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Which of the following is a powerful frequency-domain method of extracting the information regarding stability as well as the relative stability of a system without the need to evaluate the roots of the characteristic equation?
- a)Routh criterion only
- b)Root locus method only
- c)Both Routh criterion and Root locus method
- d)Nyquist criterion
Correct answer is option 'D'. Can you explain this answer?
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Which of the following is a powerful frequency-domain method of extrac...
Nyquist plot:
- Nyquist plots are the continuation of polar plots for finding the stability of the closed-loop control systems by varying ω from −∞ to ∞.
- It provides information regarding stability as well as the relative stability of a system without the need to evaluate the roots of the characteristic equation.
Nyquist stability criteria:
Encirclement:
- A point (or) a region is encircled if it inside the closed path.
- Encirclements(N) are considered as positive in the counter-clockwise direction and negative in a clockwise direction.
Nyquist stability criteria:
The Nyquist plot will encircle critical point (-1, j0) as many number of times as the difference between, the number of right side poles and zeros of the characteristic equation.
N = P - Z
Here
N = Number of encirclements of (-1, j0) by the Nyquist plot.
P = Number of right side poles of G(s) H(s)
Z = Number of right side zeros or roots of the characteristic equation (or) right side poles of the closed-loop transfer function.
For stability, 'Z' must be zero.
N = P -Z
N = P - 0
⇒ N = P
Hence, for closed-loop stability, NSC states that critical point (-1, j0) should be encircled in the counterclockwise direction as many numbers of times as the number of right side poles of G(s) H(s) by the Nyquist plot if the Nyquist contour is defined in the clockwise direction.
Note: For open-loop stable system P = 0, that means for closed-loop stability N = 0 - Z, for stability Z should be zero, it is possible if there are no encirclements made by Nyquist plot.
Note: For open-loop stable system P = 0, that means for closed-loop stability N = 0 - Z, for stability Z should be zero, it is possible if there are no encirclements made by Nyquist plot.
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Which of the following is a powerful frequency-domain method of extrac...
Nyquist plot:
- Nyquist plots are the continuation of polar plots for finding the stability of the closed-loop control systems by varying ω from −∞ to ∞.
- It provides information regarding stability as well as the relative stability of a system without the need to evaluate the roots of the characteristic equation.
Nyquist stability criteria:
Encirclement:
- A point (or) a region is encircled if it inside the closed path.
- Encirclements(N) are considered as positive in the counter-clockwise direction and negative in a clockwise direction.
Nyquist stability criteria:
The Nyquist plot will encircle critical point (-1, j0) as many number of times as the difference between, the number of right side poles and zeros of the characteristic equation.
N = P - Z
Here
N = Number of encirclements of (-1, j0) by the Nyquist plot.
P = Number of right side poles of G(s) H(s)
Z = Number of right side zeros or roots of the characteristic equation (or) right side poles of the closed-loop transfer function.
For stability, 'Z' must be zero.
N = P -Z
N = P - 0
⇒ N = P
Hence, for closed-loop stability, NSC states that critical point (-1, j0) should be encircled in the counterclockwise direction as many numbers of times as the number of right side poles of G(s) H(s) by the Nyquist plot if the Nyquist contour is defined in the clockwise direction.
Note: For open-loop stable system P = 0, that means for closed-loop stability N = 0 - Z, for stability Z should be zero, it is possible if there are no encirclements made by Nyquist plot.
Note: For open-loop stable system P = 0, that means for closed-loop stability N = 0 - Z, for stability Z should be zero, it is possible if there are no encirclements made by Nyquist plot.
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Which of the following is a powerful frequency-domain method of extracting the information regarding stability as well as the relative stability of a system without the need to evaluate the roots of the characteristic equation?a)Routh criterion onlyb)Root locus method onlyc)Both Routh criterion and Root locus methodd)Nyquist criterionCorrect answer is option 'D'. Can you explain this answer?
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Which of the following is a powerful frequency-domain method of extracting the information regarding stability as well as the relative stability of a system without the need to evaluate the roots of the characteristic equation?a)Routh criterion onlyb)Root locus method onlyc)Both Routh criterion and Root locus methodd)Nyquist criterionCorrect 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 Which of the following is a powerful frequency-domain method of extracting the information regarding stability as well as the relative stability of a system without the need to evaluate the roots of the characteristic equation?a)Routh criterion onlyb)Root locus method onlyc)Both Routh criterion and Root locus methodd)Nyquist criterionCorrect 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 Which of the following is a powerful frequency-domain method of extracting the information regarding stability as well as the relative stability of a system without the need to evaluate the roots of the characteristic equation?a)Routh criterion onlyb)Root locus method onlyc)Both Routh criterion and Root locus methodd)Nyquist criterionCorrect answer is option 'D'. Can you explain this answer?.
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Which of the following is a powerful frequency-domain method of extracting the information regarding stability as well as the relative stability of a system without the need to evaluate the roots of the characteristic equation?a)Routh criterion onlyb)Root locus method onlyc)Both Routh criterion and Root locus methodd)Nyquist criterionCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Which of the following is a powerful frequency-domain method of extracting the information regarding stability as well as the relative stability of a system without the need to evaluate the roots of the characteristic equation?a)Routh criterion onlyb)Root locus method onlyc)Both Routh criterion and Root locus methodd)Nyquist criterionCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Which of the following is a powerful frequency-domain method of extracting the information regarding stability as well as the relative stability of a system without the need to evaluate the roots of the characteristic equation?a)Routh criterion onlyb)Root locus method onlyc)Both Routh criterion and Root locus methodd)Nyquist criterionCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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