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If a feedback control system has its open loop transfer function G(s)H(s) = K/(s-2)(s2+3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will be
- a)-5
- b)10
- c)5
- d)-10
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If a feedback control system has its open loop transfer function G(s)H...
Answer: b
Explanation: The intersection point on the imaginary axis at s =0 is obtained by Routh Hurwitz criteria making s^0 row zero and getting the value K = 10.
Explanation: The intersection point on the imaginary axis at s =0 is obtained by Routh Hurwitz criteria making s^0 row zero and getting the value K = 10.
Most Upvoted Answer
If a feedback control system has its open loop transfer function G(s)H...
Root Locus Plot and Imaginary Axis Intersection
Root locus plot is a graphical representation of the locations of the roots of the characteristic equation of a feedback control system as a parameter varies. It is used to determine the stability and performance of the system. The imaginary axis intersection is a point on the imaginary axis where the root locus intersects.
In this problem, the open loop transfer function of the feedback control system is given as G(s)H(s) = K/(s-2)(s2 3s 5). The root locus plot intersects the imaginary axis at s=0.
Calculation of K Value
To find the value of K at s=0, we need to use the root locus rules. When the root locus intersects the imaginary axis, the value of K is given by K = -1/G(s)H(s) where s=0.
Substituting s=0 in the given open loop transfer function, we get G(s)H(s) = K/(-2*5) = -K/10
Therefore, K = -10*G(s)H(s)
To find the value of K at s=0, we need to substitute s=0 in the given open loop transfer function and simplify it. We get G(0)H(0) = K/(-2*5) = -K/10
Since the root locus intersects the imaginary axis at s=0, the value of K at this point is given by K = -10/G(0)H(0)
Substituting G(0)H(0) = -K/10 in the above equation, we get K = -10/(-K/10)
Simplifying the above equation, we get K = 10.
Therefore, the correct answer is option B) 10.
Root locus plot is a graphical representation of the locations of the roots of the characteristic equation of a feedback control system as a parameter varies. It is used to determine the stability and performance of the system. The imaginary axis intersection is a point on the imaginary axis where the root locus intersects.
In this problem, the open loop transfer function of the feedback control system is given as G(s)H(s) = K/(s-2)(s2 3s 5). The root locus plot intersects the imaginary axis at s=0.
Calculation of K Value
To find the value of K at s=0, we need to use the root locus rules. When the root locus intersects the imaginary axis, the value of K is given by K = -1/G(s)H(s) where s=0.
Substituting s=0 in the given open loop transfer function, we get G(s)H(s) = K/(-2*5) = -K/10
Therefore, K = -10*G(s)H(s)
To find the value of K at s=0, we need to substitute s=0 in the given open loop transfer function and simplify it. We get G(0)H(0) = K/(-2*5) = -K/10
Since the root locus intersects the imaginary axis at s=0, the value of K at this point is given by K = -10/G(0)H(0)
Substituting G(0)H(0) = -K/10 in the above equation, we get K = -10/(-K/10)
Simplifying the above equation, we get K = 10.
Therefore, the correct answer is option B) 10.
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If a feedback control system has its open loop transfer function G(s)H(s) = K/(s-2)(s2+3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will bea)-5b)10c)5d)-10Correct answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about If a feedback control system has its open loop transfer function G(s)H(s) = K/(s-2)(s2+3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will bea)-5b)10c)5d)-10Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a feedback control system has its open loop transfer function G(s)H(s) = K/(s-2)(s2+3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will bea)-5b)10c)5d)-10Correct answer is option 'B'. Can you explain this answer?.
If a feedback control system has its open loop transfer function G(s)H(s) = K/(s-2)(s2+3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will bea)-5b)10c)5d)-10Correct answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about If a feedback control system has its open loop transfer function G(s)H(s) = K/(s-2)(s2+3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will bea)-5b)10c)5d)-10Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a feedback control system has its open loop transfer function G(s)H(s) = K/(s-2)(s2+3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will bea)-5b)10c)5d)-10Correct answer is option 'B'. Can you explain this answer?.
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