PID+

[rupert]

[From Rupert Young (2014.10.01 21.00)]

Today I spent a couple of hours at the BRL (Bristol Robotics Laboratory) with a view to making use of their Robotics Innovtion Facility, that is, use their facilities to apply PCT, for free.

Apart from a quick tour of their robots most of the time was taken up with me explaining the PR/PCT approach and methodology as it would apply to robotics. I described the general theory and particularly how adaptive control could be achieved without recourse to internal models of the world and its dynamics. Although he (the BRL guy) seemed to appreciate the lack of need for models he had trouble understanding (or I had trouble explaining) what PCT adds to what are basically PID controllers. How would you explain the difference?

He wasn't very impressed with my robots, but did become more enthused after I showed a variety of demos, and we ended with him being "excited" by what we had discussed. What particularly seemed to sway him was Rick's catching-baseball demo. Cheers Rick!

They are going to sign me up to the RIF and he is going to look out for areas where the approach could be applied to real-world problems; and I will return soon to look in detail at their Baxter robot (http://www.rethinkrobotics.com/baxter/) with a view to implementing PCT.

So, all in all a promising start.

···

--

Regards,
Rupert

[MartinT]

[Martin Taylor 2014.10.01.16.32]

Try this passage from a draft of my chapter for LCS IV.

---------quote---------
Control loops in PCT are true control loops in the engineering
sense, and are mathematically the same as those of classical control
systems (Figure 1, top panel), though they differ conceptually. 
Figure 1. Control diagrams compared. (Top) A Classical control
diagram, and (Bottom) a PCT diagram
In a classical description of a control unit (Figure 1, top), the
arrow entering from the left is the “input”, which provides the
value that the designer wishes to have appear at the output of the
“load”, which may be variable. The small circle at the left
represents a comparator that provides as its output an “error”
signal that represents the difference between the “input” and the
“output”. The value of the output is sent directly to the comparator
according to the usual diagram, though there must be some
transformation between, say, the output RPM of a motor and the input
voltage that specifies the desired output. The input is not RPM, and
the output is not voltage.
The Powers (“PCT”) interpretation of a control system is
mathematically and functionally the same as that of an engineered
control loop, but conceptually different. The difference is
important in imagining the way control units function in a living
system. In Figure 1 (bottom), the white upper area is inside a
living organism, and shows the components of an elementary control
unit (ECU). The ECU itself consists of the Perceptual Input Function
(PIF — though the word “Input” is sometimes omitted), the comparator
(the small circle where the Reference enters) and the Output
function, together with their connecting links, all in the white
upper area. In the grey area is the “environment” of the ECU,
through which the feedback pathway goes. The ECU has a “reference”
input from elsewhere inside the organism, functionally equivalent to
to the classical “input” shown in the upper diagram.
The classical “Output” in the top figure appears as “Input” in the
PCT representation of the same loop. The variability of the
classical “Load” is represented explicitly in the PCT diagram as a
“Disturbance”. The lower circle in the PCT diagram represents a
“Complex Environmental Variable” that is influenced both by the
“Output” and by the “Disturbance”. Only the arrows in the grey
“External Environment” area at the bottom refer to connections into
and out of the control loop through the ECU’s outer environment.
Although the two diagrams look very different, they represent the
same functions apart from the frequent omission of the Perceptual
Input Function in the classical diagram. The important difference is
in the conceptual pictures they display. The omission of the PIF
implies that the designer of the controller knows exactly what is
measured at the output and what is represented at the input. In PCT,
the PIF defines what aspects of the indefinitely complex outer world
are involved in control. It specifies the form and nature of the
CEV, and converts sensory effects due to the CEV into a form that
can be compared with the reference signal value. Whereas the
classical diagram shows an input that dictates a value to be taken
by an output in the face of a varying load, the PCT diagram
emphasizes that the reference value comes from an inner world rather
than the external environment, and that the reference value is
compared not to the value of something in the environment but to a
perception, an internal value. These differences are not functional.
They are conceptual. And they matter.
There is one other conceptual difference between the two diagrams.
It is not in the way the control system itself functions, but in
what influence on the outer environment is considered important. In
the classical diagram, the “Output” that matters is variation at the
point at which the feedback signal is connected. To the designer of
the classical control system, this effect on the environment is the
reason the control loop exists at all. In the PCT diagram, that
point is the CEV, and the reason for the existence of the control
loop is to stabilize the internal representation of the CEV, the
perceptual signal value. Both control loops do, in practice, have
effects on their environments other than their effect on the
controlled variable, but PCT diagrams often make these side-effect
influences explicit, whereas they are usually omitted in the
classical diagram even though a designer of the larger system may
need to take them into account.
These differences between the conceptual rationales for designing
engineered control loops and for discovering biological control
loops should not be allowed to obscure the fact that every
engineering principle that applies to a hardware control loop also
applies to a biological control loop. It is worth re-emphasising
that control is control, whether it be implemented in crafted solid
metal like a Watt governor, in a mess of electronics, in sequences
of chemical reactions, or in biological purposeful behaviour. The
functional and mathematical relations are the same in all of them.
----------end quote--------
Martin
PS. Comments welcomed

···

  [From Rupert Young (2014.10.01 21.00)]




  .... I described the general theory and particularly how adaptive

control could be achieved without recourse to internal models of
the world and its dynamics. Although he (the BRL guy) seemed to
appreciate the lack of need for models he had trouble
understanding (or I had trouble explaining) what PCT adds to what
are basically PID controllers. How would you explain the
difference?

[rsmarken]

[From Rick Marken (2014.10.01.1510)]

···

Martin Taylor (2014.10.01.16.32)–

  [From Rupert Young (2014.10.01 21.00)]




  .... I described the general theory and particularly how adaptive

control could be achieved without recourse to internal models of
the world and its dynamics. Although he (the BRL guy) seemed to
appreciate the lack of need for models he had trouble
understanding (or I had trouble explaining) what PCT adds to what
are basically PID controllers. How would you explain the
difference?

Try this passage from a draft of my chapter for LCS IV.

---------quote---------

Control loops in PCT are true control loops in the engineering

sense, and are mathematically the same as those of classical control
systems (Figure 1, top panel), though they differ conceptually…

These differences between the conceptual rationales for designing

engineered control loops and for discovering biological control
loops should not be allowed to obscure the fact that every
engineering principle that applies to a hardware control loop also
applies to a biological control loop. It is worth re-emphasising
that control is control, whether it be implemented in crafted solid
metal like a Watt governor, in a mess of electronics, in sequences
of chemical reactions, or in biological purposeful behaviour. The
functional and mathematical relations are the same in all of them.

----------end quote--------



Martin



PS. Comments welcomed

RM: This description of the difference between the “classical” or “engineering” view of a control system and the PCT view is absolutely wonderful. Great work Martin. It overlaps to a great extent what I say in my paper for LCS IV but I think that is a good thing; it’s an important point and I think it will be good to have this level of concurrence on it in a volume honoring the person who had the insight that you describe so well (better than I do, I must admit) in the passage above.

Best regards

Rick

–
Richard S. Marken, Ph.D.
Author of Doing Research on Purpose.
Now available from Amazon or Barnes & Noble

[Kent]

[From Kent McClelland 2014.10.01.17.07]

I’m not clear about the mathematics of it, but doesn’t a PID controller also make use of the derivative (rate of change) of the PIF in its equations, as well as the usual “leaky integrator” term that appears in the PCT equations?

I guess my question is whether there’s a mathematical difference between a PID controller and the standard PCT model, as well as the conceptual difference that Martin points out very clearly in the excerpt from his chapter.

···

[From Rupert Young (2014.10.01 21.00)]

… I described the general theory and particularly how adaptive control could be achieved without recourse to internal models of the world and its dynamics. Although he (the BRL guy) seemed to appreciate the lack of need for models he had trouble understanding
(or I had trouble explaining) what PCT adds to what are basically PID controllers. How would you explain the difference?

[rsmarken]

[From Rick Marken (2014.10.01.1550)]

···

Kent McClelland 2014.10.01.17.07]

I’m not clear about the mathematics of it, but doesn’t a PID controller also make use of the derivative (rate of change) of the PIF in its equations, as well as the usual “leaky integrator” term that appears in the PCT equations?Â

RM:  I think the proportional, integral and derivative refer to the functions that transform error into output. My experience is that each can be used as the output function but which works best – P, I or D – depends on the dynamics of the variable being controlled. But Wikipedia shows all three functions being used simultaneously, probably with differential weights to get the best quality pf  control. But I’m pretty sure that the P,I and D functions in PID controlled are output functions that convert error to output, not input functions that fconvery sensory inputs to perceptions.Â

BestÂ

Rick

Â

I guess my question is whether there’s a mathematical difference between a PID controller and the standard PCT model, as well as the conceptual difference that Martin points out very clearly in the excerpt from his chapter.

