# Test: Control System- 2

## 20 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: Control System- 2

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Attempt Test: Control System- 2 | 20 questions in 60 minutes | Mock test for GATE preparation | Free important questions MCQ to study GATE Electrical Engineering (EE) 2023 Mock Test Series for GATE Exam | Download free PDF with solutions
QUESTION: 1

Solution:
QUESTION: 2

### The transfer function of a second order system is given as The peak (A) value of the output for unit  step input is

Solution:    QUESTION: 3

### If the resonant peak of the system is B, then the value of B/A is

Solution:    QUESTION: 4

A portion of the polar plot of an open-loop transfer function is shown in the given figure The phase margin and gain margin will be respectively

Solution:

Phase margin = 90° − 30° = 60° Gain margin = 1/0.75

QUESTION: 5

The open-loop transfer function of a unity negative feedback system is The polar plot of the system will be

Solution: The polar plot intersects with the negative real axis as in making imaginary term of G(jω) to be zero, the solution exists.

QUESTION: 6

The compensator would provide a maximum phase shift of

Solution:

Maximum phase shift    QUESTION: 7

A step input is applied to a system with the transfer function The output response will be

Solution:     QUESTION: 8

Which one of the following characteristic equations of result in the stable operation of the feedback system?

Solution:

For stable operation, all coefficients of the characteristic equation should be real and have the same sign and none of the coefficients should be zero.

QUESTION: 9

Consider the following statements:
Routh-Hurwitz criterion gives
1. absolute stability
2. the number of roots lying on the right half of the s-plane
3. the gain margin and phase margin
Which of these statements are correct?

Which of these statements are correct?

Solution:

Routh - Hurwitz criterion gives absolute stability and the number of roots lying on the right half of the s-plane but it does not tell about the gain margin and phase margin.

QUESTION: 10

The polar plot (for positive frequencies) for the open-loop transfer function of a unity feedback control system is shown in the given figure The phase margin and the gain margin ofthe system are respectively

Solution: QUESTION: 11

For the given network, the maximum phase lead φm of V0 with respect to Vi is Solution:          QUESTION: 12

For the system dynamics described by differential equationy+3y+2y=u(t) the transfer function of the system represented in controllable canonical form is The matrix A would be

Solution:

General representation of phase variable representation:      QUESTION: 13

For the signal flow diagram shown in the given figure, the transmittance between x2 and x1 is Solution:    QUESTION: 14

Consider the mechanical system shown in the given figure. If the system is set into motion by unit impulse force, the equation of the resulting oscillation will be Solution:    QUESTION: 15

Nyquist plot shown in the given figure is for a type

1. Solution:  (i) When a pole is added at negative real axis, the tail of the plot remains at the same position whereas head of plot shifts by 90° in clockwise direction.

(ii) When a pole is added at origin, both the tail and head of the plot shift by 90° in clockwise direction.

QUESTION: 16

An open loop transfer function of a unity feedback control system has two finite zeros, two poles at origin and two pairs of complex conjugate poles. The slope of high frequency asymptote in Bode magnitude plot will be

Solution:

No. of poles, n = 6
No. of zeros, m = 2
Slope of high frequency asymptote
= −20 (n−m)
= −20 (6−2)

QUESTION: 17

Match List-I (Pole-zero plot of linear control system) with
List-II (Responses of the system) and select the correct answer:
Codes:    Codes:

A    B    C  D

Solution:
QUESTION: 18

The unit impulse response of a system having transfer function K/(s + α) is shown below. The value of α is Solution:   QUESTION: 19

The transfer function of a phase lead network as shown in the figure below is  The values of R1 and R2 are respectively

Solution:   QUESTION: 20

The forward path transfer function of a unity feedback system is given by The frequency response of this system will exhibit the resonance peak at

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