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# lecture4 - Lec 4 Graphical System Representations and...

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1 Lec 4 . Graphical System Representations and Simplifications • Block Diagrams • Signal Flow Graphs and Mason’s Formula • Reading: 3.9-3.10 Block Diagrams Graphical representation of interconnected systems – In practice, a system may consist of multiple subsystems: the output of one subsystem may be the input to another subsystem – Each subsystem is represented by a functional block, labeled with the corresponding transfer function – Blocks are connected by arrows to indicate signal flow directions Advantage – Easy for visualization purpose – Can represent a class of similar systems

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2 Basic Components of Block Diagrams (Functional) block Summing point + G ( s ) X ( s ) Y ( s ) Y ( s ) = G ( x ) X ( s ) + ¡ Branch point Y ( s ) Z ( s ) Z ( s ) = X ( s ) ¡ Y ( s ) X ( s ) Y ( s ) Z ( s ) Z ( s ) = Y ( s ) = X ( s ) Signal flow X ( s ) X ( s ) Cascaded/Parallel Connected Systems Cascaded systems: Parallel connected systems: + G 1 ( s ) G 2 ( s ) G 1 ( s ) G 2 ( s ) U ( s ) Y ( s ) U ( s ) Y ( s ) Z ( s ) Y 1 ( s ) Y 2 ( s ) + + G ( s ) = Y ( s ) U ( s ) G ( s ) = Y ( s ) U ( s )
3 (Negative) Feedback Connected Systems Feedback connected systems: U ( s ) Y ( s ) + + ¡ E ( s ) B ( s ) G ( s ) H ( s ) Feedforward transfer function (FTF) : Open-loop transfer function (OTF): B ( s ) E ( s ) = G ( s ) H ( s ) Y ( s ) E ( s ) = G ( s ) Y ( s ) U ( s ) = Closed-loop transfer function: Positive Feedback Connected Systems U ( s ) Y ( s ) + + E ( s ) B ( s ) G ( s ) H ( s ) Y ( s ) U ( s ) = Closed-loop transfer function: + Remark: can be thought of as negative feedback connected system with feedback element – H ( s )

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4 Unity Feedback System Unity feedback connected systems: H ( s )=1 U ( s ) Y ( s ) + + ¡ E ( s ) G ( s ) Y ( s ) U ( s ) = Closed-loop transfer function: B ( s ) Feedback Control System U ( s ) Y ( s ) + + ¡ G
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lecture4 - Lec 4 Graphical System Representations and...

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