Motor Dead Range
Due to static friction the servo motor has an input voltage threshold below which
the motor will not move. The friction is primarily due to the brushes within the
servo motor. A graph of the input voltage versus cart velocity might look something
like the following:
To compensate for this non-linearity we can add to our calculated control voltage
the corresponding threshold voltage. If the calculated control voltage is positive
we add the threshold voltage to the control voltage to compensate for the
deadrange, and if the calculated voltage is negative we add a negative threshold
voltage to the control voltage to compensate for the deadrange. A graph of the
transfer function would look something like:
Note that this function is the inverse of the previous function.
It thus cancels out the non-linearity of the motor-cart system
due to static friction making the system appear more linear.