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Root Locus



For both the P and PD controllers in problem 7.1, you are asked to plot positions of the poles (and zeroes) for a variety of different controller GAINS.
This is essentially what 'root locus' is all about: mapping out where poles will move as controller gain changes.

You can use the matlab command rlocus to map out the poles and zeroes for a given 'loop transmission' (aka the 'open-loop transfer function').

For these and future control systems, try to take note of correspondence between the controller gain, the pole (and zero) locations and the resulting transient (step) response of a system. (As discussed, the real and imaginary parts of stable poles describe decay and oscillation characteristics of the system.)

(See the suggested readings from Nise and Ogata for more information about root locus.)
gonzo@mit.edu page 6 (of 10) 2.010 Tutorial #7, 5-Nov-00