1. The problem statement, all variables and given/known data
I am trying to write a block diagram as a transfer function.
2. Relevant equations
3. The attempt at a solution
Let ##G = \frac{1}{s}##, ##H = \frac{K}{Js + a}##, and ##L= K_f##. Then wouldn't the closed loop transfer function be written as
$$
\frac{\frac{HLG}{1+HL}}{1 + \frac{HLG}{1+HL}} = \frac{KK_f}{s^2J + (KK_f + a)s + KK_f}
$$
I only ask because the book has it as
$$
\frac{K}{s^2J + (KK_f + a)s + K}
$$
and I don't see how that was obtained.
I am trying to write a block diagram as a transfer function.
2. Relevant equations
3. The attempt at a solution
Let ##G = \frac{1}{s}##, ##H = \frac{K}{Js + a}##, and ##L= K_f##. Then wouldn't the closed loop transfer function be written as
$$
\frac{\frac{HLG}{1+HL}}{1 + \frac{HLG}{1+HL}} = \frac{KK_f}{s^2J + (KK_f + a)s + KK_f}
$$
I only ask because the book has it as
$$
\frac{K}{s^2J + (KK_f + a)s + K}
$$
and I don't see how that was obtained.
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