This document is a lecture on block diagram operations and transfer functions for a mechatronics systems design course. It includes objectives, concepts, terminology, transformations, reductions, and examples of working through block diagrams and deriving overall transfer functions. Students are assigned homework problems involving simplifying and reducing given block diagrams.

1. Week 10 Data Presentation System
Part 1
Professor Charlton S. Inao
PE-6282 Mechatronics System Design
Defence Engineering College
Bishoftu, Ethiopia

2. Instructional Objectives
To understand and manipulate the following:
1)Block diagrams operations to represent control system
2) Canonical Form of feedback control system
3) Block diagram Transformation
4) Block diagram Reduction
5) Examples
6) Homework and Assignment
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3. 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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4. Transfer Function : Generalized Statement
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5. Concept of Transfer Function
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6. Terminology of Transfer Function
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8. Block diagram transformations
Source: Owonbulu

10. Block Diagram Algebra and
Transfer Functions (Source: Schaum’s Outline- more complete)
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13. Summary of Block Diagram
reduction
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14. Summary of Block Diagram
Reduction
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15. Block Diagram Simplification
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16. Block Diagram Simplification
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17. Block Diagram Simplification
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18. Block Diagram Simplification
C(s)+ G(s)H(s)C(s)=G(s)R(s)
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19. Block Diagram Simplification
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20. Example 1
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21. Example 2
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22. Example 3
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23. Example 4
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24. Example 5
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25. Breaker: Sample Problems from Control
Engineering by W. Bolton
Simplify the following block diagrams
Solution
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26. Problem: What is the over all transfer
function of the following systems.
Answers:
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27. Continuation……..
Example 6
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28. Example 6
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29. Example 6
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30. Example 7 : Multiple Loop
Feedback Control System
The denominator equation would be:

31. Step 1

32. Step 2
1
G4

33. Step 3

34. Step 4 multiply cascaded blocks
Step 5 Eliminating a feedback loop

35. Step 5 Eliminating a feed back loop
Rule
2
G G G
G G H
-
2 3 4
3 4 1
H
( )
1
1
4
3 4 1
G
G G H
-
2 3 4
G G G
1 -

36. * 1
2
H
( )
G G G
2 3 4
G G G
-
1
1
4
G G H
3 4 1
2 3 4
3 4 1
G
G G H
-
1 -
* 1
2
H
( )
G G G
2 3 4
G G H
3 4 1
G G G
1
)
-
G G H
-
1 (
1
1
4
3 4 1
2 3 4
-
3 4 1 3 4 1
G
G G H G G H
- -
* 1 )
2
H
( )
-
- -
1
1 (
1
4
3 4 1
3 4 1
3 4 1
G
G G H
G G H
G G H
2 3 4
2 3 4
G G G
G G G
-
Step 6

37. G G
2 3
-
- +
-
G G H
2 3 2
1
then
* 1 1
( )
*
1
1
1
G G H
3 4 1
2
3 4 1
3 4 1
3 4 1
- +
H
G G H
G G H
G G H
2 3 4
4
4
2 3 4
G G G
G
G
G G G
Multiply cascade blocks
Step 7

38. From
Eliminating a feedback loop
Rule:
3
G G G G
1 2 3 4
G G H G G H
3 4 1 2 3 2
G G G G
1 2 3 4
3 4 1 2 3 2
)
1
1 (
1
H
G G H G G H
- +
-
- +
Step 8

39. 3
G G G G
G G H G G H
3 4 1 2 3 2
G G G G
1 2 3 4
- -
3 4 1 2 3 2
G G H G G H
- +
3 4 1 2 3 2
3 4 1 2 3 2
1 2 3 4
)
1
(
1
1
1
H
G G H G G H
G G H G G H
- +
- +
- +
G G G G
1 2 3 4
Rs Ys
1 G G H G G H G G G G H
- + +
3 4 1 2 3 2 1 2 3 4 3
Over all
transfer
function

40. Example 8
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41. parallel
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43. Example 9
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46. Example 10
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48. Example 10 Final Answer
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49. Assignment /Homework
Reduce/Simplify the following block diagram into its overall transfer function,
isolating block H1
Problem No. 1
Solution
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50. Problem No. 2
Simplify the block diagram by isolating feedback transfer function H2
Solution
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51. Problem No.3
Solution
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52. Problem No.4 Reduce the block diagram of the Fig. below to
canonical form, isolating block K in the forward loop.
Solution
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53. Problem No. 5. Reduce the block diagram below into
open loop form.
Solution
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