On Oct 1, 2014, at 3:37 PM, Martin Taylor wrote:

[Martin Taylor 2014.10.01.16.32]

[From Rupert Young (2014.10.01 21.00)]

… I described the general theory and particularly how adaptive control could be achieved without recourse to internal models of the world and its dynamics. Although he (the BRL guy) seemed to appreciate the lack of need for models he had trouble understanding
(or I had trouble explaining) what PCT adds to what are basically PID controllers. How would you explain the difference?

Try this passage from a draft of my chapter for LCS IV.

---------quote---------

Control loops in PCT are true control loops in the engineering sense, and are mathematically the same as those of classical control systems (Figure 1, top panel), though they differ conceptually.



Figure 1. Control diagrams compared. (Top) A Classical control diagram, and (Bottom) a PCT diagram

In a classical description of a control unit (Figure 1, top), the arrow entering from the left is the “input�, which provides the value that the designer wishes to have appear at the output of the “load�, which may be variable. The small circle at the left
represents a comparator that provides as its output an “error� signal that represents the difference between the “input� and the “output�. The value of the output is sent directly to the comparator according to the usual diagram, though there must be some
transformation between, say, the output RPM of a motor and the input voltage that specifies the desired output. The input is not RPM, and the output is not voltage.

The Powers (“PCT�) interpretation of a control system is mathematically and functionally the same as that of an engineered control loop, but conceptually different. The difference is important in imagining the way control units function in a living system.
In Figure 1 (bottom), the white upper area is inside a living organism, and shows the components of an elementary control unit (ECU). The ECU itself consists of the Perceptual Input Function (PIF — though the word “Inputâ€? is sometimes omitted), the comparator
(the small circle where the Reference enters) and the Output function, together with their connecting links, all in the white upper area. In the grey area is the “environment� of the ECU, through which the feedback pathway goes. The ECU has a “reference� input
from elsewhere inside the organism, functionally equivalent to to the classical “input� shown in the upper diagram.

The classical “Output� in the top figure appears as “Input� in the PCT representation of the same loop. The variability of the classical “Load� is represented explicitly in the PCT diagram as a “Disturbance�. The lower circle in the PCT diagram represents a
“Complex Environmental Variable� that is influenced both by the “Output� and by the “Disturbance�. Only the arrows in the grey “External Environment� area at the bottom refer to connections into and out of the control loop through the ECU’s outer environment.

Although the two diagrams look very different, they represent the same functions apart from the frequent omission of the Perceptual Input Function in the classical diagram. The important difference is in the conceptual pictures they display. The omission of
the PIF implies that the designer of the controller knows exactly what is measured at the output and what is represented at the input. In PCT, the PIF defines what aspects of the indefinitely complex outer world are involved in control. It specifies the form
and nature of the CEV, and converts sensory effects due to the CEV into a form that can be compared with the reference signal value. Whereas the classical diagram shows an input that dictates a value to be taken by an output in the face of a varying load,
the PCT diagram emphasizes that the reference value comes from an inner world rather than the external environment, and that the reference value is compared not to the value of something in the environment but to a perception, an internal value. These differences
are not functional. They are conceptual. And they matter.

There is one other conceptual difference between the two diagrams. It is not in the way the control system itself functions, but in what influence on the outer environment is considered important. In the classical diagram, the “Output� that matters is variation
at the point at which the feedback signal is connected. To the designer of the classical control system, this effect on the environment is the reason the control loop exists at all. In the PCT diagram, that point is the CEV, and the reason for the existence
of the control loop is to stabilize the internal representation of the CEV, the perceptual signal value. Both control loops do, in practice, have effects on their environments other than their effect on the controlled variable, but PCT diagrams often make
these side-effect influences explicit, whereas they are usually omitted in the classical diagram even though a designer of the larger system may need to take them into account.

These differences between the conceptual rationales for designing engineered control loops and for discovering biological control loops should not be allowed to obscure the fact that every engineering principle that applies to a hardware control loop also applies
to a biological control loop. It is worth re-emphasising that control is control, whether it be implemented in crafted solid metal like a Watt governor, in a mess of electronics, in sequences of chemical reactions, or in biological purposeful behaviour. The
functional and mathematical relations are the same in all of them.

----------end quote--------

Martin

PS. Comments welcomed

–
Richard S. Marken, Ph.D.
Author of  Doing Research on Purpose.Â
Now available from Amazon or Barnes & Noble

[Kent]

OK, that explanation clarifies things a bit for me. Thanks, Rick.

Kent

···

Kent McClelland 2014.10.01.17.07]

I’m not clear about the mathematics of it, but doesn’t a PID controller also make use of the derivative (rate of change) of the PIF in its equations, as well as the usual “leaky integrator” term that appears in the PCT equations?

RM: I think the proportional, integral and derivative refer to the functions that transform error into output. My experience is that each can be used as the output function but which works best – P, I or D – depends on the dynamics of the variable being
controlled. But Wikipedia shows all three functions being used simultaneously, probably with differential weights to get the best quality pf control. But I’m pretty sure that the P,I and D functions in PID controlled are output functions that convert error
to output, not input functions that fconvery sensory inputs to perceptions.

Best

Rick

I guess my question is whether there’s a mathematical difference between a PID controller and the standard PCT model, as well as the conceptual difference that Martin points out very clearly in the excerpt from his chapter.

On Oct 1, 2014, at 3:37 PM, Martin Taylor wrote:

[Martin Taylor 2014.10.01.16.32]

[From Rupert Young (2014.10.01 21.00)]

… I described the general theory and particularly how adaptive control could be achieved without recourse to internal models of the world and its dynamics. Although he (the BRL guy) seemed to appreciate the lack of need for models he had trouble understanding
(or I had trouble explaining) what PCT adds to what are basically PID controllers. How would you explain the difference?

Try this passage from a draft of my chapter for LCS IV.

---------quote---------

Control loops in PCT are true control loops in the engineering sense, and are mathematically the same as those of classical control systems (Figure 1, top panel), though they differ conceptually.

<ControlDiagramsCompared.jpg>

Figure 1. Control diagrams compared. (Top) A Classical control diagram, and (Bottom) a PCT diagram

In a classical description of a control unit (Figure 1, top), the arrow entering from the left is the “input�, which provides the value that the designer wishes to have appear at the output of the “load�, which may be variable. The small circle at the left
represents a comparator that provides as its output an “error� signal that represents the difference between the “input� and the “output�. The value of the output is sent directly to the comparator according to the usual diagram, though there must be some
transformation between, say, the output RPM of a motor and the input voltage that specifies the desired output. The input is not RPM, and the output is not voltage.

The Powers (“PCT�) interpretation of a control system is mathematically and functionally the same as that of an engineered control loop, but conceptually different. The difference is important in imagining the way control units function in a living system.
In Figure 1 (bottom), the white upper area is inside a living organism, and shows the components of an elementary control unit (ECU). The ECU itself consists of the Perceptual Input Function (PIF — though the word “Inputâ€? is sometimes omiitted), the comparator
(the small circle where the Reference enters) and the Output function, together with their connecting links, all in the white upper area. In the grey area is the “environment� of the ECU, through which the feedback pathway goes. The ECU has a “reference� input
from elsewhere inside the organism, functionally equivalent to to the classical “input� shown in the upper diagram.

The classical “Output� in the top figure appears as “Input� in the PCT representation of the same loop. The variability of the classical “Load� is represented explicitly in the PCT diagram as a “Disturbance�. The lower circle in the PCT diagram represents a
“Complex Environmental Variable� that is influenced both by the “Output� and by the “Disturbance�. Only the arrows in the grey “External Environment� area at the bottom refer to connections into and out of the control loop through the ECU’s outer environment.

Although the two diagrams look very different, they represent the same functions apart from the frequent omission of the Perceptual Input Function in the classical diagram. The important difference is in the conceptual pictures they display. The omission of
the PIF implies that the designer of the controller knows exactly what is measured at the output and what is represented at the input. In PCT, the PIF defines what aspects of the indefinitely complex outer world are involved in control. It specifies the form
and nature of the CEV, and converts sensory effects due to the CEV into a form that can be compared with the reference signal value. Whereas the classical diagram shows an input that dictates a value to be taken by an output in the face of a varying load,
the PCT diagram emphasizes that the reference value comes from an inner world rather than the external environment, and that the reference value is compared not to the value of something in the environment but to a perception, an internal value. These differences
are not functional. They are conceptual. And they matter.

