure for Objective Question 12.
13. A typical control system is shown in Figure P4.62. Assuming RðsÞ ¼ 1=s; the steady-state error is (a) 1
1þ K (b) K
(c) Zero (d) 1
½IES (EC) 1995 14. The velocity-error constant Kvof a feedback system of a closed-loop transfer function
CðsÞ RðsÞ¼
GðsÞ 1þ GðsÞHðsÞ is
(a) Kv¼ Lims!0sG sð ÞH sð Þ (b) Kv¼ Lims!0s1þG sG sð ÞH sð Þð Þ (c) Kv¼ Lim
s!0sG sð Þ (d) Kv¼ Lims!0s 1½ þ G sð ÞH sð Þ
½IES (EC) 1998 15. In the derivation of expression for peak percent overshoot
Mp¼ exp ffiffiffiffiffiffiffiffiffiffiffiffiffi 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.
½GATE (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 ¼ 0 (b) a¼ 1 (c) a 4 (d) For no value of a 1 s + 20 s + 40 s(s + 10) + – R(s) K C(s)
½GATE (EE) 1992 17. A system has the following transfer function
G sð Þ ¼ 100 sð þ 5Þ s þ 50ð Þ s4ðsþ 10Þ sð2þ 3s þ 10Þ 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
½IES (EE) 1998 18. 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
½IES (EE) 1999 19. Consider the following statements regarding system shown in Figure P4.65, where m ¼ mass,
B ¼ frictional coefficient and K ¼ spring constant: 1. It represents a conservative system.
2. It has a natural frequency of undamped oscillation of pffiffiffiffiffiffiffiffiffiK=m: 3. It has a time constant of m/K of these statements.
2 s51 s s a + + + 1 4 s +
Figure P4.63 Figure for Objective Question 16.
K s(s + 2s) – + C(s) K 1 + 0.025 Input = Unit step
Figure P4.64 Figure for Objective Question 18.
(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
½IAS 1997
20. In Figure P4.66, spring constant is K, viscous friction coefficient is B, mass is M and the system output motion is x(t) corresponding to input force F(t). Which of the following parameters relates to the above system?
Here
1. The constant¼ 1=M
2. Damping coefficient ¼ B= 2 pffiffiffiffiffiffiffiKM 3. Natural frequency of oscillation¼pffiffiffiffiffiffiffiffiffiffiK=M
½IES (EE) 1995 21. The step response of a system is cðtÞ ¼ 1 5etþ 10e2t 6e3t. The impulse response of the
system is
(a) 5et 20e2tþ 18e3t (b) 5et 20e2tþ 18e3t (c) 5etþ 20e2tþ 18e3t (d) 5etþ 20e2t 18e3t
½IAS 2003 22. Given a unity feedback with
G sð Þ ¼ K s sð þ 4Þ
B = 0 m
Figure P4.65 Figure for Objective Question 4.
M k
F(t) x(t)
the value of K for damping ratio of 0.5 is
(a) 1 (b) 16
(c) 4 (d) 2
½IAS 2003 23. A unity-feedback control system has a forward-path transfer function G(s) is given by
G sð Þ ¼ 10 1ð þ sÞ s2ðsþ 1Þ s þ 5ð Þ The steady-state error due to unit parabolic input
rðtÞ ¼ t2 2UðtÞ is (a) Zero (b) 0.5 (c) 1.0 (d) Infinite ½IAS 2003 24. Damping factor and undamped natural frequency for a position control system is given by
(a) 2pffiffiffiffiffiKJ; pffiffiffiffiffiKJrespectively (b) K 2fJ; ffiffiffiffiffiffiffiffi K=J p respectively (c) f 2p ;ffiffiffiffiffiKJ ffiffiffiffiffiffiffiffi K=J p respectively (d) J 2pffiffiffiffiffiKf; ffiffiffiffiffi KJ p respectively ½IES (EE) 1992 25. Match List I (Time Domain Specification) with List II (Equation for Finding Its Value), and select the
correct answer using the codes given below the lists.
List I (Time Domain Specification) List II (Equation for Finding Its Value)
A. Peak overshoot 1.=ðvn ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 p Þ B. Peak time 2. 4= vð nÞ
C. Rise time 3. expð=pffiffiffiffiffiffiffiffiffiffiffiffiffi1 2Þ% D. Settling time (2%) 4. p fcos1½=ðvn
ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 p Þg 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 ½IAS 2004 26. 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 afluctuating error.
½IES (EE) 1992 27. If the time response of a system is given by the following equation
y tð Þ ¼ 5 þ 3 sin vt þ ð 1Þ þ e3tsinðvt þ 2Þ þ e5t then the steady-state part of the above response is given by
(a) 5þ 3 sin vt þ sð 1Þ (b) 5þ 3 sin vt þ ð 1Þ þ e3tsinðvt þ 2Þ
(c) 5þ e5t (d) 5
½IES (EE) 1996 28. The impulse response of a system is 5e10t; its step response is equal to
(a) 0:5e10t (b) 5ð1 e10tÞ
(c) 0:5ð1 e10tÞ (d) 10ð1 e10tÞ
½IES (EE) 1996 29. The transfer function of a system is 10/(1þ 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) Infinity
½IES (EE) 1996 30. The unit-impulse response of a second-order system is 1=6e0:8tsin 0:6tð Þ . 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
½IES (EE) 2003 31. A second-order control system has
M jwð Þ ¼ 100
100 v2þ 10pffiffiffi2jv Its Mp(peak magnitude) is
(a) 0.5 (b) 1
(c)pffiffiffi2 (d) 2
½IES (EE) 2003 32. Consider the following system, shown in Figure P4.67, where x(t) ¼ sin t. What will be the response
y(t) in the steady state?
