The Root Locus

Root Locus plots are a very useful way to predict the behavior of a closed loop system as some parameter of the system (typically a gain) is changed.  This web page attempts to demystify the process. The various parts are more-or-less stand alone, so if you want to skip one or more, that should not be a problem.  If you are only interested in a quick lesson on how to make root locus plots, examine part 3 in conjunction with part 5.  A MatLab program designed to help learn to sketch Root Locus plots is described in part 6.

The documents are:

  1. Why is the root locus important?
  2. A Derivation of Root Locus Rules.
  3. Some examples (1, 2, 3, 4, 5) - (combined into one file)
  4. Root Locus Characteristics (for design).  (not completed)
  5. A table summarizing Root Locus Rules.  (The complementary root locus).
  6. RLocusGui:  A software tool for learning to sketch Root Locus plots by hand.
  7. The Matlab files discussed in these documents.

Documents 1-6 combined into one file (for easier printing).