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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