Explore topic-wise MCQs in Control Systems.

This section includes 283 Mcqs, each offering curated multiple-choice questions to sharpen your Control Systems knowledge and support exam preparation. Choose a topic below to get started.

51.

The performance specifications for a unity feedback control system having an open-loop transfer function
G(s) =
K
are
s(s + 1)(s + 2)

(i) Velocity error coefficient KV > 10 sec 1
(ii) Stable closed-loop operation. The value of K, satisfying the above specifications, is

A. K > 6
B. 6 < K < 10
C. K > 10
D. K > 20
Answer» E.
Discussion
52.

A linear stable invariant system is forced with an input given below
x (t) = A sin t
x (t) [G (s) ] y (t)
Under steady-state conditions, the output y (t) of the system will be

A. A sin ( t + ), where = tan
B. |G (j )|
C. | G (j ) | A sin [ t + < G (j )]
D. | G (j ) | A sin [2 t + < G (j )]
E. AG (j ) sin [ t + G (j )]
Answer» C. | G (j ) | A sin [ t + < G (j )]
Discussion
53.

The asymptotic approximation of the log-magnitude versus frequency plot of a minimum phase system with real poles and one zero is shown in figure. Its transfer function is

A.
B.
Answer» E.
Discussion
54.

The transfer function of a compensating network is of the form
1 + Ts
1 + Ts

If this is a phase-lag network, the value of should be

A. exactly equal to 0
B. between 0 and 1
C. exactly equal to 1
D. greater than 1
Answer» C. exactly equal to 1
Discussion
55.

The transfer function C/ R of the system shown in the figure is

A.
B.
Answer» C.
Discussion
56.

The open-loop transfer function of a system is given by
G(s) H(s) =
K(s + 1)(s + 3)
s2 + 4s + 8

Its root locus diagram is

A. Fig:- A
B. Fig:- B
C. Fig:- C
D. Fig:- D
Answer» B. Fig:- B
Discussion
57.

A unity feedback system has the open-loop transfer function
G(s) =
1
(s 1)(s + 2)(s + 3)

The Nyquist plot of G(s) encircles the origin

A. never
B. once
C. twice
D. thrice
Answer» C. twice
Discussion
58.

A unity feedback system has an open-loop transfer function of the from
KG(s) =
K(s + a)
; b > a
s2(s + b)

Which of the loci system in figure can be a valid root-loci for the system?

A. Fig:- A
B. Fig:- B
C. Fig:- C
D. Fig:- D
Answer» B. Fig:- B
Discussion
59.

The characteristic equation of a closed loop system is given by s4 + 6s3 + 11s2 + 6s + K = 0 Stable closed loop behaviour can be ensured when gain K is such that

A. 0 < K < 10
B. K > 10
C. K <
D. 0 < K 20
Answer» B. K > 10
Discussion
60.

For a standard feedback control loop, the sensitivity of the closed-loop transfer function T to forward path gain G and feedback path gain H are
SGTSHT
A. -1/(1 + GH)-1(1 + GH)
B. -GH/(1 + GH)-H/(1 + GH)
C. G/(1 + GH)1/(1 + GH)
D. 1/(1 + GH)-GH/(1 +GH)
A. A
B. B
C. C
D. D
Answer» E.
Discussion
61.

The system with transfer function
K
s2(1 + sT)

is operated in closed-loop with unity feedback. The closed-loop system is

A. stable
B. unstable
C. marginally stable
D. conditionally stable
Answer» C. marginally stable
Discussion
62.

The transfer function G (s) is
K
s2(1 + sT)
. This open-loop system will be

A. stable
B. unstable
C. marginally stable
D. conditionally stable
Answer» B. unstable
Discussion
63.

Consider the following statements with reference to the block diagram of a control system given in the figure
1. For G2 = 0, the system is open-loop.
2. For G1 = 0, the system is closed-loop.
3. For G2 = H = 1, the system is closed-loop 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
Answer» D. 1 and 3 are correct
Discussion
64.

The unit impulse response of a system is given by C (t) = 0.5 e t/2. Its transfer function is

A. 1/(s + 2)
B. 1/(1 + 2s)
C. 2/(1 + 2s)
D. 2/(s + 2)
Answer» C. 2/(1 + 2s)
Discussion
65.

The open-loop transfer function of a unity negative feed back control system is given by
G(s) =
K(s + 2)
(s + 1)(s - 7)

the stability 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
Answer» C. stable and unstable
Discussion
66.

