Difference between revisions of "User:DukeEgr93/RL Example"

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(Created page with "This page is a sandbox to go over an example of how to analyze a non-unity feedback system with proportional control. This will include stability analysis, steady-state error...")
 
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* The overall transfer function is: $$T=\frac{KG}{1+KGH}$$; this is the system we will use to determine stability and transient characteristics.
 
* The overall transfer function is: $$T=\frac{KG}{1+KGH}$$; this is the system we will use to determine stability and transient characteristics.
 
* The equivalent forward path for an equivalent unity feedback system is: $$G_{eq}=\frac{KG}{1+KGH-KG}$$; this is the system we will use to determine steady state error.
 
* The equivalent forward path for an equivalent unity feedback system is: $$G_{eq}=\frac{KG}{1+KGH-KG}$$; this is the system we will use to determine steady state error.
 +
 +
== Specific Processes ==
 +
=== Breakaway / Break-in ===
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* Make the root locus plot
 +
* Move a pole to a location where it meets another pole (i.e. a critical pole)
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* To get the gain, select the compensator $$C$$ from the '''Controllers and Fixed Blocks''' portion of the '''Data Browser''' at the far left.  The gain $$K$$ will be the value of the block.
 +
* To get the pole and zero locations,

Revision as of 19:00, 26 July 2020

This page is a sandbox to go over an example of how to analyze a non-unity feedback system with proportional control. This will include stability analysis, steady-state error determination, sketching a basic root locus plot, using computational tools to gather information for a more refined sketch, using MATLAB to generate a root locus plot, and finally using Maple or MATLAB to satisfy certain design criteria using the concept of a root locus plot.

Introduction

This page will use the system as shown in Figure 8.1 of Nise 8e. Sections 8.1-8.3 develop the mathematics behind a root locus plot. The keys are as follows:

  • The overall transfer function is: $$T=\frac{KG}{1+KGH}$$; this is the system we will use to determine stability and transient characteristics.
  • The equivalent forward path for an equivalent unity feedback system is: $$G_{eq}=\frac{KG}{1+KGH-KG}$$; this is the system we will use to determine steady state error.

Specific Processes

Breakaway / Break-in

  • Make the root locus plot
  • Move a pole to a location where it meets another pole (i.e. a critical pole)
  • To get the gain, select the compensator $$C$$ from the Controllers and Fixed Blocks portion of the Data Browser at the far left. The gain $$K$$ will be the value of the block.
  • To get the pole and zero locations,