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BLOCK DIAGRAMSBLOCK

DIAGRAMS (Textbook^ Ch.5)(

BLOCK^ DIAGRAMS

As you already know, a subsystem is represented as a block with an input, anoutput, and a transfer function. Many^ systems

are^ composed^

of^ multiple^ subsystems

When^ multiple

Many^ systems

are^ composed^

of^ multiple^ subsystems.

When^ multiple

subsystems are interconnected, a few more schematic elements must be addedto the block diagram. These new elements are

summing^ junctions

and^ pickoff^ points

All component

These new elements are

summing^ junctions

and^ pickoff^ points

. All component

parts of a block diagram for a linear, time-invariant system are shown in thefollowing figure.

Parallel^ Form

Following figure shows an example of parallel subsystems Again, we can find the equivalent transfer function by writing the output ofeach subsystem The equivalent transfer function iseach subsystem. The equivalent transfer function is

Feedback^ Form

The^ feedback^ system

forms^ the^ basis

for^ our^ study^

of^ control^ systems

engineering.

Moving^ Blocks

to^ Create^ Familiar

Forms

The figures below shows equivalent block diagrams.

Example‐^1

Reduce^ the^ block

diagram^ shown^ in

the^ figure^ below

to^ a^ single^ transfer

function.^ First,^ the^ three^ summing

junctions can^ be^ collapsed^

into^ a^ single summing^ junction.

Example‐^2

Reduce^ the^ block

diagram^ shown^ in

the^ figure^ below

to^ a^ single^ transfer

function.^ First, move G2(s) to the left^ past^ the^ pickoff

point^ to create^ parallel^ subsystems,and^ reduce^ the

feedback system consisting of G3(s) andH3(s).

Example‐^2

ctd.

First, move G2(s) to the leftpast^ the^ pickoff

point^ to create^ parallel^

subsystems,p y^ , and^ reduce^ the

feedback system consisting of G3(s) andH3(s)H3(s).Second,^ reduce^ the

parallel pair consisting of 1/G2(s) and unity, and push G1(s) to theright^ past^ the^

summing junction,^ creating

parallel subsystems in the feedback.Third, collapse the summing junctions,^ add^

the^ two feedback^ elements

together, and^ combine^ the

last^ two cascaded blocks.