Back Lash and Describing Function for second order system
Backlash can occur in geared positional systems where there is
some play between the teeth of the gears. This effect adds a
phase delay to the system and can make a second order system
oscillatory. Describing function analysis can be used to analyse
the behaviour of this system. More information on describing
function analysis can be found in Modern Control Engineering
by K Ogata, published by Prentice Hall. In describing function analysis a Fourier series analysis is done of the backlash transfer
characteristics to derive a function relating the magnitude
and phase of the fundamental component in the fourier series.
The result can be plotted as shown in the red curve in the
applet below. This is plotted with the magnitude vs phase of
the linear transfer function(yellow plot below).
The frequency of the point of intersection is determined,
in this case w = 1.57. The
amplitude of the backlash vs phase is also plotted with
the same axes(green curve). The intersection of the w line with this curve give the amplitude
of the backlash which is also the amplitude of the resulting
oscillations(in this case ~ 2).
Gif image below shows how applet should appear.
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COPYRIGHT © 2006 Cuthbert Nyack.