The document discusses control systems engineering and reducing multiple subsystems using block diagrams. It covers block diagram topologies like cascade, parallel, and feedback forms. It shows how to apply algebra to summing junctions and pickoff points when reducing block diagrams. An example problem demonstrates the step-by-step process of reducing a block diagram with multiple feedback loops into an equivalent single-loop feedback system.

1. ME 176
Control Systems Engineering
Reduction of Multiple Subsystems
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2. Block Diagrams:
Elements:
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3. Block Diagrams: Topologies
Cascade Form:
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4. Block Diagrams: Topologies
Cascade Form:
Exception: Assumption that the interconnected subsystems do not
load adjacent subsystems.
Use K (amplifier), it has
high-impedance input so
it does not load previus
network. And has low
impedance output so it
looks like a pure voltage
source to subsequent
networks
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5. Block Diagrams: Topologies
Parallel Form:
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6. Block Diagrams: Topologies
Feedback Form:
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7. Block Diagrams: Moving Blocks
Algebra for Summing Junctions:
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8. Block Diagrams: Moving Blocks
Algebra for Pickoff Points:
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9. Block Diagrams: Example
Steps:
a) Collapse suming junction.
b) Form equivalent cascade system in
the forward and feedback paths.
c) Form equivalent feedback system
and multiply by cascaded G1(s).
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10. Block Diagrams: Example
Move G2(s) to the left past pickoff point to create parallel subsystems.
Reduce feedback system consisting of G3(s) and H3(s).
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11. Block Diagrams: Example
Reduce parallel pair of 1/G2(s) and unity.
Push G1(s) past right summing junction.
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12. Block Diagrams: Example
Collapse summing junction and two feedback elements.
Combine last two cascade blocks.
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13. Block Diagrams: Example
Reduce the remaining feedback system.
Combine last two cascade blocks.
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14. Analysis and Design of Feedback Systems:
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15. Analysis and Design of Feedback Systems:
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