PCT Formal Model - Car in Lane Example

[From Fred Nickols (2015.11.15.1028)]

Shown below is another example (PNG). This one pertains to the car’s position in a lane.

Corrections? Comments?

image00136.png

Regards,

Fred Nickols, CPT

DISTANCE CONSULTING

“Assistance at a Distance”

The Knowledge Workers’ Tool Room

Be sure you measure what you want.

Be sure you want what you measure.

[From Bruce Nevin (2015.11.15.11:42)]

Ever notice how when you’re rounding a curve your reference is relative to the inside boundary of the curve? Contemplating this, it seemed to me that on a straight road my references for finding the center are the two edges.

image00136.png

···

On Sun, Nov 15, 2015 at 10:28 AM, Fred Nickols fred@nickols.us wrote:

[From Fred Nickols (2015.11.15.1028)]

Â

Shown below is another example (PNG). This one pertains to the car’s position in a lane.

Â

Corrections? Comments?

Â

Â

Regards,

Â

Fred Nickols, CPT

DISTANCE CONSULTING

“Assistance at a Distance�

The Knowledge Workers’ Tool Room

Be sure you measure what you want.

Be sure you want what you measure.

Â

Â

[From Fred Nickols (2015.11.15.1500)]

I suspect we use different reference points; indeed, I doubt there are any universal reference points when it comes to driving. We are of different heights; we sit differently in our seats; we learned to drive differently, etc., etc.

I gauge being in the center of the lane based on the alignment of the car’s hood ornament with the right lane marker or edge of the road.

In a curve to the left, at highway speed, momentum “throwsâ€? the car to the right. I stay focused on the right front fender and keeping it clear of the right lane marker or road edge.Â

On a curve to the right, momentum “throws� the car toward the center line. Then I focus on the center line, keeping my left front fender clear of the center line.

Fred Nickols

image00136.png

···

From: Bruce Nevin [mailto:bnhpct@gmail.com]
Sent: Sunday, November 15, 2015 1:41 PM
To: CSG
Subject: Re: PCT Formal Model - Car in Lane Example

[From Bruce Nevin (2015.11.15.11:42)]

Ever notice how when you’re rounding a curve your reference is relative to the inside boundary of the curve? Contemplating this, it seemed to me that on a straight road my references for finding the center are the two edges.

On Sun, Nov 15, 2015 at 10:28 AM, Fred Nickols fred@nickols.us wrote:

[From Fred Nickols (2015.11.15.1028)]

Shown below is another example (PNG). This one pertains to the car’s position in a lane.

Corrections? Comments?

Regards,

Fred Nickols, CPT

DISTANCE CONSULTING

“Assistance at a Distance�

The Knowledge Workers’ Tool Room

Be sure you measure what you want.

Be sure you want what you measure.

[From Rick Marken (2015.11.15.1600)]

image00136.png

···

 Fred Nickols (2015.11.15.1028)–

Â

FN: Shown below is another example (PNG). This one pertains to the car’s position in a lane.

Â

FN:Corrections? Comments?

RM: This one really is perfect, right off the bat. By George, I think you’ve got it! (I am NOT being condescending;-)

BestÂ

RickÂ

Â

Â

Â

Regards,

Â

Fred Nickols, CPT

DISTANCE CONSULTING

“Assistance at a Distance�

The Knowledge Workers’ Tool Room

Be sure you measure what you want.

Be sure you want what you measure.

Â

Â

Richard S. MarkenÂ

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

[Bruce Nevin (2015.11.16.08:10 ET)]

Avoidance of the edges is what I had in mind. Hood ornament relative to right margin, left fender relative to left margin. “Centered in lane” is a byproduct of these two. As in the Crowd demo, avoidance of getting too close. It can be modeled as alignment of center of car with center of road, and the model will be successful, until you introduce certain disturbances.

  1. Block perception of the center of the lane but keep edges open (on a track where the driver is assured that the lane is clear of obstacles!). I predict no degradation of control of what the observer sees as “car in center of lane”.
  2. Block perception of one or both edges. (There’s no marking in the center.) I predict some wandering around relative to what the observer identifies as the lane.

image00136.png

···

On Sun, Nov 15, 2015 at 3:05 PM, Fred Nickols fred@nickols.us wrote:

[From Fred Nickols (2015.11.15.1500)]

Â

I suspect we use different reference points; indeed, I doubt there are any universal reference points when it comes to driving. We are of different heights; we sit differently in our seats; we learned to drive differently, etc., etc.

