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blockdiagram9

# blockdiagram9 - G G =(7 Combining equations(6 and(7 29 29...

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Block Diagrams Q UESTION 9 For the block diagram shown in Figure 9.1, determine the transfer functions ( 29 ( 29 Y s R s , ( 29 ( 29 1 E s R s , ( 29 ( 29 2 E s R s , and ( 29 ( 29 3 E s R s . G 6 (s) G 2 (s) G 1 (s) G 5 (s) G 3 (s) G 4 (s) G 7 (s) R(s) + - E 1 (s) + + - + + - E 2 (s) E 3 (s) Y(s) Figure 9.1 The block diagram with all of the signals labeled is given in Figure 9.2. Writing an equation for the first summing junction 1 1 2 7 E R G E G Y = - - (1) Writing an equation for the second summing junction [ ] 2 2 1 3 1 2 3 1 E G E G E G G E = + = + (2) Writing an equation for the third summing junction 3 5 2 4 1 E G E G E Y = + - (3) Writing an equation for the output

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Block Diagrams 6 3 Y G E = (4) Multiplying equation (3) by G 6 and combining with equation (4) 5 6 2 4 6 1 6 Y G G E G G E G Y = + - (5) Rearranging equation (5) and combining with equation (2) [ ] ( 29 6 4 6 5 6 2 3 1 1 G Y G G G G G G E + = + + (6) Combining equations (1), (2), and (6) and rearranging ( 29 ( 29 ( 29 ( 29 4 6 5 6 2 3 6 4 6 7 5 6 7 2 3 1 2 3 6 1 1 G G G G G G Y R G G G G G G G G G G G G G + +
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Unformatted text preview: G G + + = + + + + + + + (7) Combining equations (6) and (7) ( 29 ( 29 ( 29 6 1 6 4 6 7 5 6 7 2 3 1 2 3 6 1 1 1 G E R G G G G G G G G G G G G G + = + + + + + + + (8) Combining equations (2), (6), and (7) ( 29 ( 29 ( 29 ( 29 ( 29 6 2 3 2 6 4 6 7 5 6 7 2 3 1 2 3 6 1 1 1 G G G E R G G G G G G G G G G G G G + + = + + + + + + + (9) Combining equations (4) and (7) and rearranging ( 29 ( 29 ( 29 ( 29 4 5 2 3 3 6 4 6 7 5 6 7 2 3 1 2 3 6 1 1 G G G G E R G G G G G G G G G G G G G + + = + + + + + + + (10) G 6 (s) G 2 (s) G 1 (s) G 5 (s) G 3 (s) G 4 (s) G 7 (s) R(s) +-E 1 (s) G 1 E 2 + +-+ +-E 2 (s) E 3 (s) G 2 E 1 G 5 E 2 Y(s) G 7 Y G 3 E 1 G 4 E 1 Figure 9.2 2 Block Diagrams 3...
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