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Routh-Hurwitz Stability MCQs for Electrical Engineering (EE) Exam
It covers all Important Questions with answers on Routh-Hurwitz Stability for the Electrical Engineering (EE) exam. The questions are based on important topics. Details about the questions:- Topic: Routh-Hurwitz Stability
- Type of Questions: MCQs with solutions
- Number of Questions: 50
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A Routh table is shown in fig. The location of pole on RHP, LHP and imaginary axis are
- a)1, 2, 4
- b)1, 6, 0
- c)1, 0, 6
- d)None of the above
Correct answer is 'A'. Can you explain this answer?
A Routh table is shown in fig. The location of pole on RHP, LHP and imaginary axis are
a)
1, 2, 4
b)
1, 6, 0
c)
1, 0, 6
d)
None of the above
 | Jaya Yadav answered |
If the system is given with the unbounded input then nothing can be clarified for the stability of the system.
For which of the following values of K, the feedback system shown in the below figure is stable?
- a)K < 0
- b)K > 0
- c)0 < K < 54
- d)0 < K < 70
Correct answer is option 'D'. Can you explain this answer?
For which of the following values of K, the feedback system shown in the below figure is stable?
a)
K < 0
b)
K > 0
c)
0 < K < 54
d)
0 < K < 70
 | Rhea Reddy answered |
The characteristic equation is
1 + G (s) H (s) = 0
or,
1 + G (s) H (s) = 0
or,
or, s3 + 10s2 + (21 + K )s + 13 K= 0
For stability, 13K > 0 or K > 0
Also,
or, K < 70
Hence, 0 < K< 70 (For stability).
Consider the following statements regarding the characteristic equation of a system given by:
s4 + 5s3 + 25+10 = 0
1. The system is unstable.
2. The system is stable.
3. Number of roots with zero real part - 0
4. Number of roots with positive real part - 4
5. Number of roots with negative real part = 2
Which of the above statements are correct?- a)2 and 3
- b)1 and 3
- c)2, 3 and 4
- d)1, 3 and 5
Correct answer is option 'D'. Can you explain this answer?
Consider the following statements regarding the characteristic equation of a system given by:
s4 + 5s3 + 25+10 = 0
1. The system is unstable.
2. The system is stable.
3. Number of roots with zero real part - 0
4. Number of roots with positive real part - 4
5. Number of roots with negative real part = 2
Which of the above statements are correct?
s4 + 5s3 + 25+10 = 0
1. The system is unstable.
2. The system is stable.
3. Number of roots with zero real part - 0
4. Number of roots with positive real part - 4
5. Number of roots with negative real part = 2
Which of the above statements are correct?
a)
2 and 3
b)
1 and 3
c)
2, 3 and 4
d)
1, 3 and 5
 | Anirban Gupta answered |
The Routh’s array is
Since there are two sign changes in first column of Routh’s array, therefore the system is unstable.
Number of roots with positive real part = 2
Number of roots with negative real part = 2
Number of roots with zero real part = 0
Since there are two sign changes in first column of Routh’s array, therefore the system is unstable.
Number of roots with positive real part = 2
Number of roots with negative real part = 2
Number of roots with zero real part = 0
The transfer function of a system is 
The system is then which one of the following?- a)Non-minimum phase function
- b)Low-pass system
- c)Second-order system
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
The transfer function of a system is
The system is then which one of the following?
The system is then which one of the following?
a)
Non-minimum phase function
b)
Low-pass system
c)
Second-order system
d)
None of the above
 | Ashutosh Majumdar answered |
Since one pole (s .= 1) lies in RH s-plane, therefore the system is unstable.
Which of the following is the correct statement?
A minimum phase network is one whose transfer function has- a)zeros in the right hand s-plane and poles in the left hand s-plane.
- b)zeros and poles in the left hand s-plane.
- c)zeros in the left hand s-plane and poles in the right hand s-plane.
- d)arbitrary distribution of zeros and poles in the S-plane.
Correct answer is option 'B'. Can you explain this answer?
Which of the following is the correct statement?