Â

I gauge being in the center of the lane based on the alignment of the car’s hood ornament with the right lane marker or edge of the road.

Â

In a curve to the left, at highway speed, momentum “throwsâ€? the car to the right. I stay focused on the right front fender and keeping it clear of the right lane marker or road edge.Â

Â

On a curve to the right, momentum “throws� the car toward the center line. Then I focus on the center line, keeping my left front fender clear of the center line.

Â

Fred Nickols

Â

From: Bruce Nevin [mailto:bnhpct@gmail.com]
Sent: Sunday, November 15, 2015 1:41 PM
To: CSG
Subject: Re: PCT Formal Model - Car in Lane Example

Â

[From Bruce Nevin (2015.11.15.11:42)]

Â

Ever notice how when you’re rounding a curve your reference is relative to the inside boundary of the curve? Contemplating this, it seemed to me that on a straight road my references for finding the center are the two edges.

Â

On Sun, Nov 15, 2015 at 10:28 AM, Fred Nickols fred@nickols.us wrote:

[From Fred Nickols (2015.11.15.1028)]

Â

Shown below is another example (PNG). This one pertains to the car’s position in a lane.

Â

Corrections? Comments?

Â

Â

Regards,

Â

Fred Nickols, CPT

DISTANCE CONSULTING

“Assistance at a Distance�

The Knowledge Workers’ Tool Room

Be sure you measure what you want.

Be sure you want what you measure.

Â

Â

Â

[From Bruce Abbott (2015.11.16.2210 EST)]

Fred Nickols (2015.11.15.1028) –

Shown below is another example (PNG). This one pertains to the car’s position in a lane.

Corrections? Comments?

What is the output, Qo?

What happens if there is a constant wind blowing across the road from the right? Will the car still be centered in the lane?

Bruce A.

image00136.png

Regards,

Fred Nickols, CPT

DISTANCE CONSULTING

“Assistance at a Distance”

The Knowledge Workers’ Tool Room

Be sure you measure what you want.

Be sure you want what you measure.

···

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[Fred Nickols (2015.11.17.0528)]

image00136.png

···

From: Bruce Abbott [mailto:bbabbott@frontier.com]
Sent: Monday, November 16, 2015 10:12 PM
To: csgnet@lists.illinois.edu
Subject: RE: PCT Formal Model - Car in Lane Example

[From Bruce Abbott (2015.11.16.2210 EST)]

Fred Nickols (2015.11.15.1028) –

Shown below is another example (PNG). This one pertains to the car’s position in a lane.

Corrections? Comments?

What is the output, Qo?

[Fred Nickols] The output is turning the steering wheel.

What happens if there is a constant wind blowing across the road from the right? Will the car still be centered in the lane?

[Fred Nickols] That wind is a disturbance; its effects will be detected as part of comparing p and r and will be compensated for in Qo. I assume that if the wind is constant the wheel will be turned slightly more to the right than would be the case if there were no wind.

Bruce A.

Regards,

Fred Nickols, CPT

DISTANCE CONSULTING

“Assistance at a Distance”

The Knowledge Workers’ Tool Room

Be sure you measure what you want.

Be sure you want what you measure.


No virus found in this message.
Checked by AVG - www.avg.com
Version: 2016.0.7227 / Virus Database: 4457/11007 - Release Date: 11/15/15

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Checked by AVG - www.avg.com
Version: 2016.0.7227 / Virus Database: 4457/11007 - Release Date: 11/15/15

[From Bruce Abbott (2015.11.17.0740 EST)]

Fred Nickols (2015.11.17.0528) –

Bruce Abbott (2015.11.16.2210 EST)

What is the output, Qo?

The output is turning the steering wheel.

Yes – at this level of description. (The error signal doesn’t drive the steering wheel directly; there is another level of control, hidden within the output function, that operates the muscles that turn the steering wheel.)

What happens if there is a constant wind blowing across the road from the right? Will the car still be centered in the lane?

That wind is a disturbance; its effects will be detected as part of comparing p and r and will be compensated for in Qo. I assume that if the wind is constant the wheel will be turned slightly more to the right than would be the case if there were no wind.

That’s fine as far as it goes, but it stops short of answering the question: With a constant wind blowing from the right, will the car still be centered in the lane?

