Control Systems and Equilibrium Systems

[From Bruce Abbott (2013.12.27.1050 EST)]

Recently I distinguished between control systems and equilibrium systems. In this post I thought I’d provide an example in which both are involved.

Like many of us, I have a problem keeping my weight down where I want it to be. Over time I gradually put on body fat until my jeans don’t fit and I’m faced with either replacing my wardrobe with larger sizes or getting serious about losing the excess weight. This happens even though I know that being overweight is uncomfortable, unsightly, and a threat to my overall health. I don’t WANT to be overweight. So why do I keep gaining the weight back?

We know that the body includes physiological control systems that initiate feeding from time to time. The food consumed is digested and nutrients enter the blood stream. Some of these are used by the body for repairs or growth, some to fuel metabolism; any excess is stored away as carbohydrates or fat. As the nutrients are depleted in the blood stream, these stores are drawn upon to supply the necessary fuel and materials until the next feeding.

The level of body fat that gets stored away over time depends directly on the rate of caloric intake and inversely on the rate at which those calories are “burned” through metabolic processes. Although we consume thousands of calories in a year, body weight (a measure of stored fat) typically changes only a couple of pounds over that period, this despite variations in the caloric content of our food, amount of exercise, ambient temperature, and so on. How is this stability achieved? Under what conditions is this stability overcome and we gain a significant amount of weight?

The answer, in so far as we know it, is rather complicated. For starters, there is a control system that works over a relatively short time-span (a matter of hours). As glucose (blood sugar) levels fall due to metabolism and the completion of digestion, the liver begins to convert stored carbohydrate (glycogen) into blood sugar and releases it into the bloodstream. This activity also activates sensors that inform the brain of the liver’s activity. We begin to feel hungry (a perception). Our reference for hunger usually is zero; the error drives output that results in a complex set of behaviors that normally result in feeding. Feeding brings nutrient levels up, blood sugar rises and the liver reverses its conversion process, turning excess blood sugar into glycogen and storing it away. Additional nutrients not immediately consumed are stored as fat in the fat cells.

That’s a simplified picture of the process – other factors can also lead to a perception of hunger, and we may eat for reasons other than hunger – but this picture is I think adequate for our purpose here.

There appears to be another control system that works on a longer time-scale and involves the level of stored fat. Fat cells release a hormone whose concentration is proportional to the level of stored fat. Receptors in the brain perceive this hormonal signal. This signal also contributes to the perception of hunger, but how it interacts with the short-term, meal-initiating hunger control system is a detail I’m not clear on. It might turn the gain up on the hunger-control system, so that smaller levels of hunger would lead to more frequent meals and/or larger consumption during meals. Or it might amplify the hunger perception itself. (There are other possibilities as well.) We do know that in some individuals a genetic error renders the hormone’s receptors nonfunctional; such individuals report being in a continuous state of hunger and have to be prevented from eating too much if they are not to become morbidly obese. But for most of us the receptors work as they should.

This fat-regulation system seems to have the ability to affect stored fat levels in two ways: by altering how much we consume and by changing our metabolic rate. Metabolic rate increases when body weight gain increases by around 10%, thus tending to burn off more of the calories we consume. Similarly, metabolic rate decreases when body weight falls by about 10%, thus helping to conserve our stores of energy.

With these control systems at work, why do so many of us end up carrying around more body fat than we would like? According to “set-point” theory, the body’s fat-regulation system has a set-point (reference level) that differs from person to person. Some of us have a higher set-point than others. One piece of evidence for this view comes from a study involving women who normally were quite obese but who had succeeded in losing the excess weight through diet and exercise. These women were haunted by thoughts of food and had to continually fight the impulse to give in and indulge. But more tellingly, these women no longer had their monthly periods. Cessation of the feminine cycle is an adaptive response of the female body to starvation. Although now weighing about normal for women their age, these women’s systems were acting as though the women were starving, or in other words, at a level of fat storage well below set-point. As for those individuals with defective receptors, their set-points may be at normal values, but their systems perceive that the body-fat level is zero and constantly act in an attempt to bring it up.

