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QUESTION: 1

An under damped second order system having a transfer function of the form

has a frequency response plot shown in fig.

Q. The system gain K is

Solution:

From the fig. P6.5.1-2, |T(j0)| = 1

QUESTION: 2

An under damped second order system having a transfer function of the form

has a frequency response plot shown in fig.

Q. The damping factor ξ is approximately

Solution:

The peak value of T(jω) occurs when the denominator of function |T(jω)|^{2} is minimum i.e. when

QUESTION: 3

Consider the Bode plot of a ufb system shown in fig.

Q. The steady state error corresponding to a rampinput is

Solution:

The Bode plot is as shown in fig.

QUESTION: 4

Consider the Bode plot of a ufb system shown in fig.

The damping ratio is

Solution:

From Fig.:

QUESTION: 5

The Nyquist plot of a open-loop transfer function G(jω)H(jω) of a system encloses the (-1, j0) point. The gain margin of the system is

Solution:

If Nyquist plot encloses the point (-1, j0), the system is unstable and gain margin is negative.

QUESTION: 6

Consider a ufb system

The angle of asymptote, which the Nyquist plotapproaches as ω → 0 is

Solution:

Hence, the asymptote of the Nyquist plot tends to an angle of -90° as ω→ 0.

QUESTION: 7

If the gain margin of a certain feedback system isgiven as 20 dB, the Nyquist plot will cross the negativereal axis at the point

Solution:

Since system is stable, it will cross at s = -0.1

QUESTION: 8

The transfer function of an open-loop system is

The Nyquist plot will be of the form

Solution:

Hence (B) is correct option.

QUESTION: 9

Consider a ufb system whose open-loop transfer function is

The Nyquist plot for this system is

Solution:

Due to s there will be a infinite semicircle. Hence (C) is correct option.

QUESTION: 10

The open loop transfer function of a system is

The Nyquist plot for this system is

Solution:

∠GH(jw) = -270°+ 2 tan-1ω

For ω = 0, GH(jω) = ∞∠ -270°

For ω = 1 , ∠GH(jω) = -180°

For ω = ∞, GH(jω) = 0 ∠ - 90°

As ω increases from 0 to ∞, phase goes -270° to -90°.

Due to s^{3} term there will be 3 infinite semicircle.

QUESTION: 11

For the certain unity feedback system

The Nyquist plot is

Solution:

∠GH(j(ω) = -90 °- tan^{-1} ω - tan^{-1} 2ω - tan^{ -1} 3ω,

For ω = 0, GH(jω) = ∞∠ - 90°,

For ω = ∞, GH(jω) = 0∠- 360°,

Hence (A) is correct option.

QUESTION: 12

The Nyquist plot of a system is shown in fig. The open-loop transfer function is

The no. of poles of closed loop system in RHP are

Solution:

The open-loop poles in RHP are P = 0. Nyquist path enclosed 2 times the point (-1 + j0). Taking clockwise encirclements as negative N = -2.

N = P - Z, -2 = 0 -Z , Z = 2 which implies that two poles of closed-loop system are on RHP.

QUESTION: 13

The open-loop transfer function of a feedback control system is

Q. The Nyquist plot for this system is

Solution:

QUESTION: 14

If the damping of the system becomes equal to zero, which condition of the resonant frequency is likely to occur?

Solution:

QUESTION: 15

A unity feedback system has the open loop transfer function G(s)=1/((s−1)(s+2)(s+3))

The Nyquist plot of GG encircle the origin

Solution:

QUESTION: 16

The open-loop transfer function of a feedback system is

Q. The Nyquist plot of this system is

Solution:

QUESTION: 17

The open-loop transfer function of a feedback system is

The system is stable for K

Solution:

RHP poles of open-loop system P = 1, Z = P - N .

For closed loop system to be stable, Z = 0, 0 =1 - N ⇒N = 1

There must be one anticlockwise rotation of point (-1+ j0). It is possible when K > 1.

QUESTION: 18

A unity feedback system has open-loop transfer function

Q. The Nyquist plot for the system is

Solution:

The intersection with the real axis can be calculated as {GH(jω)} = 0, The condition gives ω(2ω^{2} -1) = 0

With the above information the plot in option (C) is correct.

QUESTION: 19

A unity feedback system has open-loop transfer function

Q. The phase crossover and gain crossover frequenciesare

Solution:

The Nyquist plot crosses the negative real axis

Hence phase crossover frequency is

The frequency at which magnitude unity is

QUESTION: 20

A unity feedback system has open-loop transfer function

The gain margin and phase margin are

Solution:

∠GH(jω) = -90°- tan^{-1} ω- tan^{-1} 2ω ,

At unit gain ω_{1} = 0.57 rad/sec,

Phase at this frequency is ∠GH(jω_{1}) = -90°- tan^{-1} 0.57 -tan^{-1} 2(0.57) = -168.42°

Phase margin = -168.420+180° = 11.6°

Note that system is stable. So gain margin and phase margin are positive value. Hence only possible option is (D).

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