Stability Analysis and Root Locus - Control Systems - Electronics & Communication Engineering Previous Year Questions

1

2012 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2012

The feedback system shown below oscillates at 2 rad/s when

A

\(K = 2 \) and \(a = 0.75 \)

B

\(K = 3 \) and \(a = 0.75 \)

C

\(K = 4 \) and \(a = 0.5 \)

D

\(K = 2 \) and \(a = 0.5 \)

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2

2014 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2014 [Session 1]

Consider the feedback system shown in the figure. The Nyquist plot of \(G(s)\) is also shown. Which one of the following conclusions is correct?

A

\(G(s)\) is an all-pass filter

B

\(G(s)\) is a strictly proper transfer function

C

\(G(s)\) is a stable and minimum-phase transfer function

D

The closed-loop system is unstable for sufficiently large and positive \(k\)

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3

2014 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2014 [Session 1]

The phase margin in degrees of \(G(s) = \frac{10}{(s+0.1)(s+1)(s+10)}\) calculated using the asymptotic Bode plot is ______.

A

B

C

D

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4

2014 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2014 [Session 3]

In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus?

A

\(\frac{s+4}{(s+2)(s+6)(s+7)}\)

B

\(\frac{s+4}{(s+1)(s+2)(s+7)}\)

C

\(\frac{s+7}{(s+1)(s+2)(s+4)}\)

D

\(\frac{s+1}{(s+7)(s+4)}\)

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5

2014 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2014 [Session 4]

Consider a transfer function \(G_p(s) = \frac{ps^2+3ps-2}{s^2+(3+p)s+(2-p)}\) with \(p\) a positive real parameter. The maximum value of \(p\) until which \(G_p\) remains stable is ________.

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6

2014 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2014 [Session 4]

The characteristic equation of a unity negative feedback system is \(1 + KG(s) = 0\). The open loop transfer function \(G(s)\) has one pole at 0 and two poles at -1. The root locus of the system for varying \(K\) is shown in the figure. The constant damping ratio line, for \(\xi=0.5\), intersects the root locus at point A. The distance from the origin to point A is given as 0.5. The value of \(K\) at point A is ________.

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7

2016 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2016 [Session 1]

A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer function

A

encircles the s-plane point \(-1 + j0\) in the counterclockwise direction as many times as the number of right-half s-plane poles.

B

encircles the s-plane point \(0 - j1\) in the clockwise direction as many times as the number of right-half s-plane poles.

C

encircles the s-plane point \(-1 + j0\) in the counterclockwise direction as many times as the number of left-half s-plane poles.

D

encircles the s-plane point \(-1 + j0\) in the counterclockwise direction as many times as the number of right-half s-plane zeros.

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8

2016 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2016 [Session 1]

The open-loop transfer function of a unity-feedback control system is \( G(s) = \frac{K}{s^2+5s+5} \) The value of K at the breakaway point of the feedback control system's root-locus plot is __________

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9

2016 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2016 [Session 2]

The number and direction of encirclements around the point \( -1 + j0 \) in the complex plane by the Nyquist plot of \( G(s) = \frac{1-s}{4+2s} \) is

A

zero.

B

one, anti-clockwise.

C

one, clockwise.

D

two, clockwise.

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10

2016 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2016 [Session 2]

In the feedback system shown below \(G(s) = \frac{1}{(s+1)(s+2)(s+3)}\) . The positive value of \(k\) for which the gain margin of the loop is exactly 0 dB and the phase margin of the loop is exactly zero degree is ______

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11

2016 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2016 [Session 3]

The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as

\(s^3\)	1	\((2K + 3)\)
\(s^2\)	\(2K\)	4

The range of \(K\) for which the system is stable is

A

\(-2.0 < K < 0.5\)

B

\(0 < K < 0.5\)

C

\(0 < K < \infty\)

D

\(0.5 < K < \infty\)

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12

2016 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2016 [Session 3]

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as
\[G(s) = \frac{K(s+2)}{s^2 + 2s + 2} \quad \text{and} \quad H(s) = 1,\]
respectively. If the variable parameter \(K\) is real positive, then the location of the breakaway point on the root locus diagram of the system is __________

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13

2017 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2017

A unity feedback control system is characterized by the open-loop transfer function G(s) = 2(s + 1) / (s3 + ks2 + 2s + 1). The value of k for which the system oscillates at 2 rad/s is ________

A

P to Q

B

P to R

C

P to S

D

P to T

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14

2017 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2017

A unity feedback control system is characterized by the open-loop transfer function G(s) = 10K(s + 2) / (s3 + 3s2 + 10). The Nyquist path and the corresponding Nyquist plot of G(s) are shown in the figures below. If 0 < K < 1, then the number of poles of the closed-loop transfer function that lie in the right-half of the s-plane is

A

0

B

1

C

2

D

3

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15

2018 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2018

The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE:

A

Both the criteria provide information relative to the stable gain range of the system.

B

The general shape of the Nyquist plot is readily obtained from the Bode magnitude plot for all minimum-phase systems.

C

The Routh criterion is not applicable in the condition of transport lag, which can be readily handled by the Nyquist criterion.

D

The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.

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16

2018 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2018

The figure below shows the Bode magnitude and phase plots of a stable transfer function \(G(s) = \frac{n_0}{s^3 + d_2 s^2 + d_1 s + d_0}\).

Consider the negative unity feedback configuration with gain \(k\) in the feedforward path. The closed loop is stable for \(k < k_0\). The maximum value of \(k_0\) is ________.

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17

2019 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2019

Consider a unity feedback system, as in the figure shown, with an integral compensator \( \frac{K}{s} \) and open-loop transfer function \( G(s) = \frac{1}{s^2 + 3s + 2} \) where \( K > 0 \). The positive value of K for which there are exactly two poles of the unity feedback system on the \( j\omega \) axis is equal to ___________ (rounded off to two decimal places).

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18

2020 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2020

The pole-zero map of a rational function \(G(s)\) is shown below. When the closed contour \(\Gamma\) is mapped into the \(G(s)\)-plane, then the mapping encircles

A

the origin of the \(G(s)\)-plane once in the counter-clockwise direction.

B

the origin of the \(G(s)\)-plane once in the clockwise direction.

C

the point \(-1 + j0\) of the \(G(s)\)-plane once in the counter-clockwise direction.

D

the point \(-1 + j0\) of the \(G(s)\)-plane once in the clockwise direction.

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19

2020 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2020

The loop transfer function of a negative feedback system is G(s)H(s) = K(s+11) / [s(s+2)(s+8)]. The value of K, for which the system is marginally stable, is __________.

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20

2020 · Electronics & Communication Engineering · Control Systems · Stability Analysis and Root Locus

Electronics & Communication Engineering (EC) 2020

The characteristic equation of a system is $s^3 + 3s^2 + (K + 2)s + 3K = 0$. In the root locus plot for the given system, as K varies from 0 to ∞, the break-away or break-in point(s) lie within

A

$(-1, 0)$.

B

$(-2, -1)$.

C

$(-3, -2)$.

D

$(-\infty, -3)$.

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