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A lead compensator network includes a parallel combination of R and C in the feed-forward
path. If the transfer function of the compensator is GC(S) = s+2/s+4. the value of RC is
______________.
path. If the transfer function of the compensator is GC(S) = s+2/s+4. the value of RC is
______________.
Correct answer is '0.5'. Can you explain this answer?
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Lead Compensator Network and Transfer Function
A lead compensator network is a type of compensator used in control systems to improve the stability and response of a system. The network includes a parallel combination of resistor (R) and capacitor (C) in the feed-forward path. The transfer function of the compensator is given by GC(S) = s^2/s^4, where s is the Laplace variable.
Finding the Value of RC
To find the value of RC, we need to equate the transfer function of the compensator to the desired transfer function. In this case, the desired transfer function is given by the lead compensator network. Therefore, we have:
GC(S) = s^2/s^4 = (1 + RCs)/(1 + 2RCs + RCs^2)
Multiplying the numerator and denominator of the right-hand side by s^2, we get:
s^2/s^4 = (s^2 + RCs^3)/(s^2 + 2RCs^3 + RCs^4)
Equating the numerator and denominator of both sides, we obtain:
s^2 = s^2 + RCs^3
2RC = 1
RC = 0.5
Therefore, the value of RC is 0.5.
Conclusion
In summary, a lead compensator network includes a parallel combination of resistor and capacitor in the feed-forward path. The transfer function of the compensator is given by GC(S) = s^2/s^4. To find the value of RC, we equate the transfer function of the compensator to the desired transfer function and solve for RC. In this case, the value of RC is 0.5.
A lead compensator network is a type of compensator used in control systems to improve the stability and response of a system. The network includes a parallel combination of resistor (R) and capacitor (C) in the feed-forward path. The transfer function of the compensator is given by GC(S) = s^2/s^4, where s is the Laplace variable.
Finding the Value of RC
To find the value of RC, we need to equate the transfer function of the compensator to the desired transfer function. In this case, the desired transfer function is given by the lead compensator network. Therefore, we have:
GC(S) = s^2/s^4 = (1 + RCs)/(1 + 2RCs + RCs^2)
Multiplying the numerator and denominator of the right-hand side by s^2, we get:
s^2/s^4 = (s^2 + RCs^3)/(s^2 + 2RCs^3 + RCs^4)
Equating the numerator and denominator of both sides, we obtain:
s^2 = s^2 + RCs^3
2RC = 1
RC = 0.5
Therefore, the value of RC is 0.5.
Conclusion
In summary, a lead compensator network includes a parallel combination of resistor and capacitor in the feed-forward path. The transfer function of the compensator is given by GC(S) = s^2/s^4. To find the value of RC, we equate the transfer function of the compensator to the desired transfer function and solve for RC. In this case, the value of RC is 0.5.
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A lead compensator network includes a parallel combination of R and C in the feed-forwardpath. If the transfer function of the compensator is GC(S) = s+2/s+4.the value of RC is______________.Correct answer is '0.5'. Can you explain this answer?
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A lead compensator network includes a parallel combination of R and C in the feed-forwardpath. If the transfer function of the compensator is GC(S) = s+2/s+4.the value of RC is______________.Correct answer is '0.5'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A lead compensator network includes a parallel combination of R and C in the feed-forwardpath. If the transfer function of the compensator is GC(S) = s+2/s+4.the value of RC is______________.Correct answer is '0.5'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lead compensator network includes a parallel combination of R and C in the feed-forwardpath. If the transfer function of the compensator is GC(S) = s+2/s+4.the value of RC is______________.Correct answer is '0.5'. Can you explain this answer?.
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