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 = 14, when the value of K is

A. 4355
B. 2436
C. 9600
D. 2463
Answer» C. 9600
Discussion
67.

In the root-locus for open-loop transfer function
G (s)H (s) =
K(s + 6)
(s + 3) (s + 5)

the break away and break-in' points are located respectively at

A. 2 and 1
B. 2.47 and 4.42
C. 7.58 and 7.23
D. 4.42 and 7.58
Answer» E.
Discussion
68.

The close-loop transfer function of a control system is given by
C(s)
=
1
R(s)1 + s
For the input r (t) = sin t, the steady state value of C(t) is equal to

A.
B. 1
C.
Answer» E.
Discussion
69.

For a unit step input, a system with forward path transfer function G(s) = 20/s2 and feedback path transfer function H(s) = (s + 5) has a steady state output of

A. 20
B. 5
C. 0.2
D. zero
Answer» E.
Discussion
70.

The error response of a second order system to a step input is obtained as
E (t) = 1.66 e 8t sin (6t + 37 ).
The damping ratio is

A. 0.4
B. 0.5
C. 0.8
D. 1.0
Answer» D. 1.0
Discussion
71.

The open loop transfer function of a unity feedback control system is given by
G (s) =
K(s + 2)
s(s2 + 2s + 2)

The centroid and angles of root locus asymptotes are respectively

A. zero and + 90 , 90
B. 2/3 and + 60 , 60
C. zero and + 120 , 120
D. 2/3 and 90 and 90 , + 90
Answer» B. 2/3 and + 60 , 60
Discussion
72.

The Laplace transform of the function i(t) is
I (s) =
10s + 4
s(s + 1)(s2 + 4s + 5)

Its final value will be

A. 4/5
B. 5/4
C. 4
D. 5
Answer» B. 5/4
Discussion
73.

A linear discrete-time system has the characteristic equation, z3 0.81z = 0
The system

A. is stable
B. is marginally stable
C. is unstable
D. stability cannot be assessed from the given information.
Answer» B. is marginally stable
Discussion
74.

A lag compensation network
(i) increases the gain of the original network without affecting stability
(ii) reduces the steady state error
(iii) reduces the speed of response
(iv) permits the increase of gain if phase margin is acceptable. In the above, correct statements are

A. All
B. (i) and (ii)
C. (ii), (iii) and (iv)
D. (iii) and (ii)
Answer» B. (i) and (ii)
Discussion
75.

Consider a feedback control system with loop transfer function
G(s) H(s) =
K(1 + 0 5s)
s(1 + s) (1 + 2s)

The type of the closed loop system is

A. zero
B. one
C. two
D. three
Answer» C. two
Discussion
76.

The open-loop transfer function of the given Bode plot is

A.
B.
Answer» B.
Discussion
77.

The transfer function of a linear system is the

A. ratio of the output V
B. 1 (t)
C. ratio of the derivatives of the output and the input.
D. ratio of the Laplace transform of the output and that of the input with all initial conditions zeros.
E. None of these
Answer» D. ratio of the Laplace transform of the output and that of the input with all initial conditions zeros.
Discussion
78.

A second order system is given as
G(s) =
K
(1 + 1s) (1 + 2s)

If the gain K is increased, then the phase margin

A. gets increased
B. gets decreased
C. is unaffected
D. gets decreased and becomes stable
Answer» C. is unaffected
Discussion
79.

G (s) =
1
s(1 + 6s)

the system is

A. stable
B. unstable
C. marginally stable
D. conditionally stable
Answer» D. conditionally stable
Discussion
80.

In the following, pick out the linear systems.
(i)
d2y(t)
+ a1
dy(t)
+ a2y(t) = u(t)
dt2dt

(ii) y
dy(t)
+ a1y(t)= a2u(t)
dt

(iii) 2
d2y
+ t
dy
+ t2y(t) =5
dt2dt
A. (i) and (ii)
B. (i) only
C. (i) and (iii)
D. (ii) and (iii)
Answer» D. (ii) and (iii)
Discussion
81.