x(t) y(t)
1
s s
+
(a) sin(t 458)=pffiffiffi2 (b) sin(tþ 458)=pffiffiffi2 (c)pffiffiffi2etsin t (d) sin t cos t
½IES (EE) 2004 33. 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
½IES (EE) 2004 34. Which of the following equations gives the steady-state error for a unity-feedback system excited by
usð Þ þ tut sð Þ þ tt 2 us 2 (a) 1 2þ Kp þ 1 Kv þ 1 Ka (b) 1 1þ Kp þ 1 Kv þ 2 Ka (c) 1 Kp þ 1 Kv þ 1 Ka (d) 1 1þ Kp þ 1 Kv þ 1 Ka ½IES (EE) 2004 35. The steady-state error, due to a ramp input for a type-2 system, is equal to
(a) Zero (b) Infinite
(c) Non-zero number (d) Constant
½IES (EE) 2001 36. 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 tð 2Þ3 tð Þ? (a) 3 1þ Kp 3 2Ka (b) 3 1þ Kp þ 6 Ka (c) 3 1þ Kp 3 Ka (d) 3 1þ Kp 6 Ka ½IES (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 cðtÞ ¼ 1 þ 1:25e6tsinð8t tan11:333Þ; t 0
The 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
½IAS 2000
39. If a second-order system has poles atð1 jÞ, then the step response of the system will exhibit a peak value at
(a) 4.5 s (b) 3.5 s
(c) 3.14 s (d) 1 s
½IAS 2001 40. 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
½IES (EE) 1992 42. 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
½IES (EE) 1993 43. The open-loop transfer function of a unity feedback control system is given by
G sð Þ ¼ K s sð þ 1Þ
If the gain K is increased to infinity, then the damping ratio will tend to become
(a) 1=pffiffiffi2 (b) 1
(c) 0 (d) 1
½IES (EE) 1993 44. The transfer system of a control system is given as
T sð Þ ¼ K x2þ 4s þ K
where K is the gain of the system in radians/amp. For this system to be critically damped, the value of K should be
(a) 1 (b) 2
(c) 3 (d) 4
½IES (EE) 1996 45. Consider the following statements with reference to a system with velocity-error constant,
Kc ¼ 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
½IES (EE) 2003 46. The response cðtÞ to a system is described by the differential equation
d2c tð Þ dt2 þ 4
dc tð Þ
dt þ 5c tð Þ ¼ 0 The system response is:
(a) Undamped (b) Underdamped
(c) Critically damped (d) Oscillatory
½IES (EC) 1999 47. Consider the following transfer functions:
1: 1 s2þ s þ 1 2: 4 s2þ 2s þ 4 3: 2 s2þ 2s þ 2 4: 1 s2þ 2s þ 1 5: 3 s2þ 6s þ 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
½IES (EE) 2004 48. The open-loop transfer function of a unity-feedback control system is given by
G sð Þ ¼ K s sð þ 1Þ
If the gain K is increased to infinity, then the damping ratio will tend to become
(a) Zero (b) 0.707
(c) Unity (d) Infinite
½IES (EE) 2005 49. Consider the following statements in connection with the differential equation
4d 2y
dt2þ 36y ¼ 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 infinite.
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
½IES (EE) 2005 50. A second-order system exhibits 100% overshoot. Its damping coefficient is:
(a) Equal to 0 (b) Equal to 1
(c) Less than 1 (d) Greater than 1
½IES (EE) 1998 51. For a second-order system
2d 2y dt2þ 4
dy
dtþ 8y ¼ 8x the damping ratio is
(a) 0.1 (b) 0.25
(c) 0.333 (d) 0.5
½IES (EC) 1992 52. 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 constant
½IES (EC) 1992 53. A unity-feedback control system has a forward-path transfer function equal to
42:25 s sð þ 6:5Þ
The unit-step response of this system, starting from rest, will have its maximum value at a time equal to
(a) 0 sec (b) 0.56 sec
(c) 5.6 sec (d) Infinity
½IES (EC) 1993 54. 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 s2þ 6s þ 9 1. Zero B. 30 s2þ 6s 2. 0.2 C. 30 s2þ 9s 2. 0.3 D. sþ 1 s2 4. Infinity
Codes: A B C D A B C D
(a) 1 2 3 4 (b) 4 3 2 1
(c) 1 3 2 4 (d) 4 2 3 1
½IES (EC) 1993 55. A plant has the following transfer function
GðsÞ ¼ 1
s2þ 0:2s þ 1
For a step input, it is required that the response settles to within 2% of itsfinal value. The plant settling time is
(a) 20 s (b) 40 s
(c) 35 s (d) 45 s
½IES (EC) 2003 56. A second-order control system is defined by the following differential equation:
4d 2c tð Þ dt2 þ 8
dc tð Þ
dt þ 16c tð Þ ¼ 16u tð Þ
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
½IES (EE) 2001 57. Assuming the transient response of a second-order system to be given by
c tð Þ ¼ 1 e 4t ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 p sinðvn ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 p þ Þ the setting time for the 5% criterion will be
(a) 1/4 s (b) 3/4 s
(c) 5/4 s (d) 4 s
½IES (EC) 1994 58. Consider the systems with the following open-loop transfer functions:
1: 36 s sð þ 3:6Þ 2: 100 s sð þ 5Þ 3: 6:25 s sð þ 4Þ
The correct sequence of these systems in increasing order of the time taken for the unit-step response to settle is
(a) 1, 2, 3 (b) 3, 1, 2
(c) 2, 3, 1 (d) 3, 2, 1
½IES (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. s2þ 15s þ 26:25 1. Undamped B. s2þ 5s þ 6 2. Under-damped C. s2þ 20:25 3. Critically damped D. s2þ 4:55s þ 42:25 4. Overdamped Codes: A B C D A B C D (a) 1 2 3 4 (b) 2 3 1 4 (c) 4 3 1 2 (d) 1 2 4 3 ½IES (EC) 1994 60. 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
½IES (EC) 1995 61. A system has an open-loop transfer function
G sð Þ ¼ 10 s sð þ 1Þ s þ 2ð Þ What is the steady-state error when it is subjected to the input
r tð Þ ¼ 1 þ 2t þ3 2t 2? (a) Zero (b) 0.4 (c) 4 (d) infinity ½IES (EC) 1995 62. 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:
2 s2 + 7s + 2 + – R(s) C(s) K
Figure P4.68 Figure for Objective Question 60.
