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Control System Lecture-4.pdf, Summaries of Algebra

▻ Take -off Point :- The output signal can be applied to two or more points from a take-off point. Block Diagram Reduction Techniques. ▻ Rule 1 :- For Blocks ...

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Control System
Block Diagram Reduction Techniques
Content
Review of Last Lecture.
Need of Block Diagram.
Block Diagram Reduction Technique.
Examples of Block Diagram Reduction.
Learning Objectives
Able to understand the need of Block
diagram in Control System.
Able to apply various rule of block
diagram reduction techniques.
Block Diagram Algebra
Block diagram is a shorthand, graphical
representation of a physical system,
illustrating the functional relationships
among its components.
OR
A Block Diagram is a shorthand pictorial
representation of the cause-and-effect
relationship of a system.
Block Diagram Algebra
Entire complicated system can be
completely represented by connecting
different blocks.
One block corresponds to one element of
system.
A corresponding block is drawn by inserting
a transfer function of that element inside the
block
.
Components of a Block Diagram
for a LTI System
System components are alternatively
called elements of the system.
Block diagram has four components:
Signals
System/ block
Summing junction
Pick-off/ Take-off point
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Control System

Block Diagram Reduction Techniques

Content

 Review of Last Lecture.  Need of Block Diagram.  Block Diagram Reduction Technique.  Examples of Block Diagram Reduction.

Learning Objectives

 Able to understand the need of Block diagram in Control System.  Able to apply various rule of block diagram reduction techniques. Block Diagram Algebra  Block diagram is a shorthand, graphical representation of a physical system, illustrating the functional relationships among its components. OR  A Block Diagram is a shorthand pictorial representation of the cause-and-effect relationship of a system. Block Diagram Algebra  Entire complicated system can be completely represented by connecting different blocks.  One block corresponds to one element of system.  A corresponding block is drawn by inserting a transfer function of that element inside the block. Components of a Block Diagram for a LTI System  System components are alternatively called elements of the system.  Block diagram has four components:  SignalsSystem/ blockSumming junctionPick-off/ Take-off point

Element of Block Diagram  Summing Point :- Two or more signals can be added or subtracted at summing point.  Take - off Point :- The output signal can be applied to two or more points from a take-off point. Block Diagram Reduction Techniques  Rule 1 :- For Blocks in Series/Cascade

- Gain of blocks connected in series gets multiplied with each other. Block Diagram Reduction Techniques  **Rule 2 :- For Blocks in Parallel

  • Gain of blocks connected in parallel gets added algebrically.** Block Diagram Reduction Techniques  Rule 3 :- Elimination of Feedback loop For – ve f/b : +ve sign in above expression & vice-versa. Block Diagram Reduction Techniques  Rule 4 :- Associative law for summing point
  • Order of summing point can be changed if two or more summing points are in series. . Block Diagram Reduction Techniques  Rule 5 :- Shift summing point before block .

Example 1: Cont…. Example 1: Cont…. Example 1: Cont…. Example 1: Cont…. Example 2: Example 2: Cont….

Example 2: Cont…. Example 2: Cont…. Example 2: Cont…. Example 2: Cont…. Example 2: Cont…. Example 3:

Example 4: Example 4: Cont…. Example 4: Cont…. Example 4: Cont…. Example 4: Cont…. Example 4: Cont….

Example 4: Cont…. Example 4: Cont…. Example 4: Cont…. According to Rule 4 Example 5: Example 5: Cont….

Example 6: Cont…. Example 6: Cont…. Example 6: Cont…. Example 6: Cont…. Example 6: Cont…. Example 6: Cont….

Example 7: Example 7: Cont…. Example 7: Cont…. Example 7: Cont…. Example 7: Cont…. Example 7: Cont….

Example 8: Cont…. Example 8: Cont…. Example 8: Cont…. Example 8: Cont…. Example 8: Cont…. Example 9:

Example 9: Cont…. Example 9: Cont…. Example 9: Cont…. Example 9: Cont…. Example 10: Example 10: Cont….

Example 10: Cont…. Summary

 Significance of Block Diagram.  Block Diagram Reduction Techniques.  Examples of Block Diagram Reduction.