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.

1.

Consider a unit feedback control system with open-loop transfer function
G (s) = K/ [s (s + 1)].
The steady state error of the system due to a unit step input is

A. zero
B. K
C. 1/ K
D.
Answer» B. K
Discussion
2.

Bode plot of a stable system is shown in figure below. The transfer function of the system is

A.
B.
C. None of these
Answer» C. None of these
Discussion
3.

Given: KK1 = 99; s = j1 rad/s, the sensitivity of the closed-loop system (shown in the figure) to variation in parameter K is approximately

A. 0.01
B. 0.1
C. 1.0
D. 10
Answer» C. 1.0
Discussion
4.

The state representation of a second order system is
x1 = x1 u, x2 = x1 2x2 + u
Consider the following statements regarding the above system:
1. The system is completely state controllable.
2. If x1 is the output, then the system is completely output controllable.
3. If x2 is the output, then the system is completely output controllable. 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
5.

The number of roots of s3 + 5 s2 + 7 s + 3 = 0 in the left half of the s-plane is

A. zero
B. one
C. two
D. three
Answer» E.
Discussion
6.

The maximum phase shift that can be provided by a lead compensator with transfer function
Gc(s) =
1 + 6s
1 + 2s

is

A. 15
B. 30
C. 45
D. 60
Answer» C. 45
Discussion
7.

An integral controller is used to improve the transient response of a first order system. If G (s) = 1/1 + s and the system is operated in closed-loop with unity feedback, what is the value of Ti if integral controller transfer function is 1/Ti s to provide damping ratio of 0.5?

A. 0.5
B. 2
C. 1
D. 4
Answer» D. 4
Discussion
8.

The open loop transfer function of a unity feedback control system is given by:
G(s) =
K
s(s + 1)

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

A. 1/ 2
B. 1
C. 0
D.
Answer» D.
Discussion
9.

A process with open-loop model
G(s) =
Ke sT4
s + 1

is controlled by a PID controller. For this process

A. the integral mode improves transient performance.
B. the integral mode improves steady-state performance
C. the derivative mode improves transient performance
D. the derivative mode improves steady-state performance.
E. B and C both
Answer» F.
Discussion
10.

The first 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 s-plane is

A. 0
B. 2
C. 3
D. 4
Answer» C. 3
Discussion
11.

The characteristic equation of a unity feedback control system is given by s3 + K1s2 + s + K2 = 0. Consider the following statements in this regard
1. For a given of K1, all the root-locus branches will terminate at infinity for K2 in the positive direction.
2. For a given value of K2, all the root-locus branches will terminate at infinity for variable K1 in the positive direction.
3. For a given value of K2, only one root-locus branch will terminate at infinity for 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
Answer» B. 3 alone is correct
Discussion
12.

Given a unity feedback system with open-loop transfer function.
G(s) =
K
s(s + 1)(s + 2)

the root locus plot of the system is of the form

A. Fig:- A
B. Fig:- B
C. Fig:- C
D. Fig:- D
Answer» B. Fig:- B
Discussion
13.

Consider the following statements regarding a first order system with a proportional (P) controller which exhibits an offset to a unit step input.
1. increase the gain of the P controller
2. add derivative mode
3. add integral mode 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» C. 2 and 3 are correct
Discussion
14.

If the closed-loop transfer function of unity negative feedback system is given by
T(s) =
an-1 s+an
sn + a1sn-1 + ........+an-1s+an

then the steady state error for a unit ramp is

A. an. an 1
B. an. an 2
C. an 2. an
D. Zero
Answer» D. Zero
Discussion
15.

The transfer function of a system is 1/1 + sT. The input to this system is u(t). The output would track this system but the error would be

A. 0
B. T
C.
D. T
E. T/2
Answer» B. T
Discussion
16.

Given G(s) =
1 - Is
s(s + 2)

The system with the transfer function is operated in a close-loop with unity feedback. The closed loop system is

A. stable
B. unstable
C. marginally stable
D. conditionally stable
Answer» B. unstable
Discussion
17.

The position and acceleration error coefficients for the open-loop transfer function
G(s) =
K
s2(s + 10) (s + 100)

respectively are

A. zero and infinity
B. infinity and zero
C. K/100 and zero
D. infinity and K/100
Answer» E.
Discussion
18.

The overshoot of the system
16K
s(s2 + 2s + 16

for a step input applied would be

A. 60%
B. 40%
C. 20%
D. 10%
Answer» C. 20%
Discussion
19.

The transfer function of transportation lag is e sT. If the lag is small as compare to the time constant of the system, it can be approximated by