A minimum phase network is one whose transfer function has
A minimum phase network is one whose transfer function has
a)
zeros in the right hand s-plane and poles in the left hand s-plane.
b)
zeros and poles in the left hand s-plane.
c)
zeros in the left hand s-plane and poles in the right hand s-plane.
d)
arbitrary distribution of zeros and poles in the S-plane.
 | Anjali Choudhury answered |
Explanation:
Minimum Phase Network:
A minimum phase network is a type of linear time-invariant (LTI) system in which all the zeroes and poles of the transfer function lie in the left-half of the s-plane. The transfer function of a minimum phase network is a causal and stable function that can be factored into a product of two terms: a minimum phase term and a delay term. The minimum phase term has all its zeroes and poles in the left-half of the s-plane, while the delay term has a pole at the origin.
Transfer Function:
The transfer function of a minimum phase network is given by:
H(s) = e^(-Ds) * G(s)
where D is a positive constant, G(s) is the minimum phase transfer function, and e^(-Ds) is the delay term. The transfer function H(s) can be expressed as a product of the minimum phase term G(s) and the delay term e^(-Ds). The minimum phase term G(s) is a causal and stable function that has all its zeroes and poles in the left-half of the s-plane. The delay term e^(-Ds) is a non-causal and unstable function that has a pole at the origin.
Properties of Minimum Phase Network:
The following are some of the properties of a minimum phase network:
- All the zeroes and poles of the transfer function lie in the left-half of the s-plane.
- The step response of a minimum phase network is faster than that of a non-minimum phase network with the same magnitude response.
- The phase response of a minimum phase network is always less than or equal to the phase response of a non-minimum phase network with the same magnitude response.
- The impulse response of a minimum phase network decays faster than that of a non-minimum phase network with the same magnitude response.
Answer:
Option 'B' is the correct statement. A minimum phase network is one whose transfer function has zeros and poles in the left-hand s-plane.
Minimum Phase Network:
A minimum phase network is a type of linear time-invariant (LTI) system in which all the zeroes and poles of the transfer function lie in the left-half of the s-plane. The transfer function of a minimum phase network is a causal and stable function that can be factored into a product of two terms: a minimum phase term and a delay term. The minimum phase term has all its zeroes and poles in the left-half of the s-plane, while the delay term has a pole at the origin.
Transfer Function:
The transfer function of a minimum phase network is given by:
H(s) = e^(-Ds) * G(s)
where D is a positive constant, G(s) is the minimum phase transfer function, and e^(-Ds) is the delay term. The transfer function H(s) can be expressed as a product of the minimum phase term G(s) and the delay term e^(-Ds). The minimum phase term G(s) is a causal and stable function that has all its zeroes and poles in the left-half of the s-plane. The delay term e^(-Ds) is a non-causal and unstable function that has a pole at the origin.
Properties of Minimum Phase Network:
The following are some of the properties of a minimum phase network:
- All the zeroes and poles of the transfer function lie in the left-half of the s-plane.
- The step response of a minimum phase network is faster than that of a non-minimum phase network with the same magnitude response.
- The phase response of a minimum phase network is always less than or equal to the phase response of a non-minimum phase network with the same magnitude response.
- The impulse response of a minimum phase network decays faster than that of a non-minimum phase network with the same magnitude response.
Answer:
Option 'B' is the correct statement. A minimum phase network is one whose transfer function has zeros and poles in the left-hand s-plane.
According to Hurwitz criterion, the characteristic equations4 + 8s3 + 18s2 + 16s + 5 = 0 is- a)Stable
- b)Marginally stable
- c)Conditionally stable
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
According to Hurwitz criterion, the characteristic equation
s4 + 8s3 + 18s2 + 16s + 5 = 0 is
a)
Stable
b)
Marginally stable
c)
Conditionally stable
d)
None of these
 | Engineers Adda answered |
Concept:
The Routh Stability Criterion is used to test the stability of an LTI system. The conditions for stability are:
- All the coefficients of the characteristic Equation must be present and must have the same sign.
- It is necessary and sufficient that each term of the first column of the Routh Array of the Characteristic Equation is positive for the system to be stable, i.e. there should not be any sign changes in the first column of each row.
- The number of sign changes represents the number of roots on the right side of the s-plane.
- If the first term in any row of Routh Array is zero while the rest of the row has at least one non-zero term. Because of this term, the terms in the next row will become infinite.
- When all elements in any row of the Routh array are zero. This condition indicates that there are symmetrical/imaginary roots in the s-plane.
