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

Kevin,

Ok, lets see if I can't stir this pot a bit more:

a) Double integrating acceleration to control position is sometimes
called an inertial guidance system. I has worked ok in the past for
ICBM's, but they work with somewhat coarser tolerances than we want. :)
In other words, I think we concur on this point.

b) Deriving velocity from position seems to have more potential as a
useful technique. It is certainly true that we will always have some
error in our calculated instantaneous velocity. What I'm not so sure of
is how this compares to the errors involved in reading a DC tach.

Plus, I'm still hung up on the idea that instantaneous position is the
thing we really want to control, rather than velocity. We do want to
maintain a more or less constant feed rate, and there are clear limits
to the accelerations we can tolerate, but as long as the cutter is
always in the right place at the right time the part should come out the
right shape.

The real issue here, I think, is maintaining coordinated motion.
Intuitively, I seems to me that if one has fine enough position
feedback, that should be sufficient.

Ok, anyone care to straighten me out on this?

Jeff

On Wed, 29 Nov 2000 16:31:56 -0500, Kevin wrote:

>
>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
>