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The open loop DC gain of unity negative feedback system with closed loop transfer function
s + 4/(s2 + 7s + 13) is ________
Correct answer is '0.444'. Can you explain this answer?
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The open loop DC gain of unity negative feedback system with closed l...
Open Loop DC Gain:
The open-loop DC gain of a feedback system refers to the gain of the system when the frequency is zero or very low. In other words, it represents the gain of the system at DC or for steady-state input signals.
Given Information:
The closed-loop transfer function of the system is given as 4/(s^2 + 7s + 13).
Closed-Loop Transfer Function:
The closed-loop transfer function is obtained by applying negative feedback to the open-loop transfer function. In this case, the open-loop transfer function is 4/(s^2 + 7s + 13), and the closed-loop transfer function is the overall transfer function of the system.
DC Gain Calculation:
To find the open-loop DC gain, we need to evaluate the closed-loop transfer function at s = 0. This is because at DC, the Laplace variable 's' is replaced by '0' in the transfer function.
Substituting s = 0 in the closed-loop transfer function:
H(0) = 4/((0)^2 + 7(0) + 13)
= 4/13
≈ 0.308
Therefore, the open-loop DC gain of the system is approximately 0.308.
Correction:
The given correct answer is '0.444', which is different from the calculated value of 0.308. It is possible that there might be a mistake in the given closed-loop transfer function or a typographical error in the provided answer.
To verify the correct answer, please double-check the closed-loop transfer function or consult the source of the problem statement.
The open-loop DC gain of a feedback system refers to the gain of the system when the frequency is zero or very low. In other words, it represents the gain of the system at DC or for steady-state input signals.
Given Information:
The closed-loop transfer function of the system is given as 4/(s^2 + 7s + 13).
Closed-Loop Transfer Function:
The closed-loop transfer function is obtained by applying negative feedback to the open-loop transfer function. In this case, the open-loop transfer function is 4/(s^2 + 7s + 13), and the closed-loop transfer function is the overall transfer function of the system.
DC Gain Calculation:
To find the open-loop DC gain, we need to evaluate the closed-loop transfer function at s = 0. This is because at DC, the Laplace variable 's' is replaced by '0' in the transfer function.
Substituting s = 0 in the closed-loop transfer function:
H(0) = 4/((0)^2 + 7(0) + 13)
= 4/13
≈ 0.308
Therefore, the open-loop DC gain of the system is approximately 0.308.
Correction:
The given correct answer is '0.444', which is different from the calculated value of 0.308. It is possible that there might be a mistake in the given closed-loop transfer function or a typographical error in the provided answer.
To verify the correct answer, please double-check the closed-loop transfer function or consult the source of the problem statement.
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Community Answer
The open loop DC gain of unity negative feedback system with closed l...
H(s) = 1 for unity feedback
For DC gain s = 0
So, open loop gain G(0) = 4/9 = 0.444
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The open loop DC gain of unity negative feedback system with closed loop transfer functions + 4/(s2 + 7s + 13) is ________Correct answer is '0.444'. Can you explain this answer?
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