[Hans Blom, 960718]
(Bruce Abbott (960717.1400))
You are going a very long way around to avoid accepting my assertion that
there are constant disturbances to biological control systems, requiring
constant action to correct.
Bruce, what I object to is to say that a _control_ system must
correct constant "disturbances". Not that constant correctional
action might be required. Let's analyze the loop. We need a simple DC
analysis only.
reference ---> +
>---> gain G ---->---
perception -> - | action a
> >
+ + <---- world W --<----
^
>
----<------ gain D ---<--- disturbance d
Action a = G (r - p)
Perception p = W a + D d,
where D can be any function, depending on where d enters. D = W and
D = 1 may be considered special cases. But that doesn't matter now.
The above leads to
p = WGr - WGp + Dd
p (1 + WG) = WGr + Dd
WG D
p = ------ r + ------ d
1 + WG 1 + WG
We see that, since d is not equal to zero, the second term creates an
offset, a constant difference between perception and reference. We
can distinguish several cases:
a) WG >> D, usually meaning that G is large. If the controller's
output path contains an integrator, this is the case. Then there is
no offset. But note also that the constant "disturbance" can be
neglected, because it has no effect at all. In a more complete
analysis of this case, thus, one may consider d to have no constant
component, even though it has one. This will not introduce error.
b) Gain G is not so large that WG >> D. Note that the offset cannot
be controlled away. Thus, even in the steady state, there will be a
difference between r and p. In Bruce's "anti-gravity device", for
instance, this could mean setting r to 10 cm and finding p at 8 cm.
Not desirable.
c) We may not consider b) a problem. Just set r to 12.5 cm and you
will find p at 10 cm, where you want it. Fine. But doing so would
force us to drop any pretentions that, in our diagrams, r will stand
for something that the organism _wants_. No, it would be something
that can be manipulated, but something else (and the diagram does not
tell us what, although the formulas do) is wanted.
So these do not seem good approaches. In engineering, you see a
different approach: combat constant "disturbances" by _constant_
actions. The above diagram modifies to:
reference ---> +
----> gain G ---->-+ + -<--- constant action c
perception -> - | action a
> >
+ + <---- world W --<----
^
>
----<------ gain D ---<--- disturbance d
Action a = G (r - p) + c
Perception p = W a + D d
p = WGr - WGp + Wc + Dd
p (1 + WG) = WGr + Wc + Dd
WG W D
p = ------ r + ------ c + ------ d
1 + WG 1 + WG 1 + WG
As you see, the offset can be eliminated by choosing c = Dd/W. This
is the engineering approach. I wouldn't want to call this _control_,
although you might.
For Bruce's "anti-gravity" device, this means, for instance, that the
constant action is a steady magnetic field that lets the iron ring
float at the desired height, and to use the control system to
stabilize it in that position on which all kinds of "disturbances"
act (drafts, shocks to the device's support, etc). The obvious
advantage is that the control system needs far less power than it
would otherwise possibly be designed for. Now all it has to do is to
modulate the steady magnetic field, and that variation probably need
be not much more than a few percent.
In the "anti-gravity" device, both constant action and controlled
action use magnetic force. Such an equality of mechanisms of action
may or may not be present. Generally, it is not, because the
requirements differ: solidity versus fluidity. In our bodies, our
skeleton provides the large counterforces that keep us upright; our
musculature takes care of the (modulating) posture control.
Greetings,
Hans