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Assertion ( A ) : An addition of real pole at s = - p0 in the transfer function G(s)H(s) of a control system results in the increase of stability margin.
Reason ( R ) : An addition of real pole at s = - p0 in the transfer function G(s)H(s) will make the resultant root loci bend towards the right.
Reason ( R ) : An addition of real pole at s = - p0 in the transfer function G(s)H(s) will make the resultant root loci bend towards the right.
- 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 'D'. Can you explain this answer?
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Assertion ( A ) : An addition of real pole at s = - p0 in the transfer...
Addition of real pole to an open loop T.F. decreases the stability because root locus shifts towards right of s-plane. Hence, assertion is a false statement.
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Assertion ( A ) : An addition of real pole at s = - p0 in the transfer...
Assertion (A): Stability Margin and Real Pole Addition
- The assertion states that adding a real pole at s = -p0 in the transfer function G(s)H(s) increases the stability margin.
- This assertion is false. Adding a real pole typically decreases the stability margin because it can lead to a slower response and may cause the system to become less stable.
Reason (R): Effect on Root Loci
- The reason given is that adding a real pole at s = -p0 causes the resultant root loci to bend towards the right.
- This statement is true. Adding a pole can indeed cause the root loci to shift. However, the bending of the root loci towards the right typically implies a decrease in stability, not an increase.
Conclusion: Evaluating A and R
- Since A is false and R is true, the correct option is D: A is false but R is true.
- This means that while the reason correctly describes the behavior of root loci, it does not justify the assertion about the stability margin.
Key Takeaways
- Adding a pole generally reduces stability margin.
- Root loci bending behavior helps understand system dynamics but does not support the assertion regarding stability improvement.
This evaluation highlights the importance of understanding system dynamics in control theory, especially when analyzing how modifications to the transfer function affect system behavior.
- The assertion states that adding a real pole at s = -p0 in the transfer function G(s)H(s) increases the stability margin.
- This assertion is false. Adding a real pole typically decreases the stability margin because it can lead to a slower response and may cause the system to become less stable.
Reason (R): Effect on Root Loci
- The reason given is that adding a real pole at s = -p0 causes the resultant root loci to bend towards the right.
- This statement is true. Adding a pole can indeed cause the root loci to shift. However, the bending of the root loci towards the right typically implies a decrease in stability, not an increase.
Conclusion: Evaluating A and R
- Since A is false and R is true, the correct option is D: A is false but R is true.
- This means that while the reason correctly describes the behavior of root loci, it does not justify the assertion about the stability margin.
Key Takeaways
- Adding a pole generally reduces stability margin.
- Root loci bending behavior helps understand system dynamics but does not support the assertion regarding stability improvement.
This evaluation highlights the importance of understanding system dynamics in control theory, especially when analyzing how modifications to the transfer function affect system behavior.
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Assertion ( A ) : An addition of real pole at s = - p0 in the transfer function G(s)H(s) of a control system results in the increase of stability margin.Reason ( R ) : An addition of real pole at s = - p0in the transfer function G(s)H(s) will make the resultant root loci bend towards the right.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 'D'. Can you explain this answer?
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Assertion ( A ) : An addition of real pole at s = - p0 in the transfer function G(s)H(s) of a control system results in the increase of stability margin.Reason ( R ) : An addition of real pole at s = - p0in the transfer function G(s)H(s) will make the resultant root loci bend towards the right.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 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Assertion ( A ) : An addition of real pole at s = - p0 in the transfer function G(s)H(s) of a control system results in the increase of stability margin.Reason ( R ) : An addition of real pole at s = - p0in the transfer function G(s)H(s) will make the resultant root loci bend towards the right.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 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion ( A ) : An addition of real pole at s = - p0 in the transfer function G(s)H(s) of a control system results in the increase of stability margin.Reason ( R ) : An addition of real pole at s = - p0in the transfer function G(s)H(s) will make the resultant root loci bend towards the right.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 'D'. Can you explain this answer?.
Assertion ( A ) : An addition of real pole at s = - p0 in the transfer function G(s)H(s) of a control system results in the increase of stability margin.Reason ( R ) : An addition of real pole at s = - p0in the transfer function G(s)H(s) will make the resultant root loci bend towards the right.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 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Assertion ( A ) : An addition of real pole at s = - p0 in the transfer function G(s)H(s) of a control system results in the increase of stability margin.Reason ( R ) : An addition of real pole at s = - p0in the transfer function G(s)H(s) will make the resultant root loci bend towards the right.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 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion ( A ) : An addition of real pole at s = - p0 in the transfer function G(s)H(s) of a control system results in the increase of stability margin.Reason ( R ) : An addition of real pole at s = - p0in the transfer function G(s)H(s) will make the resultant root loci bend towards the right.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 'D'. Can you explain this answer?.
Solutions for Assertion ( A ) : An addition of real pole at s = - p0 in the transfer function G(s)H(s) of a control system results in the increase of stability margin.Reason ( R ) : An addition of real pole at s = - p0in the transfer function G(s)H(s) will make the resultant root loci bend towards the right.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 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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ample number of questions to practice Assertion ( A ) : An addition of real pole at s = - p0 in the transfer function G(s)H(s) of a control system results in the increase of stability margin.Reason ( R ) : An addition of real pole at s = - p0in the transfer function G(s)H(s) will make the resultant root loci bend towards the right.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 'D'. Can you explain this answer? tests, examples and also practice GATE tests.
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