Periodic error correction in automatic telescopes I am starting a study on automatic telescopes and the correction of their periodic error.
I found two ways of correcting it : with a CCD camera and manually by recording the error. I was wondering if it could be possible to model the error by a periodic signal in order to add it to the entry signal then correct it with a low-pass filter or an other filter ?
Quoting the most relevant parts from the Richard McDonald's Wiki on Astrophotography Mounts: Periodic Error Correction:


  Periodic Error can be reduced to an acceptable level using a variety
  of techniques, only some of which are in the range of a beginner or
  mid-level astrophotographer.
  
  
  Throw Money at the ProblemVery high-end mounts for astrophotography have very small periodic error because of the time
  and money spent on manufacturing high-precision gears. You can also
  buy higher-precision gear upgrades for some mounts. For the beginner,
  let's call this impractical. Buying a \$1000 replacement worm gear for
  your \$1000 mount is probably not a good balance.
  Don't Use GearsThis is really an extreme case of the "throw money" solution, mentioned just for fun. There are some
  very-high-end experimental drive systems showing up on the market that
  don't use worm gears, and that don't exhibit periodic error. Examples
  include direct drive systems and harmonic drives. 'Way out of our
  price range.
  AutoguidingA second guide camera and computer can be used to make frequent small corrections to the mount's pointing,
  and this can reduce or eliminate Periodic Error if the onset of the
  error is not too sudden. This is the subject of a separate article.
  Periodic Error Correction FeatureTraining PEC with hand-control Most mounts intended for astrophotography include a
  feature called Periodic Error Correction (PEC), which can be used
  alone, or in conjunction with Autoguiding. PEC is used in two phases:
  
  
  Training. During this phase you use the control panel or menus to say "Hey! Pay attention to this!" to the mount, then you manually
  keep a star perfectly centred for several worm periods. You do this by
  centering a star with a high-magnification eyepiece that includes a
  cross-hair reticle. You then stare at the star for 10 to 15 minutes
  and use the mount's hand controller to manually make the small
  adjustments necessary to keep it perfectly centred on the cross hair.
  The mount records the error corrections you supply, remembering where
  in the worm position each one was needed. By training through more
  than one worm cycle, the mount can record an average correction, in
  case you reacted slowly or over-reacted.
  Playback. Once you have trained the mount, you can turn on PEC. The mount will "play back" the recorded error correction information
  by slightly changing the speed of the Right Ascension drive to move
  ahead or back each time your manual error corrections did the same.
  This will cancel the periodic error, resulting in a smoother track.
  
  
  
  
  
  Training PEC with
  hand-control: Periodic Error Correction (PEC) button on the control
  panel of an equatorial mount.
  
  The manual training phase is quite tedious and a more modern
  alternative is to use a camera and computer - usually the same one you
  will use for auto-guiding - to track a star while the mount records
  the training information.
  
  There is even specialized software available to help collect Periodic
  Error data, analyze and smooth it, and upload it to the mount. You do
  not need such software, as the manual techniques mentioned above will
  work just fine. However, it makes a tedious job simple and pleasant,
  and you may find it a worthwhile investment. I use PEMPRO and am
  very impressed with it. It's not free, but it is inexpensive and works
  very well (and includes another feature to help achieve perfect polar
  alignment).


Quoted text and photograph source, copyright and courtesy of Richard McDonald, no copyright infringement intended. I would also highly recommend reading same author's extensive article on Autoguiding.