R(s) + C(s)
−
2 4
s +
(a) 1:1 (b) 2:1
(c) 3:2 (d) 2:3
½IES (EC) 1995 63. Consider the following overall transfer function for a unity feedback system
4 s2þ 4s þ 4
Which 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 isfinite. 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
½IES (EC) 1996 64. A first-order system is shown in Figure P4.70. Its time response to a unit-step input is given by
(a) c tð Þ ¼ 1=Tð Þet=T (b) c tð Þ ¼ Tð1 et=TÞ (c) c tð Þ ¼ ð1 et=TÞ (d) c tð Þ ¼ Tet=T
½IES (EC) 1996 65. For a unity-feedback system, the open-loop transfer function is
G sð Þ ¼ 16 sð þ 2Þ s2ðsþ 1Þ s þ 4ð Þ
What is the steady-state error if the input is r tð Þ ¼ 2 þ 3t þ 4tð 2Þu tð Þ?
(a) 0 (b) 1
(c) 2 (d) 3 ½IES (EC) 1996
66. A system has a transfer function C sð Þ R sð Þ¼
4 s2þ 1:6s þ 4
For the unit-step response, the settling time (in seconds) for 2% tolerance band is
(a) 1.6 (b) 2.5
(c) 4 (d) 5
½IES (EC) 1996
R(s) 1 C(s)
1 sT+
Figure P4.70 Figure for Objective Question 64.
67. A second-order system has the damping ratio and undamped natural frequency of oscillation vn. The settling time at 2% tolerance band of the system is
(a) 2 vn (b) 3 vn (c) 4 vn (c)vn ½IES (EC) 2000 68. 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 sð Þ ¼ 10 s2þ 14s þ 50?
(a) ess ¼ 0 (b) ess ¼ 0:83
(c) ess¼ 1 (d) ess¼ 1
½IES (EC) 2001 69. In the system shown in Figure P4.71, where
r tð Þ ¼ 1 þ 2t ðt 0Þ the steady-state value of the error eðtÞ is equal to
(a) Zero (b) 2/10
(c) 10/2 (d) Infinity
½IES (EE) 2001 70. 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
½IES (EC) 2002 71. 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
½IES (EC) 2003 r(t) + e(t) C(t) − 2 10( 1) ( 2) s s s + +
Figure P4.71 Figure for Objective Question 69.
r(t) + e(t) C(t) 2 10( 1) ( 2) s s s + + –
72. What is the unit-step response of a unity-feedback control system having forward-path transfer function
G sð Þ ¼ 80 s sð þ 18Þ?
(a) Overdamped (b) Critically damped
(c) Underdamped (d) Undamped oscillatory
½IES (EC) 2004 73. What is the steady-state error for a unity-feedback control system having
G sð Þ ¼ 1 s sð þ 1Þ due to unit-ramp input?
(a) 1 (b) 0.5
(c) 0.25 (d)pffiffiffiffiffiffiffi0:5
½IES (EC) 2005 74. Given a unity-feedback system with
G sð Þ ¼ K s sð þ 4Þ what is the value of K for a damping ratio of 0.5?
(a) 1 (b) 16
(c) 4 (d) 2
½IES (EC) 2005 75. 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 s2þ 12s þ 400 1. Undamped B. 900 s2þ 90s þ 400 2. Critically damped C. 225 s2þ 30s þ 225 3. Underdamped D. 625 s2þ 0s þ 225 4. Overdamped Codes: A B C D A B C D (a) 3 1 2 4 (b) 2 4 3 1 (c) 3 4 2 1 (d) 2 1 3 4 ½IES (EC) 2005 76. 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 roots
½IES (EC) 2005 77. Which of the following expresses the time at which second peak in step response occurs for a
second-order system? (a) vn ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 p (b) 2 vn ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 p (c) 3 vn ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 p (d) ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 p ½IES (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=ð1 þ KpÞ
(c)1 (d) 1=Kp
½GATE (EC) 1990 79. A second-order system has a transfer function given by
G sð Þ ¼ 25 s2þ 8s þ 25
If the system, initially at rest, is subjected to a unit-step input at t¼ 0, the second peak in the response will occur at
(a) s (b) =3 s
(c) 2=3 s (d)=2 s
½GATE (EC) 1991 80. A unity-feedback control system has an open-loop transfer function
G sð Þ ¼4 1ð þ 2sÞ s2ðsþ 2Þ
If the input to the system is a unit ramp, the steady-state error will be
(a) 0 (b) 0.5
(c) 2 (d) Infinity
½GATE (EC) 1991 81. The step-error coefficient of a system
G sð Þ ¼ 1 sþ 6 ð Þ s þ 1ð Þ with unity feedback is
(a) 1=6 (b) 1
(c) 0 (d) 1
½GATE (EC) 1995 82. Consider a unity-feedback control system with open-loop transfer function
G sð Þ ¼ K s sð þ 1Þ
The steady-state error of the system due to a unit-step input is
(a) Zero (b) K
(c) 1/K (d) Infinite
½GATE (EC) 1998 83. For a second-order system with the closed-loop transfer function
T sð Þ ¼ 9 s2þ 4s þ 9 the settling time for 2% band, in seconds, is:
(a) 1.5 (b) 2.0
(c) 3.0 (d) 4.0
½GATE (EC) 1999 84. If the characteristic equation of a closed-loop system is s2þ 2s þ 2 ¼ 0, then the system is
(a) Overdamped (b) Critically damped
(c) Underdamped (d) Undamped
½GATE (EC) 2001 85. Consider a system with a transfer function
G sð Þ ¼ sþ 6 Ks2þ s þ 6 Its damping ratio will be 0.5 when the value of K is
(a) 2/6 (b) 3
(c) 1/6 (d) 6
½GATE (EC) 2002 86. The transfer function of a system is
G sð Þ ¼ 100 sþ 1
ð Þ s þ 100ð Þ
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
½GATE (EE) 2002 87. For a feedback-control system of type 2, the steady-state error for a ramp input is:
(a) Infinite (b) Constant
(c) Zero (d) Interminate
½GATE (EE) 1996 88. 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)
½GATE (EE) 2000 89. A unity-feedback system has an open-loop transfer function
GðsÞ ¼ 25 sðs þ 6Þ
The peak overshoot in the step-input response of the system is approximately equal to:
(a) 5% (b) 10%
(c) 15% (d) 20%
½GATE (EE) 2000 90. 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 infinity
