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GATE Electrical Engineering (EE) Test: Modelling of Control Systems - 1


MCQ Practice Test & Solutions: Test: Modelling of Control Systems - 1 (10 Questions)

You can prepare effectively for Electrical Engineering (EE) GATE Electrical Engineering (EE) Mock Test Series 2027 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Modelling of Control Systems - 1". These 10 questions have been designed by the experts with the latest curriculum of Electrical Engineering (EE) 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 30 minutes
  • - Number of Questions: 10

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Test: Modelling of Control Systems - 1 - Question 1

The electrical time-constant of an armature- controlled dc servomotor is

Test: Modelling of Control Systems - 1 - Question 2

A mass spring system under equilibrium condition is shown in figure below.

The output displacement x(t) for M = 10 kg is given by

Detailed Solution: Question 2

The differential equation for the given system is 

or, 
Taking Laplace transform on both sides, we get: (10s2 + 30s + 20) X(s) = 1
or, 
or, 

Test: Modelling of Control Systems - 1 - Question 3

Two wheels are mechanically coupled as shown in figure below.

Here, ω1 and ω2 = angular velocities (in rad/s)
T1 and T2 = Torque (in N-m)
r1 and r2 = radius of the wheels (in cm)
θ1 and θ2 = angular displacements (in degrees)
N1, and N2 = No. of teeths on wheels
It is given that ω1 = 10 rad/s, N1 = 40, N2 - 20,
T1 = 5 N-m, r1 = 20 cm and θ1 = 20°.
Match List-I with List-ll and select the correct answer using the codes given below the lists: 

Detailed Solution: Question 3

We know that,


Test: Modelling of Control Systems - 1 - Question 4

The poles-and zeros of the transfer function  for the mechanical system shown below are respectively

Detailed Solution: Question 4

The differential equation for the given mechanical system is

Taking Laplace transform on both sides, we get

Test: Modelling of Control Systems - 1 - Question 5

Consider the mechanical system shown in figure below. 

Which one of the following circuits shows the force-voltage analogous electrical circuit for the mechanical diagram shown above?

Detailed Solution: Question 5



Thus, option (d) will be the correct circuit.

Test: Modelling of Control Systems - 1 - Question 6

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

Detailed Solution: Question 6

For mechanical rotational system, we have: 

For electrical system, we have

Comparing equations (i) and (ii), we have:

Test: Modelling of Control Systems - 1 - Question 7

Consider the mechanical system shown below:

The system is described by the differential equations:

Detailed Solution: Question 7

The free-body diagram for the two masses will be shown as below.

Hence, the differential equations for the two masses can be written as follows:

Test: Modelling of Control Systems - 1 - Question 8

Which of the following is not a desirable property of a servomotor in feedback control systems?

Detailed Solution: Question 8

Relation between electrical control system and rotor speed should be linear.

Test: Modelling of Control Systems - 1 - Question 9

Consider the following statements related to A.C. servomotors compared to D.C. servomotor used in control system applications.
1. It has less efficiency.
2. It is maintenance free.
3. It gives smooth operation.
4. It gives high power output.

Which of these statements is/are true regarding an A.C. servomotor?

Detailed Solution: Question 9

An A.C. servomotor doesn’t require brushes compared to a D.C. servomotor. So, it gives maintenance free operation. It’s efficiency is less due to low power output but, gives smooth operation.

Test: Modelling of Control Systems - 1 - Question 10

A field controlled DC servomotor is a

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