The log-magnitude plot of a system is given below.
The system is a/an

A. integrator
B. PID controller
C. PD controller
D. proportional controller
Answer» C. PD controller
Discussion
82.

A plant has the following transfer function:
G (s) =
1
(s2+ 0 2s + 1)

For a step input it is required that the response settles to within 2% of its final value. The plant setting time is

A. 20 sec
B. 40 sec
C. 35 sec
D. 45 sec
Answer» C. 35 sec
Discussion
83.

In the following pick out the time-invariant systems.
(i)
dy(t)
 + 5y(t) = u(t)
dt

(ii) t
d2y(t)
 +
dy(t)
 + 2y(t) = v(t)
dt2dt

(iii)
d2y(t)
 + 5
dy(t)
 + 6y(t) = (t)
dt2dt
A. (i) and (iii)
B. (i) and (ii)
C. (ii) and (iii)
D. (i) only
Answer» B. (i) and (ii)
Discussion
84.

The Laplace transform of f(t) is F(s).
Given F(s) =
s2 + 2

The final value f(t) is

A. infinity
B. zero
C. one
D. None of these
Answer» B. zero
Discussion
85.

Consider the following overall T.F. for a unity feedback system
=
4
s2 + 4s + 4

Which of the following statements regarding this system are correct?
1. Position error constant KP for the system is 4.
2. The system type one.
3. The velocity error constant Kv for the system is finite.
Select the correct answer code

A. 1, 2, 3
B. 1, 2
C. 2, 3
D. s1, 3
Answer» E.
Discussion
86.

The number of roots of the equation
2s4 + s3 + 3s2 + 5s + 7 = 0
that lie in the right half of s plane is

A. zero
B. one
C. two
D. three
Answer» D. three
Discussion
87.

The condition of a stability for a unity feedback control system whose open loop transfer function is given by
G(s) =
e sT
s(s + 2)
A. T < 2
B. T = 2
C. T > 2
D. 0
Answer» B. T = 2
Discussion
88.

The transfer function of the system
K
s2 (1 + sT)
operated in closed loop mode with unity feedback. The system is

A. Stable
B. Unstable
C. Conditionally stable
D. Marginally stable
Answer» C. Conditionally stable
Discussion
89.

The unit step response of a second order linear system with zero initial states is given by
C (t) = 1 + 1.25 exp ( 6t) sin (8t tan 1 1.333); t 0
The damping ratio and the undamped natural frequency of oscillation for 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
Answer» B. 0.6 and 12.5 rad/s
Discussion
90.

The Laplace transformation of f (t) is
F(s) =
=
s2 + 2

the final value of f(t) is

A. infinity
B. zero
C. one
D. None of these
Answer» E.
Discussion
91.

The transfer function of the system
K
s2 (1 + sT)
is operated in open loop mode. The system is

A. Stable
B. Unstable
C. Conditionally stable
D. Marginally stable
Answer» C. Conditionally stable
Discussion
92.

The transmittance from A to B in the signal flow graph shown in the figure is

A.
B.
C.
D.
Answer» B.
Discussion
93.

Consider the following properties attributed to state model of a system
1. State model is unique
2. State model can be derived from the system transfer function
3. State model can be derived from time variant systems. 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
Answer» D. 1 and 3 are correct
Discussion
94.

A system has transfer function
1 s
1 + s
it is a

A. non-minimum phase system
B. minimum phase system
C. low phase system
D. second order system
Answer» B. minimum phase system
Discussion
95.

A linear second-order system with the transfer function
G(s) =
49
s2 + 8s + 49

is initially at rest and is subject to a step input signal. The response of the system will exhibit a peak overshoot of

A. 16%
B. 9%
C. 2%
D. zero
Answer» D. zero
Discussion
96.

The Transfer function of a system is
K
T + s
What is the steady state error when applied u(t) to closed loop system with unity feedback

A. K + T
Answer» D.
Discussion
97.

Consider the following statements regarding time-domain analysis of a control system
1. Derivative control improves system s transient performance
2. Integral control does not improve system s steady state performance
3. Integral control can convert a second order system into a third order system. Of these statements

A. 1 and 2 are correct
B. 1 and 3 are correct
C. 2 and 3 are correct
D. 1, 2 and 3 are correct
Answer» C. 2 and 3 are correct
Discussion
98.

It is given that
G (s) =
1
s2 (s + 2)
. This system in a closed loop with unity feedback. What is the order and type of the closed loop system?

A. 2 and 3
B. 3 and 2
C. 3 and 3
D. 2 and 2
Answer» C. 3 and 3
Discussion
99.

Given: KK

A. 0.01
B. 0.1
C. 1.0
D. 10
Answer» C. 1.0
Discussion
100.

The state representation of a second order system is

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
Answer» D. 1 and 3 are correct
Discussion