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2.0 Mathematical Backgroundsummarize 2.1 continued

Block Diagrams

A block diagram is a graphical method for representing the model of a system and showing how subsystems are interconnected. Each block in a diagram has an input, output and a dynamic system (differential equation) that relates the output to the input. On this site we will always represent the dynamic system in a block diagram using a transfer function. A single block is shown in Fig 2.1.1.

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A single block is no more useful than a single transfer function. The value of a block diagram is that it allows us to model a system using a set of interconnected blocks where each block represents a small piece of the entire system.

The complication with block diagrams is that in order to solve for the response of the system, you need the differential equation or transfer function representing the entire system. This means you must combine all the blocks in a diagram into a single block.

Block Diagram Algebra - Brute Force

You can combine blocks in a block diagram using a brute force method. This approach always works, although is may require a substantial amount of algebra. There are three steps to this method.

1. Create a unique variable for the output of every block
2. Write the equation relating the input and output of each individual block
3. Use algebra to eliminate the unwanted variables from the set of equations

See the example at the bottom of this page

Block Diagram Algebra - Equivalents

While the brute force method always works, it may not be the easiest way to simplify a block diagram. In many cases, youYou can simplify a block diagram by identifying common forms or patterns of blocks and replacing those with simplified equivalent blocks. In this site we present three common forms. For additional discussion on this approach go here

Following is an example that demonstrates how to simplify a block diagram using both methods.

Simplifying a Block Diagram