# PCT and CT

**URL:** <http://discourse.iapct.org/t/pct-and-ct/8240>\
**Category:** CSG1993\
**Created:** [December 28, 1993, 5:09pm UTC](http://discourse.iapct.org/t/pct-and-ct/8240 "1993-12-28T17:09:47Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![William\_T\_Powers2](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/w/c67d28/32.png) [@William\_T\_Powers2](http://discourse.iapct.org/u/William_T_Powers2)\
**Post date:** [December 28, 1993, 5:09pm UTC](http://discourse.iapct.org/t/pct-and-ct/8240/1 "1993-12-28T17:09:47Z")

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[From Bill Powers (931228.0750 EST)]

Osmo Eerola (931228.0845 GMT) --

(In replying to Martin Taylor):

> Cannot see why "multiple input" systems could not control  
> "single output".

... and ...

> ... it is very well possible that multiple inputs can control a  
> few outputs - the output O(t) is a function of several inputs  
> I1(t), I2(t),...,In(t). There can even be several sensed  
> (perceived) variables of a process and all they control the  
> ouput in combination in a closed loop manner.

The most important parts of your statement are "is a function of"  
and "in combination." A function or combination of a set of  
inputs has just one value at a time. Thus what seem to be  
multiple degrees of freedom when seen from outside the system  
become a single degree of freedom inside the system. This is the  
basis for the hierarchical perception aspect of HPCT. When  
multiple inputs are reduced to a single representative signal, it  
is no longer possible for each input to have a unique effect on  
the output. Instead, only a function of all the inputs has a  
relationship to the output.

Because of this reduction in degrees of freedom, it is possible  
for the same set of inputs to be controlled in several different  
and independent respects. The simplest example is a system with  
two input variables. One perceptual function can compute the sum  
of the two variables, and a second one the difference. Two  
independent control systems can be set up, using two output  
actuators, such that one controls the sensed sum while the other  
controls the sensed difference. The reference signals for each  
system can be adjusted independently to cause the sum and the  
difference to be maintained at the specified levels,  
independently of each other. One control system's error signal  
affects both external variables in the same direction, and the  
other affects them in opposite directions. So both actuators are  
used by both control systems, but the effect is that of  
independently controlling two degrees of freedom of the  
environment. This is easy to simulate, by the way.

Control of this kind is handled in standard control theory, but  
in a way that obscures the principle involved (at least for me).  
When I see matrix control equations, I don't see any of these  
basic relationships. Maybe other people do. I've never seen them  
discussed in a CT text.

> From me:
> 
> > I think of controlling as something done by the whole closed  
> > loop, not by any one part of it.

> From you:  
> Sure. But one can observe the closed loop functioning by  
> measuring it from different parts:

That's true of the engineer looking at an artificial control  
system. But now consider your own control systems (the ones  
inside which you live). Now your only access to the loop is in  
the perceptual signals, the feedback signals. You can't  
experience your outputs, or the mechanisms in the external part  
of the loop. Everything you know (even about the forces you  
generate with your muscles) has to come to you through sensors,  
so all you ever experience are the feedback signals in various  
control systems.

When you look at another person behaving, you see the immediate  
and indirect environmental effects of the muscle forces, but now  
you have no access to the feedback signals or the other parts of  
the control systems inside the other person. You can't see  
directly what aspect of the environment the other person is  
perceiving, so you can't see immediately what the other person is  
controlling.

Building up a control-system model of human behavior requires  
putting these two views together into a model that explains them  
both (never forgetting that while you are watching another person  
behaving, you are still observing only your own perceptual  
signals). I haven't seen this discussed in CT textbooks, either.

> You have applied Ct to human behaviour and call it PCT.  
> The main "difference" between CT and PCT is that you  
> control perceptions, not outputs (but actually the ouputs  
> are affected, too).