½GATE (EE) 2000 91. Consider the unit-step response of a unity-feedback control system, whose open-loop transfer
functions is
GðsÞ ¼ 1 sðs þ 1Þ The maximum overshoot is equal to
(a) 0.143 (b) 0.153
(c) 0.163 (d) 0.173
½GATE (EE) 1996 92. An open-loop transfer function of a unity-feedback system is given by
K s sð þ 1Þ
If the value of gain K is such that the system is critically damped, the closed-loop poles of the system will lie at:
(a)0.5 and 0.5 (b) j0:5
(c) 0 and1 (d) 0.5 j0:5
½GATE (EE) 2002 93. 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%
½IES (EE) 2001 94. 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 15 s + 15 1 s +
½IES (EC) 1997 95. The unit-impulse response of a second-order underdamped system, starting from rest, is given by
cðtÞ ¼ 12:5e6tsin 8t; t 0
The 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
½GATE (EE) 2004 96. In the case of a second-order system described by a differential equation
Jd20 dt2 þ F
d0
dt þ k0¼ ki
where i and0 are the input and output shaft angles, the natural frequency is given by: (a)pffiffiffiffiffiffiffiffiK=J (b)pffiffiffiffiffiffiffiffiJ=K
(c)pffiffiffiffiffiKJ (d) pffiffiffiffiffiffiffiffiffiffiffiK J
½IES (EC) 1997 97. 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. K B. 1 2.1 C. 2 3. 0 D. 3 4.1=4 Codes: A B C D A B C D (a) 2 4 3 3 (b) 1 2 3 4 (c) 2 1 4 3 (d) 1 2 4 3 ½IES (EC) 2003 98. A unity-feedback second-order control system is characterized by
G sð Þ ¼ K s Jsð þ BÞ s( s + 2) K – + C(s) R(s) 1 + sP
Figure P4.74 Figure for Objective Question 95.
where J ¼ moment of inertia, K ¼ system gain and B ¼ viscous damping coefficient. The transient response specification, 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
½IES (EE) 1997 99. A linear second-order system with the transfer function
G sð Þ ¼ 49 s2þ 16s þ 49
is initially at rest and is subjected to a step-input signal. The response of the system will exhibit a peak overshoot of:
(a) 16% (b) 9%
(c) 2% (d) Zero
½IES (EE) 1998 100. The unit-impulse response of a linear time-invariant second-order system is
gðtÞ ¼ 10e8tsin 6t ðt 0Þ
The 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
½IES (EE) 1999 101. Ifða jbÞ are the complex conjugate roots of a characteristic equation of a second-order system,
then its damping coefficient and natural frequency will be respectively: (a) ffiffiffiffiffiffiffiffiffiffiffiffiffiffib a2þ b2 p and ffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2þ b2 p (b) ffiffiffiffiffiffiffiffiffiffiffiffiffiffib a2þ b2 p (c) ffiffiffiffiffiffiffiffiffiffiffiffiffiffia a2þ b2 p andpffiffiffiffiffiffiffiffiffiffiffiffiffiffia2þ b2 (d) ffiffiffiffiffiffiffiffiffiffiffiffiffiffia a2þ b2 p and a2þ b2 ½IES (EE) 2000 102. A unity-feedback control system has a forward-path transfer function
G sð Þ ¼10 1ð þ 4sÞ s2ð1þ sÞ If the system is subjected to an input
rðtÞ ¼ 1 þ t þt2
2 ðt 0Þ then the steady-state error of the system will be:
(a) Zero (b) 0.1
(c) 10 (d) Infinity
½IES (EE) 2000 103. 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 s3þ 14s2þ 56s þ k ¼ 0 then it will be stable only if: (a) 0< K < 784 (c) 10> K > 600
(b) 1< K < 64 (d) 4< K < 784
½IAS 1994 2. Thefirst two rows of Routh’s tabulation of a fourth-order system are:
s4 1 10 5
s3 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
½IAS 1996 3. Thefirst stability test showed the sign as follows:
Rows I II III IV V VI VII
Signs + + + + +
The number of roots of the system lying the right half of the s-plane is:
(a) 2 (b) 3
(c) 4 (d) 5
½IAS 1998 4. For the block diagram shown in Figure P5.21, the limiting values of K for the stability of inner loop
is 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
½IES (EE) 2000
Figure P5.21 Figure for Objective Question 4.
5. A system with the characteristic equation s4þ 2s3þ 11s2þ 18s þ 18 ¼ 0 will have a closed-loop poles 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.
½IAS 1993 6. By properly choosing the value of K, the output c(t) of the system (as shown in Figure P5.22) can be
made to oscillate sinusoidally at a frequency (in rad/s) of:
(a) 1 (b) 2
(c) 3 (d) 4
½IAS 1993 7. 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.
½IAS 1993
K s(s+1)(s+4)
c(t)
Figure P5.22 Figure for Objective Question 6.
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
½IAS 1995 9. Consider the following statements regarding the stability analysis by Routh–Hurwitz criterion.
1. For a system to be stable, all the coefficients of the characteristic equation must be present and of the same sign.
2. If a system is to be stable, there should not be any sign change in thefirst column of the Routh’s array.
3. The order of the auxillary equation obtained from the elements of the Routh’s table is always odd.
Of these statements: (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.
½IAS 1999 10. A closed-loop system is shown in Figure P5.24. The largest possible value of for which the system
would be stable is:
(a) 1 (b) 1.1
(c) 1.2 (d) 2.3
½IES (EC) 1998 11. The number of roots in the left-half of s-plane for the equation s3 4s2þ s þ 6 ¼ 0 would be
(a) 1 (b) 2
(c) 3 (d) 4
½IAS 2001 Figure P5.24 Figure for Objective Question 10.