Bruce A.

image00196.jpg

[Fred Nickols (2015.11.17.0754)]

image00196.jpg

···

From: Bruce Abbott [mailto:bbabbott@frontier.com]
Sent: Tuesday, November 17, 2015 7:42 AM
To: csgnet@lists.illinois.edu
Subject: RE: PCT Formal Model - Car in Lane Example

[From Bruce Abbott (2015.11.17.0740 EST)]

Fred Nickols (2015.11.17.0528) –

Bruce Abbott (2015.11.16.2210 EST)

What is the output, Qo?

The output is turning the steering wheel.

Yes – at this level of description. (The error signal doesn’t drive the steering wheel directly; there is another level of control, hidden within the output function, that operates the muscles that turn the steering wheel.)

What happens if there is a constant wind blowing across the road from the right? Will the car still be centered in the lane?

That wind is a disturbance; its effects will be detected as part of comparing p and r and will be compensated for in Qo. I assume that if the wind is constant the wheel will be turned slightly more to the right than would be the case if there were no wind.

That’s fine as far as it goes, but it stops short of answering the question: With a constant wind blowing from the right, will the car still be centered in the lane?

[Fred Nickols] Yes, assuming it’s not strong enough to overwhelm the driver’s attempts to keep it there.

Bruce A.

cid:image001.png@01D120BB.63B34040

[From Bruce Abbott (2015.11.17.0910 EST)]

Fred Nickols (2015.11.17.0754) –

Bruce Abbott (2015.11.17.0740 EST)

Fred Nickols (2015.11.17.0528)

Bruce Abbott (2015.11.16.2210 EST)

What is the output, Qo?

The output is turning the steering wheel.

Yes – at this level of description. (The error signal doesn’t drive the steering wheel directly; there is another level of control, hidden within the output function, that operates the muscles that turn the steering wheel.)

What happens if there is a constant wind blowing across the road from the right? Will the car still be centered in the lane?

That wind is a disturbance; its effects will be detected as part of comparing p and r and will be compensated for in Qo. I assume that if the wind is constant the wheel will be turned slightly more to the right than would be the case if there were no wind.

That’s fine as far as it goes, but it stops short of answering the question: With a constant wind blowing from the right, will the car still be centered in the lane?

[Fred Nickols] Yes, assuming it’s not strong enough to overwhelm the driver’s attempts to keep it there.

That is true in my own experience, too. But I think it is important to be aware that it is not true of the PCT model we typically use to illustrate PCT: a simple proportional controller. In such a controller, there must be a non-zero error signal to keep the steering wheel angled so as to oppose the crosswind disturbance to the car’s position in the lane. That means that, so long as the crosswind persists, the car’s position in the lane must remain at least a little to the left of the reference position. How much to the left will depend on the loop gain of the control system, with lower gains yielding greater residual error. Because real drivers are able to “zero out” the error, we can conclude that drivers are not implementing a simple proportional controller.

So then the question becomes, what is the nature of the driver’s actual control system? One possibility is that it is a proportional-integral controller. The added integral component can bring the car’s position to the reference position while maintaining a constant wind-opposing output.

PCT holds that the car’s position with respect to the lane is a controlled variable, but PCT is not wedded to a particular design of control system. A goal of PCT research is to discover how control is actually implemented within the driver’s system.

Bruce

[Fred Nickols (2015.11.17.0937)]

···

From: Bruce Abbott [mailto:bbabbott@frontier.com]
Sent: Tuesday, November 17, 2015 9:10 AM
To: csgnet@lists.illinois.edu
Subject: RE: PCT Formal Model - Car in Lane Example

[From Bruce Abbott (2015.11.17.0910 EST)]

That is true in my own experience, too. But I think it is important to be aware that it is not true of the PCT model we typically use to illustrate PCT: a simple proportional controller. In such a controller, there must be a non-zero error signal to keep the steering wheel angled so as to oppose the crosswind disturbance to the car’s position in the lane. That means that, so long as the crosswind persists, the car’s position in the lane must remain at least a little to the left of the reference position. How much to the left will depend on the loop gain of the control system, with lower gains yielding greater residual error. Because real drivers are able to “zero out” the error, we can conclude that drivers are not implementing a simple proportional controller.

[Fred Nickols] Fascinating! I was a technician in the Navy and I was taught that servomechanisms required an error signal in order to function or they would just sit there. I raised this with Bill on this list once and he said that wasn’t true. Hmm. Oh well.

[Fred Nickols (2015.11.17.0950)]

P.S.

