RE: [CAD_CAM_EDM_DRO] Servo systems (was: re:cleaning, lovejoy, black box tach....)

>-----Original Message-----
>From: Jeff Barlow [mailto:jeff@...]
>It seems obvious to me that independently measuring position, velocity,
>acceleration, and time, is, at least theoretically, redundant. Since we
>are using digital electronics we "know what time it is" for free. So,
>then, it would seem that all we really need is one of: a tach, a
>position encoder, or an accelerometer. (No, I'm not seriously suggesting
>we stick an accelerometer on the table).

Let's see if I can express this succinctly: You are asking why it is not
possible to just measure one "real" variable (position, velocity, or
acceleration) and use that to do all the controlling.

I suspect the answers are:
a) You can't measure the time derivative variables (velocity or acceleration)
and expect to integrate them (once or twice) in time to get the position; any
small error between the real and measured variable will be integrated over time
and result in an unbounded error between the actual and calculated position.
Even if the reading you started were 100% precise, you are still doing the
summation of sampled values, not the integration of a continuously varying
function, and you still get error accumulation.
b) Measuring the position and trying to calculate its derivative has a similar
problem: The computer can't calculate an instantaneous derivative, it can only
calculate differences over specific time intervals. This once again introduces
errors, since the result you get is not the derivative of the measured variable,
but is instead the slopes of a series of secants that are approximating the
measured function. Although in this case the error can probably be tuned out of
the system, there is the further problem that the calculated differential is
only available at the end of the interval over which it was measured.
Effectively you cannot know the velocity at time T until time T+(deltaT/2). This
time delay can introduce oscillatory behaviour into the system.

-Kevin Martin