Stability and Compensation - Control Systems - Electrical Engineering Previous Year Questions

1

2007 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2007

The system shown in the figure is

A

stable

B

unstable

C

conditionally stable

D

stable for input \(u_1\), but unstable for input \(u_2\)

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2

2007 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2007

The system 900/[s(s+1)(s+9)] is to be compensated such that its gain-crossover frequency becomes same as its uncompensated phase-crossover frequency and provides a 45° phase margin. To achieve this, one may use

A

a lag compensator that provides an attenuation of 20 dB and a phase lag of 45° at the frequency of 3√3 rad/s

B

a lead compensator that provides an amplification of 20 dB and a phase lead of 45° at the frequency of 3 rad/s

C

a lag-lead compensator that provides an amplification of 20 dB and a phase lag of 45° at the frequency of √3 rad/s.

D

a lag-lead compensator that provides an attenuation of 20 dB and phase lead of 45° at the frequency of 3 rad/s

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3

2007 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2007

Consider the discrete-time system shown in the figure where the impulse response of G(z) is g(0) = 0, g(1) = g(2) = 1, g(3) = g(4) = ... = 0.

This system is stable for range of values of K

A

[-1, 1/2]

B

[-1, 1]

C

[-1/2, 1]

D

[-1/2, 2]

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4

2007 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2007

If the loop gain K of a negative feedback system having a loop transfer function K(s+3)/(s+8)² is to be adjusted to induce a sustained oscillation then

A

The frequency of this oscillation must be 4/√3 rad/s

B

The frequency of this oscillation must be 4 rad/s

C

The frequency of this oscillation must be 4 or 4/√3 rad/s

D

such a K does not exist

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5

2008 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2008

Figure shows a feedback system where K > 0.

The range of K for which the system is stable will be given by

A

0 < K < 30

B

0 < K < 39

C

0 < K < 390

D

K > 390

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6

2009 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2009

The polar plot of an open loop stable system is shown below. The closed loop system is

A

always stable

B

marginally stable

C

unstable with one pole on the RH s-plane

D

unstable with two poles on the RH s-plane

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7

2009 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2009

The first two rows of Routh's tabulation of a third order equation are as follows.

\(s^3\)	2	2
\(s^2\)	4	4

This means there are

A

two roots at \(s = \pm j\) and one root in right half s-plane

B

two roots at \(s = \pm j2\) and one root in left half s-plane

C

two roots at \(s = \pm j2\) and one root in right half s-plane

D

two roots at \(s = \pm j\) and one root in left half s-plane

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8

2010 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2010

The characteristic equation of a closed-loop system is \(s(s+1)(s+3) + k(s+2) = 0, \; k > 0\). Which of the following statements is true?

A

Its roots are always real

B

It cannot have a breakaway point in the range -1 < Re[s] < 0

C

Two of its roots tend to infinity along the asymptotes Re[s] = -1

D

It may have complex roots in the right half plane

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9

2011 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2011

The open loop transfer function \(G(s)\) of a unity feedback control system is given as, \(G(s) = \frac{k\left(s+\frac{2}{3}\right)}{s^2(s+2)}\) From the root locus, it can be inferred that when \(k\) tends to positive infinity,

A

three roots with nearly equal real parts exist on the left half of the \(s\)-plane

B

one real root is found on the right half of the \(s\)-plane

C

the root loci cross the \(j\omega\) axis for a finite value of \(k; k \neq 0\)

D

three real roots are found on the right half of the \(s\)-plane

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10

2012 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 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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11

2012 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2012

G_c(s) is a lead compensator if

A

a=1, b=2

B

a=3, b=2

C

a=-3, b=-1

D

a=3, b=1

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12

2014 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2014 [Session 1]

In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of

A

only one root at the origin

B

imaginary roots

C

only positive real roots

D

only negative real roots

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13

2014 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2014 [Session 1]

For the given system, it is desired that the system be stable. The minimum value of \(\alpha\) for this condition is ______.

Check answer

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14

2014 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2014 [Session 2]

A system with the open loop transfer function \( G(s) = \frac{K}{s(s+2)(s^2+2s+2)} \) is connected in a negative feedback configuration with a feedback gain of unity. For the closed loop system to be marginally stable, the value of K is __________.

Check answer

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15

2014 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2014 [Session 3]

A single-input single-output feedback system has forward transfer function \( G(s) \) and feedback transfer function \( H(s) \). It is given that \( |G(s)H(s)| \ll 1 \). Which of the following is true about the stability of the system?

A

The system is always stable

B

The system is stable if all zeros of \(G(s)H(s) \) are in left half of the s-plane

C

The system is stable if all poles of \(G(s)H(s) \) are in left half of the s-plane

D

It is not possible to say whether or not the system is stable from the information given

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16

2016 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2016 [Session 1]

Loop transfer function of a feedback system is \(G(s)H(s) = \frac{s+3}{s^2(s-3)}\). Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of \(G(s)H(s)\) encircles \(-1+j0\)

A

once in clockwise direction

B

twice in clockwise direction

C

once in anticlockwise direction

D

twice in anticlockwise direction

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17

2016 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2016 [Session 1]

Given the following polynomial equation
\(s^3 + 5.5 s^2 + 8.5 s + 3 = 0\),
the number of roots of the polynomial, which have real parts strictly less than \(-1\), is ________.

Check answer

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18

2016 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2016 [Session 2]

The open loop transfer function of a unity feedback control system is given by \( G(s) = \frac{K(s+1)}{s(1+Ts)(1+2s)} \), \( K > 0, T > 0 \). The closed loop system will be stable if,

A

\(0 < T < \frac{4(K+1)}{K-1} \)

B

\(0 < K < \frac{4(T+2)}{T-2} \)

C

\(0 < K < \frac{T+2}{T-2} \)

D

\(0 < T < \frac{8(K+1)}{K-1} \)

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19

2016 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2016 [Session 2]

The gain at the breakaway point of the root locus of a unity feedback system with open loop transfer function \( G(s) = \frac{Ks}{(s-1)(s-4)} \) is

A

1

B

2

C

5

D

9

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20

2017 · Electrical Engineering · Control Systems · Stability and Compensation

Electrical Engineering (EE) 2017 [Session 1]

A closed loop system has the characteristic equation given by \( s^3 + Ks^2 + (K+2)s + 3 = 0 \). For this system to be stable, which one of the following conditions should be satisfied?

A

0 < K < 0.5

B

0.5 < K < 1

C

0 < K < 1

D

K > 1

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