[what's the relationship between Controller DAC resolution and mechanical precision]

In a digital position control system you are discretizing both the force you can apply (DAC counts) and the time interval over which you can apply it (sampling rate). The more DAC resolution you have, the finer increment of force you can apply. Looking at DAC resolution as delta Force and time resolution as delta Time, the "resolution" of the acceleration control capability of your system is limited by:

 

delta Acceleration = delta Force / delta Time ~ sample time / DAC bits

 

Of course, resolution is not everything, as noise limits the effective resolution of both of these parameters.

 

If you work through the physics, it turns out that the finer the resolution on acceleration control the stiffer your system can be and the smaller your following error, within the limitations of noise and mechanical hysteresis.

 

A practical answer to your question: if you are working on a high-resolution, low-friction system (air bearing/linear motors/nanometer resolution) then make sure your DAC resolution is finer than the analog noise resolution of your amplifiers/motors, i.e. 16 to 18 bits typically. If you are working on an "average" system with lots of friction and coarse resolution, then 12 bits is fine.

 

I am attaching a paper that discusses some of this; also see Precison Machine Design, by Alex Slocum, 1992

stage_resolution.pdf

[Lowpass DC Gain]

Is there an easy formula for calculating the DC gain of a lowpass from ix38 and ix39? I know the Tuning Pro takes care of this when it is used, but I need to use other methods for my gain scheduler.

 

Take a look at PMAC users manual under "manual notch specification." (in my version it is page 109) It explains it pretty well in general terms.