In stability computation, the curve representing the real surface of sliding is usually replaced by ___________

Arc of circle and Logarithmic failure

According to Bennet, non-circular slip surface may arise in ___________

Soil deposit with a specific plane of weakness

Planar surface commonly occur in __________

Embankment with specific plane of weakness

Find the number of poles in the left half plane (LHP), the right half plane (RJP) and on the jω-axis for the feedback control system as shown. Is the system stable?

2 LHP ploes; 2 RHP poles; 0 jω poles; system is stable

1 LHP poles; 3 RHP poles; 0 jω poles; system is stable

2 LHP poles; 2 RHP poles; 0 jω poles; system is unstable

2 LHP ploes; 2 RHP poles; 0 jω poles; system is stable

1 LHP poles; 3 RHP poles; 0 jω poles; system is unstable

A system with characteristic equation s4 + 2 s3 + 11 s2 + 18s + 18 = 0 will have closed loop poles such that

No pole lies on the imaginary axis of the s-plane

All poles lie in the left half of the s-plane

All poles lie in the right half of the s-plane

Two poles lie symmetrically on the imaginary axis of the s-plane

No pole lies on the imaginary axis of the s-plane

A closed-loop control system has a characteristic equation given by s3 + 2.4s2 + 1.8s + 0.5 = 0. Find out the value of a, b, c, and d using the Routh Hurwitz criterion.s311.8s22.40.5s1acs0bd

a = 1.59, b = 0.5, c = 0, d = 0

For the feedback system given below, the transfer function \(G\left( s \right) = \frac{1}{{{{\left( {s + 1} \right)}^2}}}.\) The system CAN NOT be stabilized with

\(C\left( s \right) = \frac{1}{s}\)

\(C\left( s \right) = 1 + \frac{3}{s}\)

\(C\left( s \right) = 3 + \frac{7}{s}\)

\(C\left( s \right) = 3 + \frac{9}{s}\)

\(C\left( s \right) = \frac{1}{s}\)

a0 sn + a1 sn-1 + a2sn-2 + ...........+ an-1 s1 + an The necessary condition for system stability for the above characteristic equation is

All the coefficients of the characteristic equation should be negative and imaginary.

All the coefficients of the characteristic equation should be zero.

All the coefficient of the characteristic equation should be unity.

All the coefficients of the characteristic equation should be positive and real.

All the coefficients of the characteristic equation should be negative and imaginary.

A discrete time system is stable if all the roots of the characteristic equation lie

Outside of circle of radius equal to 3 units

Outside the circle of unit radius

Within the circle of unit radius

Outside of circle of radius equal to 3 units

On the circle of infinite radius

A unit feedback system has the open loop transfer function \(G(s) = \frac {10^4}{s(s+10)^2}\). The closed loop system is

stable at an angular frequency of 10 rad / s

Find the number of poles in the right-half plane (RHP) for the system as shown. Is the system stable?

2 RHP poles; System is unstable

3 RHP poles; System is unstable

For a stable system, poles of the transfer function

should lie entirely in the right half of the s-plane

should lie entirely in the left half of the s-plane

For making an unstable system stable

Gain of the system should be decreased.

Gain of the system should be increased.

Gain of the system should be decreased.

The number of zeros to the loop transfer function should be increased

The number of poles to the loop transfer function should be increased

Consider a unity feedback configuration with a plant and a PID controller as shown in the figure. \(G(s) = \frac{1}{(s+1)(s+3)}\) and \(C(s) = K \frac{(s+3-j)(s+3+j)}{s}\)with K being scaler. the closed loop is

only stable for K between -1 and +1

In Routh-Hurwitz Criterion, if all the elements in one row are zero, then there can be

pairs of equal roots with opposite sign

pairs of conjugate roots on imaginary axis

conjugate roots forming a quadrature in the s-plane

A plant transfer function is given as,\({\rm{G}}\left( {\rm{s}} \right) = \left( {{{\rm{K}}_{\rm{p}}} + \frac{{{{\rm{K}}_{\rm{I}}}}}{{\rm{s}}}} \right)\frac{1}{{{\rm{s}}\left( {{\rm{s}} + 2} \right)}}\)When the plant operates in a unity feedback configuration the condition for the stability of the closed-loop system is

\(2{{\rm{K}}_{\rm{I}}}{\rm{\;}} > {\rm{\;}}{{\rm{K}}_{\rm{P}}}{\rm{\;}} > {\rm{\;}}0\)

