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Rs feedforward transfer function closed loop transfer

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Unformatted text preview: R(s) Feedforward transfer function: Closed-loop transfer function: C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs ECE382 3 / 31 C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs ECE382 4 / 31 Closed-Loop Transfer Function Constructing a Block Diagram from an RC Circuit Find the transfer function Equations: Eo (s) Ei (s) Determine the closed-loop transfer function: C(s) R(s) (1) (2) and C(s) = G(s) or C(s) = G(s)E(s) E(s) E(s) = R(s) - H(s)C(s) C(s) = G(s)R(s) - G(s)H(s)C(s) ei - eo 1 = i(t); eo = i(t)dt R C Taking the Laplace Transform of the above equations, we have Ei (s) - Eo (s) = I(s), R Eo (s) = 1 I(s) sC Substituting Eq. (2) into Eq. (1): or C(s)[1 + G(s)H(s)] = G(s)R(s) C(s) G(s) = R(s) 1 + G(s)H(s) C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs (3) ECE382 5 / 31 C. S. George Lee (Purdue Univ.) Block Diagrams & Signal-Flow Graphs ECE382 6 / 31 Closed-loop System with Disturbance (I) Two inputs : R(s) and D(s) One output : C(s) Two transferfunctions : T1 (s) = C1 (s) ; T2 (s) = R(s) D(s)=0 Closed-loop System with Disturbance (II) C(s) = C1 (s) + C2 (s) = T1 (s)R(s) + T2 (s)D(s) G2 (s) = [G1 (s)R(s) + D(s)] 1 + G1 (s)G2 (s)H(s) Output, C(s) C1 (s) G1 (s)G2 (s) = R(s) D(s)=0 1 + G1 (s)G2 (s)H(s) C2 (s) G2 (s) = D(s) R(s)=0 1 + G1 (s)G2 (s)H(s) C2 (s) D(s) R(s)=0 If |G1 (s)H(s)| 1 and |G1 (s)G2 (s)H(s)| 1, then C2 (s) G2 (s) 1 =0 D(s) G (s)G (s)H(s) G (s)H(s) R(s)=0 1 2 1 C(s) = C1 (s) + C2 (s) = T1 (s)R(s) + T2 (s)D(s) C. S. George Lee (Purdue Univ.) Bl...
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