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A single-input single-output feedback system has forward transfer function G(s) and feedback transfer function H(s). It is given that |G(s)H(s)| < 1. Which of the following is true about the stability of the system?
- a)The system is always stable
- b)The system is stable if all zeros of G(s)H(s) are in left half of the s-plane
- c)The system is stable if all poles of G(s)H(s) are in left half of the s-plane
- d)It is not possible to say whether or not the system is stable from the information given
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A single-input single-output feedback system has forward transfer func...
Concept:
D(s) = 1 + G(s)H(s)
D(s) = 1 + G(s)H(s)
D(s) gives the roots of characteristic equation i.e. closed-loop poles.
Nyquist stability criteria state that the number of unstable closed-loop poles is equal to the number of unstable open-loop poles plus the number of encirclements of the origin of the Nyquist plot of the complex function D(s).
It can be slightly simplified if instead of plotting the function D(s) = 1 + G(s)H(s), we plot only the function G(s)H(s) around the point and count encirclement of the Nyquist plot of around the point (-1, j0).
From the principal of argument theorem, the number of encirclements about (-1, j0) is
N = P - Z
Where
Where P = Number of open-loop poles on the right half of s plane
Z = Number of closed-loop poles on the right half of s plane
Calculation:
For the given system, we have |G(s)H(s)| < 1
So, we may easily conclude that the Nyquist-plot intersect the negative real axis between 0 and -1 point, i.e. the Nyquist plot does not enclose the point (-1, 0) or in other words number of encirclements is zero.
⇒ N = 0
For a stable closed loop system, we must have Z = 0.
To get Z = 0, from the Nyquist criteria, P must be equal to zero.
Therefore, the system is stable if all poles of G(s)H(s) are in left half of the s-plane.
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Community Answer
A single-input single-output feedback system has forward transfer func...
Explanation:
Feedback System Stability Criteria:
In a feedback system, stability can be determined by analyzing the poles of the closed-loop transfer function. If all the poles of the closed-loop transfer function have negative real parts, then the system is stable.
Given Information:
The given condition |G(s)H(s)| < 1="" implies="" that="" the="" loop="" gain="" of="" the="" system="" is="" less="" than="" 1.="" this="" is="" a="" necessary="" but="" not="" a="" sufficient="" condition="" for="" />
Analysis:
To determine the stability of the system, we need to analyze the poles of the closed-loop transfer function G(s)H(s). If all the poles of G(s)H(s) are in the left half of the s-plane (i.e., have negative real parts), then the system is stable. This is because the poles of G(s)H(s) determine the stability of the closed-loop system.
Conclusion:
Therefore, the correct statement is option 'c) The system is stable if all poles of G(s)H(s) are in the left half of the s-plane'. This condition ensures that the system is stable based on the location of the poles of the closed-loop transfer function.
Feedback System Stability Criteria:
In a feedback system, stability can be determined by analyzing the poles of the closed-loop transfer function. If all the poles of the closed-loop transfer function have negative real parts, then the system is stable.
Given Information:
The given condition |G(s)H(s)| < 1="" implies="" that="" the="" loop="" gain="" of="" the="" system="" is="" less="" than="" 1.="" this="" is="" a="" necessary="" but="" not="" a="" sufficient="" condition="" for="" />
Analysis:
To determine the stability of the system, we need to analyze the poles of the closed-loop transfer function G(s)H(s). If all the poles of G(s)H(s) are in the left half of the s-plane (i.e., have negative real parts), then the system is stable. This is because the poles of G(s)H(s) determine the stability of the closed-loop system.
Conclusion:
Therefore, the correct statement is option 'c) The system is stable if all poles of G(s)H(s) are in the left half of the s-plane'. This condition ensures that the system is stable based on the location of the poles of the closed-loop transfer function.
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A single-input single-output feedback system has forward transfer function G(s) and feedback transfer function H(s). It is given that |G(s)H(s)| < 1. Which of the following is true about the stability of the system?a)The system is always stableb)The system is stable if all zeros of G(s)H(s) are in left half of the s-planec)The system is stable if all poles of G(s)H(s) are in left half of the s-planed)It is not possible to say whether or not the system is stable from the information givenCorrect answer is option 'C'. Can you explain this answer?
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A single-input single-output feedback system has forward transfer function G(s) and feedback transfer function H(s). It is given that |G(s)H(s)| < 1. Which of the following is true about the stability of the system?a)The system is always stableb)The system is stable if all zeros of G(s)H(s) are in left half of the s-planec)The system is stable if all poles of G(s)H(s) are in left half of the s-planed)It is not possible to say whether or not the system is stable from the information givenCorrect answer is option 'C'. 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 A single-input single-output feedback system has forward transfer function G(s) and feedback transfer function H(s). It is given that |G(s)H(s)| < 1. Which of the following is true about the stability of the system?a)The system is always stableb)The system is stable if all zeros of G(s)H(s) are in left half of the s-planec)The system is stable if all poles of G(s)H(s) are in left half of the s-planed)It is not possible to say whether or not the system is stable from the information givenCorrect answer is option 'C'. 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 A single-input single-output feedback system has forward transfer function G(s) and feedback transfer function H(s). It is given that |G(s)H(s)| < 1. Which of the following is true about the stability of the system?a)The system is always stableb)The system is stable if all zeros of G(s)H(s) are in left half of the s-planec)The system is stable if all poles of G(s)H(s) are in left half of the s-planed)It is not possible to say whether or not the system is stable from the information givenCorrect answer is option 'C'. Can you explain this answer?.
A single-input single-output feedback system has forward transfer function G(s) and feedback transfer function H(s). It is given that |G(s)H(s)| < 1. Which of the following is true about the stability of the system?a)The system is always stableb)The system is stable if all zeros of G(s)H(s) are in left half of the s-planec)The system is stable if all poles of G(s)H(s) are in left half of the s-planed)It is not possible to say whether or not the system is stable from the information givenCorrect answer is option 'C'. 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 A single-input single-output feedback system has forward transfer function G(s) and feedback transfer function H(s). It is given that |G(s)H(s)| < 1. Which of the following is true about the stability of the system?a)The system is always stableb)The system is stable if all zeros of G(s)H(s) are in left half of the s-planec)The system is stable if all poles of G(s)H(s) are in left half of the s-planed)It is not possible to say whether or not the system is stable from the information givenCorrect answer is option 'C'. 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 A single-input single-output feedback system has forward transfer function G(s) and feedback transfer function H(s). It is given that |G(s)H(s)| < 1. Which of the following is true about the stability of the system?a)The system is always stableb)The system is stable if all zeros of G(s)H(s) are in left half of the s-planec)The system is stable if all poles of G(s)H(s) are in left half of the s-planed)It is not possible to say whether or not the system is stable from the information givenCorrect answer is option 'C'. Can you explain this answer?.
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ample number of questions to practice A single-input single-output feedback system has forward transfer function G(s) and feedback transfer function H(s). It is given that |G(s)H(s)| < 1. Which of the following is true about the stability of the system?a)The system is always stableb)The system is stable if all zeros of G(s)H(s) are in left half of the s-planec)The system is stable if all poles of G(s)H(s) are in left half of the s-planed)It is not possible to say whether or not the system is stable from the information givenCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
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