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The complete Nyquist plot of the open loop transfer function G(s) H (s) of a feedback control system shown in figure,
If G(s) H (s) has one zero in right half of the s-plane, the number of poles that, the closed loop system will have in right half of s-plane is
- a)0
- b)1
- c)4
- d)3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The complete Nyquist plot of the open loop transfer function G(s) H (...
Given Nyquist plot of G(s)H(s) is shown below
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Case 1 :
Here, G(s)H(s) has one zero in the right half of s-plane i.e. Z = 1 .
According to principle of argument
N =P− Z (Anti clockwise direction) …(i)
Where,
N = Number of encirclements of Nyquist plot of G(s)H(s) about origin in anti-clockwise direction P = Number of poles of G(s)H(s) in right half of s-plane.
Z = Number of zeros of G(s)H(s) in right half of s-plane.
Here, N =−2 (anti clockwise direction)
Z = 1
From equation (i)
−2= P − 1
P = –1 …(ii)
So, poles cannot be negative in numbers so no more further discussion on this.
Case 2 : If we assume Nyquist contour in anti clockwise direction then according to principle of argument
N =P− Z (Clockwise direction) …(iii)
Where,
N = Number of encirclements of Nyquist plot of G(s)H(s) about origin in clockwise direction
P = Number of poles of G(s)H(s) in right half of s-plane.
Z = Number of zeros of G(s)H(s) in right half of s-plane.
Here, N = 2 (Clockwise direction)
Z = 1
From equation (iii)
2 = P−1
P = 3 …(iv)
According to Nyquist stability criteria
N =P− Z (Anti clockwise direction) …(v)
Where, N = Number of encirclements about (−1+ 0 j ) in clockwise direction
Z = Number of closed loop poles in right half of s-plane.
P = Number of open loop poles or poles of G(s)H(s) in right half of s-plane.
From given Nyquist plot number of encirclements about (−1+ 0 j ) is
N = 1−1= 0
Using equation (v)
0 = P−Z
Z = P
Z = 3
So here number of poles in right half of s-plane is 3.
Hence, the correct option is (D).
Most Upvoted Answer
The complete Nyquist plot of the open loop transfer function G(s) H (...
Given Nyquist plot of G(s)H(s) is shown below
Case 1 :
Here, G(s)H(s) has one zero in the right half of s-plane i.e. Z = 1 .
According to principle of argument
N =P− Z (Anti clockwise direction) …(i)
Where,
N = Number of encirclements of Nyquist plot of G(s)H(s) about origin in anti-clockwise direction P = Number of poles of G(s)H(s) in right half of s-plane.
Z = Number of zeros of G(s)H(s) in right half of s-plane.
Here, N =−2 (anti clockwise direction)
Z = 1
From equation (i)
−2= P − 1
P = –1 …(ii)
So, poles cannot be negative in numbers so no more further discussion on this.
Case 2 : If we assume Nyquist contour in anti clockwise direction then according to principle of argument
N =P− Z (Clockwise direction) …(iii)
Where,
N = Number of encirclements of Nyquist plot of G(s)H(s) about origin in clockwise direction
P = Number of poles of G(s)H(s) in right half of s-plane.
Z = Number of zeros of G(s)H(s) in right half of s-plane.
Here, N = 2 (Clockwise direction)
Z = 1
From equation (iii)
2 = P−1
P = 3 …(iv)
According to Nyquist stability criteria
N =P− Z (Anti clockwise direction) …(v)
Where, N = Number of encirclements about (−1+ 0 j ) in clockwise direction
Z = Number of closed loop poles in right half of s-plane.
P = Number of open loop poles or poles of G(s)H(s) in right half of s-plane.
From given Nyquist plot number of encirclements about (−1+ 0 j ) is
N = 1−1= 0
Using equation (v)
0 = P−Z
Z = P
Z = 3
So here number of poles in right half of s-plane is 3.
Hence, the correct option is (D).
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The complete Nyquist plot of the open loop transfer function G(s) H (s) of a feedback control system shown in figure,If G(s) H (s) has one zero in right half of the s-plane, the number of poles that, the closed loop system will have in right half of s-plane isa)0b)1c)4d)3Correct answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about The complete Nyquist plot of the open loop transfer function G(s) H (s) of a feedback control system shown in figure,If G(s) H (s) has one zero in right half of the s-plane, the number of poles that, the closed loop system will have in right half of s-plane isa)0b)1c)4d)3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The complete Nyquist plot of the open loop transfer function G(s) H (s) of a feedback control system shown in figure,If G(s) H (s) has one zero in right half of the s-plane, the number of poles that, the closed loop system will have in right half of s-plane isa)0b)1c)4d)3Correct answer is option 'D'. Can you explain this answer?.
Solutions for The complete Nyquist plot of the open loop transfer function G(s) H (s) of a feedback control system shown in figure,If G(s) H (s) has one zero in right half of the s-plane, the number of poles that, the closed loop system will have in right half of s-plane isa)0b)1c)4d)3Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
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