12. The characteristic equation of a feedback-control system is s3þ Ks2þ 5s þ 10 ¼ 0 for the system to be critically stable, the values of K should be
(a) 1 (b) 2
(c) 3 (d) 4
½IES (EE) 1999 13. 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 ½IAS 2002
14. Consider the equation 2s4þ s3þ 3s2þ 5s þ 10 ¼ 0. The number of roots this equation has in the right half of the s-plane is:
(a) One (b) Two
(c) Three (d) Four
½IAS 2003 15. 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
½IAS 2003 16. 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.
½IES (EE) 1992 17. While forming a Routh’s 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
½IES (EC) 1997 18. The characteristic equation of a closed-loop system is given by s4þ 6s3þ 11s2þ 6s þ k ¼ 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
½IES (EE) 1993 Figure P5.25 Figure for Objective Question 15.
19. By a suitable choice of the scalar parameter K, the system shown in Figure P5.26 can be made to oscillate continuously at a frequency of:
(a) 1 rad/s (b) 2 rad/s
(c) 4 rad/s (d) 8 rad/s
½IES (EE) 1993 20. The open-loop transfer functions with unity feedback are given below for different systems:
1. G sð Þ ¼ 2 sþ 2 2. G sð Þ ¼ 2 s sð þ 2Þ 3. GðsÞ ¼ 2 s2ðs þ 2Þ 4. G sð Þ ¼ 2 sð þ 1Þ s sð þ 2Þ Among these systems, the unstable system is
(a) 1 (b) 2
(c) 3 (d) 4
½IES (EE) 1993 21. The open-loop transfer function of a control system is given by
K sð þ 10Þ s sð þ 2Þ s þ að Þ
The smallest possible value of a for which this system is stable in a closed loop for all positive values of K is:
(a) 0 (b) 8
(c) 10 (d) 12
½IES (EE) 1994 22. The open-loop transfer function of a unity-feedback control system is given by
G s
ð Þ ¼
ðsþ 1K sðÞ s 7þ 2ð Þ ÞFor K > 6, the stability characteristic of the open-loop and closed-loop configuration of the system are, respectively:
(a) Stable and stable (b) Unstable and stable (c) Stable and unstable (d) Unstable and unstable
½IES (EE) 1994 Figure P5.26 Figure for Objective Question 19.
23. The open-loop transfer function of a system is given by G sð Þ ¼ K
s sð þ 2Þ s þ 4ð Þ
The value of K which will cause sustained oscillations in the closed-loop unity feedback, is:
(a) 16 (b) 32
(c) 48 (d) 64
½IES (EE) 1996 24. The characteristic equation 1þ G(s)H(s) ¼ 0 of a system is given by s4þ 6s3þ 11s2þ 6s þ
K¼ 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
½IES (EE) 1996] 25. The characteristic equation for a third-order is q(s)¼ a0s3þ a1s2þ a2sþ a3¼ 0: For the third-order system to be stable, besides that all the coefficients have to be positive, which one of the following has to be satisfied as a necessary and sufficient condition?
(a) a0a1 a2a3 (b) a1a2 a0a3
(c) a2a3 a1a0 (d) a0a3 a1a2 ½IES (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
½IES (EE) 2005 27. Consider the equation 2s4þ s3þ 3s2þ 5s þ 10 ¼ 0: How many roots does this equation have in
the right half of the s-plane?
(a) One (b) Two
(c) Three (d) Four
½IES (EE) 2005 Figure P5.27 Figure for Objective Question 26.
28. When all the roots of the characteristic equation are found in the left of an s-plane, the response due to the initial condition will:
(a) Increase to infinity as time approaches infinity (b) Decrease to zero as time approaches infinity (c) Remain constant for all time
(d) Be oscillating
½IES (EC) 1992 29. 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 þj), (1j) 1. Marginally stable B. (2 þj), (2j), (2j), (2j) 2. Unstable C.j, j, 1, 1 3. Stable Codes: A B C A B C (a) 1 2 3 (b) 3 1 2 (c) 2 3 1 (d) 1 3 2 ½IES (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 ½IES (EC) 1992
31. How many roots of the characteristic equation s5þ s4þ 2s3þ 2s2þ 3s þ 15 ¼ 0 lie in the left half of the s-plane?
(a) 1 (b) 2
(c) 3 (d) 5
½IES (EC) 1993 32. A control system is shown in Figure P5.28. The maximum value of the gain K for which the system is
stable is:
(a)pffiffiffi3 (b) 3
(c) 4 (d) 5 ½IES(EC) 1993
33. Consider the following statements regarding the number of sign change in thefirst column of Routh in respect of the characteristic equation s2þ 2as þ 4:
1. If a¼ þ", where " is near to zero, number of sign changes will be equal to zero. 2. If a¼ 0, the number of sign change will be equal to one.
3. If a ¼ "; where " ¼ 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
½IES (EC) 1994 34. The value of K for which the unity-feedback system
G sð Þ ¼ K s sð þ 2Þ s þ 4ð Þ crosses the imaginary axis is
(a) 2 (b) 4
(c) 6 (d) 48
½IES (EC) 1997 35. Thefirst column of a Routh array is:
s5 1 s4 2 s3 3=2 s2 1=3 s1 10 s0 2
Figure P5.28 Figure for Objective Question 32.
How many roots of the corresponding equation are there in the left of the s-plane?
(a) 2 (b) 3
(c) 4 (d) 5
½IES (EC) 1996 36. The characteristic equation of a system is given by 3s4þ 10s3þ 5s2þ 2 ¼ 0. This system is:
(a) Stable (b) Marginally stable
(c) Unstable (d) None of (a), (b) or (c)
½IES (EE) 2002 37. The loop transfer function of Q closed-loop system is given by
G sð ÞH sð Þ ¼ k s2ðs2þ 2s þ 2Þ The angle of departure of the root locus at s¼ 1 þ j is
(a) Zero (b) 90
(c)90 (d)180
½IES (EC) 1998 38. The Routh–Hurwitz criterion cannot be applied when the characteristic equation of the system
contains any coefficients 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
½IES (EC) 2000 39. Which one of the following characteristics equations can result in a stable operation of the feedback
system?
