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Control Systems
Stability

Practice questions from Stability.

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Q#1 Stability GATE EE 2025 (Set 1) MCQ +2 marks -0.66 marks

Let . Then the closed-loop system shown in the figure below, is

stable for all .

unstable for all .

unstable for all .

stable for all .

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Q#2 Stability GATE EE 2022 (Set 1) MCQ +1 mark -0.33 marks

The open loop transfer function of a unity gain negative feedback system is given by G(s)= . The range of k for which the system is stable, is

k > 3

k < 3

k > 5

k < 5

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Q#3 Stability GATE EE 2020 (Set 1) MCQ +2 marks -0.66 marks

Which of the following option is correct for the system shown below?

A picture containing text, clock Description automatically generated

3rd order and stable

4th order and unstable

4th order and stable

3rd order and unstable

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Q#4 Stability GATE EE 2020 (Set 1) MCQ +2 marks -0.66 marks

Consider a negative unity feedback system with the forward path transfer function , where K is a positive real number. The value of K for which the

system will have some of its poles on the imaginary axis is

9

8

7

6

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Q#5 Stability GATE EE 2019 (Set 1) MCQ +1 mark -0.33 marks

The Characteristic equation of a linear time-invariant (LTI) system is given by

The system is BIBO stable if        

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Q#6 Stability GATE EE 2018 (Set 1) MCQ +2 marks -0.66 marks

The number of roots of the polynomial, , in the open left half of the complex plane is

3

4

5

6

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Q#7 Stability GATE EE 2017 (Set 1) MCQ +1 mark -0.33 marks

A closed loop system has the characteristic equation given by . For this system to be stable, which one of the following conditions should be satisfied?

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Q#8 Stability GATE EE 2017 (Set 2) MCQ +2 marks -0.66 marks

The range of K for which all the roots of the equation are in the left half of the complex s-plane is

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Q#9 Stability GATE EE 2016 (Set 1) NAT +2 marks -0 marks

Given the following polynomial equation

,

the number of roots of the polynomial, which have real parts strictly less than -1, is ___________.

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Q#10 Stability GATE EE 2016 (Set 2) MCQ +2 marks -0.66 marks

The open loop transfer function of a unity feedback control system is given by  .`

The closed loop system will be stable if.

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Q#11 Stability GATE EE 2014 (Set 1) MCQ +1 mark -0.33 marks

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

only one root at the origin

imaginary roots

only positive real roots

only negative real roots

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Q#12 Stability GATE EE 2014 (Set 1) NAT +2 marks -0 marks

For the given system, it is desired that the system be stable. The minimum value of  for this condition is ______________.                  

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Q#13 Stability GATE EE 2014 (Set 2) NAT +2 marks -0 marks

A system with the open loop transfer function

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

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Q#14 Stability GATE EE 2012 (Set 1) MCQ +2 marks -0.66 marks

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

20.jpg

K = 2 and a = 0.75

K = 3 and a = 0.75

K = 4 and a = 0.5

K = 2 and a = 0.5

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Q#15 Stability GATE EE 2011 (Set 1) MCQ +1 mark -0.33 marks

An open loop system represented by the transfer function  is

stable and of the minimum phase type

stable and of the non-minimum phase type

unstable and of the minimum phase type

unstable and of the non-minimum phase type

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Q#16 Stability GATE EE 2009 (Set 1) MCQ +1 mark -0.33 marks

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

The means there are

Two roots at s = ±j and one root in right half s-plane.

Two roots at s = ±j2 and one root in left half s-plane.

Two roots at s = ±j and one root in right in half s-plane.

Two roots at s = ±j and one root in left half s-plane.

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Q#17 Stability GATE EE 2008 (Set 1) MCQ +2 marks -0.66 marks

Figure shows a feedback system where K>0.

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

Q67.jpg

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Q#18 Stability GATE EE 2007 (Set 1) MCQ +1 mark -0.33 marks

The system shown in the figure is         

Stable

Unstable

Conditionally stable

Stable for input , but unstable for input

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Q#19 Stability GATE EE 2007 (Set 1) MCQ +2 marks -0.66 marks

If the loop gain K of a negative feedback system having a loop transfer function is to be adjusted to induce a sustained oscillation then        

The frequency of this oscillation must be  rad/s

The frequency of this oscillation must be 4 rad/s

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

Such a K does not exist

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Q#20 Stability GATE EE 2006 (Set 1) MCQ +2 marks -0.66 marks

The algebraic equation  is given F(s) = 0 has

A single complex root with the remaining roots being real

One positive real root and four complex roots, all with positive real parts.

One negative real root, two imaginary roots and two roots with positive real parts.

One positive real root, two imaginary roots, and two roots with negative real parts.

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Q#21 Stability GATE EE 2005 (Set 1) MCQ +2 marks -0.66 marks

A unity feedback system, having an open loop gain , becomes stable when

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Q#22 Stability GATE EE 2004 (Set 1) MCQ +2 marks -0.66 marks

For the equation, , the number of roots in the left half of s-plane will be

Zero

One

Two

Three

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Q#23 Stability GATE EE 2003 (Set 1) MCQ +2 marks -0.66 marks

The loop gain GH of a closed system is given by the following expression

The value of K for which the system just becomes unstable is

K = 6

K = 8

K = 48

K = 96

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Q#24 Stability GATE EE 2000 (Set 1) MCQ +2 marks -0.66 marks

The characteristic equation of a feedback control system is:           

The number of roots in the right half of s-plane are :

Zero

1

2

3

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Q#25 Stability GATE EE 1998 (Set 1) MCQ +1 mark -0.33 marks

None of the poles of a linear control system lie in the right half of s-plane. For a bounded input, the output of this system

Is always bounded

Could be unbounded

Always tends to zero

None of the above

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Q#26 Stability GATE EE 1998 (Set 1) MCQ +2 marks -0.66 marks

The number of roots on the equation  that lie in the right half of S plane is:

Zero

One

Two

Three

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Q#27 Stability GATE EE 1997 (Set 1) NAT +2 marks -0 marks

The system represented by the transfer function  has _______ pole(s) in the right-half s-plane.  

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Q#28 Stability GATE EE 1997 (Set 1) NAT +2 marks -0 marks

Determine whether the system given by the block diagram of figure, is stable ( Yes=1, No=0)

F:\Volume-2 deepak work\07.jpg

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Q#29 Stability GATE EE 1995 (Set 1) NAT +1 mark -0 marks

Closed loop stability implies that  has only Zeros in the left half of the s-plane. (True=1, False=0)

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Q#30 Stability GATE EE 1995 (Set 1) MSQ +2 marks -0 marks

The characteristic equation for a certain feedback control system is given by    

Range of K for stability: 0<k<1.49

Range of K for stability: 0<k<1.39

Frequency of oscillation = 0.316 rad/sec

For k=5, Two roots of the characteristic equation lie in the right half plane.

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Q#31 Stability GATE EE 1994 (Set 1) NAT +1 mark -0 marks

The closed loop system, of figure, is stable if the transfer function  is stable. (True=1,False=0)

D:\1Mayu\Gate-9\JPG\JPG\1994\1994\Q2_2.7.jpg

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Q#32 Stability GATE EE 1994 (Set 1) NAT +1 mark -0 marks

The number of positive real roots of the equation,  is _______________.

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Q#33 Stability GATE EE 1992 (Set 1) MCQ +1 mark -0.33 marks

For what range of K is the following system (figure) asymptotically stable? Assume

Untitled-10.png

k<4

None of these

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