There is one other conceptual difference between the two diagrams. It is not in the way the control system itself functions, but in what influence on the outer environment is considered important. In the classical diagram, the “Output� that matters is variation
at the point at which the feedback signal is connected. To the designer of the classical control system, this effect on the environment is the reason the control loop exists at all. In the PCT diagram, that point is the CEV, and the reason for the existence
of the control loop is to stabilize the internal representation of the CEV, the perceptual signal value. Both control loops do, in practice, have effects on their environments other than their effect on the controlled variable, but PCT diagrams often make
these side-effect influences explicit, whereas they are usually omitted in the classical diagram even though a designer of the larger system may need to take them into account.

These differences between the conceptual rationales for designing engineered control loops and for discovering biological control loops should not be allowed to obscure the fact that every engineering principle that applies to a hardware
control loop also applies to a biological control loop. It is worth re-emphasising that control is control, whether it be implemented in crafted solid metal like a Watt governor, in a mess of electronics, in sequences of chemical reactions, or in biological
purposeful behaviour. The functional and mathematical relations are the same in all of them.

----------end quote--------

Martin

PS. Comments welcomed

–
Richard S. Marken, Ph.D.

Author of Doing
Research on Purpose.
Now available from Amazon or Barnes & Noble

[MartinT]

[Martin Taylor 2014.10.01.21.12]

Yep. Well put.

Martin

···

[From Rick Marken (2014.10.01.1550)]

            Kent McClelland

2014.10.01.17.07]

              I'm not clear about the mathematics of it, but

doesn’t a PID controller also make use of the
derivative (rate of change) of the PIF in its
equations, as well as the usual “leaky integrator”
term that appears in the PCT equations?

          RM:  I think the proportional, integral and derivative

refer to the functions that transform error into output.
My experience is that each can be used as the output
function but which works best – P, I or D – depends on
the dynamics of the variable being controlled. But
Wikipedia shows all three functions being used
simultaneously, probably with differential weights to get
the best quality pf control. But I’m pretty sure that the
P,I and D functions in PID controlled are output functions
that convert error to output, not input functions that
fconvery sensory inputs to perceptions.

[rupert]

···

[From Rupert Young (2014.10.02 15.00)]

  Martin, thanks, very useful.

  Though the response I was getting yesterday was, "we [robotics

control engineers] are doing that already". So, perhaps the
question should be (which you alluded to), if the there are no
functional differences why do the conceptual differences matter?
What is the + provided by PCT?

  On 01/10/2014 21:37, Martin Taylor wrote:

Regards,
Rupert

[Martin Taylor 2014.10.01.16.32]

  Try this passage from a draft of my chapter for LCS IV.

---------quote---------
Control loops in PCT are true control loops in the engineering
sense, and are mathematically the same as those of classical
control systems (Figure 1, top panel), though they differ
conceptually. 
Figure 1. Control diagrams compared. (Top) A Classical control
diagram, and (Bottom) a PCT diagram
In a classical description of a control unit (Figure 1, top), the
arrow entering from the left is the “input”, which provides the
value that the designer wishes to have appear at the output of the
“load”, which may be variable. The small circle at the left
represents a comparator that provides as its output an “error”
signal that represents the difference between the “input” and the
“output”. The value of the output is sent directly to the
comparator according to the usual diagram, though there must be
some transformation between, say, the output RPM of a motor and
the input voltage that specifies the desired output. The input is
not RPM, and the output is not voltage.
The Powers (“PCT”) interpretation of a control system is
mathematically and functionally the same as that of an engineered
control loop, but conceptually different. The difference is
important in imagining the way control units function in a living
system. In Figure 1 (bottom), the white upper area is inside a
living organism, and shows the components of an elementary control
unit (ECU). The ECU itself consists of the Perceptual Input
Function (PIF — though the word “Input” is sometimes omitted), the
comparator (the small circle where the Reference enters) and the
Output function, together with their connecting links, all in the
white upper area. In the grey area is the “environment” of the
ECU, through which the feedback pathway goes. The ECU has a
“reference” input from elsewhere inside the organism, functionally
equivalent to to the classical “input” shown in the upper diagram.
The classical “Output” in the top figure appears as “Input” in the
PCT representation of the same loop. The variability of the
classical “Load” is represented explicitly in the PCT diagram as a
“Disturbance”. The lower circle in the PCT diagram represents a
“Complex Environmental Variable” that is influenced both by the
“Output” and by the “Disturbance”. Only the arrows in the grey
“External Environment” area at the bottom refer to connections
into and out of the control loop through the ECU’s outer
environment.
Although the two diagrams look very different, they represent the
same functions apart from the frequent omission of the Perceptual
Input Function in the classical diagram. The important difference
is in the conceptual pictures they display. The omission of the
PIF implies that the designer of the controller knows exactly what
is measured at the output and what is represented at the input. In
PCT, the PIF defines what aspects of the indefinitely complex
outer world are involved in control. It specifies the form and
nature of the CEV, and converts sensory effects due to the CEV
into a form that can be compared with the reference signal value.
Whereas the classical diagram shows an input that dictates a value
to be taken by an output in the face of a varying load, the PCT
diagram emphasizes that the reference value comes from an inner
world rather than the external environment, and that the reference
value is compared not to the value of something in the environment
but to a perception, an internal value. These differences are not
functional. They are conceptual. And they matter.
There is one other conceptual difference between the two diagrams.
It is not in the way the control system itself functions, but in
what influence on the outer environment is considered important.
In the classical diagram, the “Output” that matters is variation
at the point at which the feedback signal is connected. To the
designer of the classical control system, this effect on the
environment is the reason the control loop exists at all. In the
PCT diagram, that point is the CEV, and the reason for the
existence of the control loop is to stabilize the internal
representation of the CEV, the perceptual signal value. Both
control loops do, in practice, have effects on their environments
other than their effect on the controlled variable, but PCT
diagrams often make these side-effect influences explicit, whereas
they are usually omitted in the classical diagram even though a
designer of the larger system may need to take them into account.
These differences between the conceptual rationales for designing
engineered control loops and for discovering biological control
loops should not be allowed to obscure the fact that every
engineering principle that applies to a hardware control loop also
applies to a biological control loop. It is worth re-emphasising
that control is control, whether it be implemented in crafted
solid metal like a Watt governor, in a mess of electronics, in
sequences of chemical reactions, or in biological purposeful
behaviour. The functional and mathematical relations are the same
in all of them.
----------end quote--------
Martin
PS. Comments welcomed

[From Rupert Young (2014.10.01 21.00)]

    .... I described the general theory and particularly how

adaptive control could be achieved without recourse to internal
models of the world and its dynamics. Although he (the BRL guy)
seemed to appreciate the lack of need for models he had trouble
understanding (or I had trouble explaining) what PCT adds to
what are basically PID controllers. How would you explain the
difference?

[MartinT]

[Martin Taylor 2014.10.02.11.04]

Without actually having been part of the conversation, it's hard to

know what they had in mind. Functionally, control being control, if
they were producing objects that controlled some variable to some
desired value, I suppose they had to have been “doing that already”.
If they were controlling output (PCT labelling), in other words
making the robot perform some actions accurately, like the
manipulators that put cars together, their robots will do that
movement well, but if the car body has shifted on its carrier, the
car won’t be put together very well. If they were controlling input
(see that the car windshield fits properly in its place), the
motions might be variable but the car would be properly made. If
they were controlling input, then they were using PCT, at least in
part.
The other part of the possible difference between what they were
“doing already” and PCT as applied to living things is where the
reference values come from, or if there is even a reference value at
all. An arm-on-a-post ball-catching robot can’t make the same
movements every time when the ball might arrive anywhere within its
reach. It could be designed with clever algorithms to calculate the
joint angles needed to compensate for the ball’s predicted
trajectory or even to compensate for where the ball actually is from
microsecond to microsecond, as I suspect may be the case for ones I
have see on TV, or it could be designed with a purpose to see and
perhaps to feel the ball in its “hand”, and allowed to reorganize
its hierarchic structure in the way a combination of Bill’s Arm 1
(Little Man) and Arm 2 (14 df arm) would do if the reorganization
criterion were the minimum separation of the time-space world lines
of the ball and the hand. The former “control of output” robot would
catch the ball very well, but would need a lot of new programs to be
calculated off-line if the same arm was to be used to bat the ball
to a specified spot on a wall, whereas the reorganizing one would
need no changes other than some practice time in order to
accommodate the new purpose.
Since the purpose of a robot is always provided from outside, in
contrast to the purposes of a biological entity, you can’t take that
as a discriminative criterion. Given that both systems use negative
feedback control, the real issue is whether the cleverness needed to
achieve that purpose is in the human designer or is learned by the
robot (by way of reorganization).
I’ve no idea whether this would relate to the comment that they were
“doing that already”. If they are allowing their robots to
reorganize and not supplying the algorithms to produce designed
outputs, maybe they really are using PCT, and came to that point
without knowing that it had been developed independently to describe
how living things operate. But I suppose there may be other
differences I have not considered.
Martin

···

[From Rupert Young (2014.10.02
15.00)]

    Martin, thanks, very useful.

