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hw1.1 solu 355

# hw1.1 solu 355 - 5-8 Chapter 5 Reduction of Multiple...

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5-8 Chapter 5: Reduction of Multiple Subsystems ans = Ge3(s)=G1(s)Ge1(s)Ge2(s) Transfer function: 50 s^3 - 50 s^2 - 100 s ------------------------------- s^5 + 2 s^4 + 101 s^3 + 100 s^2 ans = T(s)=Ge3(s)/(1+Ge3(s)) Transfer function: 50 s - 100 ----------------------- s^3 + s^2 + 150 s - 100 2. Push G 1 (s) to the left past the pickoff point. + - + + G 1 H 1 G 1 1 G 2 G 3 Thus, T ( s ) g32 G 1 1 g14 G 1 H 1 g167g3 g169g3 g168g3 g168g3 g183g3 g185g3 g184g3 g184g3 G 2 g14 1 G 1 g167g3 g169g3 g168g3 g168g3 g183g3 g185g3 g184g3 g184g3 G 3 g32 G 1 G 2 g14 1 g11 g12 G 3 1 g14 G 1 H 1 g11 g12 3. a. Split G 3 and combine with G 2 and G 4 . Also use feedback formula on G 6 loop.

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Solutions to Problems 5-9 Push G 2 +G 3 to the left past the pickoff point. Using the feedback formula and combining parallel blocks, Multiplying the blocks of the forward path and applying the feedback formula,
5-18 Chapter 5: Reduction of Multiple Subsystems Combine parallel pair and feedback in forward path. Combine cascade pair and apply final feedback formula yielding T ( s ) g32 5 s 2 g14 2 s 6 s 2 g14 9 s g14 6 .

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