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The characteristic equation of a closed loop control system is given by:
s2 + 2s +10 + K(s2 + 6s + 10) = 0
The angle of asymptotes for the root loci for K ≥ 0 are given by
s2 + 2s +10 + K(s2 + 6s + 10) = 0
The angle of asymptotes for the root loci for K ≥ 0 are given by
- a)180°, 360°
- b)90°, 270°
- c)90°, 180°
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The characteristic equation of a closed loop control system is given b...
Given, s2 + 2s + 10 + K(s2 + 6s + 10) = 0
Here, number of open loop poles, P = 2. Number of open loop zero, Z = 2
∴ P - Z = 0.
Angle of asymptotes are given by:
Sines P - Z = 0, therefore there are no angle of asymptotes for the root locus of the given system.
Here, number of open loop poles, P = 2. Number of open loop zero, Z = 2
∴ P - Z = 0.
Angle of asymptotes are given by:
Sines P - Z = 0, therefore there are no angle of asymptotes for the root locus of the given system.
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The characteristic equation of a closed loop control system is given b...
To find the angle of asymptotes for the root loci, we need to determine the number of poles and zeros on the real axis.
The given characteristic equation is:
s^2 + 2s + 10 + K(s^2 - 6s + 10) = 0
Expanding the equation, we get:
s^2 + 2s + 10 + Ks^2 - 6Ks + 10K = 0
(s^2 + Ks^2) + (2 - 6K)s + (10 + 10K) = 0
Comparing the coefficients of s^2, s, and the constant term, we have:
1 + K = 0 (coefficient of s^2)
2 - 6K = 0 (coefficient of s)
10 + 10K = 0 (constant term)
From the first equation, we can solve for K:
K = -1
Substituting this value of K into the second equation:
2 - 6(-1) = 0
2 + 6 = 0
8 = 0
This equation is not satisfied, which means that K = -1 is not a valid value.
Therefore, we cannot determine the angle of asymptotes for the root loci for K = -1.
The given characteristic equation is:
s^2 + 2s + 10 + K(s^2 - 6s + 10) = 0
Expanding the equation, we get:
s^2 + 2s + 10 + Ks^2 - 6Ks + 10K = 0
(s^2 + Ks^2) + (2 - 6K)s + (10 + 10K) = 0
Comparing the coefficients of s^2, s, and the constant term, we have:
1 + K = 0 (coefficient of s^2)
2 - 6K = 0 (coefficient of s)
10 + 10K = 0 (constant term)
From the first equation, we can solve for K:
K = -1
Substituting this value of K into the second equation:
2 - 6(-1) = 0
2 + 6 = 0
8 = 0
This equation is not satisfied, which means that K = -1 is not a valid value.
Therefore, we cannot determine the angle of asymptotes for the root loci for K = -1.
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The characteristic equation of a closed loop control system is given by:s2+ 2s +10 + K(s2+ 6s + 10) =0The angle of asymptotes for the root loci for K ≥ 0 are given bya)180°, 360°b)90°, 270°c)90°, 180° d)none of theseCorrect answer is option 'D'. Can you explain this answer?
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