(a) s3þ 4s2þ s 6 ¼ 0 (b) s3 s2þ 5s þ 6 ¼ 0 (c) s3þ 4s2þ 10s þ 11 ¼ 0 (d) s4þ s3þ 2s2þ 4s þ 6 ¼ 0
½IES (EC) 2000 40. Consider the following statements: Routh–Hurwitz criterion gives
1. Absolute stability
2. 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?
(a) 1, 2 and 3 (b) 1 and 2
(c) 2 and 3 (d) 1 and 3
½IES (EC) 2000 41. The given characteristic polynomial s4þ s3þ 2s þ 3 ¼ 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
42. A system has a single pole at the origin. Its impulse response will be:
(a) Constant (b) Ramp
(d) Decaying exponential (d) Oscillatory
½IES (EC) 2002 43. Match List I (Pole–zero plot of linear control system) with List II (Response of the system), and select
the correct answer using the codes given below the lists:
List I (Pole–zero 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 ½IES (EC) 2002 44. The characteristic equation of a control system is given by
s
6þ 2s
5þ 8s
4þ 12s
3þ 20s
2þ 16s þ 16s ¼ 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
½IES (EC) 2003 45. The closed-loop system shown in Figure P5.29 becomes marginally stable, if the constant K is
chosen to be:
(a) 10 (b) 20
(c) 30 (d) 40
½IES (EE) 2002
46. An open loop system has a transfer function 1
s3þ 1:5s2þ s 1
It is converted into a closed-loop system by providing negative feedback having transfer function 20(sþ 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
½IES (EC) 2004 Figure P5.29 Figure for Objective Question 45.
47. An electromechanical closed-loop control system has the characteristic equation s3þ 6Ks2þ Kþ 2
ð Þs þ 8 ¼ 0; where K is the forward gain of the system. The condition for the closed-loop stability is:
(a) K ¼ 0.528 (b) K¼ 2
(c) K ¼ 0 (d) K¼ 2528
½GATE (EC) 1990 48. The characteristic equation of a feedback control system is given by s3þ 5s2þ K þ 6ð Þ s þ K ¼ 0; where K > 0 is a scalar variable parameter. In the root–loci diagram of the system, the asymptotes of the root–locus 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)
½GATE (EC) 1991 49. 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
½GATE (EC) 1995 50. The number of roots of s3þ 5s2þ 7s þ 3 ¼ 0 in the left half of the s-plane is:
(a) Zero (b) One
(c) Two (d) Three
½GATE (EC) 1998 51. The transfer function of a system is
2s2þ 6s þ 5 sþ 1 ð Þ2
sþ 2
ð Þ
The characteristic equation of the system is:
(a) 2s2þ 6s þ 5 ¼ 0 (b) ðsþ 1Þ2ðsþ 2Þ ¼ 0
(c) 2s2þ 6s þ 5þ s þ 1ð Þ2ðsþ 2Þ ¼ 0 (d) 2s2þ 6s þ 5 s þ 1ð Þ2ðsþ 2Þ ¼ 0
½GATE (EC) 1998 52. A system described by the transfer function
H sð Þ¼ 1
s3þ s2þ Ks þ 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
½GATE (EC) 2000
53. The characteristic polynomial of a system is q sð Þ ¼ 2s5þ s4þ 4s3þ 2s2þ 2s þ 1. The system is:
(a) Stable (b) Marginally stable
(c) Unstable (d) Oscillatory
½GATE (EC) 2002 54. The open-loop transfer function of a unity feedback system is
G sð Þ ¼ K
s sð2þ s þ 2Þ s þ 3ð Þ 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
½GATE (EC) 2004 55. For the polynomial P sð Þ ¼ s5þ s4þ 2s3þ 2s2þ 3s þ 15; the number of roots that lie in the right
half of the s-plane is:
(a) 4 (b) 2
(c) 3 (d) 1
½GATE (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 ¼ 0 (b) T< 0
(c) T > 1 (d) 0< T < 1
½IES (EE) 2000 57. The open-loop transfer function of a unity-feedback control system is
G sð Þ ¼K sð þ 10Þ s þ 20ð Þ s2ðsþ 2Þ The closed-loop system will be stable, if the value of K is:
(a) 2 (b) 3
(c) 4 (d) 5
½IES (EE) 1998 Figure P5.30 Figure for Objective Question 56.
58. The number of roots of the equation 2s4þ s3þ 3s2þ 5s þ 7 ¼ 0 that lie in the right half of the s-plane is:
(a) Zero (b) One
(c) Two (d) Three
½GATE (EE) 1998 59. The characteristic equation of a feedback control system is 2s4þ s3þ 3s2þ 5s þ 10 ¼ 0. The
number of roots in the right half of the s-plane are:
(a) Zero (b) 1
(c) 2 (d) 3
½GATE (EE) 2003 60. First column elements of the Routh’s tabulation are 3, 5, 3/4, 1/2 and 2. It means that there
is/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
½IES (EC) 1999 61. The loop gain GH of a closed-loop system is given by
K s sð þ 2Þ s þ 4ð Þ
The value of K for which the system just becomes unstable, is:
(a) K ¼ 6 (b) K¼ 8
(c) K ¼ 48 (d) K¼ 96
½GATE (EE) 2003 62. A unity-feedback system having an open-loop gain
G sð ÞH sð Þ ¼K 1ð sÞ 1þ s becomes stable when:
(a) | K | > 1 (b) K> 1
(c) | K | < 1 (d) K<1
½GATE (EE) 2005 63. The algebraic equation FðsÞ ¼ s5 3s4þ 5s3 7s2þ 4s þ 20 is given. F(s) ¼ 0 has:
(a) A single complex root with the remaining roots being real
(b) One positive real root and four complex roots, all with positive real parts
(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
½GATE (EE) 2006 64. The characteristic equation of a control system is given by sðs þ 4Þðs2þ 2s þ 2Þ þ Kðs þ 1Þ ¼ 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
½IES (EE) 2005 65. Figure P5.64 shows the Nyquist plot of the open-loop transfer function G(s)H(s) of a system. If
G(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
½GATE (EC) 2003 66. For the equation s3 4s2þ s þ 6 ¼ 0; the number of roots in the left half of the s-plane will be:
(a) Zero (b) One
(c) Two (d) Three
½GATE (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
½IES (EC) 2003 2. Despite the presence of a negative feedback, control systems still have problems of instability
because 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.
