Test: Control System - 2

# Test: Control System - 2 - Electronics and Communication Engineering (ECE)

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## 20 Questions MCQ Test GATE ECE (Electronics) 2024 Mock Test Series - Test: Control System - 2

Test: Control System - 2 for Electronics and Communication Engineering (ECE) 2023 is part of GATE ECE (Electronics) 2024 Mock Test Series preparation. The Test: Control System - 2 questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Control System - 2 MCQs are made for Electronics and Communication Engineering (ECE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Control System - 2 below.
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Test: Control System - 2 - Question 1

### The represents of  in static diagram will be:

Detailed Solution for Test: Control System - 2 - Question 1

From options we can easily solve the problem

Forward paths are:

Individual loop,

Test: Control System - 2 - Question 2

### the angle of departure of the root locus at s = —1 + j is

Detailed Solution for Test: Control System - 2 - Question 2

∴​

Test: Control System - 2 - Question 3

### The open-loop transfer function of a system is . The root locus of the system is

Detailed Solution for Test: Control System - 2 - Question 3

Test: Control System - 2 - Question 4

The open-loop transfer function of a system is G(s)  =   Indicate the correct root locus diagram is

Detailed Solution for Test: Control System - 2 - Question 4

Breakaway point:

s = —3.4 is a valid breakaway point.

Test: Control System - 2 - Question 5

A negative feedback control system has a transfer function G(s)

compensator Gc(s) =   in order to achieve zero steady state error for a step input. Select 'a' and 'k' so that the overshoot to a step is approximately 5% and the settling time (with a 2% criterion) is approximately 1 second.

Detailed Solution for Test: Control System - 2 - Question 5

The characteristics equation is 1 + Gc(s) G(s) I-1(s) = 0

compare equation (i) to standard

Now,

Test: Control System - 2 - Question 6

The transfer function of a lead compensator is Gc s =    . The maximum phase shift that can be obtained from this compensator is

Detailed Solution for Test: Control System - 2 - Question 6

The standard transfer function of lead compensator is

......(i)

and given transfer function

put s = j ω then,

......(ii)

Compare equation (i) and (ii) we gt,

∴​

∴​ Maximum phase shift =

∴​

Test: Control System - 2 - Question 7

Calculate the sensitivity of the closed-loop system shown in figure below with respect to the forward path transfer function at w = 1.3 rad/sec.

Detailed Solution for Test: Control System - 2 - Question 7

Here,

and H(s) = 0.50

Test: Control System - 2 - Question 8

The magnitude plot of a transfer function is shown in figure below. The transfer function is

Detailed Solution for Test: Control System - 2 - Question 8

Initially slope is —6 dB/octave i.e. —20 dB/dec. so there must be a pole at origin. At ω = 2 rad/sec slope change to ω db/dec. so there is a zero at ω = 2

and At 0 = 10 rad/sec, slope change to —20 dB/sec. so there is a pole at ω = 10.

∴ Transfer function =

∴ K = 0

∴ Transfer function =

*Answer can only contain numeric values
Test: Control System - 2 - Question 9

The open-loop transfer function of a feedback system is

The gain margin of the system is___

Detailed Solution for Test: Control System - 2 - Question 9

*Answer can only contain numeric values
Test: Control System - 2 - Question 10

The open-loop transfer function of a feedback system is G (s)H (s) =

The value of gain k for obtaining a gain margin of 3 dB for stable system is_________

Detailed Solution for Test: Control System - 2 - Question 10

Test: Control System - 2 - Question 11

In the figure given below the phase margin and the gain margin are:

Detailed Solution for Test: Control System - 2 - Question 11

Test: Control System - 2 - Question 12

A LTI system is characterized by the homogeneous state equation The initial state is

The state transition matrix 4(t) is

Detailed Solution for Test: Control System - 2 - Question 12

Given

Test: Control System - 2 - Question 13

The state equation in the phase canonical form can be obtained from the transfer function by:

Detailed Solution for Test: Control System - 2 - Question 13

The state equation from transfer function by parallel decomposition in the phase canonical form.

Test: Control System - 2 - Question 14

Consider the system shown in figure below and investigate whether it is observable or not.

Detailed Solution for Test: Control System - 2 - Question 14

and

and

For observability:

So the System is Observable

Test: Control System - 2 - Question 15

For a (-)ve feedback second order control system in its step response, the maximum value of the output response in time domain form is given by

Q. The damping factor (damping coefficient) of this system is

Detailed Solution for Test: Control System - 2 - Question 15

From the conventional approach we have,

Give that  C(t)Imax = 1.75

∴ Mp = Maximum overshoot = 1.75 - 1.00 = 0.75

Test: Control System - 2 - Question 16

For a (-)ve feedback second order control system in its step response, the maximum value of the output response in time domain form is given by

Q. The open-loop zero frequency gain of this given unity feedback control system equals to

Detailed Solution for Test: Control System - 2 - Question 16

Closed loop transfer function

(put, H(s) = 1)

= Open loop transfer function

∴ Open loop Gain at zero frequency i.e. s

Test: Control System - 2 - Question 17

The block diogram of a feedback system is shown in figure (a).

Q. Find the minimum value of G for which the step response of the system would

exhibit an overshoot as shown in figure (b).

Detailed Solution for Test: Control System - 2 - Question 17

Closed loop transfer function:

Characteristic equation s2 + 3s + G = 0

For minimum valueof G 'ξ’ should be 0.6.

G = 6.25

Test: Control System - 2 - Question 18

The block diogram of a feedback system is shown in figure (a).

Q.  For G equal to twice this minimum value, find the time period 't' indicated in figure (b).

Detailed Solution for Test: Control System - 2 - Question 18

∴

Test: Control System - 2 - Question 19

The system shown in figure below has the oscillation of 2.5 rad/sec, and there are no poles in right half of s-plane.

Q. Determine the values of Kmar.

Detailed Solution for Test: Control System - 2 - Question 19

Since the system oscillates, it is marginally stable. The characteristic equation of the system becomes.

Now the Routh's Array is

At marginal value of k,

Again, at this value of p,

Given, ω = 2.5 rad /sec, therefore

k + 3 = 6.25

∴ k = 3.25

Test: Control System - 2 - Question 20

The system shown in figure below has the oscillation of 2.5 rad/sec, and there are no poles in right half of s-plane.

Q. Also find the value of P.

Detailed Solution for Test: Control System - 2 - Question 20

From the above solution:

at k = 3.25 then,

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## GATE ECE (Electronics) 2024 Mock Test Series

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