Difference between revisions of "User:DukeEgr93/RL Example"
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| − | 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. | + | 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. This page is based on MATLAB R2020a and Maple 2019. |
== Introduction == | == Introduction == | ||
| Line 7: | Line 7: | ||
== Specific Processes == | == Specific Processes == | ||
| + | === Creating Transfer Functions in MATLAB === | ||
| + | * Generally, start with <code>s = tf('s')</code> to define a variable that has the Control Systems Toolbox definition of the frequency variable. | ||
| + | * Use <code>s</code> to create the transfer function. Alternately, use the <code>tf</code> or <code>zpk</code> commands. | ||
| + | |||
| + | === Importing Transfer Functions to SISOtool === | ||
| + | You can start SISOtool with arguments that provide values to the four transfer functions in the default architecture. The following startup commands work: | ||
| + | <source> | ||
| + | sisotool | ||
| + | sisotool(G) | ||
| + | sisotool(G, C) | ||
| + | sisotool(G, C, H, F) | ||
| + | <source> | ||
| + | Any unspecified transfer function is a 1. You can also change transfer functions once SISOtool is running: | ||
| + | * Click the "Edit Architecture" icon in the "Control System" tab at the top | ||
| + | * Replace the Value entry for the particular transfer function you want to change with either a command that creates your desired transfer function or a variable name containing the transfer function. | ||
| + | |||
=== Breakaway / Break-in === | === Breakaway / Break-in === | ||
* Make the root locus plot | * Make the root locus plot | ||
* Move a pole to a location where it meets another pole (i.e. a critical pole) | * 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 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 | + | * To get the pole and zero locations: |
| + | ** | ||
| + | |||
| + | == References == | ||
| + | [https://www.mathworks.com/help/releases/R2020a/control/ref/controlsystemdesigner-app.html?searchHighlight=controlSystemDesigner&s_tid=doc_srchtitle Control System Designer R2020a] documentation from MATLAB | ||
Revision as of 19:31, 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. This page is based on MATLAB R2020a and Maple 2019.
Contents
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
Creating Transfer Functions in MATLAB
- Generally, start with
s = tf('s')to define a variable that has the Control Systems Toolbox definition of the frequency variable. - Use
sto create the transfer function. Alternately, use thetforzpkcommands.
Importing Transfer Functions to SISOtool
You can start SISOtool with arguments that provide values to the four transfer functions in the default architecture. The following startup commands work: <source> sisotool sisotool(G) sisotool(G, C) sisotool(G, C, H, F) <source> Any unspecified transfer function is a 1. You can also change transfer functions once SISOtool is running:
- Click the "Edit Architecture" icon in the "Control System" tab at the top
- Replace the Value entry for the particular transfer function you want to change with either a command that creates your desired transfer function or a variable name containing the transfer function.
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:
References
Control System Designer R2020a documentation from MATLAB