\({{\rm{K}}_{\rm{P}}} > \frac{{{{\rm{K}}_{\rm{I}}}}}{2} > 0\)

\(2{{\rm{K}}_{\rm{I}}}{\rm{\;}} > {\rm{\;}}{{\rm{K}}_{\rm{P}}}{\rm{\;}} > {\rm{\;}}0\)

\(2{{\rm{K}}_{\rm{I}}}{\rm{\;}} < {\rm{\;}}{{\rm{K}}_{\rm{P}}}\)

\(2{{\rm{K}}_{\rm{I}}}{\rm{\;}} > {\rm{\;}}{{\rm{K}}_{\rm{P}}}\)

63 + Mcqs in Stability Analysis Finite Slopes in Geotechnical Engineering Page 1 McqOptions

1.	In stability computation, the curve representing the real surface of sliding is usually replaced by ___________
A.	Arc of circle and Logarithmic failure
B.	Cycloid
C.	None of the mentioned
D.	All of the mentioned
Answer» B. Cycloid

Discussion

2.	The rupture mass sliding down a surface in a definite pattern resembles __________
A.	Curve
B.	Cycloid
C.	Ellipse
D.	Circle
Answer» C. Ellipse

Discussion

3.	According to Bennet, non-circular slip surface may arise in ___________
A.	Non homogeneous dam
B.	Embankment dams
C.	Homogeneous dam
D.	Soil deposit with a specific plane of weakness
Answer» D. Soil deposit with a specific plane of weakness

Discussion

4.	Planar surface commonly occur in __________
A.	Embankment with specific plane of weakness
B.	All embankments
C.	Soil deposit
D.	Foundation of infinite depth
Answer» B. All embankments

Discussion

5.	The depth factor Df for toe failure is ___________
A.	Df > 1
B.	Df < 1
C.	Df = 1
D.	Df = 0
Answer» D. Df = 0

Discussion

6.	The ratio of total depth to depth H is called _________
A.	Depth factor
B.	Slope depth
C.	Depth failure
D.	Base failure
Answer» B. Slope depth

Discussion

7.	The types of slip surface or failure surfaces are ____________
A.	4
B.	2
C.	3
D.	5
Answer» D. 5

Discussion

8.	If the failure occurs along a surface of sliding that intersect the slope at its toe, the slide is known as ___________
A.	Base failure
B.	Slope failure
C.	Face failure
D.	All of the mentioned
Answer» C. Face failure

Discussion

9.	A basic type of failure at a finite slope may occur due to ___________
A.	Slope failure and Base failure
B.	Toe failure
C.	None of the mentioned
D.	All of the mentioned
Answer» B. Toe failure

Discussion

10.	For \(G\left( s \right)H\left( s \right) = \frac{1}{{s + 2}}\) , the system is:
A.	Stable, has one zero
B.	stable, has no zeros
C.	Unstable has no zeros
D.	Unstable, has one zero
Answer» C. Unstable has no zeros

Discussion

11.	A system described by the transfer function \(H\left( s \right) = \frac{1}{{{s^3} + a{s^2} + ks + 3}}\) is stable. The constraints on a and k are
A.	a > 0, a k < 3
B.	a > 0, a k > 3
C.	a > 0, a k > 0
D.	a > 0, a k < 0
Answer» C. a > 0, a k > 0

Discussion

12.	A unity feedback control system has the open loop transfer function G(s). For the system to be stable find the range of K.\(G\left( s \right) = \frac{{K\left( {s + 13} \right)}}{{s\left( {s + 7} \right)\left( {s + 3} \right)}}\)
A.	[0, 70]
B.	[0, 80]
C.	[0, 90]
D.	[0, 75]
Answer» B. [0, 80]

Discussion

13.	A feedback system with characteristic equation s4 + 20Ks3 + 5s2 + 10s + 15 = 0 is:
A.	Stable for all values of K
B.	Stable only for K ≥ 0
C.	Stable for ∞ > K > 70
D.	Unstable for all values of K
Answer» E.

