Tick Management and Gurley Interpolation Error Correction

The purpose of "Tick Management is to use an economical, medium resolution encoder to "close the loop" for your telescope axis, which can remove all backlash and periodic error.

Tick management works like this:

You must have an encoder on your motor, and a medium resolution encoder on each of the telescope axis's on which you want to apply tick management.

Inside the SiTech servo controller, every time a new "scope tick" happens, the motor location is captured.  When a communication is sent from the servo controller to SiTechExe, the controller sends 3 items of interest to the tick management routine:

1. Motor location

2. Scope encoder location

3. Motor location when the last scope encoder location happened.


Now have a look at the image below....   You'll see that it's the telescope angle (radians) = Current Scope Tick Angle + (motor ticks per scope tick / (current motor location - the location at last scope tick) * Pi * 2).



That is how normal tick management works, and it allows you to "close the loop" using a much more economical encoder than a sub arc second encoder.


Based on what Dan pulled out of one of his body parts, plus some experience, we think that you could have at least a 10 fold resolution increase. Thus if you had an encoder that has 320,000 ticks per rev (after quadrature), you could use it with "tick Management" and have a simulated resolution of more than 3,200,000 ticks per rev. This is sub arc second, and should work fine for most amateur scopes.

There's two ways to get an encoder of this medium resolution:
1. Gear up an inexpensive USDigital ( http://www.usdigital.com )

    The advantage is low cost, and, as it turns out, slow periodic error.
    The disadvantages are:
        a. Possible slippage (if used as a roller)
        b. Adding backlash (gears)
        c. Fast periodic error (gears or timing belts),
        d. Can have a very large slow periodic error (rollers, gears or timing belts)

It turns out that a very small de-centering of the roller creates a considerable amount of slow periodic error.

2. Purchase a medium resolution Gurley Encoder. I recommend the 320,000 tick per rev (after quad).

Several SiTech customers did this option 2, and had mixed results.

Gurley Interpolation Error:
What Chuck Shaw found out was that the Gurley encoder has what we've named "Interpolation Error".
There are 5,000 lines on the gurley disk. In quadrature, this would create 20,000 ticks per rev, but Gurley uses a technic called "Interpolation".  A sine and a cosine analog signal are created from photo-electronics, that are proportional to the angle of the dark line through the glass. This signal is converted to digital, and then "stepped" through several voltage levels, enabling a higher resolution than if just purely digital. In the case of the 320,000 tick encoder, the sine and cosine are stepped to create 64 "ticks" per line, and with 5,000 lines, this creates 320,000 "ticks".

What we found, is that there is a periodic error of about 5 arc seconds for every line, or 64 ticks. Since this is a fast moving error, it's hard for an autoguider to compensate.

We should point out that this error is well within the specifications of the Gurley encoder, it's just that none of us were expecting it to be that fast of an error.

So after thinking about the problem for a few days, Dan came up with a solution. He mentioned this to Dave Rowe, who was skeptical. However, he modeled it, and found out it would work quite nicely.

Here's the concept:
There is an average number of motor encoder ticks between each scope encoder tick. This value will vary from scope tick to scope tick, depending on the interpolation error, but it is consistent for each "cell" of different 64 scope "ticks" per scope encoder line.  Dan programmed the SiTech controller to count each motor tick between the telescope encoder ticks, and put them in a 64 byte buffer. This buffer is read out to the SiTechExe program, every time the 64 "ticks" roll over to zero again (just over 17 seconds with the 5,000 line Gurley encoder, while moving at the sidereal rate).

Now the SiTechExe program averages these ticks (to average any changes because of worm gear periodic error), and then converts the 64 cells (representing motor ticks to scope ticks) into an angle. This angle is integrated, depending on which scope tick the scope encoder is currently on. Then a standard "tick management" is applied to the cell that is the current cell, to find the fractional angle of that particular cell.

Now, we hope Dan explained that ok, but I fear it will need to be re-written, but, if you don't want to understand it, then don't worry, you don't have to, just use it! Have a look at the improvement in the following pictures, you can see the uncorrected Gurley interpolation error, in relation to the corrected Interpolation Periodic Error, and also, the final improvement from the normal worm periodic error of Chucks German Equatorial Scope.

In this PemPro screenshot taken by Chuck Shaw, you can see the uncorrected Gurley interpolation error, and the Corrected interpolation error:


In this PemPro Screenshot taken by Chuck Shaw, you can see the un-corrected periodic error of his worm gear, and the Gurley tick managment, with Gurley Interpolated Periodic Error Correction on:



Authors: Dan Gray, Chuck Shaw, Dave Rowe.

Dan - Software and Firmware.

Chuck - Testing, Testing, Testing, and more Testing.

Dave - Mathematically modeled the concept, and gave programming advice.

Reference:
Gurley part numbers:
320,000 tick:
R158S05000Q5L16AN18SP04EN

500,000 tick:
R158S05000Q5L25AN18SP04EN

R158 PDF:
http://www.gpi-encoders.com/Info/R158.pdf




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