Professor Charlton S. InaoPE-6282 Mechatronics System Design

Defence Engineering College Bishoftu, Ethiopia

Week 10 Data Presentation SystemPart 1

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

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)

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:

Example 6

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Continuation……..

Example 6

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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 24G

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

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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

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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Solution