Discussion

14.	Check the system with characteristic equation F(s) = s4 + 3s3 + 2s2 + s + 1 for stability.
A.	quasi-stable
B.	Oscillatory
C.	Unstable
D.	Stable
Answer» D. Stable

Discussion

15.	Find the number of poles in the left half plane (LHP), the right half plane (RJP) and on the jω-axis for the feedback control system as shown. Is the system stable?
A.	1 LHP poles; 3 RHP poles; 0 jω poles; system is stable
B.	2 LHP poles; 2 RHP poles; 0 jω poles; system is unstable
C.	2 LHP ploes; 2 RHP poles; 0 jω poles; system is stable
D.	1 LHP poles; 3 RHP poles; 0 jω poles; system is unstable
Answer» C. 2 LHP ploes; 2 RHP poles; 0 jω poles; system is stable

Discussion

16.	A system with characteristic equation s4 + 2 s3 + 11 s2 + 18s + 18 = 0 will have closed loop poles such that
A.	All poles lie in the left half of the s-plane
B.	All poles lie in the right half of the s-plane
C.	Two poles lie symmetrically on the imaginary axis of the s-plane
D.	No pole lies on the imaginary axis of the s-plane
Answer» D. No pole lies on the imaginary axis of the s-plane

Discussion

17.	A closed-loop system is shown in the figure. The system parameter α is not known. The condition for asymptotic stability of the closed loop system is
A.	α < -0.5
B.	-0.5 < α < 0.5
C.	0 < α < 0.5
D.	α > 0.5
Answer» E.

Discussion

18.	If any root of the characteristic equation has a positive real part or if there is a repeated root on the jω-axis, then the system is
A.	Limitedly stable
B.	Conditionally stable
C.	Stable
D.	Unstable
Answer» E.

Discussion

19.	Consider a negative unity feedback system with the forward path transfer function \(\frac{{{s^2} + s + 1}}{{{s^3} + 2{s^2} + 2s + K}}\), 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 ________
A.	9
B.	8
C.	7
D.	6
Answer» C. 7

Discussion

20.	Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh’s Table of the system characteristic equation.X: The system is stable …Y: The system is unstable …Z: The test breaks down …P: … when all elements are positiveQ: … when any one element is zeroR: … when there is a change in sign of coefficients
A.	X→P, Y→Q, Z→R
B.	X→Q, Y→P, Z→R
C.	X→R, Y→Q, Z→P
D.	X→P, Y→R, Z→Q
Answer» E.

Discussion

21.	A system's open-loop transfer function is given by \(G\left( s \right) = \frac{K}{{s\left( {s + 2} \right)\left( {s + 4} \right)}}\). If the system is having a unity negative feedback, which of the following is true for such a system to be stable?
A.	K > 0
B.	0 < K < 24
C.	K < 24
D.	None of the above
Answer» C. K < 24

Discussion

22.	For the equation s3 – 4s2 + s + 6 = 0, the number of roots in the left half of s-plane will be:
A.	Zero
B.	One
C.	Two
D.	Three
Answer» C. Two

Discussion

23.	A closed-loop control system has a characteristic equation given by s3 + 2.4s2 + 1.8s + 0.5 = 0. Find out the value of a, b, c, and d using the Routh Hurwitz criterion.s311.8s22.40.5s1acs0bd
A.	a = 2, b = 0.5, c = 0, d = 1.3
B.	a = 0, b = 0, c = 0, d = 0
C.	a = 1.59, b = 0.5, c = 0, d = 0
D.	a = 4, b = 0, c = 9, d = 0.7
Answer» D. a = 4, b = 0, c = 9, d = 0.7

Discussion

24.	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 of1. a pair of real roots with opposite sign2. complex conjugate roots on the imaginary axis3. a pair of complex conjugate roots with opposite real partsWhich of the above statements are correct?
A.	Only 2
B.	2 and 3
C.	Only 3
D.	1, 2 and 3
Answer» E.

Discussion

25.	For the feedback system given below, the transfer function \(G\left( s \right) = \frac{1}{{{{\left( {s + 1} \right)}^2}}}.\) The system CAN NOT be stabilized with
A.	\(C\left( s \right) = 1 + \frac{3}{s}\)
B.	\(C\left( s \right) = 3 + \frac{7}{s}\)
C.	\(C\left( s \right) = 3 + \frac{9}{s}\)
D.	\(C\left( s \right) = \frac{1}{s}\)
Answer» D. \(C\left( s \right) = \frac{1}{s}\)

Discussion

26.	Consider the polynomial equation below:s4 + 2s3 + 3s2 + 4s + 5 = 0The number of roots with positive real part are:
A.	2
B.	3
C.	1
D.	0
Answer» B. 3

Discussion

27.	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
Answer» C. only positive real roots

Discussion

28.	Forward path transfer function of a unity feedback system is \(G\left( s \right) = \frac{K}{{\left( {s + 5} \right)\left( {s + 10} \right)\left( {s + 15} \right)}}\)Select the appropriate value of K for the system to be oscillatory.
A.	4000
B.	5250
C.	2400
D.	7500
Answer» E.