I think a driver can maintain center of lane position despite the crosswind. However, I also believe that is done within some kind of margin of error. In other words, I don’t believe center of lane position can be maintained with no visible, discernible, detectable error. Human beings, unlike computers and some other electronic devices don’t operate anywhere near the speed of light. So to me, center of lane position translates to center of lane plus or minus a bit. A standard generally comes with some tolerances. I think that, for the most part, we human beings operate on a detect and correct basis; we detect an error or the start of a deviation and we correct it.

Fred

···

From: Bruce Abbott [mailto:bbabbott@frontier.com]
Sent: Tuesday, November 17, 2015 9:10 AM
To: csgnet@lists.illinois.edu
Subject: RE: PCT Formal Model - Car in Lane Example

[From Bruce Abbott (2015.11.17.0910 EST)]

Fred Nickols (2015.11.17.0754) –

Bruce Abbott (2015.11.17.0740 EST)

Fred Nickols (2015.11.17.0528)

Bruce Abbott (2015.11.16.2210 EST)

What is the output, Qo?

The output is turning the steering wheel.

Yes – at this level of description. (The error signal doesn’t drive the steering wheel directly; there is another level of control, hidden within the output function, that operates the muscles that turn the steering wheel.)

What happens if there is a constant wind blowing across the road from the right? Will the car still be centered in the lane?

That wind is a disturbance; its effects will be detected as part of comparing p and r and will be compensated for in Qo. I assume that if the wind is constant the wheel will be turned slightly more to the right than would be the case if there were no wind.

That’s fine as far as it goes, but it stops short of answering the question: With a constant wind blowing from the right, will the car still be centered in the lane?

[Fred Nickols] Yes, assuming it’s not strong enough to overwhelm the driver’s attempts to keep it there.

That is true in my own experience, too. But I think it is important to be aware that it is not true of the PCT model we typically use to illustrate PCT: a simple proportional controller. In such a controller, there must be a non-zero error signal to keep the steering wheel angled so as to oppose the crosswind disturbance to the car’s position in the lane. That means that, so long as the crosswind persists, the car’s position in the lane must remain at least a little to the left of the reference position. How much to the left will depend on the loop gain of the control system, with lower gains yielding greater residual error. Because real drivers are able to “zero out” the error, we can conclude that drivers are not implementing a simple proportional controller.

So then the question becomes, what is the nature of the driver’s actual control system? One possibility is that it is a proportional-integral controller. The added integral component can bring the car’s position to the reference position while maintaining a constant wind-opposing output.

PCT holds that the car’s position with respect to the lane is a controlled variable, but PCT is not wedded to a particular design of control system. A goal of PCT research is to discover how control is actually implemented within the driver’s system.

Bruce

[From Rick Marken (2015.11.17.1230)]

···

Bruce Abbott (2015.11.17.0910 EST)

BA: PCT holds that the car’s position with respect to the lane is a controlled variable, but PCT is not wedded to a particular design of control system. A goal of PCT research is to discover how control is actually implemented within the driver’s system.

RM: A goal that is secondary, however, to determining what variable is actually under control (“the car’s position relative to the lane” is a good for an informal description of a possible controlled variable but it is far too vague for use in research). The primary aim of PCT research – and what distinguishes it from conventional research in the behavioral sciences – is the description of the variables that are controlled when organisms are seen to be carrying out various behaviors.

Best

Rick

Richard S. Marken

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

[From Bruce Abbott (2015.11.17.1700 EST)]

Fred Nickols (2015.11.17.0937)

Bruce Abbott (2015.11.17.0910 EST)]

That is true in my own experience, too. But I think it is important to be aware that it is not true of the PCT model we typically use to illustrate PCT: a simple proportional controller. In such a controller, there must be a non-zero error signal to keep the steering wheel angled so as to oppose the crosswind disturbance to the car’s position in the lane. That means that, so long as the crosswind persists, the car’s position in the lane must remain at least a little to the left of the reference position. How much to the left will depend on the loop gain of the control system, with lower gains yielding greater residual error. Because real drivers are able to “zero out” the error, we can conclude that drivers are not implementing a simple proportional controller.

[Fred Nickols] Fascinating! I was a technician in the Navy and I was taught that servomechanisms required an error signal in order to function or they would just sit there. I raised this with Bill on this list once and he said that wasn’t true. Hmm. Oh well.

Well, yes, servomechanisms do “require an error signal in order to function” if by that phrase you mean that changes in output are driven by changes in the error signal. But if “require an error signal in order to function” means that there must be a non-zero error signal in order to have a non-zero output, then the statement is false.

A proportional controller’s output is proportional to the size of the error. If the controlled variable is being acted upon by a constant disturbance, then the only way that such a controller can generate an opposing output is to maintain enough error to produce an opposing output equal to the disturbance. However, an integral controller’s output is proportional to the integral (sum) of the error. A continuous error in a given direction will produce a continually increasing output in a direction opposite that of the disturbance. But as the output increases, it reduces the error, thus reducing the rate at which the integral of the error increases and thus the rate at which the output increases. When the size of the output equals the size of the disturbance, the error is reduced to zero, and the integral of the error remains at its current level; consequently the output remains constant at the value that exactly counteracts the disturbance. So now we have zero error, but a nonzero output.

In bidirectional control systems, errors in the opposite direction summate negatively. If the integral of the error is already positive, the integral will decrease and, if the negative error persists, the integral eventually will become negative. The sign of the output will reverse, restoring the negative feedback relationship. The integral thus introduces a lag in the system’s response to a changing disturbance. A derivative of the error is sometimes added to the output function to reduce this delay.

[Fred Nickols (2015.11.17.0950)]

P.S.

I think a driver can maintain center of lane position despite the crosswind. However, I also believe that is done within some kind of margin of error. In other words, I don’t believe center of lane position can be maintained with no visible, discernible, detectable error. Human beings, unlike computers and some other electronic devices don’t operate anywhere near the speed of light. So to me, center of lane position translates to center of lane plus or minus a bit. A standard generally comes with some tolerances. I think that, for the most part, we human beings operate on a detect and correct basis; we detect an error or the start of a deviation and we correct it.

Excellent observation, Fred. In the example, small deviations from center-lane may not be detectible by the driver, or if detectible, not large enough to bother correcting. (The limits within which errors will produce no response from the control system is sometimes referred to as “dead-band.”) Nevertheless, even if the position of the car is not exactly at the reference value, the driver must bring the heading of the car parallel to the road, as heading errors will accumulate positional error.

Bruce A.

[From Bruce Abbott (2015.11.19.1400 EST)]

Rick Marken (2015.11.17.1230)–

Bruce Abbott (2015.11.17.0910 EST)

BA: PCT holds that the car’s position with respect to the lane is a controlled variable, but PCT is not wedded to a particular design of control system. A goal of PCT research is to discover how control is actually implemented within the driver’s system.

RM: A goal that is secondary, however, to determining what variable is actually under control (“the car’s position relative to the lane” is a good for an informal description of a possible controlled variable but it is far too vague for use in research). The primary aim of PCT research – and what distinguishes it from conventional research in the behavioral sciences – is the description of the variables that are controlled when organisms are seen to be carrying out various behaviors.

Why is it important to know what variable(s) a particular person controls when carrying out a given behavior? What can you do with that information, once you have it?

Bruce

[From Rick Marken (2015.11.2240)]

···

Bruce Abbott (2015.11.19.1400 EST)

BA: A goal of PCT research is to discover how control is actually implemented within the driver’s system.

RM: A goal that is secondary, however, to determining what variable is actually under control

BA: Why is it important to know what variable(s) a particular person controls when carrying out a given behavior? What can you do with that information, once you have it?

http://www.mindreadings.com/ControlDemo/Size.html

RM: Your conclusions about how control is implemented is completely dependent on what variable you think is being controlled. This is demonstrated rather dramatically in my “What is size” demo:

RM: Your conclusion about how control is implemented, in terms of the relationship between control actions (outputs) and stimulus “inputs” (disturbances) will be quite different depending on the variable controlled – area or perimeter. This can be seen in the graph printed at the end of the demo, which plots the relationship between output (width) and disturbance (height) variations. The relationship is linear when the controlled variable is perimeter and non-linear when the controlled variable is area. So if you didn’t know what a person was controlling in this study you could come to quite different conclusions about the relationship between the variable you manipulate (the height of the rectangle) and the subject’s “behavior” (which you define as only their actions, the width of the rectangle).

RM: I think truly understanding this would be a devastating blow to the belief system of a conventional scientific psychologist, which is why PCT has not ignored or rejected by the scientific psychology community. After all “It’s difficult to get a man to understand something when his salary depends on his not understanding it.” But I think it’s the most important thing to be understood about PCT by any psychologist who wants to do research based on PCT. PCT research has to be primarily aimed at determining the variable(s) around which an organism’s behavior (its controlling) is organized. The Test for the Controlled Variable has to be the central feature of doing research on purpose.

Best

Rick

Richard S. Marken

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