Help with Root Locus: Get into General Form for Drawing

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SUMMARY

The discussion focuses on designing a control system using root locus methods, specifically for a motor control application. The user successfully implemented a deadbeat controller but struggles with generating a root locus due to the feedback loop configuration. The challenge arises from the introduction of a zero when multiplying H(s) and G(s), which alters the root locus as the gain varies. A general form for drawing the root locus is requested to address this issue.

PREREQUISITES
  • Understanding of control systems and feedback loops
  • Familiarity with root locus techniques in control theory
  • Knowledge of state-variable feedback design
  • Proficiency in transfer function analysis
NEXT STEPS
  • Study the derivation of the root locus for feedback systems
  • Learn about the effects of pole-zero placement on system stability
  • Explore MATLAB's Control System Toolbox for root locus plotting
  • Investigate the relationship between gain and system response in feedback loops
USEFUL FOR

Control engineers, students in control systems courses, and practitioners designing motor control systems will benefit from this discussion.

formulajoe
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I had to use state-variable feedback to design a control system for a motor. I first designed a deadbeat controller, which was pretty easy.
But now I have to design another controller using root locus methods.
The gain that is varied is located in the feedback loop as shown in the picture.
I am completely lost as to how to generate a root locus with the gain in the feedback loop.
Can anybody give me a general form to get into so I can draw the root locus?
 

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The problem I am having is that when H(s) and G(s) are multiplied together, a zero is introduced because of the feedback loop. The location of this zero changes as the gain changes. So the gain cannot be varied without moving the zero. Thus every value of gain produces a different root locus.
 

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