GATE ECE Control Systems PYQs & Answers — Page 3

Questions 21–30 of 56. Imported answers require independent review unless marked reviewed.

Consider a closed-loop control system with unity negative feedback and

in the forward path, where the gain

. The complete Nyquist plot of the transfer function

is shown in the figure. Note that the Nyquist contour has been chosen to have the clockwise sense. Assume

has no poles on the closed right-half of the complex plane. The number of poles of the closed-loop transfer function in the closed right-half of the complex plane is ____________.

Diagram for Electronics and Communication Engineering question 21

Your answerChoose one option.

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The root-locus plot of a closed-loop system with unity negative feedback and transfer function

in the forward path is shown in the figure. Note that

is varied from 0 to

Select the transfer function

that results in the root-locus plot of the closed-loop system as shown in the figure.

Diagram for Electronics and Communication Engineering question 22

Your answerChoose one option.

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Consider an even polynomial

given by

where

is an unknown real parameter. The complete range of

for which

has all its roots on the imaginary axis is ________.

Your answerChoose one option.

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Two linear time-invariant systems with transfer functions

and

have unit step responses

and

, respectively. Which of the following statements is/are true?

Your answerSelect all correct options. You can choose more than one.

and

have the same percentage peak overshoot.

and

have the same steady-state value.

and

have the same damped frequency of oscillation.

and

have the same 2% settling time.

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The block diagram of a closed-loop control system is shown in the figure.

, and

are the Laplace transforms of the time-domain signals

, and

, respectively. Let the error signal be defined as

. Assuming the reference input

for all

, the steady-state error

, due to a unit step disturbance

, is ________ (rounded off to two decimal places).

Diagram for Electronics and Communication Engineering question 60

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The block diagram of a feedback control system is shown in the figure. The transfer function

of the system is

Diagram for Electronics and Communication Engineering question 13

Your answerChoose one option.

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The complete Nyquist plot of the open-loop transfer function

of a feedback control system is shown in the figure. If

has one zero in the right-half of the

-plane, the number of poles that the closed-loop system will have in the right-half of the

-plane is

Diagram for Electronics and Communication Engineering question 14

Your answerChoose one option.

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The electrical system shown in the figure converts input source current

to output voltage

Diagram for Electronics and Communication Engineering question 33

Current

in the inductor and voltage

across the capacitor are taken as the state variables, both assumed to be initially equal to zero, i.e.,

and

. The system is

Your answerChoose one option.

completely state controllable as well as completely observable

completely state controllable but not observable

completely observable but not state controllable

neither state controllable nor observable

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A unity feedback system that uses proportional-integral (PI) control is shown in the figure.

Diagram for Electronics and Communication Engineering question 48

The stability of the overall system is controlled by tuning the PI control parameters

and

. The maximum value of

that can be chosen so as to keep the overall system stable or, in the worst case, marginally stable (rounded off to three decimal places) is _____.

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The pole-zero map of a rational function

is shown below. When the closed contour

is mapped into the

-plane, then the mapping encircles

Diagram for Electronics and Communication Engineering question 11

Your answerChoose one option.

the origin of the

-plane once in the counter-clockwise direction.

the origin of the

-plane once in the clockwise direction.

the point

of the

-plane once in the counter-clockwise direction.

the point

of the

-plane once in the clockwise direction.

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GATE ECE Control Systems PYQs

Question 21

Question 22

Question 44

Question 50

Question 60

Question 13

Question 14

Question 33

Question 48

Question 11