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The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?
- a)It corresponds to a frequency greater than K
- b)It corresponds to a frequency less than K
- c)It corresponds to a frequency K
- d)Root locus of modified system never transits to unstable region
Correct answer is option 'D'. Can you explain this answer?
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The open loop poles of a third order unity feedback system are at 0,-1...
The given system is a third-order unity feedback system with open loop poles at 0, -1, and -2. The frequency corresponding to the point where the root locus of the system transits to the unstable region is denoted by K.
Introducing a zero in the open loop transfer function at -3 while keeping all the earlier open loop poles intact will affect the root locus of the system. Let's analyze the effect of this zero on the stability of the system.
Effect of Adding a Zero
- Adding a zero will introduce a break-in and breakaway point on the root locus.
- The break-in point occurs when the angle condition of the root locus intersects the real axis.
- The breakaway point occurs when two branches of the root locus meet and then diverge.
Location of Break-in and Breakaway Points
- The break-in and breakaway points occur on the real axis between the open loop poles and zeros.
- In this case, the break-in and breakaway points will occur between the poles at -2 and -3.
Modified Root Locus
- The addition of the zero at -3 will affect the root locus and its behavior.
- The modified root locus will have an additional branch that originates from the zero at -3 and moves towards the open loop poles at 0, -1, and -2.
- Depending on the gain K, this additional branch can either stay in the stable region or cross over into the unstable region.
Location of Transition to Unstable Region
- Since the additional branch of the modified root locus originates from the zero at -3, it will never intersect the real axis to the left of this zero.
- The root locus will only transit to the unstable region if it intersects the real axis to the right of the zero at -3.
- However, since the original root locus has already transited to the unstable region at a frequency denoted by K, the modified root locus will not transit again.
Therefore, the point where the root locus of the modified system transits to the unstable region is not applicable. The correct answer is option D, "Root locus of the modified system never transits to the unstable region."
Introducing a zero in the open loop transfer function at -3 while keeping all the earlier open loop poles intact will affect the root locus of the system. Let's analyze the effect of this zero on the stability of the system.
Effect of Adding a Zero
- Adding a zero will introduce a break-in and breakaway point on the root locus.
- The break-in point occurs when the angle condition of the root locus intersects the real axis.
- The breakaway point occurs when two branches of the root locus meet and then diverge.
Location of Break-in and Breakaway Points
- The break-in and breakaway points occur on the real axis between the open loop poles and zeros.
- In this case, the break-in and breakaway points will occur between the poles at -2 and -3.
Modified Root Locus
- The addition of the zero at -3 will affect the root locus and its behavior.
- The modified root locus will have an additional branch that originates from the zero at -3 and moves towards the open loop poles at 0, -1, and -2.
- Depending on the gain K, this additional branch can either stay in the stable region or cross over into the unstable region.
Location of Transition to Unstable Region
- Since the additional branch of the modified root locus originates from the zero at -3, it will never intersect the real axis to the left of this zero.
- The root locus will only transit to the unstable region if it intersects the real axis to the right of the zero at -3.
- However, since the original root locus has already transited to the unstable region at a frequency denoted by K, the modified root locus will not transit again.
Therefore, the point where the root locus of the modified system transits to the unstable region is not applicable. The correct answer is option D, "Root locus of the modified system never transits to the unstable region."
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The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?a)It corresponds to a frequency greater than Kb)It corresponds to a frequency less than Kc)It corresponds to a frequency Kd)Root locus of modified system never transits to unstable regionCorrect answer is option 'D'. Can you explain this answer?
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The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?a)It corresponds to a frequency greater than Kb)It corresponds to a frequency less than Kc)It corresponds to a frequency Kd)Root locus of modified system never transits to unstable regionCorrect answer is option 'D'. 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 The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?a)It corresponds to a frequency greater than Kb)It corresponds to a frequency less than Kc)It corresponds to a frequency Kd)Root locus of modified system never transits to unstable regionCorrect answer is option 'D'. 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 The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?a)It corresponds to a frequency greater than Kb)It corresponds to a frequency less than Kc)It corresponds to a frequency Kd)Root locus of modified system never transits to unstable regionCorrect answer is option 'D'. Can you explain this answer?.
The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?a)It corresponds to a frequency greater than Kb)It corresponds to a frequency less than Kc)It corresponds to a frequency Kd)Root locus of modified system never transits to unstable regionCorrect answer is option 'D'. 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 The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?a)It corresponds to a frequency greater than Kb)It corresponds to a frequency less than Kc)It corresponds to a frequency Kd)Root locus of modified system never transits to unstable regionCorrect answer is option 'D'. 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 The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?a)It corresponds to a frequency greater than Kb)It corresponds to a frequency less than Kc)It corresponds to a frequency Kd)Root locus of modified system never transits to unstable regionCorrect answer is option 'D'. Can you explain this answer?.
Solutions for The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?a)It corresponds to a frequency greater than Kb)It corresponds to a frequency less than Kc)It corresponds to a frequency Kd)Root locus of modified system never transits to unstable regionCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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