A. sT
B. 1 + sT
C. 1 sT
D. 1/1 + sT
Answer» D. 1/1 + sT
Discussion
20.

For the unity feedback system shown below, the steady state, when the input is
R =
3
 -
1
 +
1
ss22s3

would be

A. 1/4
B. 0
C.
D. 1/2
Answer» B. 0
Discussion
21.

G (s) =
1 s
s(s + 2)

The system with this transfer function is operated in closed-loop with unity feedback. The closedloop system is

A. stable
B. unstable
C. marginally stable
D. conditionally stable
Answer» B. unstable
Discussion
22.

The transfer function is
K
(s + 1)(s + 2)(s + 3)
.
The break point lies between

A. 0 and 1
B. 1 and 2
C. 2 and 3
D. beyond 3
Answer» C. 2 and 3
Discussion
23.

Consider the control system shown in the following figure and the statements given below.
1. The system is of second order.
2. Basically, the system is having positive feedback.
3. The system is of type 1.
4. The dimension of the output is not the same as that of the input. Of these statements

A. 1 and 2 are correct
B. 2 and 4 are correct
C. 2, 3 and 4 are correct
D. 1, 2 and 3 are correct
Answer» C. 2, 3 and 4 are correct
Discussion
24.

G (s) =
K
s(1 + sT)
.
This system is operated in closedloop with unity feedback. The closed-loop system is

A. stable
B. unstable
C. marginally stable
D. conditionally stable
Answer» E.
Discussion
25.

The transfer function of a closed-loop system is
Fk(s) =
K(s + 3)
1 + s s2 + s3

. This system is

A. stable
B. unstable
C. marginally stable
D. conditionally stable
Answer» C. marginally stable
Discussion
26.

GA (j ), GB (j ) and GC (j ) are three transfer function whose phase variations are shown in the given figure. The magnitude variation with respect to frequency is the same for both GA (j ) and GC (j ), but their phase variation is as indicated by the curves labelled A and C in the given figure. The transfer function GB (j ) is such that
C (j ) = A (j ) + B (j )
GA, GB and GC are respectively

A. minimum phase, all pass and non-minimum phase functions
B. minimum phase, non-minimum phase and all pass functions
C. all pass, minimum phase and non-minimum phase functions
D. all pass, non-minimum phase and minimum phase functions.
Answer» C. all pass, minimum phase and non-minimum phase functions
Discussion
27.

The position and velocity error coefficients for the system of transfer function
G(s) =
50
(1 + 0.1s) (1 + 2s)

respectively are

A. zero and zero
B. zero and infinity
C. 50 and zero
D. 50 and infinity
Answer» D. 50 and infinity
Discussion
28.

The overall transfer function O(s)/I(s) is

A.
B.
Answer» D.
Discussion
29.

Consider a system shown in the given flgure with
G(s) =
K(s + 1)
s3 + as2 + 2s + 1

What value of K and a should be chosen so that the system oscillates?

A. K = 2, a = 1
B. K = 2, a = 0.75
C. K = 4, a = 1
D. K = 4, a = 0.75
Answer» C. K = 4, a = 1
Discussion
30.

The maximum phase shift that can be provided by a lead compensator with transfer function
G (s) =
1 + 6s
1 + 2s
is

A. 15
B. 30
C. 45
D. 60
Answer» C. 45
Discussion
31.

Consider the following polynomials
1. s4 + 7s3 + 17s2 + 17s + 6
2. s4 + 11s3 + 41s2 + 61s + 30
3. s4 + s3 + 2s2 + 3s + 2.
Among these polynomials, those which are Hurwitz would include

A. 1 and 3
B. 2 and 3
C. 1 and 2
D. 1, 2 and 3
Answer» D. 1, 2 and 3
Discussion
32.

The magnitude-frequency response of a control system is shown in the figure. The value of 1 and 2 are respectively

A. 10 and 200
B. 20 and 200
C. 20 and 400
D. 100 and 400
Answer» D. 100 and 400
Discussion
33.

The open-loop transfer function of a unity feedback control system is: G(s) = 1/(s + 2)2 The closed loop transfer function will have poles at

