[Hans Blom, 960425]
(Bill Powers (960423.0950 MDT))
... if a higher system were manipulating the reference signals r21
and r22, the controlled variables could be changed through their
entire possible range -- while disturbances still can change them
only by about 0.25 units at most.
Bill, I don't understand that you don't understand. When you trivial-
ize the importance of the influence of external disturbances on the
values of the internal reference levels, you undermine the whole
concept of hierarchical control. Let me show you why.
A note on terminology. I will use "goal" rather than "reference
level" in order to reserve the word "level" for a "layer" of the
hierarchy. These two get kind of tangled...
Assume for a moment that goals are not modulated by disturbances but
that all goals at all levels of the hierarchy are fully determined
from above, by yet higher levels of the hierarchy. That would
effectively freeze the whole hierarchy into rigidity with respect to
the outside world, and that would make the control hierarchy
superfluous (except maybe as a set of connections); the situation
would be like having a lot of one-dimensional control systems (at the
lowest hierarchical level) WITHOUT ANY MUTUAL INTERACTION AT ALL.
Interaction between elementary control systems is obtained because
information also flows UP in the hierarchy, and this is done by
changing the goals at intermediate levels. Only through this
mechanism can information go up (and then down again through the
standard mechanism), so that individual one-dimensional control
systems can be coordinated into some grand action pattern. You know
this; you draw it this way in B:CP and later publications; yet now
you seem to miss its importance. But only through changing
intermediate goals can coordinated action exist in a hierarchical
controller. And isn't this logical? If the world changes its
behavior, I will want to change my interactions with it. Let's not
quarrel about HOW MUCH goals change due to disturbances; let's
recognize the PRINCIPLE that they NEED TO change, in HPCT.
Goals are much more influenceable when lower levels saturate.
That's the kind of answer that says "I was wrong, but I'm going to
find a way to be right anyway."
Bad mood, eh? I'm just trying to find out conditions where the effect
will be quite noticeable. Bear with me...
The loop gain of a tendon-force control system that makes the arm
model behave most realistically is about 200. ... So just erase
"physiological control systems have low loop gains" from your mind.
I stand corrected. While I was writing my post, I was very much
involved in updating our group's textbook on Measurements in
Respiration and Circulation, which made me take an improper overly
restricted view of physiology. I agree that in purely sensory-
neuro-muscular systems much higher gains occur than the figures I
mentioned, and maybe in other systems as well.
Since you have no idea of what is going on inside an "overwhelmed"
control system, what you say is most probably wrong.
If you can't see it, it ain't true? But we can do a simulation.
That's what they are for, isn't it?
I guess so. I made a fully static analysis, you introduced leaky
integrators. The steady state results ought to be the same.
Boy, are you reluctant to admit that your argument has been
destroyed!
Bad mood, Bill? What goal am I disturbing? Wow, can't you just say
that you don't see where I'm heading? Let's review the history of our
exchange and see if we can discover more than randomness.
Your problem statement and my analysis of it were fully static. At
least that is how I interpreted it. Then you replied with the results
of a control system having (leaky) integrators in its output path.
Which I know is standard for you. Which I didn't take into account.
Your mentioning integrators prompted a far too cryptic, and thus
misunderstood, response from me. Let me try to express myself more
clearly now. In the frequency domain, this time, rather than the time
domain.
Maybe the misunderstanding arose in the first place because I am not
used to talking about "loop gain" in a controller with an integrator
somewhere in its loop, where "loop gain" is more properly expressed
as a Bode or Nyquist diagram or transfer function rather than what I
take to be a single number. I will now, for your convenience, use
"loop gain". But remember that this loop gain is frequency dependent.
At zero and very low frequencies, the gain will be constant in the
case of a leaky integrator, but starting at some frequency (which
defines the system's open loop bandwidth) the loop gain decreases
with a rate of 20 dB per decade and thus will eventually approach
zero; this is the familiar first order filter characteristic. Thus,
even in a system with a large zero frequency loop gain, where the
internal goals deviate only slightly from their nominal values when
constant or very low frequency disturbances exist, disturbances at
higher and higher frequencies will modulate the goals more and more,
because there is no significant loop gain anymore to "protect" them
from disturbances. Thus, high frequencies will penetrate the hierar-
chy more than low frequencies; the highest frequencies will penetrate
without encountering any significant resistance at all. You can check
this in your simulation when you employ sinusoidal disturbances.
Now this cannot be true, of course, in reality. We know (or think)
that higher levels of the hierarchy are more stable (have longer time
constants and slower variations of goals) than more peripheral
levels. But then either the world must not contain high frequency
disturbances (but it seems it does) or another mechanism is required,
some mechanism which prevents high frequency signals from penetrating
into the hierarchy. A low pass (leaky integrator) filter, obviously,
or something like it. But where could it be found? Not in the input
function, because the combined 180 degrees phase shift would make the
controller into an oscillator. Any suggestions?
Or, shifting to psychology, is it indeed true that sudden changes in
the world that we live in cause lots of changes in what we want,
whereas very slow changes don't? And that when the sudden changes are
over, we go back to our previous life style (i.e. collection of goal
settings) again?
So, Bill, what seemed to be an insignificant remark to you initially
-- internal goals are modulated by the outside world -- may be a lot
more significant, both in terms of understanding of the hierarchy and
in terms of additional questions to be answered, than you thought.
Or am I wrong?
Greetings,
Hans
ยทยทยท
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Eindhoven University of Technology Eindhoven, the Netherlands
Dept. of Electrical Engineering Medical Engineering Group
email: j.a.blom@ele.tue.nl
Great man achieves harmony by maintaining differences; small man
achieves harmony by maintaining the commonality. Confucius