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EE3530-3.2

# EE3530-3.2 - 3.2 System Modeling Diagrams In many cases a...

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Unformatted text preview: 3.2 System Modeling Diagrams In many cases, a complex feedback control system can be conve- niently described using block diagrams. A basic input/output relationship can be shown as y ( t ) u ( t )-- H Y ( s ) = H ( s ) U ( s ) Using this basic relation, we can compute the transfer function with more complex interconnections: G 1 U 1 ( s ) H9018 H11001 H11002 G 2 Y 2 ( s ) U ( s ) G 1 G 2 H9018 H11001 H11001 Y ( s ) (a) (b) R ( s ) G 1 G 2 (c) U 1 ( s ) Y 1 ( s ) Y ( s ) Y 2 ( s ) U 2 ( s ) Y ( s ) U ( s ) H11005 G 1 H11001 G 2 H11005 Y ( s ) R ( s ) G 1 1 H11001 G 1 G 2 Y 2 ( s ) U 1 ( s ) H11005 G 1 G 2 In diagram (c), we have U 1 ( s ) = R ( s )- Y 2 ( s ) , Y 2 ( s ) = G 2 ( s ) Y ( s ) , Y ( s ) = G 1 ( s ) U 1 ( s ) Eliminating U 1 ( s ) and Y 2 ( s ), we get Y ( s ) = G 1 ( s )( R ( s )- G 2 ( s ) Y ( s )) ⇒ (1+ G 1 ( s ) G 2 ( s )) Y ( s ) = G 1 ( s ) R ( s ) Or Y ( s ) R ( s ) = G 1 ( s ) 1 + G 1 ( s ) G 2 ( s ) 1 Negative Feedback : U 1 ( s ) = R ( s )- Y 2 ( s ) Positive Feedback...
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EE3530-3.2 - 3.2 System Modeling Diagrams In many cases a...

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