A spreadsheet with Appendix- page 175, Fact of Control

(Gavin Ritz
2009.07.25.13.57NZT)

[From Rick Marken
(2009.07.21.2245)]

Thanks Rick I see in the book
there are the formulas in the appendix. Your spreadsheet doesn’t really
help that much as your reference signal is fixed and ultimatley it is the reference signal
that is key to the input quantity, the most the important thing for me is to
see the mathematical relationships at this stage.

I hope my maths is up to it, I don’t
do much math anymore. ( I used to be an engineer in another life so it doesn’t
look too foreign)

Bill do you have a spreadsheet for
the Appendix in Fact of Control so I can model Demo 3.1 myself using the
formulas. I hope this is not asking too much.

I’m beginning to get a
much better picture of PCT this way. In fact this is the best depiction I have
so far of PCT, I think this book is just great. It makes now such sense. Language
is such a poor communication tool. I could have read another hundred books on
PCT and I have read all of them and I would not have got the picture I have
now.

Regards

Gavin

···

On Tue, Jul 21, 2009 at 7:15 PM, Gavin Ritz garritz@xtra.co.nz wrote:

Hey Rick can you give me the actual
formulas for calculating the

· Perceptual Signal

· Input quantity (controlled
variable)

· Output Quantity

· Feedback Quantity

· Error Signal

I’ve attached a little spreadsheet model that I just cobbled together. It shows
how the controlled variable (which I see as equivalent to the perceptual
signal) is defined by the perceptual function. I’ve picked a very simple
perceptual function: a linear combination of three scalar physical variables,
two of which can vary independent of the actions of the system and are thus
called “disturbances”; and one of which is the physical output of the
system, which represents the feedback effect of the system’s output on it’s
input. The output function is a pure integrator. I’ve shown text versions
of both the perceptual and output functions; the actual functions are in the
cells that do the computations: the perceptual function is computed in the cell
that produces the value of the controlled variable; the output function is
computer in the cell that produces the value of the output variable.

The spreadsheet uses automatic calculation so if you enter a new value for the
reference (the blue cell to the right of “Reference”) the spreadsheet
will very quickly iterate to produce an output that brings the controlled
variable into a match with the reference. So by typing different values for the
reference you can see that the control system quickly brings the controlled
perceptual variable into a match with it. You can also type in new values
for the disturbance variables (the two blue cells above the word
“Disturbances”). Note that however these values are changed, the
output varies so as to keep the controlled variable matching the reference.

The blue cells are the only ones into which you can enter new numbers without
potentially screwing up the behavior of the control system. I’ve
highlighted the controlled variable cell in rose color just so it’s easy to
compare this value to the reference value (in blue) above it. However,
you can certainly play around with this a bit. The most drastic (and
interesting) changes would be to the perceptual or output functions. Changes to
these could make the system unstable (and, thus, go into a positive feedback,
runaway regime). But you can always leave the sheet without saving it so don’t
worry about breaking it;-)

Have a ball.

Best

Rick

Richard S. Marken PhD

rsmarken@gmail.com

[From Bill Powers (2009.07.24.2056 MDT)]

(Gavin Ritz
2009.07.25.13.57NZT)

Bill do you
have a spreadsheet for the Appendix in Fact of Control so I can model
Demo 3.1 myself using the formulas. I hope this is not asking too much.
I’m beginning to get a much
better picture of PCT this way. In fact this is the best depiction I have
so far of PCT, I think this book is just great. It makes now such sense.
Language is such a poor communication tool. I could have read another
hundred books on PCT and I have read all of them and I would not have got
the picture I have now.

Rick is the one who does the spreadsheet programming. The source code for
all the demos is included in the subfolders found in the LCS3Programs
folder (which appears on your C: drive after installation). This is
basically Pascal code as used in Borland Delphi 7. You should be able to
compile it using Borland’s Turbo Delphi; the Personal Edition is free. If
you just want to read it, the .pas files and most others are text files
you can read with a text editor – Notepad or others. Bruce Abbot rewrote
all my old Delphi programming (which he had already helped me with as I
converted my old DOS programs for Windows) and turned it into
object-oriented code, cleaning up a lot of garbage in the
process.

The Appendix is the real-stuff math by Richard Kennaway. No code for that
– just write to Richard with any questions about it. Unfortunately the
Appendix isn’t well heralded so it looks like a continuation of my
writing until you get to the end where Richard’s name is. That will be
fixed in the next printing.

I really wish these demos had been there when B:CP was published, but I
didn’t know how to do that then. I started working on demos in earnest in
the mid 1980s after the Control Systems Group was formed. The first
tracking experiments were programmed in the 70s, first on a DEC PDP-8-S
that I bought for $7000 I couldn’t afford, then on a home-built
“microcomputer” I built from kits for a couple of hundred
bucks. Much faster. It was a big deal when I added a ten megabyte hard
drive to it, to supplement the 80 kilobyte floppy disks. The CPU was a 2
megahertz Z-80. My present computer is more than 1000 times as fast and
has 12,000 times as much hard drive storage and 30,000 times as much RAM.
Yet I was programming in Turbo Pascal 0.9 back then and getting pretty
decent results (with a little assembler programming in critical places to
make the programs run fast enough).

The present demos have taken a lot of work and learning since then. They
are definitely a lot better than large gobs of words for showing what PCT
means. I’m glad you’re enjoying the book.

Best,

Bill P