Our regulatory systems appear to respond strongly to deviations that fall below the reference level. We don’t appear to respond as strongly to deviations in the other direction. When overweight, we may not feel as hungry, on average, as we might otherwise feel, which normally would lead to less calorie intake and weight-loss. But we eat for reasons other than hunger. We eat because we like the taste. We eat to combat boredom. We eat when we feel anxious. (Weight gain is a side-effect of our attempts to control these other perceptions.) We eat out of habit, because it’s time to eat. And as we gain weight, it becomes more difficult and less pleasurable to exercise, so we do less of it.

With more calories coming in and fewer being burned off, more and more fat gets stored away. Here’s where equilibrium comes into play: Our weight continues to rise until the extra calories burned in hauling around all that extra weight equals the number of excess calories being consumed.

Several years ago there was a debate among researchers in this field about whether body weight reflects a set-point (reference level) or a “settling point,” by which they meant settling to an equilibrium value. It was an ill-framed debate, because, as I hope I’ve made clear, we don’t have to choose between these two explanations. Both are involved in the determination of body weight (or more accurately, level of stored body fat).

Bruce

[From Rick Marken (2013.12.28.1130)]

Bruce Abbott (2013.12.27.1050 EST)--

BA: Recently I distinguished between control systems and equilibrium systems.
In this post I thought I�d provide an example in which both are involved.

RM: Very nice post, Bruce. But I'm not convinced that both control and
equilibrium are involved in weight control. What you call equilibrium
seems to me to be a case of a side effect of control changing the
feedback connection between output and controlled variable. You say:

BA: With more calories coming in and fewer being burned off, more and more fat
gets stored away. Here�s where equilibrium comes into play: Our weight
continues to rise until the extra calories burned in hauling around all that
extra weight equals the number of excess calories being consumed.

RM: It seems to me that the build up of fat is a side effect of
controlling for calories. Assuming that calories are the controlled
variable, then the environmental components of the control loop can be
written as:

C = k.f* E - k.d * M

where C is calories, E is eating, M is metabolism, k.f is the feedback
function and k.d is the disturbance function. So in this case, eating
is done to control calories at some reference level, and eating is
done must offset the loss of calories due to metabolism. In more
generic terms, C is the controlled quantity, E is the system's output
and M is the disturbance.

What you are saying above in terms of an "equilibrium system" is that
if calories are controlled at an excess level -- greater than 0 --
then the unburned calories are stored as fat, increasing a person's
weight and thus the rate of metabolism(he rate at which calories are
burned). This is equivalent to saying that weight (Kg) has an effect
on the disturbance function, k.d: k.d = a* Kg. Increases in Kg lead to
increases in k.d. Thus, the effect of metabolism on calories increases
as weight increases. Of course, it's also the case that weight is a
function of calories: Kg = b*C. So once C is being controlled at some
fixed level (C becomes nearly constant) then weight remains nearly
constant, as does k.d.

Note that an "equilibrium system" is not involved in this control
system analysis of "weight control". The only aspect of the
"equilibrium" analysis that is included in this analysis is the
relationship between weight and the effects of metabolism: k.d = a *
Kg. It's important to include such biophysical relationships in any
model of control in living control systems; but there is no need to
invoke (or include) a special property of these systems called
"equilibrium" in this model.

BA: Several years ago there was a debate among researchers in this field
about whether body weight reflects a set-point (reference level) or a �settling
point,� by which they meant settling to an equilibrium value. It was an
ill-framed debate, because, as I hope I�ve made clear, we don�t have to
choose between these two explanations. Both are involved in the
determination of body weight (or more accurately, level of stored body fat).

RM: This is exactly the debate occurring in the area of motor control.
Latash et al (as well as people like Feldman, Kelso, Turvey, and many
other "big names" in the area that I can't recall right now) are in
the "settling point" (equilibrium) school; PCT is in the "control"
school.

I think the debate could not be clearer and we have to choose between
these two explanations of purposive behavior. The debate should be
easily resolved using the TCV. I believe it hasn't been resolved (and
the laurels triumphantly carried off by the control school) because
equilibrium theory provides what seems like a non-teleological
explanation of purposive behavior. And when people are controlling for
a point of view (that there is no such thing as purpose), disturbances
(such as the fact that control is occuring) are easily brushed aside.