Application:
A(s) = s4 + 8s3 + 18s2 + 16s + 5
Forming the Routh array, we get:
Since there are no sign changes in the first column of the Routh array, we conclude that the system is stable.
Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:
1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.
2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.
3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.
Which of these statements is/are not correct?- a)2 and 3 oniy .
- b)1, 2 and 3
- c)1 only
- d)1 and 2 only
Correct answer is option 'B'. Can you explain this answer?
Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:
1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.
2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.
3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.
Which of these statements is/are not correct?
1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.
2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.
3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.
Which of these statements is/are not correct?
a)
2 and 3 oniy .
b)
1, 2 and 3
c)
1 only
d)
1 and 2 only
 | Athul Banerjee answered |
• Routh-Hurwitz criterion is not applicable if characteristic equation has coefficients which are exponential or complex.
• It is not applied in z-piane because z-piane having unit circle is the stability boundary of discrete-data system.
• Statement-3 is also false because no. of sign change in 1st column of Routh’s array indicates the number of roots with positive real part or roots lying in RH s-plane.
• It is not applied in z-piane because z-piane having unit circle is the stability boundary of discrete-data system.
• Statement-3 is also false because no. of sign change in 1st column of Routh’s array indicates the number of roots with positive real part or roots lying in RH s-plane.
The characteristic equation of a second order discrete-data system is given by:
F(z) = z2+ z+ 0.25 = 0
The above system is- a)stable
- b)marginally stable
- c)unstable
- d)asymptotically stable
Correct answer is option 'A'. Can you explain this answer?
The characteristic equation of a second order discrete-data system is given by:
F(z) = z2+ z+ 0.25 = 0
The above system is
F(z) = z2+ z+ 0.25 = 0
The above system is
a)
stable
b)
marginally stable
c)
unstable
d)
asymptotically stable
 | Nilesh Joshi answered |
For a second order discrete- data system given by:
F(z) = a2z2 + a1z + a0 = 0
to be stable, the necessary and sufficient conditions are:
F(1) > 0
F(-1) > 0 and |a0| < a2
Here, F(z) = z2 + z + 0.25
So, = 0.25, a1 = 1, a2 = 1
Thus, F(1) - 12+ 1 + 0.25 = 2.25 > 0
F(-1) = 1 -1 + 0.25 = 0.25 > 0
and la0l = 0.25 < a2 = 1 Since ail the conditions are satisfied, therefore given system is stable.
F(z) = a2z2 + a1z + a0 = 0
to be stable, the necessary and sufficient conditions are:
F(1) > 0
F(-1) > 0 and |a0| < a2
Here, F(z) = z2 + z + 0.25
So, = 0.25, a1 = 1, a2 = 1
Thus, F(1) - 12+ 1 + 0.25 = 2.25 > 0
F(-1) = 1 -1 + 0.25 = 0.25 > 0
and la0l = 0.25 < a2 = 1 Since ail the conditions are satisfied, therefore given system is stable.
What is the stability of the system s3 + s2 + s + 4 = 0 using Hurwitz criteria?- a)Unstable
- b)Stable
- c)Critically stable
- d)Marginally stable
Correct answer is option 'A'. Can you explain this answer?
What is the stability of the system s3 + s2 + s + 4 = 0 using Hurwitz criteria?
a)
Unstable
b)
Stable
c)
Critically stable
d)
Marginally stable
| | Engineers Adda answered |
Concept:
To find the closed system stability by using RH criteria we require a characteristic equation.
Whereas in remaining all stability techniques we require open-loop transfer function.
The nth order general form of CE is a0 sn + a1 sn-1 + a2sn-2 + __________an-1 s1 +
an RH table shown below:
Necessary condition
All the coefficients of the characteristic equation should be positive and real.
Sufficient Conditions for stability:
1. All the coefficients in the first column should have the same sign and no coefficient should be zero.
2. If any sign changes in the first column, the system is unstable. And the number of sign changes = Number of poles in right of s-plane.
Calculation:
With the help of the
Routh table explained in the concept we can extend the calculation.
So in the first column, there are two sign changes, the system is unstable
Routh Hurwitz criterion is used to determine- a)peak response of the system
- b)time response of the system
- c)absolute stability of the system
- d)roots of the characteristic equation graphically
Correct answer is option 'C'. Can you explain this answer?
