The State-Variable Analysis - MCQ Test


20 Questions MCQ Test Mock Tests Electronics & Communication Engineering GATE 2020 | The State-Variable Analysis - MCQ Test


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This mock test of The State-Variable Analysis - MCQ Test for Railways helps you for every Railways entrance exam. This contains 20 Multiple Choice Questions for Railways The State-Variable Analysis - MCQ Test (mcq) to study with solutions a complete question bank. The solved questions answers in this The State-Variable Analysis - MCQ Test quiz give you a good mix of easy questions and tough questions. Railways students definitely take this The State-Variable Analysis - MCQ Test exercise for a better result in the exam. You can find other The State-Variable Analysis - MCQ Test extra questions, long questions & short questions for Railways on EduRev as well by searching above.
QUESTION: 1

The state-space representation for a system is

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

Solution:





Substituting the values,

QUESTION: 2

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

Q.   ​ ​ ​

Solution:


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



QUESTION: 3

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

Q. 

Solution:

Fourth order hence four state variable

QUESTION: 4

A state-space representation of a system is given by

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

Solution:




QUESTION: 5

Solution:





QUESTION: 6

Solution:



QUESTION: 7

Consider the system shown in fig.

The controllability matrix is

Solution:



QUESTION: 8

Consider the system shown in fig.

The observability matrix is

Solution:


QUESTION: 9

Consider the system shown in fig.

The system is

Solution:

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

QUESTION: 10

Consider the system shown in fig.

Q. The controllability matrix for this system is

Solution:




QUESTION: 11

Consider the system shown in fig.

The observability matrix is

Solution:




QUESTION: 12

Consider the system shown in fig.

Q. The system is

Solution:

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.

QUESTION: 13

A state flow graph is shown in fig.

​ ​ ​

Q.The state and output equation for this system is

Solution:

QUESTION: 14

A state flow graph is shown in fig.

The system is

Solution:

det OM = 0. Thus system is not observable

det CM = -1. Thus system is controllable.

QUESTION: 15

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

Solution:


vc and iL are state variable.

Hence equation are 

QUESTION: 16

For the network shown in fig. The output is

iR(t). The state space representation is

Solution:


Hence v1 and i3 are state variable.



QUESTION: 17

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

Q. The state variable may be

Solution:

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.

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  

Solution:




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

QUESTION: 19

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

Q. The matrix B is  

Solution:

QUESTION: 20

Consider the network shown in fig.

Q. The state variable may be

Solution:

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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