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The compensator Gc(s) =5(1+0.3s)/(1+0.1s) would provide a maximum phase shift of:
- a)20°
- b)45°
- c)30°
- d)60°
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The compensator Gc(s) =5(1+0.3s)/(1+0.1s) would provide a maximum phas...
Answer: c
Explanation: Maximum phase shift sin^(-1) [(1-α)/(1+α)] and sin^(-1)[1/2] = 30°
Explanation: Maximum phase shift sin^(-1) [(1-α)/(1+α)] and sin^(-1)[1/2] = 30°
Most Upvoted Answer
The compensator Gc(s) =5(1+0.3s)/(1+0.1s) would provide a maximum phas...
The compensator has a transfer function of:
Gc(s) = 5(1+0.3s)/(1+0.1s)
To determine the maximum phase shift provided by this compensator, we need to find the frequency at which the phase shift is maximum. This frequency can be found by setting the derivative of the phase shift with respect to frequency to zero:
d/dw [arctan(0.3w/1) - arctan(0.1w/1)] = 0
0.3/(1+(0.3w)^2) - 0.1/(1+(0.1w)^2) = 0
0.3/(1+(0.3w)^2) = 0.1/(1+(0.1w)^2)
0.3(1+(0.1w)^2) = 0.1(1+(0.3w)^2)
0.3 + 0.03w^2 = 0.1 + 0.03w^2
0.2 = 0.03w^2
w = sqrt(6.67) or w = -sqrt(6.67)
Since we are only interested in positive frequencies, the maximum phase shift occurs at w = sqrt(6.67):
arctan(0.3*sqrt(6.67)/1) - arctan(0.1*sqrt(6.67)/1) = 20.1 degrees
Therefore, the compensator provides a maximum phase shift of approximately 20 degrees.
Gc(s) = 5(1+0.3s)/(1+0.1s)
To determine the maximum phase shift provided by this compensator, we need to find the frequency at which the phase shift is maximum. This frequency can be found by setting the derivative of the phase shift with respect to frequency to zero:
d/dw [arctan(0.3w/1) - arctan(0.1w/1)] = 0
0.3/(1+(0.3w)^2) - 0.1/(1+(0.1w)^2) = 0
0.3/(1+(0.3w)^2) = 0.1/(1+(0.1w)^2)
0.3(1+(0.1w)^2) = 0.1(1+(0.3w)^2)
0.3 + 0.03w^2 = 0.1 + 0.03w^2
0.2 = 0.03w^2
w = sqrt(6.67) or w = -sqrt(6.67)
Since we are only interested in positive frequencies, the maximum phase shift occurs at w = sqrt(6.67):
arctan(0.3*sqrt(6.67)/1) - arctan(0.1*sqrt(6.67)/1) = 20.1 degrees
Therefore, the compensator provides a maximum phase shift of approximately 20 degrees.
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