    Though the response I was getting yesterday was, "we [robotics

control engineers] are doing that already". So, perhaps the
question should be (which you alluded to), if the there are no
functional differences why do the conceptual differences matter?
What is the + provided by PCT?

Regards,
Rupert

[_Erling_Jorgensen]

[From Erling Jorgensen (2014.10.02 14:00EDT)]

Rupert Young (2014.10.01 21.00)
I described the general theory and particularly how adaptive control could be

achieved without recourse to internal models of the world and its dynamics.
Although he (the BRL guy) seemed to appreciate the lack of need for models he
had trouble understanding (or I had trouble explaining) what PCT adds to what
are basically PID controllers. How would you explain the difference?

Rupert Young (2014.10.02 15.00)
Though the response I was getting yesterday was, "we [robotics control

engineers] are doing that already". So, perhaps the question should be (which
you alluded to), if the there are no functional differences why do the
conceptual differences matter? What is the + provided by PCT?

Hi Rupert,

EJ: It's a useful question your BRL contact raises, particularly for our
getting a clearer idea of what we are proposing. My understanding is as
follows. I'm drawing here on the "PID Controller" article in Wikipedia, which
is readily accessible and quite clearly written for those less versed in these
concepts (not the situation of your BRL contact.)

EJ: As was noted by others, PCT primarily uses a form of PI (Proportional,
Integral) function as its output, rather than a PID function (which adds the
derivative component.) This means most of the gain in a typical PCT control
loop is incorporated into the output term, although there are placeholders for
environmental feedback function gain and perceptual input function gain. The
output term is also typically made discrete, and thus uses an integrating
rather than an integral function. We call it a "leaky integrator." One of
the side effects of the leaky portion, I believe, is to leave a small residual
error -- what the Wikipedia article calls "droop" -- because proportional
controllers require non-zero error to stay operative.

EJ: The chief advantage of the PCT approach, to my mind, is to provide what
the article calls "cascaded PID control." This is a way to get better dynamic
performance from linear PID controllers. The key idea is that the output of
one PI(D) controller provides the set point reference for another PI(D)
controller. This is a prime feature of Hierarchical PCT. There seem to be
several distinct benefits from this approach.

EJ: 1) Additional degrees of freedom. Parameters are not collapsed into a
single equation, driving control of a single process variable. Rather, there
is finer-grained control of more than one perception.

EJ: 2) Differential time constants. The article clearly describes how the
outer loop has a long time constant, while the inner loop can respond much
more quickly. HPCT expands on that concept even more, by providing multiple
inter-nested loops, with progressively shorter time constants when descending
the hierarchy. This partitions the overall control task, and improves overall
dynamic performance.

EJ: 3) Reducing or eliminating recourse to feed-forward (open-loop) control.
When some of the time constants in item (2) above are extremely fast, there
may be less need for internal models to predict the effects of system
characteristics or of future disturbances. Such variables can be handled
directly, in real time, by closed-loop feedback control. Essentially the
environment is allowed to model itself.

EJ: 4) Differential tuning to the physics at different points in the process.
Having different PI controllers tuned to different perceptions (what the
article calls "process variables") allows a better approximation of the
physics applicable to each one.

EJ: 5) Partitioning the perceptions themselves. When PCT uses cascaded
control, it does not simply measure the same variable at two different spots,
(which is the example offered in the Wikipedia article.) PCT attempts to have
a lower loop control a constituent perception of a higher loop, as a means of
its own implementation. The result is that the control task for the higher
loop is simplified. Fast-changing dynamics from disturbances are handled at a
lower level, while the higher level monitors a different and slower overall
measure of the results of control.

EJ: An example of (5) would be Powers' PCT simulation of control of an
inverted pendulum. If I am remembering the details correctly, Position
control of the bob supplies the reference for Velocity control of the cart,
since position is integrated velocity. Velocity control supplies Acceleration
control of the cart, since velocity is integrated acceleration. Acceleration
control supplies the reference for Force control against the cart, since
acceleration is integrated force.

EJ: 6) Graded changes of reference. Cascaded PI control seems to get away
from step changes in the set points, which do not seem very plausible
biologically anyway. This is akin to what the article calls "set point
ramping."

EJ: An interesting case can be made with regard to derivative control, by
incorporating the rate of change of the error over time. This is meant as a
predictive approximation of future error, to refine overall stability of the
system. Standard PCT control loop equations do not seem to include this form
of control, although in HPCT the rate of change of any variable in itself can
become an object of perception, which we call Transition control.

EJ: However, I would make the case that in human control systems at least,
the Emotional system of the body is connected to the rate of error change over
time. I am not sure over how broad a scale the error would be measured. But
different emotions may well correlate with the slope of error change, and
whether it is rising or falling. The output of such a system seems to make
broad systemic changes in the body, albeit reversible and subject to decay
over time.

EJ: These changes seem to affect performance characteristics of the body. As
such, this is more like altering parameters of control, or the gain parameter
itself. This may be a form of Derivative control, operating on a systemic
basis, rather than for individual control loops. Alternatively, it may be a
form of what the Wikipedia article calls "PID gain scheduling," where
parameters are adjusted to different operating conditions.

EJ: The above list of advantages seems to be a decided plus when it comes to
the form of negative feedback control incorporated into Perceptual Control
Theory. Yes, it is based on PID control, or at least PI control. But it is
primarily a form of cascaded PI control, which confers a host of benefits.

EJ: Hope this is helpful. BTW, I expect to utilize some of the above wording
and formulations in the article I am writing for the Living Control Systems VI
edited book.

All the best,
Erling

[Kent]

[From Kent McClelland 2014.10.02.1638]

Nice summary, Erling! It clarified some things for me, too. I'm glad to hear that you're contributing to the LCS IV book.

Kent

···

On Oct 2, 2014, at 4:19 PM, Erling Jorgensen wrote:

[From Erling Jorgensen (2014.10.02 14:00EDT)]

Rupert Young (2014.10.01 21.00)
I described the general theory and particularly how adaptive control could be

achieved without recourse to internal models of the world and its dynamics.
Although he (the BRL guy) seemed to appreciate the lack of need for models he
had trouble understanding (or I had trouble explaining) what PCT adds to what
are basically PID controllers. How would you explain the difference?

Rupert Young (2014.10.02 15.00)
Though the response I was getting yesterday was, "we [robotics control

engineers] are doing that already". So, perhaps the question should be (which
you alluded to), if the there are no functional differences why do the
conceptual differences matter? What is the + provided by PCT?

Hi Rupert,

EJ: It's a useful question your BRL contact raises, particularly for our
getting a clearer idea of what we are proposing. My understanding is as
follows. I'm drawing here on the "PID Controller" article in Wikipedia, which
is readily accessible and quite clearly written for those less versed in these
concepts (not the situation of your BRL contact.)

EJ: As was noted by others, PCT primarily uses a form of PI (Proportional,
Integral) function as its output, rather than a PID function (which adds the
derivative component.) This means most of the gain in a typical PCT control
loop is incorporated into the output term, although there are placeholders for
environmental feedback function gain and perceptual input function gain. The
output term is also typically made discrete, and thus uses an integrating
rather than an integral function. We call it a "leaky integrator." One of
the side effects of the leaky portion, I believe, is to leave a small residual
error -- what the Wikipedia article calls "droop" -- because proportional
controllers require non-zero error to stay operative.

EJ: The chief advantage of the PCT approach, to my mind, is to provide what
the article calls "cascaded PID control." This is a way to get better dynamic
performance from linear PID controllers. The key idea is that the output of
one PI(D) controller provides the set point reference for another PI(D)
controller. This is a prime feature of Hierarchical PCT. There seem to be
several distinct benefits from this approach.