A. 2, 2
B. 2, 1
C. 2, j1
D. 2, j2
Answer» D. 2, j2
Discussion
34.

The maximum phase shift that can be obtained by using a lead compensator with transfer function
G(s) =
(1 + 0.15s)
(1 + 0.05s)

is equal to

A. 15
B. 30
C. 45
D. 60
Answer» C. 45
Discussion
35.

In the system shown in the figure,
r (t) = sin t
The steady-state response c(t) will exhibit a resonance peak at a frequency of

A. 4 rad/sec
B. 2
C. 2 rad/sec
D.
Answer» C. 2 rad/sec
Discussion
36.

For the transfer function
G(s) H(s) =
1
s(s + 1) (s + 0 5)

the phase cross-over frequency is

A. 0.5 rad/sec
B. 0.707 rad/sec
C. 1.732 rad/sec
D. 2 rad/sec
Answer» C. 1.732 rad/sec
Discussion
37.

The value of A matrix in X = AX for the system described by the differential equation + 2y + 3y = 0 is

A.
B.
C.
Answer» E.
Discussion
38.

Which one of the following statements are true of a type 1 system having unit gain in the forward path and a unity feedback?
1. Positional error constant Kp is equal to infinity
2. Acceleration error constant Ka is equal to zero
3. Steady-state error ess to a unit step displacement input is equal to one. 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
Answer» C. 2 and 3
Discussion
39.

Consider the following statements with reference to phase lead compensator.
1. increases the margin of stability
2. speeds up transient response
3. does not affect the system error constant. Of these statements

A. 2 and 3 are correct
B. 1 and 2 are correct
C. 1 and 3 are correct
D. 1, 2 and 3 are correct
Answer» C. 1 and 3 are correct
Discussion
40.

The open-loop transfer function with unity feedback are given below for different systems
1. G(s) =
2
s + 2

2. G(s) =
2
s(s + 2)

3. G(s) =
2
s2(s + 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
Answer» D. 4
Discussion
41.

Consider the following statement 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
42.

G(s) =
1 + s
s(1 + 0 5s)
. The corner frequencies are

A. 0 and 1
B. 0 and 2
C. 0 and 1
D. 1 and 2
Answer» E.
Discussion
43.

Given that the transfer function G (s) is
K
s2(1 + sT)
State the type and order of the system

A. 2 and 3
B. 3 and 2
C. 3 and 3
D. 2 and 2
Answer» B. 3 and 2
Discussion
44.

The second order system defined by
25
s2 + 5s + 25

is given a step input. The time taken for the output to settle within 2% of input is

A. 1.2 sec
B. 1.6 sec
C. 2 sec
D. 0.4 sec
Answer» C. 2 sec
Discussion
45.

The Nyquist plot given in figure corresponds to the system whose transfer function is

A. 1/(s + 1)
B.
C. 1/(s + 1)
D. (s + 1)/s
E. 1/s + 1
Answer» C. 1/(s + 1)
Discussion
46.

If the characteristic equation of a system is 3 + 14s2 + 56s + K = 0, then it will be stable only if

A. 0 < K < 784
B. 1 < K < 64
C. 10 > K > 660
D. 4 < K < 784
Answer» B. 1 < K < 64
Discussion
47.

A lead compensating network
(i) improves response time
(ii) increases resonant frequency
(iii) stabilizes the system with low phase margin
(iv) enables moderate increase in gain without affecting stability The correct statements are

A. All
B. (i) and (iv)
C. (ii) and (iii)
D. (ii) and (iv)
Answer» B. (i) and (iv)
Discussion
48.

A system is represented by
dy
+ 2y = 4t u(t)
dt

The ramp component in the forced response will be

A. t u (t)
B. 2t u (t)
C. 3t u (t)
D. 4t u (t)
Answer» C. 3t u (t)
Discussion
49.

The transfer function of a system is given by
G (j ) =
K
 K <
1
(j ) (j T + 1)T

Which one of the following is the Bode plot of this

A. Fig: - A
B. Fig: - B
C. Fig: - C
D. Fig: - D
Answer» D. Fig: - D
Discussion
50.

Which one of the following system is completely state controllable?

A.
B.
Answer» B.
Discussion