week 10 part 1 pe 6282 block diagrams
DESCRIPTION
ModelingTRANSCRIPT
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Professor Charlton S. InaoPE-6282 Mechatronics System Design
Defence Engineering College Bishoftu, Ethiopia
Week 10 Data Presentation SystemPart 1
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Instructional ObjectivesTo understand and manipulate the following:1)Block diagrams operations to represent
control system2) Canonical Form of feedback control system3) Block diagram Transformation4) Block diagram Reduction5) Examples6) Homework and Assignment
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Concept of Transfer FunctionBlock Diagram: Pictorial representation of functions performed by each
component of a system and that of flow of signals.
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Transfer Function : Generalized Statement
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Concept of Transfer Function
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Terminology of Transfer Function
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Block diagram transformationsSource: Owonbulu
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Block Diagram Algebra and Transfer Functions (Source:
Schaum’s Outline- more complete)
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Summary of Block Diagram reduction
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Summary of Block Diagram Reduction
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Block Diagram Simplification
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Block Diagram Simplification
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Block Diagram Simplification
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Block Diagram Simplification
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C(s)+ G(s)H(s)C(s)=G(s)R(s)
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Block Diagram Simplification
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Example 1
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Example 2
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Example 3
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Example 4
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Example 5
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Simplify the following block diagrams
Solution
Breaker: Sample Problems from Control Engineering by W. Bolton
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Problem: What is the over all transfer
function of the following systems.
Answers:
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Example 6
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Continuation……..
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Example 6
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Example 6
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Example 7 : Multiple Loop Feedback Control System
The denominator equation would be:
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Step 1
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Step 24G
1
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Step 3
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Step 4 multiply cascaded blocks
Step 5 Eliminating a feedback loop
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Step 5 Eliminating a feed back loop
Rule
)(1
1
4
2
143
143
G
H
HGG
HGG
432
432
GGG
GGG
-1
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)(
1*
1
1
4
2
143
143
G
H
HGG
HGG
432
432
GGG
GGG
-1
)(
1*
1
)
1
(11
4
2
143143
143
143
G
H
HGGHGG
HGGHGG
432
432
GGG
GGG
-
)(
1*
)
1
(11
4
2
143
143
143
G
H
HGG
HGGHGG
432
432
GGG
GGG
Step 6
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232
32
HGG
GG1
1*
1
)(*
1
11
143
2
143
143
143
HGG
then
H
HGG
HGGHGG
432
4
4
432
GGG
GG
GGG
Multiply cascade blocks
Step 7
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Eliminating a feedback loop
Rule:
From
3232143
4321
232143
4321
)1(1
1
HHGGHGG
GGGGHGGHGG
GGGG
Step 8
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3232143
4321
232143
232143
232143
4321
)1(
1
11
HHGGHGG
GGGG
HGGHGG
HGGHGGHGGHGG
GGGG
34321232143
4321
1 HGGGGHGGHGG
GGGG
Rs Ys
Over all transfer function
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Example 8
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parallel
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Example 9
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Example 10
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Example 10 Final Answer
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Assignment /Homework
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Reduce/Simplify the following block diagram into its overall transfer function, isolating block H1
Solution
Problem No. 1
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Problem No. 2
Solution
Simplify the block diagram by isolating feedback transfer function H2
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Problem No.3
Solution
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Problem No.4 Reduce the block diagram of the Fig. below to canonical form, isolating block K in the forward loop.
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Solution
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Problem No. 5. Reduce the block diagram below into open loop form.
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Solution