EJ: 1) Additional degrees of freedom. Parameters are not collapsed into a
single equation, driving control of a single process variable. Rather, there
is finer-grained control of more than one perception.

EJ: 2) Differential time constants. The article clearly describes how the
outer loop has a long time constant, while the inner loop can respond much
more quickly. HPCT expands on that concept even more, by providing multiple
inter-nested loops, with progressively shorter time constants when descending
the hierarchy. This partitions the overall control task, and improves overall
dynamic performance.

EJ: 3) Reducing or eliminating recourse to feed-forward (open-loop) control.
When some of the time constants in item (2) above are extremely fast, there
may be less need for internal models to predict the effects of system
characteristics or of future disturbances. Such variables can be handled
directly, in real time, by closed-loop feedback control. Essentially the
environment is allowed to model itself.

EJ: 4) Differential tuning to the physics at different points in the process.
Having different PI controllers tuned to different perceptions (what the
article calls "process variables") allows a better approximation of the
physics applicable to each one.

EJ: 5) Partitioning the perceptions themselves. When PCT uses cascaded
control, it does not simply measure the same variable at two different spots,
(which is the example offered in the Wikipedia article.) PCT attempts to have
a lower loop control a constituent perception of a higher loop, as a means of
its own implementation. The result is that the control task for the higher
loop is simplified. Fast-changing dynamics from disturbances are handled at a
lower level, while the higher level monitors a different and slower overall
measure of the results of control.

EJ: An example of (5) would be Powers' PCT simulation of control of an
inverted pendulum. If I am remembering the details correctly, Position
control of the bob supplies the reference for Velocity control of the cart,
since position is integrated velocity. Velocity control supplies Acceleration
control of the cart, since velocity is integrated acceleration. Acceleration
control supplies the reference for Force control against the cart, since
acceleration is integrated force.

EJ: 6) Graded changes of reference. Cascaded PI control seems to get away
from step changes in the set points, which do not seem very plausible
biologically anyway. This is akin to what the article calls "set point
ramping."

EJ: An interesting case can be made with regard to derivative control, by
incorporating the rate of change of the error over time. This is meant as a
predictive approximation of future error, to refine overall stability of the
system. Standard PCT control loop equations do not seem to include this form
of control, although in HPCT the rate of change of any variable in itself can
become an object of perception, which we call Transition control.

EJ: However, I would make the case that in human control systems at least,
the Emotional system of the body is connected to the rate of error change over
time. I am not sure over how broad a scale the error would be measured. But
different emotions may well correlate with the slope of error change, and
whether it is rising or falling. The output of such a system seems to make
broad systemic changes in the body, albeit reversible and subject to decay
over time.

EJ: These changes seem to affect performance characteristics of the body. As
such, this is more like altering parameters of control, or the gain parameter
itself. This may be a form of Derivative control, operating on a systemic
basis, rather than for individual control loops. Alternatively, it may be a
form of what the Wikipedia article calls "PID gain scheduling," where
parameters are adjusted to different operating conditions.

EJ: The above list of advantages seems to be a decided plus when it comes to
the form of negative feedback control incorporated into Perceptual Control
Theory. Yes, it is based on PID control, or at least PI control. But it is
primarily a form of cascaded PI control, which confers a host of benefits.

EJ: Hope this is helpful. BTW, I expect to utilize some of the above wording
and formulations in the article I am writing for the Living Control Systems VI
edited book.

All the best,
Erling

[rsmarken]

[From Rick Marken (2014.10.02.2120)]

Erling Jorgensen <tel:%282014.10.02%2014>(2014.10.02 14:00EDT)

Hi Rupert,

EJ: It's a useful question your BRL contact raises, particularly for our
getting a clearer idea of what we are proposing. My understanding is as
follows. I'm drawing here on the "PID Controller" article in Wikipedia, which
is readily accessible and quite clearly written for those less versed in these
concepts (not the situation of your BRL contact.)

EJ: As was noted by others, PCT primarily uses a form of PI (Proportional,
Integral) function as its output, rather than a PID function (which adds the
derivative component.) This means most of the gain in a typical PCT control
loop is incorporated into the output term, although there are placeholders for
environmental feedback function gain and perceptual input function gain. The
output term is also typically made discrete, and thus uses an integrating
rather than an integral function. We call it a "leaky integrator." One of
the side effects of the leaky portion, I believe, is to leave a small residual
error -- what the Wikipedia article calls "droop" -- because proportional
controllers require non-zero error to stay operative...

RM: This is a excellent post, Erling. Clear, concise and accurate! You seemed to me channeling Bill Powers when you wrote it. Thank you.
RM: I will just add that it is very difficult to say what PCT can contribute to robotics since PCT is the application of control theory to the _reverse engineering_ of control systems that have already been "built": mainly living control systems. But all the things you mention are useful ideas for the builder of control systems, particularly the idea of basing construction of the robot on an architecture that is a hierarchy of control systems. I think that's what Rupert has been doing with his little demo robots. His robots may not control the lower level perceptions as well as other robots but his robot controls a higher level perception -- a sequence, I believe -- and the sequence is indeed a controlled perceptual input, not just a pre-programmed sequence of outputs. If the sequence is disturbed the robot goes back to the point where it left off to complete the sequence. Rupert's robot is a pretty impressive demonstration of PCT, I think!
Thanks again, Erling, for this wonderful post. Definitely a keeper. Like Kent, I am \also glad to know that you are contributing a chapter to LCS IV.
Best regards
Rick
PS. OK, I will just say that your only mistake -- a trivial and irrelevant one -- was to say that force is integrated acceleration. Force is proportional actually proportional to acceleration -- F = ma -- the constant of proportionality being the mass of the object being accelerated.
Again, super post Erling. >

···

EJ: The chief advantage of the PCT approach, to my mind, is to provide what
the article calls "cascaded PID control." This is a way to get better dynamic
performance from linear PID controllers. The key idea is that the output of
one PI(D) controller provides the set point reference for another PI(D)
controller. This is a prime feature of Hierarchical PCT. There seem to be
several distinct benefits from this approach.

EJ: 1) Additional degrees of freedom. Parameters are not collapsed into a
single equation, driving control of a single process variable. Rather, there
is finer-grained control of more than one perception.

EJ: 2) Differential time constants. The article clearly describes how the
outer loop has a long time constant, while the inner loop can respond much
more quickly. HPCT expands on that concept even more, by providing multiple
inter-nested loops, with progressively shorter time constants when descending
the hierarchy. This partitions the overall control task, and improves overall
dynamic performance.

EJ: 3) Reducing or eliminating recourse to feed-forward (open-loop) control.
When some of the time constants in item (2) above are extremely fast, there
may be less need for internal models to predict the effects of system
characteristics or of future disturbances. Such variables can be handled
directly, in real time, by closed-loop feedback control. Essentially the
environment is allowed to model itself.

EJ: 4) Differential tuning to the physics at different points in the process.
Having different PI controllers tuned to different perceptions (what the
article calls "process variables") allows a better approximation of the
physics applicable to each one.

EJ: 5) Partitioning the perceptions themselves. When PCT uses cascaded
control, it does not simply measure the same variable at two different spots,
(which is the example offered in the Wikipedia article.) PCT attempts to have
a lower loop control a constituent perception of a higher loop, as a means of
its own implementation. The result is that the control task for the higher
loop is simplified. Fast-changing dynamics from disturbances are handled at a
lower level, while the higher level monitors a different and slower overall
measure of the results of control.

EJ: An example of (5) would be Powers' PCT simulation of control of an
inverted pendulum. If I am remembering the details correctly, Position
control of the bob supplies the reference for Velocity control of the cart,
since position is integrated velocity. Velocity control supplies Acceleration
control of the cart, since velocity is integrated acceleration. Acceleration
control supplies the reference for Force control against the cart, since
acceleration is integrated force.

EJ: 6) Graded changes of reference. Cascaded PI control seems to get away
from step changes in the set points, which do not seem very plausible
biologically anyway. This is akin to what the article calls "set point
ramping."

EJ: An interesting case can be made with regard to derivative control, by
incorporating the rate of change of the error over time. This is meant as a
predictive approximation of future error, to refine overall stability of the
system. Standard PCT control loop equations do not seem to include this form
of control, although in HPCT the rate of change of any variable in itself can
become an object of perception, which we call Transition control.

EJ: However, I would make the case that in human control systems at least,
the Emotional system of the body is connected to the rate of error change over
time. I am not sure over how broad a scale the error would be measured. But
different emotions may well correlate with the slope of error change, and
whether it is rising or falling. The output of such a system seems to make
broad systemic changes in the body, albeit reversible and subject to decay
over time.

