From: POWERS_W%FLC@VAXF.COLORADO.EDU (William T. Powers)
Newsgroups: bit.listserv.csg-l
Subject: Loose control systems
Date: 5 Nov 92 20:59:58 GMT
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
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 [From Bill Powers (921105.1300)]

 Jeff Hunter (921104)--

 >Your contention is that "proper" control systems have loop gains of
 >at least -5 (preferably -10 to -100). I believe that this rule-of-
 >thumb of yours may be a result of the specs of the systems you
 >designed. I also believe that this is too constrained a definition
 >to describe the majority of control systems in living organisms.

 No, it is a result of the measured parameters of all the control
 systems we have investigated experimentally. Most such systems have
 gains well over -30 and some have measured -200. In visual control
 tasks it is in the thousands -- these control systems seem to use
 integrating outputs, with an effective steady-state gain too high to
 measure accurately. Even the E. coli system has a high loop gain,
 although there is a very large noise component. When a disturbance is
 applied to an E. coli model, its average value is cancelled
 perfectly, implying a very high loop gain. Of course it has a low
 bandwidth; E. coli can't resist disturbances that vary too rapidly.

 >A "good" control system keeps its error within a specified distance
 >of zero for a specified percentage of the time for a given class of
 >disturbances.

 You're free to set your own criteria, of course, but in my book this
 would be a control system that works only intermittently and has no
 control at all within the "specified distance." In all the examples
 of ordinary behavior that I know about, control is much better than
 my relaxed rule of thumb. Driving a car, balancing a checkbook,
 walking or running, adjusting the contrast on a TV set, baking a
 cake, typing letters, looking at things, singing, riding a bicycle,
 drawing a picture, solving an equation, measuring a length, shopping
 for groceries --- the list is really endless. In all these behaviors,
 perceptions are controlled so closely that their deviations from the
 intended states are at the lower limits of detection, despite
 disturbances of all sorts.

 >The control systems you describe generally have a small
 >tolerence for error, quick response time, and make few assumptions
 >about the pattern of disturbances (although they implicitly assume
 >an upper limiton their magnitude).

 "Small tolerance" for error" is a strange way of putting it. A
 control system maintains the error as low as it can, given its loop
 gain. The response time is whatever it is -- some systems are slow
 and some are fast. Control systems make no assumptions at all --
 there is no equipment in them for doing that, and anyway they do not
 sense "the pattern of disturbances". Their action is based strictly
 on perceiving the controlled variable itself. They work no
 differently when the disturbance is caused by invisible events, or
 when multiple disturbing effects are present, randomly varying, at
 the same time. If a disturbance that is too large appears, control
 will simply fail: the output will become as large as it can, and if a
 larger output is needed, control is lost.
 >For example the machine you described to etch diffraction
 >gratings (am I remebering this correctly?) must be accurate to
 >within .1 microns, must react in fractions of a second, and
 >probably assumed that earthquakes were rare.

 The sensing of the position of the ruling diamond was accurate to
 about 0.01 wavelength of laser light, or about 0.006 microns. The
 machine itself was accurate to about one wavelength, or 0.6 microns.
 A normal disturbance was corrected in about 1/4 second. If an
 earthquake had happened, the system would have been able to resist
 the slow waves but not the fastest ones.

 >If the squirrel cannot make assumptions about the pattern
 >of summer and winter days then it must be able to survive
 >indefinitely in winter. I'm not sure what such a squirrel would
 >look like, but it would be big to keep surface heat losses down.
 >(Maybe a mammoth?)

