2. 71 2. 5
FIGURE 8. P and PID comparison. Here, the P controller is set at a very low gain and
struggles to get within three degrees of the goal position of 50 degrees. The integral
term in the PID controller tightens up the output shaft right at 50 degrees.
The setup is crude, but will
demonstrate some of the
functionality of the controller. The
heavy mass acts as, well, the mass;
the tape operates as a spring; and
the thrust washer acts as the
damper. A program was written in
Ubuntu to initially set the motor at
the zero position, set the gains,
then set the motor to a position of
50 degrees. Immediately after, the
program reads the motor position
internally and outputs the position
and time to a file, where the data
can then be plotted.
Two different comparison tests
were executed, comparing a
standard P controller to a PD, and
then a PID controller. Figure 7
shows a P controller where the gain
is set fairly high. This results in an
overshoot of the output angle. By
implementing a small amount of a
FIGURE 9. Gear concepts: a) The desired power transmission
of gears; b) To realize the desired motion, a string can link the
two discs; and c) By introducing a second string, the gears
can transmit power in both directions.
60 SERVO 01.2012
FIGURE 11. Using the markings in Figure 10, an involute
shape is built incrementally.
FIGURE 10. A close-up of Figure 9b, with markings
showing the position of the string and angles of each
disc as power is transmitted.
FIGURE 12. The involute shape as created from
unravelling a string from a circle.