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For a discussion of using a CCD imager to train the PEC see this link. PEC-CCD
For an example of the data obtained after PEC correction is applied see this link. PEC-WORM Data
The purpose of the Precision Error Correction (PEC) is to correct for mechanical irregularities in the RA motion of the telescope caused by imperfections in the drive. This is a very clever idea, much used in professional telescopes and I commend Meade for implementing it quite elegantly in the LX200 design. A basic problem with all telescope drives, including professional drives, is that there are mechanical irregularities in the gears and worm which drive the worm wheel that points the optical tube. These irregularities occur with a period determined by the speed of rotation of the gears. For the LX200 design, which has a worm wheel of 180 teeth, this period is 8 minutes long.
The basic concept is to correct the speed of the drive motor to compensate for the fact that the worm drives the worm wheel a bit faster or slower as it rotates. This is done by going into a training mode and manually training the computer to compensate for the mechanical defects. This is a good but not perfect solution to correcting mechanical problems in the worm to worm wheel interface. It can not do a perfect job because correcting for one turn of the worm takes account of only one tooth of the worm wheel. It can however remove as much as 90% of the irregularity.
Basic Operation of the RA Drive
In order to understand the details of how the computer can be used to correct mechanical irregularities in the worm, it is necessary to understand how the RA drive works in the first place. Thus a rather detailed description of the RA drive is given first. If you are thoroughly familiar with this material skip to the PEC operational details below. (PEC Operation)
The LX200 Right Ascension drive (RA drive) consists of a small DC motor which drives a small gear reducer train, which turns the worm which in turn drives the worm wheel that points the telescope on the RA axis. The RA axis moves 360 degrees in a sidereal day. Since the LX200 worm wheel has 180 teeth, the worm that drive it rotates at one turn every 8 minutes. The small gear reduction train has a reduction ratio of 60 times so the drive motor rotates once every 8 seconds. This is a very slow speed for a DC motor and thus it has to be controlled by a digital signal. The motor shaft has on it an encoder which has 90 openings and is viewed through a bi-quad mask. The bi-quad encoder has two output signals (from photocells) which are in quadrature. These signals are deciphered with appropriate logic to give two new signals. One of the signals indicates the direction of rotation and the other tells how fast the encoder shaft (motor shaft) is rotating. When the RA axis is moving at sidereal rate, the encoder puts out 45 pulses per second.
Speed control is maintained by the computer which puts out a command pulses at a nominal rate of 45 pulses per second. The motor shaft must move the encoder disk to match this rate. When the motor gets behind, the computer delivers more current to it to speed it up and vice versa. In this way, the computer can control the motor shaft position very accurately. Notice that the computer sends the command in pulses per second and the motor shaft must respond. This is the key concept which explains the ability of the PEC to control the motion of the worm. The computer can adjust the number of pulses to speed up or slow down the motor.
Note that this drive is NOT a stepper motor drive. It is a DC motor with a shaft encoder. The effect of the encoder is to make the motor move from position to position in a way similar to that of the stepper. But the principle of operation is quite different.
With a pulse rate of 45 per second, each pulse corresponds to 0.333 arc seconds of motion of the optical tube assembly (OTA). This sounds very accurate, and it is. But, is must be emphasized that the control element is on the motor shaft. There is considerable lash in the gear reduction and worm drive mechanisms. Thus the basic accuracy is not transferred to the motion of the OTA. The mechanical inaccuracies are the reason the PEC is needed. With the computer generating the correct 45 pulses per second, the OTA will move with a constant sidereal rate but will wobble back and forth with respect to the stellar sphere, typically by as much as 50 arc seconds, due to mechanical irregularities in the drive. In modern professional telescopes such irregularities are compensated for with computer correction systems not unlike that used in the LX200 system.
For those interested in details, when the worm turns one time, the first gear in the reduction train turns 4 times, the second turns 36 times and the motor shaft turns 60 times. The gear ratios are 44 to 11, 36 to 9 and 30 to 8 respectively.
All in all, this is a very fine and very precise way to control a telescope. It can be seen that a GOTO action can be initiated by knowing a location and moving the OTA to a new location by having the computer command the motor shaft to turn a given number of times. The computer gets the necessary move information from internal tables and even corrects for atmospheric refraction. The declination drive works in an almost identical way.
How the PEC Corrects Mechanical Problems
A major irregularity in the mechanical drive system is the fact that the worm is not perfect. Making a nearly perfect worm would require very high precision and a very high cost manufacturing process. In the LX series of telescopes it is typical to find that the wobble caused by worm irregularities is often 50 arc seconds. This is not a severe problem for viewing but is impossibly large for imaging of any sort. There is no telescope which does not have to have some sort of guiding used to keep it on target to within a few arc seconds or so. This includes the best professional telescopes. Fortunately, with the rather fine control provided by the LX computer controlled drive it is possible to greatly reduce one of the worst of the mechanical problems. This is the mechanical irregularities in the worm which repeat for every turn of the worm shaft.
This is done in the following way. The worm shaft is indexed by means of a small magnet inserted in the shaft which triggers a pulse at what is set as the beginning of the worm cycle. The 8 minute period of the shaft is divided into 200 intervals of 2.4 seconds each. When the telescope is put in the "Learn" mode, it emits a beep at the start of the cycle and a beep every 2.4 seconds. It is the job of the operator to guide on a star as accurately as possible for the 8 minutes by pressing the East and West keys on the keypad. This is usually done at a high magnification of 300X or so. The computer interprets the key presses and stores this information in a file. After the training (Learn) cycle is complete, the computer will play back this correction record in synchronism with the worm shaft and thus slow it or speed it to correct for the original irregularities.