½GATE (EC) 2005 3. The open-loop transfer function of unity-feedback control system is
G sð Þ ¼ K
s sð þ aÞ s þ bð Þ ; 0< a b The system is stable if:
(a) 0< K <aþ b ab (b) 0< K < ab aþ b (c) 0< K < ab a þ bð Þ (d) 0< K <a bðaþ bÞ ½IES (EC) 2000 4. The open-loop transfer function of a unity feedback control system is given by
G sð Þ ¼ K sð þ 2Þ s sð2þ 2s þ 2Þ
The centroid and angles of root locus asymptotes are respectively: (a) Zero andþ90; 90 (b)2/3 and þ60; 60 (c) Zero andþ120; 120 (d)2/3 and 90; þ90
½IAS 1993 5. The open-loop transfer function is given by
G sð Þ H sð Þ ¼K sð þ 1Þ s þ 3ð Þ s2þ 4s þ 8
Its root locus diagram is
½IAS 1994 6. Which of the following are the features of the breakaway point in the root-locus of a closed-loop control
system with the characteristic equation 1þ KG1ð Þ Hs 1ð Þ ¼ 0?s 1. It need not always occur only on the real axis.
2. At this point G1ð Þ Hs 1ð Þ ¼ 0:s 3. At this pointdk
ds¼ 0:
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
½IES (EC) 1997 7. The root-locus plot of an open-transfer function
GH sð Þ ¼ K s sð þ 2Þ s þ 4ð Þ is
½IAS 1996 8. To improve the stability and time response of a control system, poles are often added to the system
transfer function. In this context, which one of the following pairs is correctly matched? (a) Zero poles: makes the system stable and slow responding
(b) One pole: makes the system less stable and slow responding (c) Two poles: makes the system less stable and fast responding
(d) Three poles: makes the system conditionally stable and fast responding
½IAS 1997 9. Consider the following statements regarding root loci:
1. All root loci start from respective poles of G(s) H(s).
2. All root loci end at the respective zeros of G(s) H(s) or go to infinity. 3. The root loci are symmetrical about the imaginary axis of the s-plane. 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
½IAS 1997 10. If the open-loop transfer function of a feedback system is given by
G sð Þ H sð Þ ¼ K
s sð þ 2Þ sð2þ 2s þ 5Þ then the centroid of the asymptotes will be:
(a)1, 0 (b) 1, 0
(c) 0,1 (d) 0, 1
½IAS 1998 11. Consider the following statements regarding the root-locus technique for analyzing linear control
systems:
1. Root-locus is the locus of the roots of the characteristic equation as the closed-loop gain K is varied from zero to infinity.
2. The number of branches of the root-loci is equal to the number of poles of the open-loop transfer function.
3. For a particular point in the s-plane to lie on the root-locus, the angle criteria to be satisfied is 2Iþ 1
ð Þ; where I ¼ 0; 1; 2: Of these statements:
(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.
½IAS 1999 12. Figure P6.25 shows root-loci of the open-loop transfer function G(s)H(s) of a system. Consider the
following inferences drawn from thefigure:
1. It has no zero. 2. It is a stable system. 3. It is a second order system.
Which of these inferences are correct?
(a) 1, 2 and 3 (b) 1 and 2
(c) 2 and 3 (d) 1 and 3
½IAS 2000
13. The characteristic equation of a unity-feedback control system is given by s3þ K1s2þ s þ K2¼ 0: Consider the following statements in this regard:
1. For a given value of K1, all the root-locus branches will terminate at infinity for K2in the positive direction.
2. For a given value of K2, all the root-locus branches will terminate at infinity for the variable K1 in the positive direction.
3. For a given value of K2, only one root-locus branch will terminate at infinity for the variable K1 in the positive direction.
Of these statements:
(a) 1 and 2 are correct (b) 3 alone is correct (c) 2 alone is correct (d) 1 and 3 are correct
½IES (EE) 1993
σ
jω
s-plane
14. The transfer function for a system is
G sð Þ ¼ K sð þ 2Þ sþ 1
ð Þ s þ 3ð Þ s þ 4ð Þ ; k> 0
Two branches (loci) of the plot directed along asymptotes are centered at a point:
(a)3 (b)4
(c)2 (d)1
½IAS 2001 15. The root-locus plot of a system having open-loop transfer function
G sð Þ H sð Þ ¼ K sð þ 10Þ s þ 70ð Þ s3ðsþ 100Þ s þ 200ð Þ will have angle of asymptotes as:
(a) 608, 1008 (b) 608, 1808, 3008
(c) 608, 1208, 1808 (d) 608, 908, 1208
½IAS – 2003 16. The intersection of root locus branches with the imaginary axis can be determined by use of:
(a) Nyquist criterion (b) Routh’s criterion
(c) Polar plot (d) None of above
½IES (EE) 1992 17. Which of the following is not necessarily valid for root-locus pattern?
(a) The nfinite zeros and m poles are plotted on the s-plane. Then (m – n) indicates the number of non-finite zeros.
(b) The number of poles gives the number of loci.
(c) A value of s on the real axis is a point on the root locus, if the total number of poles and zeros on the real axis to the right of the point is even.
(d) There are as many asymptotes as non-finite zeros.
½IES (EE) 1992 18. The root locus of a unity feedback system is shown in Figure P6.26. The open-loop transfer function is
given by:
Figure P6.26 Figure for Objective Question 18.
(a) K s sð þ 1Þ s þ 2ð Þ (b) K sð þ 1Þ s sð þ 2Þ (c)K sð þ 2Þ s sð þ 1Þ (d) Ks sþ 1 ð Þ s þ 2ð Þ ½IES (EE) 1993 19. Given the unity-feedback system with
G sð Þ ¼ K s sð þ 1Þ s þ 2ð Þ The root-locus of the system is given by
½IES (EE) 2004 20. Figure P6.27 shows the root-locus of open-loop transfer function of a control system
* pole zero origin
PQ¼ 2:6 ¼ PQ0 RP¼ 1:4 OR¼ 2:0 OQ¼ 1:4 ¼ OQ0
j
ω σj
ω σj
ω σj
ω σ (a) (b) (c) (d)The value of the forward-path gain K at the point P is:
(a) 0.2 (b) 1.4
(c) 3.4 (d) 4.8
½IES (EE) 1994 21. For a unity-negative feedback control system, the open-loop transfer function is
G sð Þ ¼ K s sð þ 1Þ s þ 2ð Þ The root-locus plot of the system is:
½IES (EC) 1999 jω R P Q Q σ
Figure P6.27 Figure for Objective Question 20.
