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This mock test of State Variable Analysis - 1 for Electrical Engineering (EE) helps you for every Electrical Engineering (EE) entrance exam.
This contains 10 Multiple Choice Questions for Electrical Engineering (EE) State Variable Analysis - 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Which one of the following information is necessary to formulate the problem of control systems optimization?

Solution:

QUESTION: 2

For arbitrary pole placement, the following combination is necessary.

Solution:

QUESTION: 3

For a linear time invariant system, an optimal controller can be designed if

Solution:

An optimal controller for an LTI system can be designed provided the system is both controllable and observable

QUESTION: 4

The eigen values of linear system are the location of

Solution:

Eigen value are given by | sI - A | = 0, which is the location of poles.

QUESTION: 5

If the system matrix of a linear time invariant continuous system is given by

Its characteristic equation will be given by

Solution:

Characteristic equation is

or, s^{2} + 5s + 2 = 0

QUESTION: 6

The state-variable description of a linear autonomous system is is a two-dimensional state vector and A is a matrix given by

The poles of the system are located at

Solution:

Poles of given system are given by

QUESTION: 7

Assertion (A): The eigen values of a linear continuous-data time invariant system controls the stability of the system.

Reason (R): The roots of the characteristic equation are the same as the eigen values of system matrix A of the state equations.

Solution:

QUESTION: 8

The vector matrix differential equation of a system is given by

The state transition matrix of the system is

Solution:

We have:

QUESTION: 9

The system matrix of a continous time system is given by:

The characteristic equation is

Solution:

The characteristic equation | sI - A | = 0.

Now, | sI - A | = 0

or, (s + 5) [(s + 5)^{2} + 0] + 1 (0 - 0) + 0 = 0

or, (s + 5)^{3} = 0 or s^{3} + 15s^{2} + 75s + 125 = 0

QUESTION: 10

A system is described by the following equations:

The transfer function of the system is

Solution:

Transfer function is given by

Given,

and

Now,

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