Discussion

29.	a0 sn + a1 sn-1 + a2sn-2 + ...........+ an-1 s1 + an The necessary condition for system stability for the above characteristic equation is
A.	All the coefficients of the characteristic equation should be zero.
B.	All the coefficient of the characteristic equation should be unity.
C.	All the coefficients of the characteristic equation should be positive and real.
D.	All the coefficients of the characteristic equation should be negative and imaginary.
Answer» D. All the coefficients of the characteristic equation should be negative and imaginary.

Discussion

30.	Find the range of K for the system shown in the figure to be stable.Where \(G\left( s \right) = \frac{K}{{{s^2} + 2s + 4}}\) and \(H\left( s \right) = \frac{1}{{{s^2} + 3s + 5}}\)
A.	-5 < K < -2
B.	-1 < K < 1
C.	-2 < K < 0
D.	All of the above
Answer» E.

Discussion

31.	Consider the following statements with respect to Routh-Hurwitz criterion:1. It can be used to determine relative stability2. It is valid only for real coefficients of the characteristic equation.3. It is applicable only for non-linear systems.4. It does not provide the exact location of closed-loop poles in left or right-half of s-planeWhich of the above statements are correct?
A.	1, 2 and 3 only
B.	3 and 4 only
C.	1, 2 and 4 only
D.	1, 2, 3 and 4
Answer» D. 1, 2, 3 and 4

Discussion

32.	A discrete time system is stable if all the roots of the characteristic equation lie
A.	Outside the circle of unit radius
B.	Within the circle of unit radius
C.	Outside of circle of radius equal to 3 units
D.	On the circle of infinite radius
Answer» C. Outside of circle of radius equal to 3 units

Discussion

33.	A unit feedback system has the open loop transfer function \(G(s) = \frac {10^4}{s(s+10)^2}\). The closed loop system is
A.	stable
B.	marginally stable
C.	unstable
D.	stable at an angular frequency of 10 rad / s
Answer» D. stable at an angular frequency of 10 rad / s

Discussion

34.	Consider the stability of the system shown in the figure when analysed with a positive real value of gain K in1. open-loop configuration2. closed-loop configurationWhich of the following statements is correct?
A.	Both 1 and 2 are stable
B.	1 is stable and 2 is unstable
C.	1 is unstable and 2 is stable
D.	Both 1 and 2 are unstable
Answer» D. Both 1 and 2 are unstable

Discussion

35.	If the system is stable by producing an output signal with constant amplitude and constant frequency of oscillations for bounded Input, then it is known as _______.
A.	Constant stable system
B.	Absolutely stable system
C.	Conditionally stable system
D.	Marginally stable system
Answer» E.

Discussion

36.	How many roots of the following equation lie in the right-half of s-plane?2s4 + s3 + 2s2 + 5s + 10 = 0
A.	1
B.	2
C.	3
D.	4
Answer» C. 3

Discussion

37.	A closed loop system has the characteristic equation given by s3 + Ks2 + (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
Answer» E.

Discussion

38.	Find the number of poles in the right-half plane (RHP) for the system as shown. Is the system stable?
A.	2 RHP poles; System is unstable
B.	2 RHP poles; System is stable
C.	3 RHP poles; System is unstable
D.	3 RHP poles; System is stable
Answer» B. 2 RHP poles; System is stable

Discussion

39.	Find the locations of any two roots of the characteristic equation F(s) = s4 + 2s3 + 11s2 + 18s + 18 = 0
A.	± J9
B.	± j3
C.	0, 9
D.	+j9, -j2
Answer» C. 0, 9

Discussion

40.	For a stable system, poles of the transfer function
A.	should lie entirely in the right half of the s-plane
B.	should lie on the Y-axis
C.	should lie entirely in the left half of the s-plane
D.	should lie at the origin
Answer» D. should lie at the origin

Discussion

41.	For making an unstable system stable
A.	Gain of the system should be increased.
B.	Gain of the system should be decreased.
C.	The number of zeros to the loop transfer function should be increased
D.	The number of poles to the loop transfer function should be increased
Answer» B. Gain of the system should be decreased.

