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Consider the following statements:
Routh-Hurwitz criterion gives:
1. Absolute stability
2. The number of roots lying on the right half of the s-plane
3. The gain margin and the phase margin
Routh-Hurwitz criterion gives:
1. Absolute stability
2. The number of roots lying on the right half of the s-plane
3. The gain margin and the phase margin
- a)1,2 and3
- b)1 and 2
- c)2 and 3
- d)1 and 3
Correct answer is option 'B'. Can you explain this answer?
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Consider the following statements:Routh-Hurwitz criterion gives:1. Abs...
Explanation: Routh-Hurwitz criterion gives absolute stability and number of roots lying on the right half of the s-plane.
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Consider the following statements:Routh-Hurwitz criterion gives:1. Abs...
Answer:
The Routh-Hurwitz criterion is a mathematical technique used to determine the stability of a linear time-invariant system. It is based on the examination of the coefficients of the characteristic equation of the system. The characteristic equation is obtained by equating the denominator of the transfer function of the system to zero.
The Routh-Hurwitz criterion gives us information about the stability of the system and the number of roots lying on the right-half of the s-plane. Let's look at each statement in detail:
1. Absolute stability:
The Routh-Hurwitz criterion can determine whether a system is absolutely stable or not. If all the coefficients in the first column of the Routh array are positive, then the system is absolutely stable. If there is at least one coefficient in the first column that is zero or negative, then the system is not absolutely stable.
2. The number of roots lying on the right half of the s-plane:
The Routh-Hurwitz criterion can also determine the number of roots lying on the right half of the s-plane. The number of sign changes in the first column of the Routh array corresponds to the number of roots with positive real parts. If there are no sign changes in the first column, then all the roots are in the left half of the s-plane and the system is stable. If there is one sign change, then there is one root in the right half of the s-plane, indicating marginal stability. If there are more than one sign changes, then there are multiple roots in the right half of the s-plane, indicating instability.
3. The gain margin and the phase margin:
The Routh-Hurwitz criterion does not directly give information about the gain margin and the phase margin of a system. The gain margin and the phase margin are measures of the robustness of a system's stability with respect to changes in gain and phase. These measures are typically obtained through other techniques such as the Bode plot or the Nyquist plot.
Therefore, the correct answer is option 'B', which states that the Routh-Hurwitz criterion gives information about absolute stability and the number of roots lying on the right half of the s-plane. It does not directly provide information about the gain margin and the phase margin.
The Routh-Hurwitz criterion is a mathematical technique used to determine the stability of a linear time-invariant system. It is based on the examination of the coefficients of the characteristic equation of the system. The characteristic equation is obtained by equating the denominator of the transfer function of the system to zero.
The Routh-Hurwitz criterion gives us information about the stability of the system and the number of roots lying on the right-half of the s-plane. Let's look at each statement in detail:
1. Absolute stability:
The Routh-Hurwitz criterion can determine whether a system is absolutely stable or not. If all the coefficients in the first column of the Routh array are positive, then the system is absolutely stable. If there is at least one coefficient in the first column that is zero or negative, then the system is not absolutely stable.
2. The number of roots lying on the right half of the s-plane:
The Routh-Hurwitz criterion can also determine the number of roots lying on the right half of the s-plane. The number of sign changes in the first column of the Routh array corresponds to the number of roots with positive real parts. If there are no sign changes in the first column, then all the roots are in the left half of the s-plane and the system is stable. If there is one sign change, then there is one root in the right half of the s-plane, indicating marginal stability. If there are more than one sign changes, then there are multiple roots in the right half of the s-plane, indicating instability.
3. The gain margin and the phase margin:
The Routh-Hurwitz criterion does not directly give information about the gain margin and the phase margin of a system. The gain margin and the phase margin are measures of the robustness of a system's stability with respect to changes in gain and phase. These measures are typically obtained through other techniques such as the Bode plot or the Nyquist plot.
Therefore, the correct answer is option 'B', which states that the Routh-Hurwitz criterion gives information about absolute stability and the number of roots lying on the right half of the s-plane. It does not directly provide information about the gain margin and the phase margin.
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