EGGN Block Diagrams Tyrone Vincent Lecture Contents Block Diagram Elements

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EGGN307: Block Diagrams Tyrone Vincent Lecture 11 Contents 1 Block Diagram Elements 1.1 Block Diagram Simplifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Other Manipulations 2.1 Moving Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 Quiz Yourself 3.1

Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1 Block Diagram Elements Block Diagram Elements Block diagrams are graphical representations of algebraic equations )= System )= )+ Summing Junction 1.1 Block Diagram Simplifications Block Diagram Simplifications: Systems in Series Systems that are in series or cascade can be combined by multiplying This work is licensed under the Creative Commons

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)= )= )= Block Diagram Simplifications: Systems in Parallel Systems in parallel can be combined by adding )= )+ )+ )=( )+ )) Block Diagram Simplifications: Systems in Feedback )= )=
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Eliminating )= )( )) Solving for )+ )= (1+ )) )= )= 1+ We will use this simplification often in this course.

Block Diagram Simplifications: Feedback Simplification )= 1+ 1+ 1.2 Example Example 1 Simplify the following block diagram. All variables are functions of s. Example 1: Step 1 Combine systems in parallel
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Example 1: Steps 2 and 3 Combine feedback systems Combine systems in series 1+( 1+( 2 Other Manipulations Untangling Loops Sometimes, loops interfere with each other 2.1 Moving Elements Moving Summers Summing can be done in any order )=( )+ ))+ )=( )+ ))+ Moving Pick-off points Pick-off points can be taken anywhere on a line
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Moving Pick-off points

around blocks Pick-off points can be moved around a block by adding blocks 2.2 Example Example 2 Let’s return to this example
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Example 2: Equivalent Diagram Example 2: Simplified +1 1+ +1 +1)( +1) 1+ Backup Plan If you ever get stuck - just convert back to algebra relationships and solve by hand Add variable names at inputs to blocks Write equations for all variables, solve for transfer function The equations are HR
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Eliminate HR 1+ 1+ Eliminate 1+ 1+ 1+ 1+ (1+ )(1+ 1+ 3 Quiz Yourself 3.1 Questions 1. Simplify the following block diagram 2. Simplify the

following block diagram
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3.2 Solutions 1.
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2.