Routh Hurwitz criterion is used to determine
a)
peak response of the system
b)
time response of the system
c)
absolute stability of the system
d)
roots of the characteristic equation graphically
| | Engineers Adda answered |
Routh-Hurwitz criterion:
- Using the Routh-Hurwitz method, the stability information can be obtained without the need to solve the closed-loop system poles. This can be achieved by determining the number of poles that are in the left-half or right-half plane and on the imaginary axis.
- This involves checking the roots of the characteristic polynomial of a linear system to determine its stability.
- It is used to determine the absolute stability of a system.
Important points
Other methods of determining stability include:
Root locus:
- This method gives the position of the roots of the characteristic equation as the gain K is varied.
- With Root locus (unlike the case with Routh-Hurwitz criterion), we can do both analysis (i.e., for each gain value we know where the closed-loop poles are) and design (i.e., on the curve we can search for a gain value that results in the desired closed-loop poles).
Nyquist plot:
- This method is mainly used for assessing the stability of a system with feedback.
- While Nyquist is a graphical technique, it only provides a limited amount of intuition for why a system is stable or unstable, or how to modify an unstable system to be stable.
Techniques like Bode plots, while less general, are sometimes a more useful design tool.
The characteristic equation of a system is given by s3 + s + 2 - 0.What are the number of roots in the right half s-plane and on the jω-axis respectively?- a)3, 0
- b)2, 1
- c)1,2
- d)2,0
Correct answer is option 'D'. Can you explain this answer?
The characteristic equation of a system is given by s3 + s + 2 - 0.
What are the number of roots in the right half s-plane and on the jω-axis respectively?
a)
3, 0
b)
2, 1
c)
1,2
d)
2,0
| | Manisha Rane answered |
The characteristic equation of the system is given by:
s^3 + s + 2 = 0
To determine the number of roots in the right half s-plane, we need to evaluate the real parts of the roots. Since the equation is a third-degree polynomial, it can have up to three roots.
To find the roots, we can use the Routh-Hurwitz stability criterion. This method involves creating a Routh array using the coefficients of the characteristic equation:
1 2
1 0
2
To determine the number of roots in the right half s-plane, we count the number of sign changes in the first column of the Routh array. In this case, there is one sign change (from 1 to 2), so there is one root in the right half s-plane.
To determine the number of roots on the jω-axis, we count the number of sign changes in the first column of the Routh array after substituting jω for s. In this case, there are no sign changes, so there are no roots on the jω-axis.
s^3 + s + 2 = 0
To determine the number of roots in the right half s-plane, we need to evaluate the real parts of the roots. Since the equation is a third-degree polynomial, it can have up to three roots.
To find the roots, we can use the Routh-Hurwitz stability criterion. This method involves creating a Routh array using the coefficients of the characteristic equation:
1 2
1 0
2
To determine the number of roots in the right half s-plane, we count the number of sign changes in the first column of the Routh array. In this case, there is one sign change (from 1 to 2), so there is one root in the right half s-plane.
To determine the number of roots on the jω-axis, we count the number of sign changes in the first column of the Routh array after substituting jω for s. In this case, there are no sign changes, so there are no roots on the jω-axis.
The characteristic polynomial of a linear system is given as s4 + 3s3 + 5s2 + 6s + K + 10 = 0. What should be the condition on K so that the system is stable?- a)-10 < K < -4
- b)K > 10
- c)K > -4
- d)K > -10
Correct answer is option 'A'. Can you explain this answer?
The characteristic polynomial of a linear system is given as s4 + 3s3 + 5s2 + 6s + K + 10 = 0. What should be the condition on K so that the system is stable?
a)
-10 < K < -4
b)
K > 10
c)
K > -4
d)
K > -10
| | Engineers Adda answered |
Concept:
The characteristic equation for a given open-loop transfer function G(s) is
1 + G(s) H(s) = 0
To find the closed system stability by using RH criteria we require a characteristic equation. Whereas in remaining all stability techniques we require open-loop transfer function.
The nth order general form of CE is
RH table shown below:
Necessary condition: All the coefficients of the characteristic equation should be positive and real.
