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This mock test of Test: The State-Variable Analysis for Electronics and Communication Engineering (ECE) helps you for every Electronics and Communication Engineering (ECE) entrance exam.
This contains 20 Multiple Choice Questions for Electronics and Communication Engineering (ECE) Test: The State-Variable Analysis (mcq) to study with solutions a complete question bank.
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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:

(s^{3} + a_{2}s^{2} + a_{1}s + a_{0})C(s) = b_{0}R(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 C_{M} = 0. Hence system is not controllable. det O_{M }= 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 O_{M} 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 O_{M} = 0. Thus system is not observable

det C_{M} = -1. Thus system is controllable.

QUESTION: 15

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

Solution:

v_{c} and i_{L} are state variable.

Hence equation are

QUESTION: 16

For the network shown in fig. The output is

i_{R}(t). The state space representation is

Solution:

Hence v_{1} and i_{3} 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. v_{C }and i_{L} are available in differential form and linearly independent. Hence v_{C }and i_{L} 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. i_{2} ,i_{4} and v_{o} are available in differentiated form hence these are state variable.

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