So I think the best thing for us (PCT people) to do is mind our own
business. That is, just do the research and demonstrations of how
control theory (PCT) can account for purposeful behavior, ignore (as
best as we can) the often incredibly arcane noise coming from the
equilibrium crowd and train students in the application of control
theory to the undertsanding of living systems (ie. teach PCT)

Best

Rick

···

--
Richard S. Marken PhD
www.mindreadings.com

The only thing that will redeem mankind is cooperation.
                                                   -- Bertrand Russell

[Martin Taylor 2013.12.28.14.56]

[From Rick Marken (2013.12.28.1130)]

Bruce Abbott (2013.12.27.1050 EST)--
BA: Recently I distinguished between control systems and equilibrium systems.
In this post I thought I�d provide an example in which both are involved.

...[much omitted]...

BA: Several years ago there was a debate among researchers in this field
about whether body weight reflects a set-point (reference level) or a �settling
point,� by which they meant settling to an equilibrium value. It was an
ill-framed debate, because, as I hope I�ve made clear, we don�t have to
choose between these two explanations. Both are involved in the
determination of body weight (or more accurately, level of stored body fat).

RM: This is exactly the debate occurring in the area of motor control.
Latash et al (as well as people like Feldman, Kelso, Turvey, and many
other "big names" in the area that I can't recall right now) are in
the "settling point" (equilibrium) school; PCT is in the "control"
school.

Apart from the point made much earlier by Bruce, that the main difference between control and "ball-in-a-bowl" systems is the source of the restorative energy, there's zero difference between "settling point" and "control". I think you are thinking of something else behind these words -- the mechanism that adjusts the settling point and that produces the equilibrium. The action of control is to produce an equilibrium between the influences of the output and the disturbance on the environmental variable that corresponds to the perceptual signal. The effect of the reference is to adjust the "settling point" where this equilibrium occurs. That's exactly what I understand Latash et al., to be saying is the mechanism behind their observations. On that point I have no quarrel with their paper.

To keep contrasting these words is as counterproductive to scientific argument as was the earlier continued opposition of "stability" and "control". It is simple obfuscation, and rather annoying when the overt point of CSGnet is to advance understanding of PCT. To contrast mechanisms where mechanisms have been specified, on the other hand, is valuable. And in a situation where PCT does explain published observations with a specific mechanism, it is valuable to point out that no mechanism has been offered if such is the case.

Martin

Your arguments really are about mechanisms

[From Bruce Abbott (2013.12.28.1930 EST)]

Martin Taylor 2013.12.28.14.56 --

Rick Marken (2013.12.28.1130)

Bruce Abbott (2013.12.27.1050 EST)
BA: Recently I distinguished between control systems and equilibrium

systems.

In this post I thought I'd provide an example in which both are involved.

...[much omitted]...

BA: Several years ago there was a debate among researchers in this
field about whether body weight reflects a set-point (reference
level) or a "settling point," by which they meant settling to an
equilibrium value. It was an ill-framed debate, because, as I hope
I've made clear, we don't have to choose between these two
explanations. Both are involved in the determination of body weight (or

more accurately, level of stored body fat).

RM: This is exactly the debate occurring in the area of motor control.
Latash et al (as well as people like Feldman, Kelso, Turvey, and many
other "big names" in the area that I can't recall right now) are in
the "settling point" (equilibrium) school; PCT is in the "control"
school.

MT: Apart from the point made much earlier by Bruce, that the main
difference between control and "ball-in-a-bowl" systems is the source of the
restorative energy, there's zero difference between "settling point" and
"control". I think you are thinking of something else behind these words --
the mechanism that adjusts the settling point and that produces the
equilibrium. The action of control is to produce an equilibrium between the
influences of the output and the disturbance on the environmental variable
that corresponds to the perceptual signal. The effect of the reference is to
adjust the "settling point" where this equilibrium occurs. That's exactly
what I understand Latash et al., to be saying is the mechanism behind their
observations. On that point I have no quarrel with their paper.

My example pertaining to hunger and feeding borrowed the term "settling
point" from the literature on feeding, where it refers to the values at
which an equilibrium system such as the ball-in-a-bowl settles, in contrast
to a control system, which has a "set point" that the system actively
strives to match its perceptions to. If we think of stored body fat as water
in a leaky bucket, consuming food (beyond the immediate metabolic need)
leads to storage of the excess as fat in the "fat reservoir" provided by fat
cells (equivalent to the bucket). Metabolism draws on these reserves,
metabolism playing the role of the hole in the bucket. As the level of
stored fat rises, metabolic rate increases (due to the extra force needed to
carry the heavier body around and the larger muscles that develop to support
that activity), just as the rising water level in the bucket increases the
pressure at the bottom of the bucket, forcing water through the hole at a
faster rate. The level of stored fat (or the level of the water in the
bucket) rises until the caloric loss due to metabolism equals the rate of
caloric input through feeding.