Yes, the outputs are affected, too, as well as the external  
variables that the outputs act upon. Let's try to reach agreement  
on what "output" means in PCT. The basic output of a higher  
organism consists of muscle contractions. Muscle contractions are  
a physical effect of neural signals that depends ONLY on the  
neural signals (disturbances capable of altering the muscle  
contractions independently of the neural signals' effect would  
hardly ever occur, and then only under very unusual  
circumstances). In general, we use the word output to mean the  
immediate effect of an actuator device on the part of the  
physical world that it directly acts upon.

The parallel in the world of electromechanical system would be  
found in a motor used as an output device. The electronic signal  
entering the motor is like the neural signal in the living  
organism. This electronic signal (operating through a power  
output stage) causes current to flow through the windings of the  
motor, with the result that a torque is exerted on the armature.  
It would be very unusual to find any external agency that could  
alter this torque, so the torque (the static torque at least) is  
a direct measure of the immediate effect of the electronic system  
on its environment. We define that as the output of the control  
system.

This lets us distinguish between the physical outputs generated  
by a control system and the effects those outputs have on the  
rest of the physical world. In the human system, the muscle  
contraction has the immediate effect of stretching the elastic  
part of the muscle between its attachments. This is a purely  
passive, mechanical, physical effect involving the series spring  
constant of the muscle. It is the stretching of this "spring"  
that produces a force tending to pull the attachments of the  
muscle together. The shortest feedback loop in the human body  
involves sensors embedded in the tendons that fasten the muscles  
to the bones. These tendon signals do not measure the output of  
the control system (the shortening of the contractile part of the  
muscle), but a physical effect of that output (the stretching of  
the series spring element, and hence the force applied to the  
tendon). This is a negative feedback loop, with the comparator  
residing in the spinal cord as a spinal motor neuron. The error  
signal is the output of this neuron, and it enters the muscle to  
cause the contractile elements to shorten. The feedback from the  
tendon receptor inhibits (proportionally) the output of the  
spinal motor neuron, making the feedback negative

We can apply this same principle to the artificial system with a  
motor as an output device. The output of the electronic control  
system is the torque applied to the armature of the motor. The  
immediate result is to create a twisting moment on the shaft that  
connects the motor to the load. The shaft "winds up" slightly,  
and this slight torsion produces a torque at the other end of the  
shaft, determined by the torsional spring constant of the shaft.  
That torque tends to accelerate the load.

In the human system, the actual force applied to a tendon when  
the contractile fibers shorten depends not only on the  
contraction, but on the angle at the joint. If the joint angle  
changes, the series spring element in the muscle will lengthen or  
shorten even with the contractile part in a constant state of  
contraction. The joint angle, in turn, depends on external loads  
and inertial forces (if the angle is changing). So the net force  
sensed in the tendon is affected not only by the muscle  
contraction, but by external disturbances of various kinds.

This applies in the artificial control system as well. The  
angular position of the load can be disturbed by external forces  
and inertial effects, independently of the motor's torque. The  
acceleration of the load is thus not completely determined by the  
torque applied to the armature of the motor and the springiness  
of the shaft; it is also affected, just as much, by externally  
applied torques and by the moment of inertia of the load. The  
acceleration, velocity, and position of the load are affected  
BOTH by the output of the motor (the torque applied to the  
armature) AND external torques and loads.

Therefore measurements of the state of the load are not the same  
as measurements of the output of the motor, with output defined  
as we do in PCT. I trust that you agree with this analysis so  
far. Any actual engineering design has to take these factors into  
account. These details tend to get lost in conceptual diagrams,  
but in building any real control system they must be considered  
just as laid out here.

The tendon "reflex" is a force or torque control system. When you  
press a finger against a tabletop, this force control system is  
used to make the applied force vary in a precise way, with the  
tabletop preventing any angular accelerations or velocities from  
developing. The reason that this is a force control system is  
that force is \_sensed\_ by the system. The muscle contraction can  
have different effects under different physical circumstances; it  
is the fact that tendon receptors sense force, and not velocity  
or position, that makes this a force control system.

