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Derive an expression for the closed loop transfer function: h(s) = Y(s) ---- R(s) for a gain k = 10
Derive an expression for the closed loop transfer function:
h(s) = Y(s)
----
R(s) for a gain k = 10.
Work i have done so far:
Ea(s) = R(s) - B(s) = R(s) - H(s)Y(s)
Because the output is related to the actuating signal by G(s), we have
Y(s) = G(s) Ea(s)
Therefore:
Y(s) = G(s) [R(s) - H(s)Y(s)]
Now, solving for Y(s), we obtain:
Y(s) [ 1 + G(s)H(s) ] = G(s)R(s)
Therefore the transfer function relating the output Y(s) to the input R(s) is:
Y(s) = G(s)
---- -------------------------------
R(s) 1 + G(s) H(s)
Now, as the gain is equal to 10, I'm not sure if i have to just substitute that value into the last equation or not?
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