The debate was whether body fat level is actively controlled ("set point")
or merely settles to passive equilibrium value ("settling point").

This usage is unfortunate in the present context because it suggests that
only passive equilibrium systems exhibit a settling point.

In fact, as you explain, the term "settling point" as more commonly used is
simply the stable value to which a system settles under constant conditions,
and can be observed in any stable dynamic system, whether passive (the leaky
bucket and ball-in-bowl examples) or active (control systems). Control
systems exhibit that kind of settling point when the disturbance and
reference inputs to the system are constant.

Bruce

[From Rick Marken (2013.12.28.1640)]

If nothing else this dialog should put to rest any notion that I have
any claim to the title of "Crown Prince" of PCT. I can hardly be the
Crown PRince if everyone disagrees with me. And clearly everyone does
disagree with me. Oh, except me;-)

Martin Taylor (2013.12.28.14.56) --

MT: Apart from the point made much earlier by Bruce, that the main difference
between control and "ball-in-a-bowl" systems is the source of the
restorative energy, there's zero difference between "settling point" and
"control".

RM: The fact that control and "ball in a bowl" (equilibrium) behaviors
have different explanations means that they are different phenomena.
Latash et al treat purposive behavior (like moving a limb) as an
equilibrium phenomenon and give an equilibrium explanation for it. I
treat purposive behavior as a control phenomenon and give a control
theory (PCT) explanation for it.

>MT: To keep contrasting these words is as counterproductive to scientific
argument as was the earlier continued opposition of "stability" and
"control".

RM: I am contrasting the phenomena, not the words; equilibrium
phenomena (like the ball in the bowl), which I was also referring to
using the word "stability" are not the same as control phenomena.

MT: It is simple obfuscation, and rather annoying when the overt
point of CSGnet is to advance understanding of PCT.

RM: From my perspective I find the failure to distinguish behavior
like that of the ball in the bowl (call it "equilibrium" or
"stability" or "attractor" or whatever you like) from control behavior
to be extremely annoying because, for me, the first principle of PCT
is that behavior (the behavior of living systems) IS control. The idea
that behavior is the control of _perception_ comes from properly
applying control theory as an explanation of the behavior called
"control".

MT: To contrast mechanisms where mechanisms have been specified, on the other hand,
is valuable.

RM: That's true when the mechanisms are alternative models of the
_same_ phenomenon. But in this case we are dealing with two different
kinds of phenomena that are explained by very different kinds of
mechanism. The mechanism that explains the behavior of the ball in the
bowl is (as I noted before) the open-loop causal model of physics
(Newton's laws); the mechanism that explains the behavior of a
person's finger tracking another person's finger is the closed-loop
casual model of control theory (Powers' laws).

MT: And in a situation where PCT does explain published observations with a specific
mechanism, it is valuable to point out that no mechanism has been offered if
such is the case.

RM: PCT doesn't provide the mechanism that explains the ball in the
bowl because the ball in the bowl is not a control phenomenon; it's
already explained by Newtonian physics. PCT does provide an
explanation of purposive limb movement because limb movement is a
control phenomenon. Latash et al are making things confusing by
referring to limb movement as an equilibrium phenomenon. They are
getting away with it because they are observing limb movement in a
situation in which these movements look like an equilibrium phenomena.
So they are deceiving themselves into thinking that they are not
observing control and then concluding that control theory can't
explain what they are observing. This seems like pretty bad
obfuscating to me.

You say (or imply) that Latash et al have made observations that PCT
can't explain. Please tell me what they are. I believe they must be
the observations reported in Figure 1. I actually am not sure what
that Figure shows. So if you can explain what the Figure shows I'll
see if I can come up with a PCT explanation as well as a way to
determine who's explanation is better.

Best regards

Rick

···

--
Richard S. Marken PhD
www.mindreadings.com

The only thing that will redeem mankind is cooperation.
                                                   -- Bertrand Russell

[From Bruce Abbott (2013.12.28.2015 EST)]

Rick Marken (2013.12.28.1130) --

Bruce Abbott (2013.12.27.1050 EST)

BA: Recently I distinguished between control systems and equilibrium

systems.

