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This is a very brief discussion of control systems, especially those used on telescopes. Understand that this is a overview of the parts of the system and how they interact to control the position of the telescope. This is not a discussion of control theory which is a major concentration in electrical engineering. My purpose is to clarify some of the misconceptions I so often see in posts to various web sites and to perhaps clarify the terminology that should be used to describe these control systems.
Control systems can be categorized as open loop or closed loop or sometimes a combination of the two schemes. What these terms mean needs to be clarified. A control system generally has an input and an output. In the case of a telescope, the input is a command, usually from a computer, to point in a specified direction. The output is the mechanical motion of the telescope to reach that location. There are two coordinate numbers used to specify the position. These are usually Declination and Right Ascension. (call them Dec and RA) Or, they may be altitude and azimuth. Each can be easily converted to the other. The way the control system work is the two directions is almost symmetrical so only one direction of motion need be considered to understand the concepts of control.
Clearly a number in a computer has to be processed by a lot of intervening electrical and mechanical transformations to become mechanical position. These are myriad. We do not need to consider the details at the moment. Just consider that there is an input, a control system and an output. When we look at the output as related to the input with an open loop control system, we are usually disappointed in the result. This situation lead to the concept, in the 1930s, of actually measuring the output and sending a signal back to the controller to tell how close it is to the correct output. This is the concept of feedback control. It has become vital to all control systems and is even applied to biological and economic systems these days. The concept is very important and has some subtle implications. If the feedback is in error or too strong, the control system errors can be made worse or the system can even become unstable. (like the stock market or some biological functions) We find that feedback control was used in mechanical systems many years ago. Examples are the governors on steam engines or the water flow through a mill. A modern one is the cruise control in you automobile.
The theory of how these systems operate is called control theory and is studied by electrical engineers, mechanical engineers and many others. It is rare that an open loop control system, one in which there is no feedback will be adequate for precision systems. One might consider how manually pointing a telescope is a closed loop control system. This is one in which the observer is the feedback element. Say you want to go to an object at declination "d" and you have a declination scale on the telescope. First you look at the scale and move the telescope to Dec "d". Right there is a feedback process. Your arm moves the telescope, or you push a button to move it, your eye tells you when you are at the right point and you stop the motion. That is closed loop feedback. With a good scale you can get to within a fraction of a degree of the desired position. Now you look through the telescope and see the object in the finder. You then move the telescope slowly to center the object. This is also feedback control. The loop that is closed consists of: the movement of the object in the eyepiece, your eye, your brain, your finger on the control and the actual motion of the telescope. Even the concept of the loop gain of the system is in this example. With a low power eyepiece you can point with a certain accuracy. If you go to a high power eyepiece you can point more accurately. The higher eyepiece power has increased the loop gain of the system and has increased the accuracy of the feedback element in the system at the same time.
Now all of these concepts can be applied to automated pointing systems. Here is how. If you have what is called an absolute pointing system, the telescope axis will have a very precise feedback element called an absolute encoder which tells the system where the telescope is actually pointing in absolute terms. This can be done, but the cost of the system is very high and the final accuracy limited by the precision of the encoder used. Absolute encoders of reasonable accuracy cost, say $400, are usually only accurate to a part in 4000. That is about 5 arc minutes. This is not bad for pointing, it generally will put your field of view on the object. Then you can use the human feedback control system to move the object to the center of the field. This level of pointing is generally not good enough for CCD imagers which have a small field of view. To make use of this absolute encoder, you need to have a computer that reads the encoder and compares this value to the desired value and sends a signal to the telescope which tells it to move until the encoder position matches the desired position. This can and has been done in many systems but the cost is high.
There is a second way to point the telescope. It is called the differential location system. This is the system used in most telescope control schemes since it uses relatively inexpensive encoders called differential encoders. The differential scheme requires you to tell the telescope exactly where it is pointed and how far to move to get to the next object. Most amateur telescope systems work with these differential encoders. The demands on the computer are slightly greater since it has to be calibrated and keeps track of exactly where it is pointed but the encoders are much cheaper and can count differential position to an arc second or so. Computing power is cheap so this system is almost universally used. Unfortunately, each move of the telescope depends on the accuracy of the previous move and so errors accumulate. The pointing accuracy achieved is usually only to a few arc minutes in the final complete system.
So it seems that pointing to a few arc minutes is not only possible but a reasonable goal. (Note this is only the initial pointing to a new position, not the final tracking accuracy which has to be much, much better especially for imaging.)
Several examples of how the closed loop feedback is accomplished will now be described. Most systems use the differential system so it will be covered in more detail. There are several manifestations of the differential system. One is the closed loop system which includes the actual pointing position of the telescope as measured by an encoder on the shaft of the OTA. This pointing system thus includes all of the electrical and mechanical parts of the system. The accuracy of such a system depends only upon the accuracy of the encoder used to report the position of the OTA. All mechanical and electrical errors are reduced by the gain of the feedback system. In these systems, the controller moves the telescope until the encoder reports the correct position, limited only by its own ability to differentiate position. Here again, the accuracy for an encoder connected directly to the OTA shaft is about a part in 8000 for the best encoders. (2.5 arc minutes) However, the encoder can be geared up by 5 to 10 times to improve the positional sensitivity. The gearing up mechanism must of course be accurate. It can be made accurate mechanically because the forces in this link are very tiny and high precision gears can by used. One can get differential pointing accuracy of 10 to 20 arc seconds with these systems. Many commercial and amateur pointing systems use this method.