 Saying that the squirrel "makes assumptions" about such things is an
 anthropomorphism. If you want to understand how the squirrel works,
 you have to propose a model of the control systems involved. For
 example, in warm weather, the squirrel's metabolism is turned down
 and it needs less food; therefore it gathers less. The reference
 level for amount of food eaten varies, presumably because it is the
 output of a more global control system that monitors a number of
 physiological variables, keeping them near reference levels. When the
 weather begins getting colder, the squirrel's reference-metabolism is
 increased, and it gathers more and more food; the control systems
 actually set the reference level higher than immediately necessary so
 food accumulates. When the weather is cold enough, the attempt to
 maintain body weight and other functions at their reference levels
 begins to fail, and other control systems come into play, preserving
 the life of the organism by reducing the metabolism to reduce the
 rate at which reserves are used. This leads to the state of
 hibernation.

 There are many control systems involved in the overall behavior of a
 squirrel. They are probably all "good" control systems, in my terms.
 Out of their operation come the superficially-observable actions that
 we classify as foraging, food-storing, putting on fat, hibernating,
 and so forth. What we see are only symptoms of the actual control
 processes and the interactions among control systems.

 >In reality species (through evolution) have a long history of the
 >climate. Squirrels "know" that they can expect the winter to end
 >(and have a fair estimate of how long winters are).

 I doubt very much whether any such knowledge resides in a squirrel.
 Squirrels have evolved to the point where the actions of their
 control systems are sufficient for most squirrels to survive most
 winters. There is no need to say that the control systems themselves
 know anything about winter and summer: a season is much too complex a
 concept to be perceived by a squirrel. The squirrel can perceive
 temperature and the state of its own physiology. I think that giving
 it any more sophisticated abilities is unnecessary and fanciful.
 >Many control systems in living organisms make similar
 >assumptions about the pattern of disturbances they will encounter.

 This is too metaphorical for me. Control systems don't make
 assumptions about disturbances. They control variables. Where do you
 put the assumption-maker in a control system diagram?
 -----------------------------------------------------------------
 RE: your program.

 >The "gain" of the controlled system is (at most) -0.5, and
 >indeed the error is often non-zero. However it keeps the
 >environment within 8 units of zero 93% of the time.

 That's a meaningless way of evaluating the control system. With a
 gain of -0.5, the effect of a disturbance on the controlled variable
 would be reduced to 1/(1 + 0.5) or 2/3 of the value it would have had
 with no control at all. So 2/3 of the effect of the disturbance goes
 uncorrected. If that's good enough for some purpose, then there's not
 much point in using any control system at all. You'd only gain 33%
 over a system that just took the effects and suffered them. I know
 you will respond, "But maybe that 33% makes all the difference!" If
 so, OK. But you still don't have a system with much ability to
 control what is happening to it. It's just lucky that control this
 poor suffices. That is not true for most of the variables that
 organisms have to control.

 I haven't run your program yet, but have no reason to doubt your
 description of its behavior.

 I think you badly underestimate the quality and number of the control
 systems that are actually involved in real behavior. Most variables
 that are of importance to organisms are maintained very accurately at
 their reference levels under all normal conditions. For any organism
 there are conditions that strain the control processes and even
 overwhelm them; when that is the case the organism just suffers the
 consequences. It can do no better than its best. When things get bad
 enough it dies.

 You are imagining an environment in which there are only slight
 fluctuations in conditions, so that only a slight capacity for
 control is enough to assure survival, or where the system is pushed
 to its limits, and a small increase in control capacity will have
 critical effects. Such situations might exist. But by focusing on
 them, you ignore the vast array of circumstances in which control
 must be and is precise and quick. You ignore, in fact, all the major
 phenomena of behavior, which your model would be totally incapable of
 reproducing. Phenomena such as the way a squirrel climbs a tree and
 jumps from limb to limb; the way it spots food and finds its way to
 it and picks it up and carries it back to its nest; the way the
 squirrel evades a chasing cat and scolds a pestering bird; the way
 the squirrel simply stands up and walks. By looking at fringe
 phenomena and tiny effects, you are missing all the big obvious
 foreground effects that need explaining and that only control theory
 can explain.
 A loose control system controls loosely. Of course. But organisms
 don't.
 -----------------------------------------------------------------
Best,

Bill P.
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU