## Question

###### Asap Problem 1) (25 Pts.) C(s) a) Simplify the below block diagram to find the overall...

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Problem 1) (25 Pts.) C(s) a) Simplify the below block diagram to find the overall system transfer function G(s)R Show your work including all intermediate block diagrams you may require. b) Given input r(t) is a unit step, find output time response c(t). (Hint: By MATLAB might be easiest).

## Answers

For negative feed back l(s)/R(s) = G(s)/1 + G(s) + (s) reducing the red circled black first G(s) = 2/ s H(s) = 1 C(S)/R(s) = 2/s/1 + 1 times 2/s = (2/s + 2) Now G(S) = 2/s(s + 2) H(s) = 1 so C(S)/R(S) = G(S)/1 + G(S) + H(S) = 2/4 (S + 2)/1 + 2/ s(s + 2) C(S)/R(S) = 2/(s^2 + 2s + 2) \r\n C(S)/R(S) = 2/(S^2 + 2S + 2) C(S) = 2 R(S)/(S^2 + S + 2) as R(S) = unit step R (S) = (1/S) C(S) = 2/S(S^2 + 2S + 2) using partial fraction C(S) = 1/S - (S + 2 0/S^2 + 2S + 2 = 1 /S - (s + 1)

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