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Which one of the following is not a property of root loci ?
- a)The root locus is symmetrical about jw axis
- b)They start from the open loop poles and terminate at the open loop zeros.
- c)The breakaway points are determined from dK/ds = 0
- d)Segments of the real axis are part of the root locus, if and only if, the total number of real poles and zeros to their right is odd
Correct answer is option 'A'. Can you explain this answer?
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Which one of the following is not a property of root loci ?a)The root ...
-The root locus of a feedback system is the graphical representation in the complex s-plane of the possible locations of its closed-loop poles for varying values of a certain system parameter. The points that are part of the root locus satisfy the angle condition.
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-The Root Locus Plot technique can be applied to determine the dynamic response of the system. This method associates itself with the transient response of the system and is particularly useful in the investigation of stability characteristics of the system.
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Which one of the following is not a property of root loci ?a)The root ...
Explanation:
The root locus is a graphical representation of the possible locations of the closed-loop poles as a parameter, typically the gain, of the system is varied. It is a useful tool for analyzing the stability and transient response of a control system.
Properties of root loci:
1. Symmetry about the jw axis: This property states that the root locus is symmetrical about the imaginary axis. The complex conjugate poles and zeros are always symmetrically placed with respect to the imaginary axis. This property helps in analyzing the stability of the system.
2. Starting and terminating points: The root locus starts from the open-loop poles and terminates at the open-loop zeros. This means that as the gain is varied, the poles of the closed-loop system move from the original positions (open-loop poles) towards the open-loop zeros.
3. Breakaway and break-in points: The breakaway points are the points on the root locus where the real axis is tangent to the locus. They represent the values of the gain at which the system transitions from having complex poles to real poles. The breakaway points can be determined by taking the derivative of the characteristic equation with respect to the gain and setting it equal to zero, i.e., dK/ds = 0.
4. Real axis segments: Segments of the real axis are part of the root locus if and only if the total number of real poles and zeros to their right is odd. This property helps in determining the stability of the system. If the number of real poles and zeros to the right of a point on the real axis is odd, then that point lies on the root locus.
The incorrect property:
The incorrect property is option A - "The root locus is symmetrical about the jw axis." This is not a property of root loci. The root locus is symmetric about the real axis, not the imaginary axis (jw axis). The complex conjugate poles and zeros are symmetrically placed with respect to the real axis, not the imaginary axis. The root locus can have branches extending in both the upper and lower half-planes with respect to the real axis, but there is no specific symmetry about the imaginary axis.
Therefore, option A is the correct answer as it does not accurately describe a property of root loci.
The root locus is a graphical representation of the possible locations of the closed-loop poles as a parameter, typically the gain, of the system is varied. It is a useful tool for analyzing the stability and transient response of a control system.
Properties of root loci:
1. Symmetry about the jw axis: This property states that the root locus is symmetrical about the imaginary axis. The complex conjugate poles and zeros are always symmetrically placed with respect to the imaginary axis. This property helps in analyzing the stability of the system.
2. Starting and terminating points: The root locus starts from the open-loop poles and terminates at the open-loop zeros. This means that as the gain is varied, the poles of the closed-loop system move from the original positions (open-loop poles) towards the open-loop zeros.
3. Breakaway and break-in points: The breakaway points are the points on the root locus where the real axis is tangent to the locus. They represent the values of the gain at which the system transitions from having complex poles to real poles. The breakaway points can be determined by taking the derivative of the characteristic equation with respect to the gain and setting it equal to zero, i.e., dK/ds = 0.
4. Real axis segments: Segments of the real axis are part of the root locus if and only if the total number of real poles and zeros to their right is odd. This property helps in determining the stability of the system. If the number of real poles and zeros to the right of a point on the real axis is odd, then that point lies on the root locus.
The incorrect property:
The incorrect property is option A - "The root locus is symmetrical about the jw axis." This is not a property of root loci. The root locus is symmetric about the real axis, not the imaginary axis (jw axis). The complex conjugate poles and zeros are symmetrically placed with respect to the real axis, not the imaginary axis. The root locus can have branches extending in both the upper and lower half-planes with respect to the real axis, but there is no specific symmetry about the imaginary axis.
Therefore, option A is the correct answer as it does not accurately describe a property of root loci.
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Which one of the following is not a property of root loci ?a)The root locus is symmetrical about jw axisb)They start from the open loop poles and terminate at the open loop zeros.c)The breakaway points are determined from dK/ds = 0d)Segments of the real axis are part of the root locus, if and only if, the total number of real poles and zeros to their right is oddCorrect answer is option 'A'. Can you explain this answer?
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Which one of the following is not a property of root loci ?a)The root locus is symmetrical about jw axisb)They start from the open loop poles and terminate at the open loop zeros.c)The breakaway points are determined from dK/ds = 0d)Segments of the real axis are part of the root locus, if and only if, the total number of real poles and zeros to their right is oddCorrect answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Which one of the following is not a property of root loci ?a)The root locus is symmetrical about jw axisb)They start from the open loop poles and terminate at the open loop zeros.c)The breakaway points are determined from dK/ds = 0d)Segments of the real axis are part of the root locus, if and only if, the total number of real poles and zeros to their right is oddCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following is not a property of root loci ?a)The root locus is symmetrical about jw axisb)They start from the open loop poles and terminate at the open loop zeros.c)The breakaway points are determined from dK/ds = 0d)Segments of the real axis are part of the root locus, if and only if, the total number of real poles and zeros to their right is oddCorrect answer is option 'A'. Can you explain this answer?.
Which one of the following is not a property of root loci ?a)The root locus is symmetrical about jw axisb)They start from the open loop poles and terminate at the open loop zeros.c)The breakaway points are determined from dK/ds = 0d)Segments of the real axis are part of the root locus, if and only if, the total number of real poles and zeros to their right is oddCorrect answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Which one of the following is not a property of root loci ?a)The root locus is symmetrical about jw axisb)They start from the open loop poles and terminate at the open loop zeros.c)The breakaway points are determined from dK/ds = 0d)Segments of the real axis are part of the root locus, if and only if, the total number of real poles and zeros to their right is oddCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following is not a property of root loci ?a)The root locus is symmetrical about jw axisb)They start from the open loop poles and terminate at the open loop zeros.c)The breakaway points are determined from dK/ds = 0d)Segments of the real axis are part of the root locus, if and only if, the total number of real poles and zeros to their right is oddCorrect answer is option 'A'. Can you explain this answer?.
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