Difference between revisions of "User:DukeEgr93/RL Example"
Jump to navigation
Jump to search
(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...") |
|||
| Line 5: | Line 5: | ||
* 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 === | ||
| + | * 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, | ||
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,