EJ: These changes seem to affect performance characteristics of the body. As
such, this is more like altering parameters of control, or the gain parameter
itself. This may be a form of Derivative control, operating on a systemic
basis, rather than for individual control loops. Alternatively, it may be a
form of what the Wikipedia article calls "PID gain scheduling," where
parameters are adjusted to different operating conditions.

EJ: The above list of advantages seems to be a decided plus when it comes to
the form of negative feedback control incorporated into Perceptual Control
Theory. Yes, it is based on PID control, or at least PI control. But it is
primarily a form of cascaded PI control, which confers a host of benefits.

EJ: Hope this is helpful. BTW, I expect to utilize some of the above wording
and formulations in the article I am writing for the Living Control Systems VI
edited book.

All the best,
Erling

--
Richard S. Marken, Ph.D.
Author of <http://www.amazon.com/Doing-Research-Purpose-Experimental-Psychology/dp/0944337554/ref=sr_1_1?ie=UTF8&qid=1407342866&sr=8-1&keywords=doing+research+on+purpose&gt;Doing Research on Purpose.
Now available from Amazon or Barnes & Noble

[wmansell]

I agree! Erling, this post is wonderful, and I am about to post it to all my non-PCT engineering colleagues! And of course glad that you are all LCS-IV writers!
Talk to you soon,
Warren

···

On Fri, Oct 3, 2014 at 5:18 AM, Richard Marken rsmarken@gmail.com wrote:

–
Dr Warren Mansell
Reader in Clinical Psychology
School of Psychological Sciences
2nd Floor Zochonis Building
University of Manchester
Oxford Road
Manchester M13 9PL
Email: warren.mansell@manchester.ac.uk

Tel: +44 (0) 161 275 8589

Website: http://www.psych-sci.manchester.ac.uk/staff/131406

See teamstrial.net for further information on our trial of CBT for Bipolar Disorders in NW England

The highly acclaimed therapy manual on A Transdiagnostic Approach to CBT using Method of Levels is available now.

Check www.pctweb.org for further information on Perceptual Control Theory

[From Rick Marken (2014.10.02.2120)]

Erling Jorgensen (2014.10.02 14:00EDT)

Hi Rupert,

EJ: It’s a useful question your BRL contact raises, particularly for our

getting a clearer idea of what we are proposing. My understanding is as

follows. I’m drawing here on the “PID Controller” article in Wikipedia, which

is readily accessible and quite clearly written for those less versed in these

concepts (not the situation of your BRL contact.)

EJ: As was noted by others, PCT primarily uses a form of PI (Proportional,

Integral) function as its output, rather than a PID function (which adds the

derivative component.) This means most of the gain in a typical PCT control

loop is incorporated into the output term, although there are placeholders for

environmental feedback function gain and perceptual input function gain. The

output term is also typically made discrete, and thus uses an integrating

rather than an integral function. We call it a “leaky integrator.” One of

the side effects of the leaky portion, I believe, is to leave a small residual

error – what the Wikipedia article calls “droop” – because proportional

controllers require non-zero error to stay operative…

RM: This is a excellent post, Erling. Clear, concise and accurate! You seemed to me channeling Bill Powers when you wrote it. Thank you.

RM: I will just add that it is very difficult to say what PCT can contribute to robotics since PCT is the application of control theory to the reverse engineering of control systems that have already been “built”: mainly living control systems. But all the things you mention are useful ideas for the builder of control systems, particularly the idea of basing construction of the robot on an architecture that is a hierarchy of control systems. I think that’s what Rupert has been doing with his little demo robots. His robots may not control the lower level perceptions as well as other robots but his robot controls a higher level perception – a sequence, I believe – and the sequence is indeed a controlled perceptual input, not just a pre-programmed sequence of outputs. If the sequence is disturbed the robot goes back to the point where it left off to complete the sequence. Rupert’s robot is a pretty impressive demonstration of PCT, I think!

Thanks again, Erling, for this wonderful post. Definitely a keeper. Like Kent, I am \also glad to know that you are contributing a chapter to LCS IV.

Best regards

Rick

PS. OK, I will just say that your only mistake – a trivial and irrelevant one – was to say that force is integrated acceleration. Force is proportional actually proportional to acceleration – F = ma – the constant of proportionality being the mass of the object being accelerated.

Again, super post Erling.

EJ: The chief advantage of the PCT approach, to my mind, is to provide what

the article calls “cascaded PID control.” This is a way to get better dynamic

performance from linear PID controllers. The key idea is that the output of

one PI(D) controller provides the set point reference for another PI(D)

controller. This is a prime feature of Hierarchical PCT. There seem to be

several distinct benefits from this approach.

EJ: 1) Additional degrees of freedom. Parameters are not collapsed into a

single equation, driving control of a single process variable. Rather, there

is finer-grained control of more than one perception.

EJ: 2) Differential time constants. The article clearly describes how the

outer loop has a long time constant, while the inner loop can respond much

more quickly. HPCT expands on that concept even more, by providing multiple

inter-nested loops, with progressively shorter time constants when descending

the hierarchy. This partitions the overall control task, and improves overall

dynamic performance.

EJ: 3) Reducing or eliminating recourse to feed-forward (open-loop) control.

When some of the time constants in item (2) above are extremely fast, there

may be less need for internal models to predict the effects of system

characteristics or of future disturbances. Such variables can be handled

directly, in real time, by closed-loop feedback control. Essentially the

environment is allowed to model itself.

EJ: 4) Differential tuning to the physics at different points in the process.

Having different PI controllers tuned to different perceptions (what the

article calls “process variables”) allows a better approximation of the

physics applicable to each one.

EJ: 5) Partitioning the perceptions themselves. When PCT uses cascaded

control, it does not simply measure the same variable at two different spots,

(which is the example offered in the Wikipedia article.) PCT attempts to have

a lower loop control a constituent perception of a higher loop, as a means of

its own implementation. The result is that the control task for the higher

loop is simplified. Fast-changing dynamics from disturbances are handled at a

lower level, while the higher level monitors a different and slower overall

measure of the results of control.

EJ: An example of (5) would be Powers’ PCT simulation of control of an

inverted pendulum. If I am remembering the details correctly, Position

control of the bob supplies the reference for Velocity control of the cart,

since position is integrated velocity. Velocity control supplies Acceleration

control of the cart, since velocity is integrated acceleration. Acceleration

control supplies the reference for Force control against the cart, since

acceleration is integrated force.

EJ: 6) Graded changes of reference. Cascaded PI control seems to get away

from step changes in the set points, which do not seem very plausible

biologically anyway. This is akin to what the article calls "set point

ramping."

EJ: An interesting case can be made with regard to derivative control, by

incorporating the rate of change of the error over time. This is meant as a

predictive approximation of future error, to refine overall stability of the

system. Standard PCT control loop equations do not seem to include this form

of control, although in HPCT the rate of change of any variable in itself can

become an object of perception, which we call Transition control.

EJ: However, I would make the case that in human control systems at least,

the Emotional system of the body is connected to the rate of error change over

time. I am not sure over how broad a scale the error would be measured. But

different emotions may well correlate with the slope of error change, and

whether it is rising or falling. The output of such a system seems to make

broad systemic changes in the body, albeit reversible and subject to decay

over time.

EJ: These changes seem to affect performance characteristics of the body. As

such, this is more like altering parameters of control, or the gain parameter

itself. This may be a form of Derivative control, operating on a systemic

basis, rather than for individual control loops. Alternatively, it may be a

form of what the Wikipedia article calls “PID gain scheduling,” where

parameters are adjusted to different operating conditions.

EJ: The above list of advantages seems to be a decided plus when it comes to

the form of negative feedback control incorporated into Perceptual Control

Theory. Yes, it is based on PID control, or at least PI control. But it is

primarily a form of cascaded PI control, which confers a host of benefits.

EJ: Hope this is helpful. BTW, I expect to utilize some of the above wording

and formulations in the article I am writing for the Living Control Systems VI

edited book.

All the best,

Erling

–
Richard S. Marken, Ph.D.
Author of Doing Research on Purpose.
Now available from Amazon or Barnes & Noble

[MartinT]

[Martin Taylor 2014.10.03.06.43]

Useful post, Erling. Just one small correction to add to Rick's. It is about the two sentences starting "The output term" in the middle of the paragraph quoted below.

