Test: State Variable Analysis - 1

# Test: State Variable Analysis - 1 - Electrical Engineering (EE)

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## 10 Questions MCQ Test GATE Electrical Engineering (EE) 2024 Mock Test Series - Test: State Variable Analysis - 1

Test: State Variable Analysis - 1 for Electrical Engineering (EE) 2023 is part of GATE Electrical Engineering (EE) 2024 Mock Test Series preparation. The Test: State Variable Analysis - 1 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: State Variable Analysis - 1 MCQs are made for Electrical Engineering (EE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: State Variable Analysis - 1 below.
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Test: State Variable Analysis - 1 - Question 1

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

Test: State Variable Analysis - 1 - Question 2

### For arbitrary pole placement, the following combination is necessary.

Test: State Variable Analysis - 1 - Question 3

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

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

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

Test: State Variable Analysis - 1 - Question 4

The eigen values of linear system are the location of

Detailed Solution for Test: State Variable Analysis - 1 - Question 4

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

Test: State Variable Analysis - 1 - Question 5

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

Its characteristic equation will be given by

Detailed Solution for Test: State Variable Analysis - 1 - Question 5

Characteristic equation is

or, s2 + 5s + 2 = 0

Test: State Variable Analysis - 1 - 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

Detailed Solution for Test: State Variable Analysis - 1 - Question 6

Poles of given system are given by

Test: State Variable Analysis - 1 - 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.

Test: State Variable Analysis - 1 - Question 8

The vector matrix differential equation of a system is given by

The state transition matrix of the system is

Detailed Solution for Test: State Variable Analysis - 1 - Question 8

We have:

Test: State Variable Analysis - 1 - Question 9

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

​The characteristic equation is

Detailed Solution for Test: State Variable Analysis - 1 - Question 9

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 s3 + 15s2 + 75s + 125 = 0

Test: State Variable Analysis - 1 - Question 10

A system is described by the following equations:

The transfer function of the system is

Detailed Solution for Test: State Variable Analysis - 1 - Question 10

Transfer function is given by

Given,

and

Now,

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## GATE Electrical Engineering (EE) 2024 Mock Test Series

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