This document discusses techniques for reducing block diagrams containing multiple subsystems into simplified equivalent representations. It provides several examples of reducing block diagrams by moving pick-off points, combining subsystems in parallel and cascade configurations, and using block diagram mathematics to obtain equivalent transfer functions. The goal is to demonstrate how complex multi-subsystem diagrams can be reduced into more concise single-system representations through systematic application of block diagram reduction methods.

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Control Systems
Block Diagram reduction

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Block diagram of inertial navigation system

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Elevator block diagram

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Summary of Block diagram mathematics

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Reduction of Multiple Subsystems – Example 1
Reduce the multiple subsystems into one system

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Reduction of Multiple Subsystems – Example
Feedback
Move backward of pick-off point

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Reduction of Multiple Subsystems – Example
Parallel.
Move forward summing point. Then
cascade.

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Reduction of Multiple Subsystems – Example
Cascade Form
Parallel Form

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Reduction of Multiple Subsystems – Example
Feedback
form

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Reduction of Multiple Subsystems – Example 2
Cascade
and
Parallel

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Reduction of Multiple Subsystems – Example
)(sR


s
s
12

s s
)(sR


s
1



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Reduction of Multiple Subsystems – Example
)(sR


s
s
12

s
1 )(sC
s


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Reduction of Multiple Subsystems – Example
Move
backward of
pick-off point
)(sR


s
s
12

s
1 )(sC
s

)(sR


s
s
12

s
1 )(sC
s
s
s
1
1
Actually,


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Reduction of Multiple Subsystems – Example
Move
backward of
pick-off point
)(sR


s
s
12

s
1 )(sC
s

)(sR


s
s
12

s
1 )(sC
s
s
s
1
1
Actually,


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Reduction of Multiple Subsystems – Example
Parallel and
Cascade
)(sR


s
s
12

s
1 )(sC
s
s

)(sR















ss
s
112
)(sC
s2
 
sss
s
sss
s
ss
s
s
sR
sC
s
ss
s
s
s
s
s
s
s
ss
s
s
sR
sC
22
1
)22(
1
22
1
)(
)(
22
1
2
21
1
1
21
1
)(
)(
42
3
3
3
3
3
3
2
3
2
2
3
2
2





































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Reduction of Multiple Subsystems – Example
sss
s
sR
sC
22
1
)(
)(
42
3




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Reduction of Multiple Subsystems – Example 3

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Reduction of Multiple Subsystems – Example 3

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Reduction of Multiple Subsystems – Example 3

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Reduction of Multiple Subsystems – Example 3

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Reduction of Multiple Subsystems – Example 3

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Reduction of Multiple Subsystems – Example 3

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Reduction of Multiple Subsystems – Example 3