User:DukeEgr93/RL Example

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,