Discussion

42.	Consider a unity feedback configuration with a plant and a PID controller as shown in the figure. \(G(s) = \frac{1}{(s+1)(s+3)}\) and \(C(s) = K \frac{(s+3-j)(s+3+j)}{s}\)with K being scaler. the closed loop is
A.	only stable for K > 0
B.	only stable for K between -1 and +1
C.	only stable for K < 0
D.	stable for all values of K
Answer» B. only stable for K between -1 and +1

Discussion

43.	None of the poles of a linear control system lies in the right-half of s-plane. For a bounded input, the output of this system
A.	is always bounded
B.	could be unbounded
C.	always tends to zero
D.	None of the above
Answer» C. always tends to zero

Discussion

44.	If the characteristic equation of a feedback control system is given by s4 + 20s3 + 15s2 + 2s + k = 0 Then the range of values of K for the system to be stable will be
A.	1 < K < 2.49
B.	0 < K < 1.49
C.	1 < K < 4.49
D.	0 < K < 3.49
Answer» C. 1 < K < 4.49

Discussion

45.	In Routh-Hurwitz Criterion, if all the elements in one row are zero, then there can be
A.	pairs of equal roots with opposite sign
B.	pairs of conjugate roots on imaginary axis
C.	conjugate roots forming a quadrature in the s-plane
D.	all of the above
Answer» E.

Discussion

46.	If all the roots of the characteristic equation have negative real parts, the system is
A.	Stable
B.	Unstable
C.	Marginally stable
D.	Conditionally stable
Answer» B. Unstable

Discussion

47.	A plant transfer function is given as,\({\rm{G}}\left( {\rm{s}} \right) = \left( {{{\rm{K}}_{\rm{p}}} + \frac{{{{\rm{K}}_{\rm{I}}}}}{{\rm{s}}}} \right)\frac{1}{{{\rm{s}}\left( {{\rm{s}} + 2} \right)}}\)When the plant operates in a unity feedback configuration the condition for the stability of the closed-loop system is
A.	\({{\rm{K}}_{\rm{P}}} > \frac{{{{\rm{K}}_{\rm{I}}}}}{2} > 0\)
B.	\(2{{\rm{K}}_{\rm{I}}}{\rm{\;}} > {\rm{\;}}{{\rm{K}}_{\rm{P}}}{\rm{\;}} > {\rm{\;}}0\)
C.	\(2{{\rm{K}}_{\rm{I}}}{\rm{\;}} < {\rm{\;}}{{\rm{K}}_{\rm{P}}}\)
D.	\(2{{\rm{K}}_{\rm{I}}}{\rm{\;}} > {\rm{\;}}{{\rm{K}}_{\rm{P}}}\)
Answer» B. \(2{{\rm{K}}_{\rm{I}}}{\rm{\;}} > {\rm{\;}}{{\rm{K}}_{\rm{P}}}{\rm{\;}} > {\rm{\;}}0\)

Discussion

48.	Determine the range of K for stability of unity feedback system whose open loop transfer function is G(s)=K/s(s+1)(s+2)
A.	10
B.	15
C.	6
D.	0
Answer» E.

Discussion

49.	If repeated poles of a system lie on the imaginary axis, the system will be
A.	Stable
B.	Conditionally stable
C.	Marginally stable
D.	Unstable
Answer» E.

Discussion

50.	Consider a closed loop system with transfer function \(\frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{{{s^2} + 2s + 8}}{{{s^3} + 2{s^2} + 6s + 10}}\).Find the number of poles in right half of s plane and in he left half of s plane.
A.	3, 1
B.	0, 3
C.	3, 2
D.	5, 4
Answer» C. 3, 2

Discussion

Explore topic-wise MCQs in Geotechnical Engineering.

In stability computation, the curve representing the real surface of sliding is usually replaced by ___________

The rupture mass sliding down a surface in a definite pattern resembles __________

According to Bennet, non-circular slip surface may arise in ___________

Planar surface commonly occur in __________

The depth factor Df for toe failure is ___________

The ratio of total depth to depth H is called _________

The types of slip surface or failure surfaces are ____________

If the failure occurs along a surface of sliding that intersect the slope at its toe, the slide is known as ___________

A basic type of failure at a finite slope may occur due to ___________

For \(G\left( s \right)H\left( s \right) = \frac{1}{{s + 2}}\) , the system is:

A system described by the transfer function \(H\left( s \right) = \frac{1}{{{s^3} + a{s^2} + ks + 3}}\) is stable. The constraints on a and k are

A unity feedback control system has the open loop transfer function G(s). For the system to be stable find the range of K.\(G\left( s \right) = \frac{{K\left( {s + 13} \right)}}{{s\left( {s + 7} \right)\left( {s + 3} \right)}}\)

A feedback system with characteristic equation s4 + 20Ks3 + 5s2 + 10s + 15 = 0 is:

Check the system with characteristic equation F(s) = s4 + 3s3 + 2s2 + s + 1 for stability.