There is provision to run the training several times and to average the results to improve the correction. One "Learn" and one "Update" session is generally enough to reduce the irregularities to about 10% of what they were. The final accuracy is typically 3 to 10 arc seconds and this may be considered a very fine result. While not perfect, this level of error makes it possible to guide with much reduced demands on either manual guiding or with an automatic guiding system.
More Detail About How the PEC Works
In order to see what the mechanical problem with the worm is, it is necessary to consider what the mechanical errors are in terms of their distribution around the 360 degrees of the worm. The worm reaches the same point every 360 degrees while the worm wheel moves one tooth. It would be nice if the wobble of the worm surface was rather uniformly distributed over this 360 degrees. Unfortunately this is not the case. Some parts of the worm surface are very smooth and regular and some parts have larger bumps and wiggles. This is somewhat like a ramp with steeper and less steep inclines and perhaps a speed bump or two. Data recently published on the web and my own measurements on two worms have shown that there is often smooth motion followed by sudden shifts in the OTA and then a sudden motion back. See: PEC-WORM for a short description and data on actual original OTA errors and corrected operation.
It is thus necessary to have a system with frequent enough corrections to compensate not only the long slow variations but to also correct for the bumps. Rates of motion have been observed as large as 0.5 arc second per degree of rotation of the worm shaft. This is a very fast motion when observing through a high power eyepiece. It is difficult to correct this movement when guiding manually. This means that hundreds of corrections need to be made in a single turn of the worm shaft and they need to be made very quickly. The LX200 system allows for 200 corrections for each turn of the worm. This is done by detecting the start of the cycle, through the magnetic shaft switch and keeping track of the 200 sections over the 8 minute cycle in the computer.
The operator then manually guides the telescope as accurately as possible and the computer keeps track of the corrections for each interval. There are 108 pulses delivered to the drive motor in each interval. This is done as follows:
The 8 minute worm cycle is divided into 200 bins within the computer. Since there are 45 pulses per second to drive at sidereal rate, there are 108 pulses in each bin or 21,600 pulses per worm cycle. The values stored in each bin are nominally set to 108. On "Erase," the values are initialized to 108. When "Learn" is selected the values are also initialized to 108 and are then modified by the training process which is done in the "Learn" mode. When "Update" is selected the values in the bins are not reset at the start of training. During either learn or update training, any previously stored PEC corrections are not applied to the drive. Thus the RA axis is driven at a fixed rate of 108 pulses per 2.4 second period at a constant rate during both learn and update.
During each 2.4 second period the currently active bin has the number of user added or removed pulses combined with the nominal number of 108. In the learn mode, this new value is stored in the appropriate bin. In the update mode, this value is averaged with the value already in the bin. After the training, the system plays back the number of pulses in the bins which then adjusts the pulse rate so that in the 2.4 seconds that the bin is active, the indicated number of pulses are fed to the motor drive circuit evenly over this period. This has the effect of averaging any corrections over the 2.4 second period. This operation has the effect of speeding up and slowing down the drive uniformly over each period as required to correct for mechanical errors in the worm.
Rapid changes in drive motion are not tracked over the 2.4 second periods so that abrupt "bumps" or "valleys" on the worm gear or worm wheel which occur more quickly than 2.4 seconds may result in an abrupt image shift. More frequent pushes of the E/W buttons might increase guiding accuracy since this tactic avoids overlap between bins and prevents over correction that might occur from one segment to the other. The averaging of the new training with the stored training (previous value) has the effect of geometrically weighing the older trainings So, in the case of the learn mode the training value is stored but in the case of the update the training value, it is averaged with the older value. That is, the older trainings become less significant and the most recent training becomes one-half of the stored correction. This implies that the most recent training is the most heavily weighted and thus the most important. A poor update can spoil an otherwise well trained worm. Note that since one can spoil good training with a final bad training session, the averaging algorithm used is not the best. For this averaging scheme to work well, training requires that you make more or less random errors in training and that you get better at training if you do a learn and several updates afterward. In my opinion it would be better to playback the PEC during training and then allow for corrections, which would be small, to be weighted into the values that are stored, thus perfecting the training in a systematic way as you do more and more training.
Off center mounting of the worm wheel can be a problem if you train on one part of the worm wheel and then operate on another part. This may explain why you can have a well trained PEC and then on another night find the PEC less effective. It must be remembered that one cycle of the worm trains the entire worm but on only one tooth of the 180 tooth worm wheel. For this reason, a permanently mounted telescope should have the drive clutches locked so that the trained part of the worm wheel is used at all times. (only one-half of the worm wheel is ever used in this case.)
After training, the total pulse value that appears on the hand controller should nominally be 21,600. Differences from this value are due to poor training or a crystal that is slightly off frequency. This effect may be due to a highly asymmetrical error in the worm itself. The deviation from 21,600 represents a very slow RA drift which is not a problem while guiding manually or with a CCD imager. Note that when the PEC is turned off, the training vanishes.
If one can reduce the worst of the irregularities by a factor of ten, which is certainly possible, the worst rates of deviation will usually be only 0.05 arc seconds per degree of rotation of the worm shaft. Thus, with very good PEC correction in place, the residual errors should be correctable with careful manual guiding and certainly easily corrected with automatic guiding with a CCD imager. Without good PEC training, manual correction is exceedingly difficult and automated guiding often impossible. The exception to this is in the accidental case that a particular drive has almost no errors. Such cases have been reported but they are likely very unusual. Even the finest Byer's research quality gears have only a 10 arc second rating. By the time one gets to the one arc second guiding condition, other effects such as telescope mechanical instability, wind induced motion and atmospheric wobble will take over in blurring a star image.
There are are a variety of issues that relate to PEC training. One of the interesting ones is using the CCD imager guiding signals to do the training of the PEC. There have been a number of reported successes using this technique. See: (PEC-CCD)
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