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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?
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Most Upvoted Answer
Which of the following is the correct comment on stability based on un...
Concept:
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 Routh array
The number of poles lie on the right half of s plane = number of sign changes
Calculation:
Characteristic equation: s4 + 2ks3 + s2 + 5s + 5 = 0
By applying the Routh tabulation method,
The system to become stable, the sign changes in the first column of Routh table must be zero.
For all the values of k > 2.5,
gives negative values.
Therefore, the given system is unstable for all the values of k.
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 Routh array
The number of poles lie on the right half of s plane = number of sign changes
Calculation:
Characteristic equation: s4 + 2ks3 + s2 + 5s + 5 = 0
By applying the Routh tabulation method,
The system to become stable, the sign changes in the first column of Routh table must be zero.
For all the values of k > 2.5,
gives negative values.Therefore, the given system is unstable for all the values of k.
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Community Answer
Which of the following is the correct comment on stability based on un...
Explanation:
To determine the stability of the feedback system with the characteristic equation s^4 + 2ks^3 + s^2 + 5s + 5 = 0, we need to analyze the roots of the characteristic equation.
- Characteristics of the roots:
The system will be stable if all the roots of the characteristic equation have negative real parts. If any root has a positive real part, the system will be unstable.
- Analysis:
Considering the given characteristic equation, the coefficient of s^4 is 1, which is positive. This indicates that the system has at least one pole at the origin (s = 0). The coefficient of s^3 is 2k, where k is unknown. For stability, this coefficient must be negative. However, since k is unknown and could be positive, zero, or negative, we must consider all cases.
- Conclusion:
Since the coefficient of s^3 can take any value (positive, zero, or negative) depending on the value of k, the system can have poles with positive real parts for certain values of k. Therefore, the system is unstable for all values of k.
Therefore, the correct statement is:
a) Unstable for all the values of k.
To determine the stability of the feedback system with the characteristic equation s^4 + 2ks^3 + s^2 + 5s + 5 = 0, we need to analyze the roots of the characteristic equation.
- Characteristics of the roots:
The system will be stable if all the roots of the characteristic equation have negative real parts. If any root has a positive real part, the system will be unstable.
- Analysis:
Considering the given characteristic equation, the coefficient of s^4 is 1, which is positive. This indicates that the system has at least one pole at the origin (s = 0). The coefficient of s^3 is 2k, where k is unknown. For stability, this coefficient must be negative. However, since k is unknown and could be positive, zero, or negative, we must consider all cases.
- Conclusion:
Since the coefficient of s^3 can take any value (positive, zero, or negative) depending on the value of k, the system can have poles with positive real parts for certain values of k. Therefore, the system is unstable for all values of k.
Therefore, the correct statement is:
a) Unstable for all the values of k.
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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 kb)Stable for zero value of kc)Stable for positive value of kd)Stable for all the values of kCorrect answer is option 'A'. Can you explain this answer?
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