%284%29%20Reduction%20of%20Multiple%20Subsystems

%284%29%20Reduction%20of%20Multiple%20Subsystems -...

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eduction of Multiple Reduction of Multiple Subsystems Chapter 6
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Introduction (section 5.1 from the book) Objective : to reduce a system composed of block-diagram of multiple subsystems into representation of a single input- output bock diagram. We want to represent a complex system with a transfer function which yields an explicit input-output dependence. •T wo techniques: wo tec ques: i) Direct solution from the block-diagram representation, ii) Indirect solution with using signal-flow graphs . 2 © 2010 Farrokh Sharifi
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Block-diagrams (section 5.2 from the book) • A example of a complex systems composed of multiple subsystems Subsystems are introduced by adding summing junctions and pick-off points. 3 © 2010 Farrokh Sharifi
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lock- iagrams Block diagrams ascade form: Cascade form: • The blocks are connected in series. The transfer function is a product of the subsystems ’ transfer functions. • Assumption: the output of each subsystem is not affected by the adjacent subsystems. 4 © 2010 Farrokh Sharifi
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lock- iagrams Block diagrams arallel form: Parallel form: The transfer function is a sum of the subsystems’ transfer functions. 5 © 2010 Farrokh Sharifi
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lock- iagrams Block diagrams eedback form: Feedback form: Output: or: en substitute into the error then substitute into the error equation: solve for d it is obtained: and it is obtained: 6 © 2010 Farrokh Sharifi
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lock- iagrams Block diagrams eedback form: Feedback form: Note: (-) feedback results in 1+GH (+) feedback results in 1- GH 7 © 2010 Farrokh Sharifi
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lock- iagrams Block diagrams • The relationship (output/input) C (s)/ R (s) is called closed-loop transfer function . • The product G (s) H (s) is called open-loop transfer function , or loop gain . efore exploiting the three introduced forms: cascade parallel Before exploiting the three introduced forms: cascade, parallel and feedback, often the system blocks need to be rearranged first. Next we examine a few examples of block moves. 8 © 2010 Farrokh Sharifi
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lock- iagrams Block diagrams • Moving the block G ( s ) to the left of a summing junction: Note that for both the right and the left block diagram in the figure above, the output is: 9 © 2010 Farrokh Sharifi
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lock- iagrams Block diagrams • Moving the block G ( s ) to the right () Xs Rs Gs of a summing junction: ) () R sG s sGs    X s () () RsGs Note that for both the right and the left block diagram, the output is: 10 © 2010 Farrokh Sharifi
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lock- iagrams Block diagrams • Moving the block G ( s ) to the left or right of a pick-off point: 11
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lock- iagrams: ummary Block diagrams: Summary 12 © 2010 Farrokh Sharifi
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lock- iagrams: ummary Block diagrams: Summary 13 © 2010 Farrokh Sharifi
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lock- iagrams Block diagrams Example: Reduce the given block diagram to a single block: • Note that the problem can be solved in different ways; Of course, the final transfer function must be identical, even if you solve it your your own way.
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This note was uploaded on 02/20/2011 for the course MEC 709 taught by Professor Sharifi during the Fall '11 term at Ryerson.

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%284%29%20Reduction%20of%20Multiple%20Subsystems -...

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