In this post I thought I'd provide an example in which both are involved.

RM: Very nice post, Bruce. But I'm not convinced that both control and
equilibrium are involved in weight control. What you call equilibrium seems
to me to be a case of a side effect of control changing the feedback
connection between output and controlled variable. You say:

BA: With more calories coming in and fewer being burned off, more and
more fat gets stored away. Here's where equilibrium comes into play:
Our weight continues to rise until the extra calories burned in
hauling around all that extra weight equals the number of excess calories

being consumed.

RM: It seems to me that the build up of fat is a side effect of controlling
for calories. Assuming that calories are the controlled variable, then the
environmental components of the control loop can be written as:

C = k.f* E - k.d * M

where C is calories, E is eating, M is metabolism, k.f is the feedback
function and k.d is the disturbance function. So in this case, eating is
done to control calories at some reference level, and eating is done must
offset the loss of calories due to metabolism. In more generic terms, C is
the controlled quantity, E is the system's output and M is the disturbance.

RM: What you are saying above in terms of an "equilibrium system" is that if
calories are controlled at an excess level -- greater than 0 -- then the
unburned calories are stored as fat, increasing a person's weight and thus
the rate of metabolism(he rate at which calories are burned). This is
equivalent to saying that weight (Kg) has an effect on the disturbance
function, k.d: k.d = a* Kg. Increases in Kg lead to increases in k.d. Thus,
the effect of metabolism on calories increases as weight increases. Of
course, it's also the case that weight is a function of calories: Kg = b*C.
So once C is being controlled at some fixed level (C becomes nearly
constant) then weight remains nearly constant, as does k.d.

I didn't suggest that calories are controlled. But if I had, I wouldn't
posit that a reference level greater than zero is an "excess level." But
let's assume that calories are being taken in at a rate faster than they are
being consumed. That means that the reference level for calorie intake in
your system is higher than what the body needs to support growth, repair,
and metabolism. Can you think of a reason why this would be the case?

There is some evidence that feeding is modulated by the calorie content of
the food -- at least in lab rats. If you provide a lower calorie diet, they
increase the amount the rats consume. But whether the rat possesses sensors
for calorie content hasn't been established, so there may be some other
factor, correlated with calorie content, that is being sensed. Or the
observed effect of reduced calories in the food may go back to reduced
stores of glycogen in the liver or loss of body fat.

RM: Note that an "equilibrium system" is not involved in this control system
analysis of "weight control". The only aspect of the "equilibrium" analysis
that is included in this analysis is the relationship between weight and the
effects of metabolism: k.d = a * Kg. It's important to include such
biophysical relationships in any model of control in living control systems;
but there is no need to invoke (or include) a special property of these
systems called "equilibrium" in this model.

You appear to have missed the part where I stated that there appears to be a
fat-control system that regulates fat level around a set point, which
differs from person to person. Folks with a high set-point would consume
more calories than they expend until the fat levels approximate the
reference value. After that, one might presume that any fat gain beyond
that point would lead to reduced intake. I think you will agree that this
is a control system analysis.

Those of us who tend to gain more weight than we would like may simply have
a higher reference level for body fat, but observation of my own behavior
suggests something different. I often eat even though I'm not hungry
(suggesting that there's no error in the relevant control systems). I may
be full, but that pie and ice cream looks mighty good. I'm bored, so I'm
munching on potato chips to provide some pleasant sensory input. When I do
that, my weight gradually increases.

This suggests that my weight gain may be more of a side-effect of using
pleasurable foods to control other variables. It pushes my weight (fat
content) well above its reference level. That weight will stabilize at the
equilibrium value between calorie intake and calorie expenditure, just as
water in that leaky bucket stabilizes when water flow in matches water flow
out. My fat control system has already dialed hunger down to zero (let's
assume), so there's not much more it can do to regain control over fat
levels. So there's your passive equilibrium system at work.

Bruce

[From Bruce Abbott (2013.12.29.0845 EST)]

Rick Marken (2013.12.28.1640) --

RM: If nothing else this dialog should put to rest any notion that I have
any claim to the title of "Crown Prince" of PCT. I can hardly be the Crown
Prince if everyone disagrees with me. And clearly everyone does disagree
with me. Oh, except me;-)

from the Crown Prince, much is expected. With great power comes great
responsibility! ;->

Bruce