A quasi-analytical Describing Function (DF) for the Karnopp stick-slip friction
model is presented, and compared with the numerically computed DF (Baril,
1996), and with experimental measurements. Its phase lag is shown to be
dictated by the static-to-dynamic friction ratio, and is generally limited to
32.5 deg.
A DF for the exact physical Nordin-Gutman backlash model is presented, and
compared with the numerically computed DF in Nordin (2000). The proper backlash
contact condition in analytically defined in the phase-plane.
It is shown that the friction and backlash models and their DFs are duals of
each other, and hence the common engineering practice to fight backlash with
friction has got an analytical foundation. The minimum friction level to
eliminate backlash induced limit cycles is computed, as well as the minimum
dither frequency to eliminate friction induced limit cycles.
The DF models can facilitate robust control design, and be used in real-time
adaptive control algorithms.

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