Question
The transfer function of the system below is
___________Solution
We are asked to find the transfer function C(s)/R(s) of the given feedback control system.
Identify the structure ● Forward path: G(s) ● Feedback path: H(s) ● Summing point: adds R(s) and + B(s) (where B(s) = output through feedback). So, E(s) = R(s) + B(s) But B(s) = H(s)C(s) Express output C(s) = G(s)E(s) = G(s)[R(s) + H(s)C(s)] Rearrange C(s) = G(s)R(s) + G(s)H(s)C(s) Bring terms with C(s) together: C(s) – G(s)H(s)C(s) = G(s)R(s) C(s)[1 – G(s)H(s)] = G(s)R(s) Transfer function C(s)/R(s) = G(s) / [1 – G(s)H(s)]
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