[Martin Taylor 2018.02.18,15.10]
But he didn't quote you, did he? I requote, with particular
emphases:
Yes, that is what I wrote, as quoted above.
The energy claims are indeed true, but I think irrelevant.
Equilibrium occurs when the restorative force (or more generally,
influence) is equal to the disturbing force, with no reference to
energy, since at every point in the movement from the
pre-disturbance equilibrium to the with-disturbance equilibrium, the
energy supplied by the disturbing influence is available for
restoration of the original state, allowing for the losses you
mention.
Why would you think there might be something wrong with it?
The truth of this is less evident. If you do an asymptotic analysis
of a control system with a reference value of zero, using the usual
symbols s_sensory input, p = perception, r=reference, e=error,
o=output, g = gain and d=disturbance you get:
p = s = o+d
  = ge + d
  = g(r-p) + d
p(1+g) = gr+d
p = (gr+d)/(1+g).
Set r = 0
p = d/(1+g)
p is proportional to d for all values of g.
Now, for the equilibrium system, asymptotically p = f(d). The
function f(.) depends on the physical structure. If the structure is
an ideal spring that obeys Hooke’s Law, then p is proportional to d,
and an appropriate choice of spring constant can produce
asymptotically the same result as the control system, no matter what
the value of g. Maybe the same is true of the leaky bucket, but I think some
manipulation of the definitions of disturbance and perception might
be required to make it true of the bowl, because the shape of the
bowl determines the vertical and horizontal components of the effect
of gravity as a function of height above the bowl bottom. If you
define the disturbing force to be horizontal, then it takes a very
specific bowl shape to make the asymptotic height proportional to d
(and what might “p” represent if not the height?). If you define
disturbance as force parallel to the bowl side and the force exceed
that of gravity (i.e. the weight of the ball), then the perceptual
value (the height of the ball) can go to infinity. The same is true
if d is a vertical force, except then either the ball doesn’t move
or it shoots up to infinity.
So sometimes there’s a mathematical identity between the asymptotic
results of control and of the operation of an equilibrium system,
sometimes there isn’t. But I think your point was more that there
could be mathematical identity between an equilibrium system and a
control system, rather than that they are always mathematically
equivalent (which you can indeed make happen by a careful choice to
f(.) and corresponding redefinition of d and p). It is less easy to
say that the dynamics of the two types of system are likely to
produce indistinguishable results, though again it is possible. All of this is rather beside the point, which has very little to do
with dynamics. A single control loop can be looked at in many ways,
especially if you ignore energy considerations. You can look at the
pure S-R nature of the internal processing, you can look at the
behavioural illusion that shows how the S-R processes must conform
to the nature of the environmental feedback path, you can look at
the emergent “control” property of the entire loop, you can compare
the output versus the perceptual sides of the loop, you can search
for the controlled variable. It is up to you. The point of PCT is that we do NOT much worry about single loops. As
soon as you get into multi-level control, everything changes. No
longer is a loop’s internal process identical to an S-R process.
Within a lower-level loop the variable reference value ensures that
control requires different outputs to achieve similar results. Apart
from that, multi-level control allows for “the same results by
different means”, which is very different from S-R.
Martin
···
On 2018/02/18 1:14 PM, Bruce Abbott
wrote:
[From BruceAbbott (2018.02.18.1315 EST)]
Â
[Martin Taylor 2018.02.17.23.29]
[RickMarken 2018-02-17_18:03:26]
Â
 BruceAbbott (2018.02.17.1750 EST)–
...[RM] A negative feedback system (N system) is a
control system (see Powers, 1978). So if
equilibrium systems are N systems they are
control systems. But you say they are not
control systems because they don’t get their
disturbance resisting energy from an outside
source but, rather, from the disturbance itself
(per Richard’s criterion). But “disturbance
resistance” implies that there is a variable
being controlled.
Why? Is the push of a ball up the side of a bowl not resistedby gravity?
Soit sounds like you are saying that an
equilibrium system controls (in the sense that
is acts to resist disturbance to a controlled
variable) but it is not a control system because
it gets all its energy for this disturbance
resistance from the disturbance itself, which is
not enough energy to resist the disturbance.
That last part "which is not enough energy to resist thedisturbance" has absolutely nothing to do with anything. You
brought it up out of your imagination, entire and complete.
The preceding part is also wrong: "it gets all its energy for
this disturbance resistance from the disturbance itself. Not
correct. The energy used by the disturbance in an equilibrium
system is stored as potential energy, which may be available
to restore the system to its initial state when the
disturbance goes to zero. It isn’t used in any way to “resist”
the disturbance. There is no such thing as “energy for
disturbance resistance” in this situation, in contrast to the
control situation in which there is.
Â
Rick wasjust quoting me about the restoring force in an equilibrium
system coming from the disturbance itself.Â
So it sounds like you are saying that anequilibrium system controls (in the sense that is acts to resist
disturbance to a controlled variable) but it is not a control
system because it gets all its energy
for this disturbance resistance from the disturbance itself, which
is not enough energy to resist the disturbance.
If you pushthe ball up the side of the bowl, thereby disturbing its
position relative to the bottom of the bowl, the energy you
expend is stored in the potential energy of the lifted
ball. When you remove the disturbance, this potential
energy gets converted to kinetic energy as gravity pulls the
ball back toward the bottom. This energy has “come from the
disturbance itselfâ€? rather than from some other source.Â
This restorative energy cannot exceed the energy that was
expended to lift the ball and in the absence of frictional
or other losses would exactly equal it.
Â
In thisexample it is the force of gravity, acting on the mass of
the ball, that supplies the resistance to the disturbing
force. Similarly, the energy expended to compress a spring
is stored in the spring. The spring resists being
compressed; once the compressing force is removed the force
stored in the compressed spring acts to restore the spring
to its former uncompressed state.
Â
The classic“leaky bucket� provides another example of an equilibrium
system. As the bucket fills, the water level in the bucket
rises, which increases the pressure exerted by the water on
the bottom of the bucket. This pressure forces water out
the hole in the bottom, and does so at an increasing rate as
the pressure increases. Eventually the rate at which the
water squirts out the bottom equals the rate at which the
water is being added, and the water-level stabilizes at that
equilibrium value. If increasing the flow of water into the
bucket is viewed as a disturbance to the water’s level, this
system resists that disturbance by increasing the rate at
which the water flows out of the hole as the water level in
the bucket rises further. If we then reduce the inflow back
to its previous value, the water level will return to its
pre-disturbance value. The extra pressure exerted by the
higher water level came from the disturbance (gravity acting
on the additional mass of water) and now acts to reduce the
water level until it reaches its former equilibrium value.
Â
If there’ssomething wrong with this analysis I’d like to hear about.
ÂMathematically, this equates to a negative feedback system
with a gain of no more than 1.0.
Â
Bruce