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Off the top of my head there is generalised minimum variance control where a cost function is used to minimise the effort and the errort simultaneously.....this is a fairly complex affair but the idea is nevertheless important....it has many successful applications that apply to energy saving and improved accuracy (crushing of limestone, manufacture of paper, focusing of telescopes....)
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No doubt someone has written a neuro-fuzzy-generalised minimum variance-self-tuning -PID controller....:-)
Not everyone agrees with such uneccessary complexity....i guess it is application specific...but ....my original questions were really regarding saving energy whilst NOT introducing complexity for the operator.....
The PID is the workhorse......and is understood universally...this is true ...but is is it the most cost efficient....consider a 1% increase in efficiency for allthe PID controllers in a large chemical processing plant...over the lifetime....
I am suggesting that it would be worthwhile to, at least, consider..the implications of introducing a more complex controller (for a set typeof processing models...benchmarks) and write the software in such a way that the tuning be indistinguisable from a normal PID.....a tall order perhaps...
Setanta
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This is the general idea
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You are striking on some very common issues. The first step in ANY control problem is to identify the true process objectives. This may be energy, quality, response to upset, or one of many other conditions.
Consider altitude control on an aircraft. At 30,000 feet, with a full load of passenger receiving dinner, the main concern is smooth control response. But when you are landing, it is precise control, and definitely no overshoot!!!
You can find a number of studies on control performance at: http://www.expertune.com/r.asp?f=newsgroup&l=articles.html
In fact, a control conference reviewing practical applications is scheduled for April, 2007. http://www.expertune.com/UG2007.html
I am currently writing a text for the bio-pharmaceutical industry, which will consume the next 6 montsh. Such a practical book for the general industry is needed. If you are seriously interested in publishing a book on practical applications of control, including REAl sensors, REAL controllers, and REAL valves, contact me via email.
-George
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Peter Nachtwey wrote:

The ones I find hardest are the ones that are designed by engineers who really aren't control engineers, then are presented to me with the comment "we just know this should work right, but we can't figure out why it doesn't" :-).

I have been thinking that the world needs "The Art of Control Systems Engineering" in a book, similar to "The Art of Electronics" by Horowitz and Hill.
Most of the control books out there don't talk about the down & dirty aspects of sticky or compliant actuators, sensors with dead spots or inconsistent quantization, mechanisms that change their behavior if the bearings aren't preloaded or the bolts aren't snugged tight, and all those other 'touchy-feely' aspects of control. Even mine only devotes a chapter or two to coping with these effects, and the effects themselves could have been given more print space if I had wanted a much longer book.
This is not something that I could write by myself, and I'm not sure that it could be done with less than four people (which would be a nightmare). Why? I know a fairly large corner of low-end aerospace and high-end embedded control, but I have no practical experience with industrial control such as Peter does. Folks like Peter have experience with industrial control, but I'll bet you that neither of us has much mileage with Matlab-generated pipe dreams, and how to make them really work in actual control systems. If there is anyone out there who could write the whole book from practical experience, they could charge $500 an hour for their time, and they'd never want to do the writing.
Perhaps when I'm old enough to retire I'll know enough to start...

Books certainly take me a lot of work. I find the actual writing part easy; my Master's thesis is long enough for a small book, and it was not a big deal, because I just took the fallout from designing a radio and I wrote it down in a (hopefully) clear and concise manner.
"Applied Control Theory for Embedded Systems", however, took significantly more work, but not in the writing. What had me tearing my hair out, off and on for years, was designing the flow of the book so that it would be a self-study guide, deciding what I could leave out and what I must put in, and designing all of the examples so they actually worked like they said they did.
I know of people who just write and write and write. I stand in awe of them. I simply don't know how they do it, at least if they are writing good books.
"Applied Control Theory for Embedded Systems" -- http://www.wescottdesign.com/actfes/actfes.html .
"A DGPS/Radiobeacon Receiver for Minimum Shift Keying with Soft Decision Capabilities: A Thesis Submitted to the Faculty of the Worcester Polytechnic Institute" -- http://www.wescottdesign.com/articles/MSK/mskTop.html

--

Tim Wescott
Wescott Design Services
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"real systems"
I'm also interested in finding better solutions and developed a program: http://home.arcor.de/janch/janch/_control/20070103-control-e /
EXAMLPE
Page 1: example data Page 2: well approximated ODEs (system transfer functions) Page 3: implementation example
The basic idea is not just using PID (=PID^1) but e.g. PID^5 as well, and 'calculate' the necessary parameters in advance (off line).
That means find the best compensation device ('real controller' for a 'real system').
Applications are thought to be in chemical plants and power stations.
--
Regards/Gre Jan C. Hoffmann
http://home.arcor.de/janch/janch/menue.htm
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The solution of higher order continuous DE's is intriguing but ......what does it represent.....
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JCH wrote:

I think you need to add a quantizing function to the PV so the PV has no more resolution that the 'real' feedback device you would be using. Then run your simulations using PID^5 and tell us what happens.
Peter Nachtwey
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See equation (25) and Fig. 9 c for simple implementation: http://home.arcor.de/janch/janch/_news/20070123-control /
I stated before G1*G7 = 1
1 F(s) closed loop = --------------- 1 1 + ----------- K1*K7*G1*G7
Total open loop amplification = K1*K7 (not time-relevant)
P-Band of controller ~ 1/K1
--
Regards/Gre Jan C. Hoffmann
http://home.arcor.de/janch/janch/menue.htm
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That doesn't answer the question about the quantizing of the feed back and how you can take the 5th derivative of the PV using your PD^5.
I also find it odd that on your website that your process has only zeros and your controller has only poles. A PD has a gain and a zero which is in consistent with the your equations on your website.
Peter Nachtwey
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That's all about.
Therefore I have written a program that can find the cofficients for differential equations up to PD^5: http://home.arcor.de/janch/janch/_control/20070103-control-e / See page 2 for finding DE (second line from bottom) from data points page 1, and see example implementation on page 3 for PD^3 with 3 integrators and calculated coefficients.

Again: http://home.arcor.de/janch/janch/_news/20070123-control / Gain for PD^n: K1 is P-amplification Gain for process^n: K7 PD^n control will have a remaining error (eps) depending on K1. K1 can be set. With high precision compensation eps can be very small. The integrational part (I) normally used in PID controllers will not be necessairy.
Sorry, I don't see problems so far. See for more explanation: http://home.arcor.de/janch/janch/_news/20070124-control /
A_i coefficients belong to process^3 B_i coefficients belong to PD^3
A_i coeffcients (process^n) are not known, but 'can be calculated' by a programm I've written. Then I use them for compensating the process (B_i=A_i).
Result:
F1(p)*F2(p) is equal to G1(s)*G7(s) Next step: consider K1 and K7 K1*F1(p)*K2*F2(p) is equal to K1*G1(s)*K7*G7(s)
--
Regards/Gre Jan C. Hoffmann
http://home.arcor.de/janch/janch/menue.htm
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