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QUESTION: 1

With the value of "a" set for phase margin of π/4, the value of unit impulse response of the open loop system at t = 1 second is equal to

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(j_{ω}) 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 V_{0} with respect to V_{i} 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 x_{2} and x_{1} 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

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)

= −80 dB/decade

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

Solution:

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