[From Erling Jorgensen (2014.10.02 14:00EDT)]

EJ: As was noted by others, PCT primarily uses a form of PI (Proportional,
Integral) function as its output, rather than a PID function (which adds the
derivative component.) This means most of the gain in a typical PCT control
loop is incorporated into the output term, although there are placeholders for
environmental feedback function gain and perceptual input function gain. The
output term is also typically made discrete, and thus uses an integrating
rather than an integral function. We call it a "leaky integrator." One of
the side effects of the leaky portion, I believe, is to leave a small residual
error -- what the Wikipedia article calls "droop" -- because proportional
controllers require non-zero error to stay operative.

The examples and demos use an integrating output because the environmental path doesn't. In the demos, the environmental path is usually taken to be a simple connection. But if the environmental path contains integration, as it would if the output was a force applied to a mass, then the output function might well be simply proportional. If you have two integrators in a loop you run into instability problems rather quickly because of the implied phase shifts. I think it was Adam Matic who used proportional output in his real-world robot (If I have credited the wrong person, I apologise).

There's an ambiguity in your use of "discrete". On first reading, I took it to mean stepwise, but I think you probably mean that the output function is separate from the others. But I don't see how that sentence makes sense: "The output term is also typically made discrete, and thus uses an integrating rather than an integral function." I don't know what you mean by "integrating rather than integral". The integrator, when the output does integrate, is leaky because that's what real physical integrators are. Constructed ones may leak very slowly, but they leak. The ones simulated in PCT models appear to leak faster.

If you remember Bill's "Artificial Cerebellum", it was an output function tuned to the dynamics of the loop inclusive of the environmental feedback path. If the environmental feedback path had a periodic component in it, as, say, a mass on a spring, the AC would self-tune to take this into account and produce countervailing output that would not make the mass bounce up and down (much) when the reference value was for it to be at a particular elevation. That's a bit more sophisticated than a PID output function, but quite possibly something similar should be at least considered for output functions when producing control systems for real-world operation (such as in biology :-).

Martin

[_Erling_Jorgensen]

[From Erling Jorgensen (2014.10.03 0945EDT)]

Martin Taylor 2014.10.03.06.43

MT: There’s an ambiguity in your use of “discrete”. On first reading, I took
it to mean stepwise, but I think you probably mean that the output
function is separate from the others. But I don’t see how that sentence
makes sense: “The output term is also typically made discrete, and thus
uses an integrating rather than an integral function.” I don’t know what
you mean by “integrating rather than integral”. The integrator, when the
output does integrate, is leaky because that’s what real physical
integrators are.

EJ: I was simply referring to the difference between digital and analogue functions. I used the word “discrete” because that is how the Wikipedia article (on “PID controller”) classified the discussion. This is quoting from their explanation of “Discrete implementation”:

The analysis for designing a digital implementation of a PID controller in a microcontroller (MCU) or FPGA device requires the standard form of the PID controller to be discretized.^[21] Approximations for first-order derivatives are made by backward finite differences. The integral term is discretised, with a sampling time ,as follows,

EJ: Isn’t “integrating function” the term for the non-analogue version shown by the capital Sigma symbol? I was simply calling attention to that discretized form in PCT equations, which are typically made digital because they are simulated via digital computers. They also commonly use an iterative form of displaying the equations, where the previous value of the variable is inserted into the next iteration’s computation, because of the programing requirements.

EJ: Because I have benefitted so much from the patient translators, like Bill Powers, who never tired of tutoring others who may not have the same background, I try hard to make my posts inclusive for readers with varying backgrounds. When I am in doubt about an assertion, I try to signal that in some way. And I count on the community to add corrections when needed, just as you and Rick Marken have graciously done. Thanks for the discussion.

All the best,

Erling

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[rupert]

···

[From Rupert Young (2014.10.04 15.30)]

  I take your points (Martin and Erling), though it is not clear, to

me, which of these would be alien to control engineers.

  MT: I've no idea whether this would relate to the comment that

they were “doing that already”. If they are allowing their robots
to reorganize and not supplying the algorithms to produce designed
outputs, maybe they really are using PCT, and came to that point
without knowing that it had been developed independently to
describe how living things operate. But I suppose there may be
other differences I have not considered.

  It was rather that a control engineer would look at a pcs and say

that is a PI[D] controller. And he would look at a hierarchy of
pcs’s and say that’s a cascade; so nothing new to them.

  Let me come at this from a different angle (though these points

may have already been made by you, and Bill). From the
implications which arise due to PCT, that are not recognised by
control engineers, or anybody else,

1.       that it is perceptual inputs that are controlled, and never
   

behavioural outputs

1. that internal models of physical processes are not necessary

2.       that modelling observed behaviour is invalid, as it equates
   

to modelling side-effects, of control
So, how is that we both (us and control engineers) look at, what
are basically, PI[D] controllers and reach different conclusions?

  Is it simply the conceptualisation of the issues by way of the

different diagrams that we use? In other words, does the way the
PCT diagram is arranged allow us to make conclusions that do not
naturally flow from the MCT (modern control theory) diagram, even
though they are functionally the same.

  To expand on this, here's Martin's diagram again, and I refer to

the same numbers as above.

1.       Although a control engineer may acknowledge that a value is
   

being measured for the purposes of feedback, that “perception”
is not explicit in the diagram, so there is no emphasis on
perception, though to us it is of primary importance. The MCT
diagram flows from left to right, and with “output” as the
outcome of the process, it would be natural to think of the
value of “output” as the goal of the system. “Output” here is
actually the perceptual input, but has been misinterpreted as
behavioural outputs, such as muscle or motor commands. So, the
concept of control of perceptual input which is clear in the
PCT diagram is obfuscated in the MCT diagram.

1.       From the MCT diagram there seems to be a direct relationship
   

between input and output; feedback seems to be an afterthought
to correct for noise. So, it reasonably follows that if you
can replace the plant with a model of it (the plant and the
input/output relationship), then you can compute the output
independently of the actual world. This allows you to
mathematically define the scenario, making it easier to
understand and enables you to compute (predict) the next state
of the system, which seems necessary if you want it to do
something. One problem with this approach, which is
recognised, is that the complexity of models becomes
unmanageable the more complex the scenario. More importantly
though the MCT diagram doesn’t expose the fact that there is
no input/output relationship, or what is sometimes called
sensorimotor transformations. The consequence is that the
model-based approach can never be valid for building
artificial systems. As it is attempting to define a facsimile
of a real, chaotic world, it will only “work” in simulated, or
highly-controlled, environments.

1.       If it is assumed, as with the MCT diagram, that there is an
   

input/output relationship and that a model can be constructed
to represent that relationship, then it also seems reasonable
to assume that you could infer that model by observing the
output of the system. What this doesn’t appreciate, but is
more apparent from the PCT diagram, is that the output relates
to the difference between desired and actual values, which may
actually be the noise (disturbance). In other words, modelling
observed behaviour actually models the inherent variations of
the (chaotic) world and not the internal dynamics of the
system itself.
In summary, the MCT diagram leads to a number of invalid
conclusions of control of output, output generation, prediction,
models and modelling of behaviour.

    So, simply the way a behavioural system is represented in the

control engineering world signifies a conceptual blockage to
drawing many important conclusions about behaviour, and so how
to build artificial behavioural systems.

    Perhaps, coming from this angle is a way of getting beyond the

initial obvious similarities. I am thinking out aloud, but
welcome any comments.

Regards,
Rupert

[amatic]

[From Adam Matic 2014.10.04]

I think there is a difference in approach to designing control systems from the start. When it is control of input, then first you need a sensor that is measuring the variable you need to control. Next, you need a comparator and a reference signal, and then an effector that can be varied to affect the controlled variable in the needed range, with the needed resolution. That is about it.

If you think you need to ‘control the output’ then you probably need a model of the output (the plant) to predict how it will react to certain command signals, and you need to calculate the state of the thing you actually need maintained against disturbances. I only know about arm control, so I’ll take an example from there - in mainstream robotics, the procedure of moving an endpoint of the arm from point A to point B consists of finding the spatial difference, then taking into consideration arm mass, arm segment lenghts and joint motor power, and sending appropriate signals to the motors, which will then move the arm. Endpoint position is not directly measured, since that is not the thing that is, in their conception, controlled. This process (inverse kinematics and inverse dynamics) gets very complex very fast, and that is why most industrial arms have 5-6 degrees of freedom tops.

