blockdiagram1 - Block Diagrams QUESTION 1 For the block...

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Block Diagrams Q UESTION 1 For the block diagram shown in Figure 1.1, determine the transfer functions ( 29 ( 29 Y s R s , ( 29 ( 29 1 E s R s , ( 29 ( 29 2 E s R s , ( 29 ( 29 3 E s R s , and ( 29 ( 29 4 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) Y(s) E 1 (s) E 2 (s) E 3 (s) E 4 (s) + + + + + - - + + - Figure 1.1 The block diagram with all of the signals labeled is given in Figure 1.2. 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 ( 29 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 E G E Y E = - + (3) Writing an equation for the fourth summing junction
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Block Diagrams ( 29 4 3 1 4 1 3 4 1 E G E G E G G E = + = + (4) Writing an equation for the output 6 3 Y G E = (5) Combining equations (3) and (5) 5 6 2 6 6 4 Y G G E G Y G E = - + (6) Combining equations (2) and (6) and rearranging ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 6 1 6 5 6 2 3 1 6
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blockdiagram1 - Block Diagrams QUESTION 1 For the block...

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