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Drawing Differential Equations as a Block Diagram (Example Problem)
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In this video, I show an example of drawing a block diagram for a Single-Input-Single-Output (SISO) linear system described by differential equations.
Timestamps:
00:00 - Introduction
00:30 - Block Diagram Components
03:22 - Overview of steps to solve
03:56 - Example problem description
04:25 - Solving for the highest derivative (step 1)
05:08 - Drawing integrations (step 2)
06:15 - Combining signals and closing loop (step 3)
08:30 - Checking the system equation
10:20 - Combining signals for output (step 4)
11:41 - Checking the output equation
12:09 - Final answer and conclusion
If you want to see me make a video about any topic, please leave a comment below!
Errata:
• At 03:33 I say “differential equation” instead of “system equation”. While it is true that for this problem the system equation is a differential equation, The first step should be specified to be about the system equation and not the output equation. I make a note of this mistake on screen.
• I forgot to draw the input arrow for the gain block containing 6 drawn at 08:16. It should be easy to determine the direction of this signal, but the arrow should be drawn nonetheless. I make a note of this mistake on screen.
Timestamps:
00:00 - Introduction
00:30 - Block Diagram Components
03:22 - Overview of steps to solve
03:56 - Example problem description
04:25 - Solving for the highest derivative (step 1)
05:08 - Drawing integrations (step 2)
06:15 - Combining signals and closing loop (step 3)
08:30 - Checking the system equation
10:20 - Combining signals for output (step 4)
11:41 - Checking the output equation
12:09 - Final answer and conclusion
If you want to see me make a video about any topic, please leave a comment below!
Errata:
• At 03:33 I say “differential equation” instead of “system equation”. While it is true that for this problem the system equation is a differential equation, The first step should be specified to be about the system equation and not the output equation. I make a note of this mistake on screen.
• I forgot to draw the input arrow for the gain block containing 6 drawn at 08:16. It should be easy to determine the direction of this signal, but the arrow should be drawn nonetheless. I make a note of this mistake on screen.
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