Consider for example that the pole is in the upright position (angle is zero)
and it does not move (angular velocity is zero). Obviously this is the desired
situation, and therefore we don't have to do anything (speed is zero).
Let's consider another case: the pole is in upright position as before but is
in motion at low velocity in positive direction. Naturally we
would have to compensate the pole's movement by moving the platform in the
same direction at low speed.
So far we've made up two rules that can be put into a more formalized form like this:
We can summarize all applicable rules in a table:
| angle
|
speed | NH NL Z PL PH
----------+------------------------------
v NH | NH
e NL | NL Z
l Z | NH NL Z PL PH
o PL | Z PL
c PH | PH
where NH is a (usual) abbreviation for negative high, NL for negative low etc.
On the next pages we will show how these rules can be applied with concrete values for angle and angular velocity.