Sufficient Conditions for stability:
1. All the coefficients in the first column should have the same sign and no coefficient should be zero.
2. If any sign changes in the first column, the system is unstable.
And the number of sign changes = Number of poles in right of s-plane.
Calculation:
Characteristic equation: s4 + 3s3 + 5s2 + 6s + K + 10 = 0
By applying Routh tabulation method,
The system to become stable, the sign changes in the first column of the Routh table must be zero.
- 4 - K > 0 and K + 10 > 0
4 + K < 0 and K + 10 > 0
K < - 4 and K > - 10
⇒ - 10 < K < - 4
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
Correct answer is option 'D'. Can you explain this answer?
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
1. a pair of real roots with opposite sign
2. complex conjugate roots on the imaginary axis
3. a pair of complex conjugate roots with opposite real parts
Which of the above statements are correct?
a)
Only 2
b)
2 and 3
c)
Only 3
d)
1, 2 and 3
| | Engineers Adda answered |
Routh-Hurwitz Stability Criterion: It is used to test the stability of an LTI system.
The characteristic equation for a given open-loop transfer function G(s) is
1 + G(s) H(s) = 0
According to the Routh tabulation method,
The system is said to be stable if there are no sign changes in the first column of the Routh array
The number of poles lies on the right half of s plane = number of sign changes
A row of zeros in a Routh table:
This situation occurs when the characteristic equation has
- a pair of real roots with opposite sign (±a)
- complex conjugate roots on the imaginary axis (± jω)
- a pair of complex conjugate roots with opposite real parts (-a ± jb, a ± jb)
The procedure to overcome this as follows:
- Form the auxiliary equation from the preceding row to the row of zeros
- Complete Routh array by replacing the zero row with the coefficients obtained by differentiating the auxiliary equation.
- The roots of the auxiliary equation are also the roots of the characteristic equation.
- The roots of the auxiliary equation occur in pairs and are of the opposite sign of each other.
- The auxiliary equation is always even in order.
Which of the following is the correct comment on stability based on unknown k for the feedback system with characteristic s4 + 2ks3 + s2 + 5s + 5 = 0?- a)Unstable for all the values of k
- b)Stable for zero value of k
- c)Stable for positive value of k
- d)Stable for all the values of k
Correct answer is option 'A'. Can you explain this answer?
Which of the following is the correct comment on stability based on unknown k for the feedback system with characteristic s4 + 2ks3 + s2 + 5s + 5 = 0?
a)
Unstable for all the values of k
b)
Stable for zero value of k
c)
Stable for positive value of k
d)
Stable for all the values of k
| | Disha Das answered |
Explanation:
Characteristics of the given system:
- The characteristic equation of the system is s^4 + 2ks^3 + s^2 + 5s + 5 = 0.
Stability Analysis:
- The stability of a system is determined by the location of the roots of the characteristic equation in the complex plane.
- For a system to be stable, all the roots of the characteristic equation should have negative real parts.
Analysis of the given characteristic equation:
- By observing the given characteristic equation, we see that the coefficients are all positive.
- The system will have at least one root with a positive real part for any non-zero value of k.
Conclusion:
- Therefore, the system is unstable for all values of k.
- Option 'A' is the correct comment on stability based on unknown k for the feedback system with the given characteristic equation.
Characteristics of the given system:
- The characteristic equation of the system is s^4 + 2ks^3 + s^2 + 5s + 5 = 0.
Stability Analysis:
- The stability of a system is determined by the location of the roots of the characteristic equation in the complex plane.
- For a system to be stable, all the roots of the characteristic equation should have negative real parts.
Analysis of the given characteristic equation:
- By observing the given characteristic equation, we see that the coefficients are all positive.
- The system will have at least one root with a positive real part for any non-zero value of k.
Conclusion:
- Therefore, the system is unstable for all values of k.
- Option 'A' is the correct comment on stability based on unknown k for the feedback system with the given characteristic equation.
Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.
Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.- a)Both A and R are true and R is a correct explanation of A.
- b)Both A and R are true but R is not a correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'C'. Can you explain this answer?
Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.
Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.
Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.
a)
Both A and R are true and R is a correct explanation of A.
b)
Both A and R are true but R is not a correct explanation of A.
c)
A is true but R is false.
d)
A is false but R is true.
 | Rajat Kumar answered |
Poles of the closed loop transfer function is the characteristic equation of a closed loop control system. For the system to be stable all roots of characteristic equation should lie in LH s-plane. Hence reason is false.
