> I have been reading about PID in depth from textbooks and on the web,
> but am starting to feel more and more like tuning it is an art and not a
> science.

That's right.  The equations will only take you so far, because most real
world systems are not that well known or predictable.

> My first problem is that I want to
> have an operating depth of X meters and I know my current depth.  To
> move the AUV I have to set the voltage of the vertical thruster.  How do
> I relate the input to the plant (the desired depth) to the output of the
> plant (the motor voltage)?  All examples I have found assume there is a
> magical sensor that changes the output of the plant to the same units as
> the input.

The PID algorithm is driven the by the error signal, which is (desired
depth - actual depth), and which is a function of time.  Process this
error value according to the P, I and D formulas and add all the
contributions.  That's the output voltage.  (That's at a high level.  Real
world useful PID algorithms have all kinds of subtle features built in.)

Units don't matter because they represent only a proportionality constant
to the actual calculations.  The PID control values can be adjusted to any
desired proportionality constant, of which unit conversions is only one
anyway.


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