In the artificial system, what is controlled about the load  
depends on what is sensed. If a strain gauge is used to detect  
the torque applied by the load to something else, something that  
is prevented from spinning freely, then we will have a torque  
control system. If we mount an angular accelerometer on the load,  
the system will be an angular acceleration control system. If a  
tachometer is mounted on the load, sensing angular velocity, we  
will have an angular velocity control system. If we mount a  
potentiometer on the load, sensing angular position, we will have  
an angular position control system. If the load is a pinion gear  
engaging a rack, and we use a linear position sensor on the rack,  
the system will be a linear position control system. If we let  
the load be an iris diaphragm and we mount a photocell behind the  
iris, we will have a light-intensity control system.

What is controlled depends on which physical effect of a control  
system's output is sensed. The sensor, not the immediate output  
of the system, is the determining factor. In the above paragraph,  
we used exactly the same output, a torque applied to the armature  
of a motor, to control six different physical variables. What  
made the difference was not the kind of output used, but the kind  
of sensor used, and where among all the indirect effects of the  
output torque we chose to place the sensor.

By making a distinction between the output of a control system  
and physical effects of that output, we separate the controlled  
variable from the output. When disturbances are applied to the  
controlled variable, the output can now change in a way that has  
an equal and opposite effect on the controlled variable. If we  
shine a light on the iris diagraphm, disturbing the illumination  
of the photocell behind it, the motor will rotate and close the  
diaphragm until the light intensity is at its former value. If we  
increase and decrease the illumination slowly and smoothly, the  
motor will rotate in one direction and the other, and the light  
intensity at the photocell will not change appreciably (of course  
it will change a little bit). So the output of the control system  
is changing, but the \_controlled effect\_ of the output is not  
changing.

Because the sensor determines which physical effect of the  
system's output will be controlled, the controlled variable is  
defined primarily by the sensor and the signal emitted by the  
sensor. This is what "control of perception" means in the context  
of standard control theory.

I have not seen any discussion of this kind in a textbook of  
control engineering. When it comes down to a specific design,  
then of course all the details I have mentioned must be  
considered and the appropriate calculations must be done. But  
these details get left out of conceptual discussions. In your  
diagram showing G(s) and H(s) and S and P, none of the details  
was considered. The output of G(s) was simply labelled S, the  
controlled variable, with no provision for a disturbance that  
might also affect S. When such a disturbance is drawn into the  
diagram, it becomes necessary to separate the output of G(s) from  
the state of S, because now the disturbance can alter S  
independently of effects from the output of G(s). And when you do  
that, calling S the "output" becomes less justifiable -- S is not  
a measure of the actual output of the controller any more.

There is much more to say on this subject, particularly about  
controlled variables that exist only as functions of multiple  
external variables, but this is enough for now.

The control of perception concept is important in the analysis of  
human behavior, because the physical outputs of a human being  
have innumerable effects on the local environment. Most of these  
effects are not under control. The only way to find out which  
effects are controlled is to find out which are being represented  
in the perceptions of the person, and which of those perceptions  
is being compared with a reference signal to produce an error  
signal that drives the outputs. This is not like the engineering  
problem, where you start by knowing what is to be controlled and  
design the rest of the system around that. When we apply control  
theory to living systems, we do not see what is being controlled.  
All we see are the physical outputs and their multiple physical  
effects. That is not enough to tell us what the person is doing  
-- that is, which effects of the observable actions are  
intentional and under control, and which are accidental side-  
effects.

Sorry to go on for so long, but it is important to me to convince  
you that PCT is not JUST standard control theory. It is a  
detailed and orderly way of applying CT that is not taught in any  
control-system courses I have ever seen. Whether it is necessary  
for engineering students I can't say, but this careful approach  
is very necessary if we are to understand human control systems.  
Human behavior is so complex and multidimensional that one can  
easily get lost in trying to apply control theory. Without a  
detailed and systematic approach, important details can easily be  
overlooked, with the final result that the beautiful overall  
picture doesn't come into view.

> **···**
>
> --------------------------------------------------------------  
> Best,
> 
> Bill P.