For a discrete-time system to be unstable, all the poles of the z-transfer function should lie- a)on the left-half of z-plane
- b)on the right-half of z-plane
- c)outside the circle of unit radius
- d)within a circle of unit radius
Correct answer is option 'C'. Can you explain this answer?
For a discrete-time system to be unstable, all the poles of the z-transfer function should lie
a)
on the left-half of z-plane
b)
on the right-half of z-plane
c)
outside the circle of unit radius
d)
within a circle of unit radius
 | Mihir Chawla answered |
Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.
Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstable- a)Both A and R are true and R is a correct explanation of A.
- b)Both A and R are true but R is not a correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'B'. Can you explain this answer?
Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.
Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstable
Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstable
a)
Both A and R are true and R is a correct explanation of A.
b)
Both A and R are true but R is not a correct explanation of A.
c)
A is true but R is false.
d)
A is false but R is true.
 | Sravya Bajaj answered |
Both assertion and reason are individually true. The correct reason for assertion is BIBO stability criteria,
Assertion (A): If the system is stable we can determine the relative stability by the settling time of the system.
Reason (R): If the settling time is less than that of the other system then the system is said to be relatively more stable.- a)Both A and R are true and R is a correct explanation of A.
- b)Both A and R are true but R is not a correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'A'. Can you explain this answer?
Assertion (A): If the system is stable we can determine the relative stability by the settling time of the system.
Reason (R): If the settling time is less than that of the other system then the system is said to be relatively more stable.
Reason (R): If the settling time is less than that of the other system then the system is said to be relatively more stable.
a)
Both A and R are true and R is a correct explanation of A.
b)
Both A and R are true but R is not a correct explanation of A.
c)
A is true but R is false.
d)
A is false but R is true.
 | Shalini Banerjee answered |
The settling time is inversely proportional to the real part of the dominant roots. If the settling time is less compared to other system, then the system will be relatively more stable
Consider the following characteristic equation of a system:
s3 + 2Ks2 + (K+ 2) s+ 4 = 0
Which one of the following is correct?- a)The system is stable for all positive values of K.
- b)The system is unstable for all values of K.
- c)The system is stable for values of K > 0.73.
- d)The system is stable for value of K < 0.73.
Correct answer is option 'C'. Can you explain this answer?
Consider the following characteristic equation of a system:
s3 + 2Ks2 + (K+ 2) s+ 4 = 0
Which one of the following is correct?
s3 + 2Ks2 + (K+ 2) s+ 4 = 0
Which one of the following is correct?
a)
The system is stable for all positive values of K.
b)
The system is unstable for all values of K.
c)
The system is stable for values of K > 0.73.
d)
The system is stable for value of K < 0.73.
| | Sandeep Saha answered |
Given characteristic equation is,
s2 + 2Ks2 + (K + 2)s + 4 = 0
Routh’s array is:
For stability, 2K > 0 or K > 0
Also,
or K2 + 2 K - 2 > 0
Now, K2 + 2K - 2 = 0 or, K = 0.73, -2.73 For K > 0.73, K2 + 2 K - 2 > 0
(since K should be > 0)
Hence, system will be stable if K > 0.73.
s2 + 2Ks2 + (K + 2)s + 4 = 0
Routh’s array is:
For stability, 2K > 0 or K > 0
Also,
or K2 + 2 K - 2 > 0Now, K2 + 2K - 2 = 0 or, K = 0.73, -2.73 For K > 0.73, K2 + 2 K - 2 > 0
(since K should be > 0)
Hence, system will be stable if K > 0.73.
The number of sign changes in the Routh’s array indicates the number of roots lying in the- a)origin of s-plane
- b)left half of s-plane
- c)right half of s-piane
- d)centre of the s-plane
Correct answer is option 'C'. Can you explain this answer?
The number of sign changes in the Routh’s array indicates the number of roots lying in the
a)
origin of s-plane
b)
left half of s-plane
c)
right half of s-piane
d)
centre of the s-plane
 | Om Choudhury answered |
Number of sign changes in the first column of Routh’s array indicates the number of closed loop poles or roots of characteristic equation lying in the right half of s-plane.
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