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As a one-time control systems engineer there's a fourth method, though I haven't seen it attempted on amateur scopes - though I have half a mind to try as it should work well enough with say a small micro-controller - anything from a BASIC Stamp to Arduino or RaspberryPi would do...
1. Attach an auto-guider (ie a small guidescope with camera) with ST4 outputs such that the RA signals are used for azimuth and the dec signals for altitude.
2. In software, construct two "floating-integral" controllers, these are easily implemented in software, such that one controls altitude, one controls azimuth and connect the signals from the auto guider accordingly.
3. Each controller integrates the pulses from the auto guider over time, for example "up" treated as positive and "down" as negative (altitude) and "left" as positive and right as negative (azimuth). You may of course need to reverse the signs depending how you wire the motors driving the axes.
The point about integration is that a persistent error is integrated with time resulting in the controller producing a signal that cancels the error. If you this right it will probably work nicely with a time constant of a few seconds. This works very nicely with slow-moving signals as in telescopes, even with random noise added as a result of wind and atmospheric scintillation at higher frequencies which the integral controller simply averages out.
This will self-learn the right rates in a matter of seconds, much faster than the "train and track" manual method.
If you want to be really fancy you could implement a deadbeat controller algorithm, though thats tricky to tune if you haven't been taught the theory behind it. The deadbeat algorithm would be quite fast enough (two controller cycles) to correct period errors in a geartrain.
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