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Test: The State Variable Analysis - 3 - Electrical Engineering (EE) MCQ


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20 Questions MCQ Test GATE Electrical Engineering (EE) Mock Test Series 2025 - Test: The State Variable Analysis - 3

Test: The State Variable Analysis - 3 for Electrical Engineering (EE) 2024 is part of GATE Electrical Engineering (EE) Mock Test Series 2025 preparation. The Test: The State Variable Analysis - 3 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: The State Variable Analysis - 3 MCQs are made for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: The State Variable Analysis - 3 below.
Solutions of Test: The State Variable Analysis - 3 questions in English are available as part of our GATE Electrical Engineering (EE) Mock Test Series 2025 for Electrical Engineering (EE) & Test: The State Variable Analysis - 3 solutions in Hindi for GATE Electrical Engineering (EE) Mock Test Series 2025 course. Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free. Attempt Test: The State Variable Analysis - 3 | 20 questions in 60 minutes | Mock test for Electrical Engineering (EE) preparation | Free important questions MCQ to study GATE Electrical Engineering (EE) Mock Test Series 2025 for Electrical Engineering (EE) Exam | Download free PDF with solutions
Test: The State Variable Analysis - 3 - Question 1

The state-space representation for a system is

The transfer function Y(s) /U(s) is ​ ​ ​

Detailed Solution for Test: The State Variable Analysis - 3 - Question 1





Substituting the values,

Test: The State Variable Analysis - 3 - Question 2

Determine the state-space representation for the transfer function given in question. Choose the state variable as follows

Q.   ​ ​ ​

Detailed Solution for Test: The State Variable Analysis - 3 - Question 2


(s3 + a2s2 + a1s + a0)C(s) = b0R(s)
Taking the inverse Laplace transform assuming zero initial conditions 



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Test: The State Variable Analysis - 3 - Question 3

Determine the state-space representation for the transfer function given in question. Choose the state variable as follows

Q. 

Detailed Solution for Test: The State Variable Analysis - 3 - Question 3

Fourth order hence four state variable

Test: The State Variable Analysis - 3 - Question 4

A state-space representation of a system is given by

The time response of this system will be​ ​ ​ ​

Detailed Solution for Test: The State Variable Analysis - 3 - Question 4




Test: The State Variable Analysis - 3 - Question 5

Detailed Solution for Test: The State Variable Analysis - 3 - Question 5





Test: The State Variable Analysis - 3 - Question 6

Detailed Solution for Test: The State Variable Analysis - 3 - Question 6



Test: The State Variable Analysis - 3 - Question 7

Consider the system shown in fig.

The controllability matrix is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 7



Test: The State Variable Analysis - 3 - Question 8

Consider the system shown in fig.

The observability matrix is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 8


Test: The State Variable Analysis - 3 - Question 9

Consider the system shown in fig.

The system is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 9

det CM = 0. Hence system is not controllable. det OM = 1. Hence system is observable.

Test: The State Variable Analysis - 3 - Question 10

Consider the system shown in fig.

Q. The controllability matrix for this system is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 10




Test: The State Variable Analysis - 3 - Question 11

Consider the system shown in fig.

The observability matrix is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 11




Test: The State Variable Analysis - 3 - Question 12

Consider the system shown in fig.

Q. The system is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 12

Since the determinant is not zero, the 3 x 3 matrix is nonsingular and system is controllable


The rank of OM is 3. Hence system is observable.

Test: The State Variable Analysis - 3 - Question 13

A state flow graph is shown in fig.

​ ​ ​

Q.The state and output equation for this system is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 13

Test: The State Variable Analysis - 3 - Question 14

A state flow graph is shown in fig.

The system is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 14

det OM = 0. Thus system is not observable

det CM = -1. Thus system is controllable.

Test: The State Variable Analysis - 3 - Question 15

Consider the network shown in fig. The state-space representation for this network is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 15


vc and iL are state variable.

Hence equation are 

Test: The State Variable Analysis - 3 - Question 16

For the network shown in fig. The output is

iR(t). The state space representation is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 16


Hence v1 and i3 are state variable.



Test: The State Variable Analysis - 3 - Question 17

Consider the network shown in fig. This system may be represented in state space representation 

Q. The state variable may be

Detailed Solution for Test: The State Variable Analysis - 3 - Question 17

Energy storage elements are capacitor and inductor. vC and iL are available in differential form and linearly independent. Hence vC and iL are suitable for state-variable.

Test: The State Variable Analysis - 3 - Question 18

Consider the network shown in fig. This system may be represented in state space representation  

Q. If state variable are chosen as in previous question, then the matrix A is  

Detailed Solution for Test: The State Variable Analysis - 3 - Question 18




.....(i)
.....(ii)
Solving equation (i) and (ii)

Test: The State Variable Analysis - 3 - Question 19

Consider the network shown in fig. This system may be represented in state space representation  

Q. The matrix B is  

Detailed Solution for Test: The State Variable Analysis - 3 - Question 19

Test: The State Variable Analysis - 3 - Question 20

Consider the network shown in fig.

Q. The state variable may be

Detailed Solution for Test: The State Variable Analysis - 3 - Question 20

There are three energy storage elements, hence 3 variable. i2 ,i4 and vo are available in differentiated form hence these are state variable.

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