(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