blockdiagram3 - +-(5) Combining equations (3), (4), and (5)...

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Block Diagrams Q UESTION 3 For the block diagram shown in Figure 3.1, determine the transfer functions ( 29 ( 29 Y s R s , ( 29 ( 29 1 E s R s , and ( 29 ( 29 2 E s R s . G 3 (s) H 1 (s) G 2 (s) H 3 (s) H 2 (s) H 4 (s) G 1 (s) + - - R(s) E 1 (s) - - - + E 2 (s) Y(s) Figure 3.1 The block diagram with all of the signals labeled is given in Figure 3.2. Writing an equation for the first summing junction 1 2 3 2 1 2 E R G H E H E Y = - - - (1) Writing an equation for the second summing junction 2 1 1 2 2 2 4 E G E H G E H Y = - - (2) Writing an equations for the output
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Block Diagrams 2 3 2 Y G G E = (3) Rearranging equation (2) and multiplying by G 2 G 3 ( 29 ( 29 1 2 3 2 3 2 2 2 2 2 1 2 3 1 4 2 3 1 2 2 4 2 3 1 1 1 G G G Y G G E H G H G Y G G G E H G G Y E H G H G G + = + = - = + + (4) Multiplying equation (1) by G 1 G 2 G 3 [ ] 1 2 3 1 1 2 3 1 2 3 2 3 1 2 1 2 3 G G G E G G G R G G G G H H E G G G Y = -
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Unformatted text preview: +-(5) Combining equations (3), (4), and (5) and rearrange ( 29 1 2 3 2 2 4 2 3 1 2 3 1 1 2 3 1 G G G Y R H G H G G G G H H G G G = + + + + + (6) Combining equations (4) and (6) ( 29 2 2 4 2 3 1 2 2 4 2 3 1 2 3 1 1 2 3 1 1 H G H G G E Y H G H G G G G H H G G G + + = + + + + + (7) Combining equations (3) and (6) ( 29 2 1 2 2 4 2 3 1 2 3 1 1 2 3 1 E G R H G H G G G G H H G G G = + + + + + (8) G 3 (s) H 1 (s) G 2 (s) H 3 (s) H 2 (s) H 4 (s) G 1 (s) +--R(s) E 1 (s)---+ E 2 (s) Y(s) G 1 E 1 H 1 E 2 H 1 G 2 E 2 H 2 G 2 E 2 H 4 Y G 2 E 2 Figure 3.2 2...
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This note was uploaded on 02/01/2012 for the course MECH ENG 279 taught by Professor Landers during the Spring '11 term at Missouri S&T.

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blockdiagram3 - +-(5) Combining equations (3), (4), and (5)...

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