22. The closed-loop transfer function of a feedback-control system is given by C sð Þ
R sð Þ¼
K
s2þ 3 þ Kð Þs þ 2
Which one of the following diagrams represents a root locus diagram of the system for K > 0?
½IES (EE) 1996 23. The open-loop transfer function of a feedback-control system is given by
G sð Þ H sð Þ ¼ K sð þ 2Þ s sð þ 4Þ sð2þ 4s þ 8Þ
In the root-locus diagram of the system, the asymptotes of the root-loci for large values of K meet at a point 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)
24. Consider the following statements with reference to the root loci of the characteristic equation of unity-feedback control system with an open-loop transfer function of
G sð Þ ¼K sð þ 1Þ s þ 3ð Þ s þ 5ð Þ s sð þ 2Þ s þ 4ð Þ
1. Reach locus starts at an open-loop pole and ends either at an open-loop zero or infinity. 2. Reach locus starts at an open-loop pole or infinity and ends at an open-loop zero. 3. There are three separate root loci.
4. There arefive separate root loci. Which of these statements are correct?
(a) 2 and 3 (b) 2 and 4
(c) 1 and 3 (d) 1 and 4
½IES (EE) 2003 25. The loop transfer function of a system is given by
G sð Þ H sð Þ ¼K sð þ 10Þ s þ 100ð Þ s sð þ 25Þ2 The number of loci terminating at infinity is:
(a) 0 (b) 1
(c) 2 (d) 3
½IES (EE) 2003 26. A control system has
G sð Þ H sð Þ ¼ K
s sð þ 4Þ sð2þ 4s þ 20Þ ; ð0< K < Þ What is the number of breakaway points in the root locus diagram?
(a) One (b) Two
(c) Three (d) Zero
½IES (EE) 2004 27. 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 infinity is (m n). 4. The number of root loci approaching infinity is (m þ n).
Which of the statements given above are correct?
(a) 1 and 4 (b) 1 and 3
(c) 2 and 3 (d) 2 and 4
½IES (EE) 2005 28. 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?
(a) 1, 2 and 3 (b) 1 and 3
(c) 2 and 3 (d) 1 and 2
½IES (EC) 1992 29. 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 sð þ 1Þ s2þ 4s þ 5 (b) 5 sð þ 1Þ s2þ 4s þ 4 (c) 10 sð þ 1Þ s2þ 4s þ 5 (d) 10 sð þ 1Þ sþ 2 ð Þ2 ½IES (EC) 1993 30. In the root locus for open-loop transfer function
G sð Þ H sð Þ ¼ K sð þ 6Þ sþ 3 ð Þ s þ 5ð Þ 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
½IES (EC) 1994 31. If the open-loop transfer function of the system is
G sð Þ H sð Þ ¼ K sð þ 10Þ s sð þ 8Þ s þ 16ð Þ s þ 72ð Þ
then a closed-loop pole will be located at s ¼ 12 when the value of K is:
(a) 4355 (b) 5760
(c) 9600 (d) 9862
½IES (EC) 1994 Figure P6.28 Figure for Objective Question 28.
32. A unity-feedback system has
G sð Þ ¼ K s sð þ 1Þ s þ 2ð Þ In the root locus, the breakaway point occurs between:
(a) s¼ 0 and 1 (b) s¼ 1 and 1
(c) s¼ 1 and 2 (d) s ¼ 2 and 1
½IES (EC) 1995 33. The loop-transfer function of a feedback control system is given by
GðsÞ HðsÞ ¼sðs þ 2Þðs2Kþ 2s þ 2Þ The number of asymptotes of its root loci is:
(a) 1 (b) 2
(c) 3 (d) 4
½IES (EC) 1996 34. 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. Of these statements:
(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.
½IES (EC) 1998 35. The intersection of asymptotes of root-loci of a system with the open-loop transfer function
G sð Þ H sð Þ ¼ K s sð þ 1Þ s þ 3ð Þ is (a) 1.44 (b) 1.33 (c)1.44 (d)1.33 ½IES (EC) 2000 36. The root-locus plot of the system having the loop-transfer function
G sð Þ H sð Þ ¼ K
s sð þ 4Þ sð2þ 4s þ 5Þ has
(a) No breakaway point (b) Three real breakaway points
(c) Only one breakaway point (d) One real and two complex breakaway points ½IES (EC) 2001
37. An open-loop transfer function is given by
G sð Þ H sð Þ ¼ K sð þ 1Þ s sð þ 2Þ sð2þ 2s þ 2Þ It has:
(a) One zero at infinity (b) Two zeros at infinity (c) Three zeros at infinity (d) Four zeros at infinity
½IES (EC) 2001 38. Which of the following is the open-loop transfer function of the root loci shown in
Figure P6.30? (a) K s sð þ T1Þ2 (b) K sþ T1 ð Þ s þ Tð 2Þ2 (c) K sþ T ð Þ3 (d) K s2 sT 1þ 1 ð Þ ½IES (EC) 2002 39. The instrument used for plotting the root locus is called:
(a) Slide rule (b) Spirule
(c) Synchro (d) Selsyn
½IES (EC) 2002 40. A control system has
G sð Þ H sð Þ ¼ K sð þ 1Þ s sð þ 3Þ s þ 4ð Þ Root locus of the system can lie on the real axis:
(a) Between s¼ 1 and s ¼ 3 (b) Between s¼ 0 and s ¼ 4 (c) Between s¼ 3 and s ¼ 4 (d) Towards left of s¼ 4
½IES (EC) 2002 jω
r1
r2
r3 σ