Find the number of poles in the left half plane (LHP), the right half plane (RJP) and on the jω-axis for the feedback control system as shown. Is the system stable?

A system with characteristic equation s4 + 2 s3 + 11 s2 + 18s + 18 = 0 will have closed loop poles such that

A closed-loop system is shown in the figure. The system parameter α is not known. The condition for asymptotic stability of the closed loop system is

If any root of the characteristic equation has a positive real part or if there is a repeated root on the jω-axis, then the system is

Consider a negative unity feedback system with the forward path transfer function \(\frac{{{s^2} + s + 1}}{{{s^3} + 2{s^2} + 2s + K}}\), 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 ________

A system's open-loop transfer function is given by \(G\left( s \right) = \frac{K}{{s\left( {s + 2} \right)\left( {s + 4} \right)}}\). If the system is having a unity negative feedback, which of the following is true for such a system to be stable?

For the equation s3 – 4s2 + s + 6 = 0, the number of roots in the left half of s-plane will be:

A closed-loop control system has a characteristic equation given by s3 + 2.4s2 + 1.8s + 0.5 = 0. Find out the value of a, b, c, and d using the Routh Hurwitz criterion.s311.8s22.40.5s1acs0bd

For the feedback system given below, the transfer function \(G\left( s \right) = \frac{1}{{{{\left( {s + 1} \right)}^2}}}.\) The system CAN NOT be stabilized with

Consider the polynomial equation below:s4 + 2s3 + 3s2 + 4s + 5 = 0The number of roots with positive real part are:

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

Forward path transfer function of a unity feedback system is \(G\left( s \right) = \frac{K}{{\left( {s + 5} \right)\left( {s + 10} \right)\left( {s + 15} \right)}}\)Select the appropriate value of K for the system to be oscillatory.

a0 sn + a1 sn-1 + a2sn-2 + ...........+ an-1 s1 + an The necessary condition for system stability for the above characteristic equation is

Find the range of K for the system shown in the figure to be stable.Where \(G\left( s \right) = \frac{K}{{{s^2} + 2s + 4}}\) and \(H\left( s \right) = \frac{1}{{{s^2} + 3s + 5}}\)

A discrete time system is stable if all the roots of the characteristic equation lie

A unit feedback system has the open loop transfer function \(G(s) = \frac {10^4}{s(s+10)^2}\). The closed loop system is

Consider the stability of the system shown in the figure when analysed with a positive real value of gain K in1. open-loop configuration2. closed-loop configurationWhich of the following statements is correct?

If the system is stable by producing an output signal with constant amplitude and constant frequency of oscillations for bounded Input, then it is known as _______.

How many roots of the following equation lie in the right-half of s-plane?2s4 + s3 + 2s2 + 5s + 10 = 0

A closed loop system has the characteristic equation given by s3 + Ks2 + (K + 2)s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?

Find the number of poles in the right-half plane (RHP) for the system as shown. Is the system stable?

Find the locations of any two roots of the characteristic equation F(s) = s4 + 2s3 + 11s2 + 18s + 18 = 0

For a stable system, poles of the transfer function

For making an unstable system stable

Consider a unity feedback configuration with a plant and a PID controller as shown in the figure. \(G(s) = \frac{1}{(s+1)(s+3)}\) and \(C(s) = K \frac{(s+3-j)(s+3+j)}{s}\)with K being scaler. the closed loop is

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

If the characteristic equation of a feedback control system is given by s4 + 20s3 + 15s2 + 2s + k = 0 Then the range of values of K for the system to be stable will be

In Routh-Hurwitz Criterion, if all the elements in one row are zero, then there can be

If all the roots of the characteristic equation have negative real parts, the system is

Determine the range of K for stability of unity feedback system whose open loop transfer function is G(s)=K/s(s+1)(s+2)

If repeated poles of a system lie on the imaginary axis, the system will be

Consider a closed loop system with transfer function \(\frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{{{s^2} + 2s + 8}}{{{s^3} + 2{s^2} + 6s + 10}}\).Find the number of poles in right half of s plane and in he left half of s plane.