User`s guide

Root Locus Design
7-3
Root Locus Design
The root locus method is used to describe the trajectories of the closed-loop
poles of a feedback system as one parameter varies over a continuous range of
values. Typically, the root locus method is used to tune a feedback gain so as to
specify the closed-loop poles of a SISO control system.
Consider, for example, the tracking loop
where is the plant, is the sensor dynamics, and is a scalar gain to
be adjusted. The closed-loop poles are the roots of
The root locus technique consists of plotting the closed-loop pole trajectoriesin
the complex plane as varies. You can use this plot to identify the gain value
associated with a given set of closed-loop poles on the locus.
Thecommand
rltool openstheRoot LocusDesignGUI. Inadditionto plotting
the root locus,the Root Locus DesignGUI can be used to design a compensator
interactively to meet some system design specifications.
TheRootLocusDesignGUIcanbeusedto:
•Analyze the root locus plot for a SISO LTI feedback loop
• Specify feedback compensator parameters: poles, zeros, and gain
• Examine how the compensator parameters change the root locus, as well as
various open and closed-loop system responses (step response, Bode plot,
Nyquist plot, or Nichols chart)
Chapter 8 provides more detail on the Root Locus Design GUI.
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