# Test: The State-Variable Analysis

## 20 Questions MCQ Test RRB JE for Electrical Engineering | Test: The State-Variable Analysis

Description
Attempt Test: The State-Variable Analysis | 20 questions in 60 minutes | Mock test for Electronics and Communication Engineering (ECE) preparation | Free important questions MCQ to study RRB JE for Electrical Engineering for Electronics and Communication Engineering (ECE) Exam | Download free PDF with solutions
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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