A second form of differential feedback control placed the encoder on a shaft which is in the mechanical power loop but moves at a higher speed than the OTA axis. This is the system used in the LX series of telescopes. The advantage of this tactic is that the higher speed shafts are available anyway and the encoder does not have to be high precision in angular terms. The encoder differential accuracy in these systems is in the single arc second range. However, the problem with these schemes is that the encoder does not report the actual OTA position but an inferred position through the gear reducer and the worm drive. The accumulated error through the gears that form the mechanical power link between the encoder and the OTA position is easily 100 arc seconds or more. Thus while this method is theoretically very accurate, it is in practice not much better than the first method and is additionally subject to the vagaries of problems with the reducer gearing and worm drive. Loading of the system, balance and other factors make this scheme somewhat problematic. The problem is that while the high speed shaft is in the feedback loop, the OTA shaft is considerably removed from the loop.
Clearly, the better and more stable scheme is to have everything within the feedback loop if possible. That is, to have the position encoder, whether it is differential or absolute, connected directly to the OTA shaft.
So in summary, one finds that the pointing accuracy achievable depends mainly on the encoder used and the directness of the connection between the encoder and the actual OTA position. Issues of what to do with the signals once they are in electrical form are relatively easy and can be done to almost any precision desired. It appears that amateur systems, with an affordable price tag, can be made to point with an accuracy of a few arc minutes. These are adequate for most amateur uses.
There are other differential control system limitations. Since the final position of the telescope is determined by a differential move from the current location, the current location error will be reflected in the final location error. When slewing by the differential method between regions of the sky that are many degrees apart, this error plus the basic errors in the mechanical parts of the mount will usually cause disappointing goto results. One way to alleviate this problem is to use what is sometimes called precision pointing. This is a misnomer since using the technique does not change the system to a higher precision, but only seems to. What is called for, is pointing to the general location desired and then re-synchronizing the computer and mechanical system for that portion of the sky, This is done by locating and re-centering an object in the viewfinder and synchronizing. This basically means that the current reference object, which has been made accurate by the viewer, is near the desired objects. Thus the differential moves are small, the mechanical contortions are reduced and the accuracy of the pointing improved for that region of the sky. This is a perfectly legitimate way to proceed.
A computer controlled version of this technique is manifest in the fine T-point computer program provided by Bisque. This program essentially maps the locations to which your telescope points when moved over the entire sky to the actual celestial sphere. The computer remembers this mapping function and applies it to the position request being made. It then points the telescope to the actual location of the object by correcting the mechanical errors in the telescope mount. This is a very clever technique which works well for a permanently mounted telescope. The telescope has to be stable in its mechanical behavior of course since this is an open loop correction which has gone through a training session. If the telescope is mechanically very differently loaded or re-balanced or otherwise changed mechanically, The program might have to be re-trained as well. A number of different configurations can be stored and recalled as necessary.
Now for imaging none of the above pointing schemes are adequate. No telescope will track an object for more than a few minutes to an accuracy of a couple of arc seconds. (except by total accident and luck) For imaging, arc second or even sub arc second pointing accuracy are useful and sometimes even necessary. Such tracking accuracy, called guiding, is either done manually through an auxiliary telescope or with an off axis guider or it is done with a photodetector or imager. Usually an auxiliary imager is used as a guider. This sort of setup is the ultimate closed loop feedback system. In this case the sensor is actually receiving the image of the object, usually a star, and holding it in place on the image plane by feeding a corrective signal to the telescope drive. The telescope OTA is essentially locked to the motion of the celestial sphere.
To make such a system work, the system has to be stable, linear, single valued and without either dead zone or hysteresis. Now that is a mouthful. But these terms refer directly to familiar terms like solid mount, strong drives that move the telescope when told to do so, freedom from stiction and back lash. A fine mount with a good basic control system can be made to work with the feedback signal from an imager very nicely. The final problems found are usually with noise caused by mechanical defects in the telescope mount, jiggling of the mount or ultimately jiggling of the atmosphere. Any of these effects can cause the feedback system, which requires very high loop gain, to become slightly unstable. There are usually adjustments in the software that provide additional stabilizing factors to control such marginal behavior. Elements like selecting the exposure time, the star brightness and more obscure elements like aggressiveness, lash, gain and so forth are used to gain optimal guiding. These may vary greatly from system to system.
Finally, a comment about temperature control of CCD imagers may be in order. Thermal changes in the interior of the imager and at the chip can with sensitive temperature detectors be easily held to a fraction of a degree C. (Typically 0.2 C) The main requirement is that the response of the TEC be fast compared to the thermal time constants of the internal environment. It should be true, if the design is good, that holding the temperature accurately is not a problem. It is important that the cooling system have adequate cooling capability to quickly overcome any sudden change is chip temperature. Thus the cooler should probably not be run over 90% capacity under normal, relatively stable operating conditions. The thermal control system is a full fledged closed loop feedback control system. The accuracy is largely determined by the ability to measure the chip temperature accurately. This would best be done by having a temperature sensing junction built into the chip or at least mounted directly on the cold finger near the chip. Most temperature control systems in modern CCD imagers are excellent both in terms of accuracy and stability.
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