BLOCK DIAGRAMS Professor Charlton S. Inao PE-6282 Mechatronics System Design Defence Engineering College Bishoftu, Ethiopia Week 10 Data Presentation System Part 1
BLOCK DIAGRAMS
Professor Charlton S. Inao
PE-6282 Mechatronics System DesignDefence Engineering College
Bishoftu, Ethiopia
Week 10 Data Presentation SystemPart 1
INSTRUCTIONAL OBJECTIVES
To 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 FUNCTION
Block 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
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 SIMPLIFICATION0
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BLOCK DIAGRAM SIMPLIFICATION
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C(s)+ G(s)H(s)C(s)=G(s)R(s)
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 50
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SIMPLIFY THE FOLLOWING BLOCK DIAGRAMS 0
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Solution
Breaker: Sample Problems from Control Engineering by W. Bolton
PROBLEM: WHAT IS THE OVER ALL TRANSFER FUNCTION OF THE FOLLOWING SYSTEMS.
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Answers:
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Continuation……..
EXAMPLE 60
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EXAMPLE 6
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EXAMPLE 7 : MULTIPLE LOOP FEEDBACK CONTROL SYSTEM
The denominator equation would be:
Step 1
STEP 2
4G
1
STEP 3
STEP 4 MULTIPLY CASCADED BLOCKS
Step 5 Eliminating a feedback loop
STEP 5 ELIMINATING A FEED BACK LOOP
Rule
)(1
1
4
2
143
143
G
H
HGG
HGG
432
432
GGG
GGG
-1
)(
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
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
Eliminating a feedback loop
Rule:
From
3232143
4321
232143
4321
)1(1
1
HHGGHGG
GGGGHGGHGG
GGGG
Step 8
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
EXAMPLE 8
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oparallel
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EXAMPLE 90
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EXAMPLE 10
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EXAMPLE 10 FINAL ANSWER
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ASSIGNMENT /HOMEWORK0
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Reduce/Simplify the following block diagram into its overall transfer function, isolating block H1
Solution
Problem No. 1
Problem No. 20
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Solution
Simplify the block diagram by isolating feedback transfer function H2
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Problem No.3
Solution
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
PROBLEM NO. 5. REDUCE THE BLOCK DIAGRAM BELOW INTO OPEN LOOP FORM.
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