In simpler loops, such as PID, there are some differences, as Martin, Rick, Erling and others have noted. Here is an example of code for motor control:

PID loop:

pos = sensor_reading

error = set_point - pos

derivative = error - last_error

last_error = error

integral = integral + error

output = Kperror + Kd derivative + Ki * integral

end

position-velocity cascade:

pos = sensor_reading

pos_error = set_point - pos

vel_ref = Kp * pos_error

vel = pos - last_pos

last_pos = pos

vel_error = vel_ref - Kv*vel

output = vel_error

end

substituting vel_error and vel_reference, the output can be shortened to:

output = Kppos - Kvvel

or if there is slowing to:

output = output + (Kppos - Kvvel -output)/Slowing

It is interesting that Kv is actually velocity input gain, and Kp is position output gain, which allows for independent changing of gains for position and velocity loops.

This position-velocity cascade is similar to PID. The proportional term is the same. Velocity is similar, since velocity is the derivative of position, and D in PID is derivative of position error. The sign changes, but the effect is the same except there is difference in reacting to a step change is position reference.

The integral term in PID decreases the steady-state error, and I assume the slowing factor in PCT can accomplish something similar, allowing for higher position gains. Perhaps we could try modeling an electromotor with PID and with PV-cascade with slowing, and comparing the responses.

However, the position-velocity cascade is well known in engineering. Sometimes it is position-velocity-acceleration, and PCT does not bring improvements in that area, except for the use of the slowing factor. The slowing factor is a very interesting component. As Martin mentioned, in simulations it is meant to represent the slowness of the effector, such as a muscle, and in physical implementations proportional-only control might be adequate, since the slowing is in the physical motor. I’m not sure this fact is recognized in control engineering. The slowing factor also compensates for transfer delays in the loop, as demonstrated in LCSIII (the LiveBlock demo), and it is quite likely used somewhere in higher levels of control in the brain. Transfer delays can cause instability and robotics engineers use internal models to compensate for delays. I’m really not sure why they don’t just use the slowing factor.

Adam

···

On Wed, Oct 1, 2014 at 9:42 PM, Rupert Young rupert@moonsit.co.uk wrote:

[From Rupert Young (2014.10.01 21.00)]

Today I spent a couple of hours at the BRL (Bristol Robotics Laboratory) with a view to making use of their Robotics Innovtion Facility, that is, use their facilities to apply PCT, for free.

Apart from a quick tour of their robots most of the time was taken up with me explaining the PR/PCT approach and methodology as it would apply to robotics. I described the general theory and particularly how adaptive control could be achieved without recourse to internal models of the world and its dynamics. Although he (the BRL guy) seemed to appreciate the lack of need for models he had trouble understanding (or I had trouble explaining) what PCT adds to what are basically PID controllers. How would you explain the difference?

He wasn’t very impressed with my robots, but did become more enthused after I showed a variety of demos, and we ended with him being “excited” by what we had discussed. What particularly seemed to sway him was Rick’s catching-baseball demo. Cheers Rick!

They are going to sign me up to the RIF and he is going to look out for areas where the approach could be applied to real-world problems; and I will return soon to look in detail at their Baxter robot (http://www.rethinkrobotics.com/baxter/) with a view to implementing PCT.

So, all in all a promising start.

–

Regards,

Rupert

[MartinT]

[Martin Taylor 2014.10.04.10.57]

Perceptual values... "perceptual inputs" sounds as though you are

referring to the inputs to the perceptual function.
But in PCT can be useful. See Bill’s Artificial Cerebellum, which
whitens the spectrum of the loop characteristics, implicitly
modelling such things as resonances in the environmental feedback
path. The result is better control. Engineers know about
prewhitening, but I don’t know whether this is important in the
plant models. Adam [From Adam Matic 2014.10.04] says "
This process (inverse kinematics and inverse dynamics) gets very
complex very fast, and that is why most industrial arms have 5-6
degrees of freedom tops" which suggests that it is not. Certainly
PCT doesn’t need that kind of model.
I would add
4. that the PCT diagram explicitly represents the disturbance and
implicitly shows that all the output must do is match the variations
of the disturbance to oppose it, while adding whatever is needed for
the perceptual value to track the variations of the reference value.
The MCT diagram changes the emphasis to suggest that the “output” is
to match the “input”, ignoring the disturbance, which is hidden in
the “load”.
You have another possible approach, suggested by Adam’s “Endpoint
position is not directly measured, since that is not the thing that
is, in their conception, controlled.” Ask the robotics engineers
“Exactly, not approximately, what is it that your system controls?”
Then, if the answer doesn’t seem to address the problem they are
solving (or even if it does), ask “Why are you controlling that?”
or, if necessary, “How exactly is that being controlled?”. If the
problem actually involves one degree of freedom, as, for example
“Endpoint position”, and they are not sensing it and comparing with
the desired position, ask “Why not?”. If all the answers are
satisfactory, maybe they are using PCT without knowing it.
Martin

···

[From Rupert Young (2014.10.04
15.30)]

    Let me come at this from a different angle (though these points

may have already been made by you, and Bill). From the
implications which arise due to PCT, that are not recognised by
control engineers, or anybody else,

1.         that it is perceptual inputs that are controlled, and
   

never behavioural outputs

1.         that internal models of physical processes are not
   

necessary

1.         that modelling observed behaviour is invalid, as it
   

equates to modelling side-effects, of control
So, how is that we both (us and control engineers) look at, what
are basically, PI[D] controllers and reach different
conclusions?

[rupert]

It is “inputs” to the system that are being controlled rather than
outputs, and they are perceptual in nature rather than other types
of inputs familiar to control engineers, such as setpoints. There’s models and there’s models. I meant ones that require
knowledge of physical equations or physical properties, such as mass
or dimensions. As Bill said, “This adaptation method uses only the
information in the error signal: there is no teacher and no
information about the external world is needed”, in
.
One’s such as I infer from this quote, which requires knowledge of
arm dimensions,
With PCT, though, such a system can be adaptive without needing to
know the dimension.
Re-reading Powers_cerebellum.pdf now looks like what I did in
section 4.5 (Adaptive Control) of

···

[From Rupert Young (2014.10.05 15.00)]

(Martin Taylor 2014.10.04.10.57)

  Perceptual values... "perceptual inputs" sounds as though you are

referring to the inputs to the perceptual function.

  But in PCT can be useful. See Bill's Artificial Cerebellum, which

whitens the spectrum of the loop characteristics, implicitly
modelling such things as resonances in the environmental feedback
path. The result is better control. Engineers know about
prewhitening, but I don’t know whether this is important in the
plant models. Adam [From Adam Matic 2014.10.04] says "
This process (inverse kinematics and inverse dynamics) gets very
complex very fast, and that is why most industrial arms have 5-6
degrees of freedom tops" which suggests that it is not. Certainly
PCT doesn’t need that kind of model.

http://www.pctweb.org/Powers_cerebellum.pdf

http://robohub.org/automata-the-new-sci-fi-blockbuster-set-to-put-robot-ethics-under-a-spotlight/

  > “It’s the view that a robot can’t be

passive, it needs to interact to learn about itself and its
world,” says Broun. “An adaptive system can work out its own
dimensions, for example. Currently, if you change a robot’s arm,
someone has to reprogram the whole system.”

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.9589

I would add

   4. that the PCT diagram explicitly represents the disturbance and

implicitly shows that all the output must do is match the
variations of the disturbance to oppose it, while adding whatever
is needed for the perceptual value to track the variations of the
reference value. The MCT diagram changes the emphasis to suggest
that the “output” is to match the “input”, ignoring the
disturbance, which is hidden in the “load”.

  You have another possible approach, suggested by

Adam’s “Endpoint position is not directly measured, since that is
not the thing that is, in their conception, controlled.” Ask the
robotics engineers “Exactly, not approximately, what is it that
your system controls?” Then, if the answer doesn’t seem to address
the problem they are solving (or even if it does), ask “Why are
you controlling that?” or, if necessary, “How exactly is that
being controlled?”. If the problem actually involves one degree of
freedom, as, for example “Endpoint position”, and they are not
sensing it and comparing with the desired position, ask “Why
not?”. If all the answers are satisfactory, maybe they are using
PCT without knowing it.

http://youtu.be/kOjQRYmeX_o?t=33m20s

      [From Rupert Young (2014.10.04

15.30)]

      Let me come at this from a different angle (though these

points may have already been made by you, and Bill). From the
implications which arise due to PCT, that are not recognised
by control engineers, or anybody else,

1.           that it is perceptual inputs that are controlled, and
   

never behavioural outputs

1.           that internal models of physical processes are not
   

necessary

      So, how is that we both (us and control engineers) look at,

what are basically, PI[D] controllers and reach different
conclusions?