I'm newbie so I might understand more

On Thu, 16 Aug 2007 07:07:28 -0700, Boen S. Liong wrote: (top posting fixed)


Do you regularly argue with reality?
There are more control systems that are closed without anyone ever knowing the transfer function than there are systems that are designed with a person doing careful analysis. As of 20 years ago many of these were closed without any_thing_ knowing the transfer function, as well. Even today many control loops are closed around plants so nonlinear that an explicit transfer function is laughably inaccurate, and any internal approximations of plant behavior in an auto tune controller is vague and not at all like an accurate model of the real plant behavior.
The statement "An Unstable System is Obvious" is probably more true than "An Unstable System is Useless"*. So trial and error is use_ful_, because its pretty obvious when you've tuned yourself into uselessness.
Any time you approach a control system design you should assess the level of detail that needs to be done. Many control systems can be successfully implemented and tuned by keeping expectations low and tuning conservatively; some _must_ be tuned this way, if the plants are nasty. In either case, you can buy a whole lot of time saved in return for never reaching the full potential of the system.
Conversely, many control system designs must meet high expectations, indeed, if they are going to be technical or commercial successes. For such systems a careful characterization of the plant is necessary, to the point where merely extracting the transfer function is inadequate. The highest-performance systems that I work on routinely require that I work with the mechanical engineers on the design of the plant to make sure that it can be controlled to the required level of performance, and that the control algorithms take multiple nonlinearities in the plant and actuator into account. For such systems "trial and error" would, indeed, just be "error" -- but there are many more systems for which "trial and error" leads to success.
* Indeed, if the various oscillators in the machine that I'm writing this on were dead stable it would be a broken, dead, useless lump of metal and plastic.
--
Tim Wescott
Control systems and communications consulting
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Thank you. Why trial and error? Maybe something like adaptive, linearization, or stochastic control maybe better. Trial and error? Is it a method? A method call trial and error? Does it give a final state? Final value?
I still don't understand the method call trial and error. Seems to me very confusing.
Seems to me that if transfer function is not known, then we don't know about the characteristics of the process. Anyway, it's very, very confusing. And I don't think anybody will trust trial and error method. Because it an error you make and causes unstable to the system.
Recall that An Unstable System is Useless. So my conclusion is trial and error is useless, because the system can be unstable.
- Boen S. Liong.

Reducing gain will always stabilize the loop behavior. But the result maybe too bad for some applications. Therefore one can use/add more sophisticated means and regard additional values (v1', v1'', z, z', z'').
See definitions: page 1 http://home.arcor.de/janch/janch/_control/20070613-pd2 (pid)z1z2/
This makes trial-and-error tuning difficult. Control design can be very useful because the parameters can be calculated offline using an 'appropriate' process transfer function. Appropriate control equipment is necessary, e.g. fast moving cart, etc.
If the cart does not move fast then one has a different process transfer function. The time behavior of the cart is regarded as part of the process transfer function F1(s)=v1/v2.
See Fig.: page 3 http://home.arcor.de/janch/janch/_control/20070613-pd2 (pid)z1z2/
--
Regards/Gre http://home.arcor.de/janch/janch/menue.htm
Jan C. Hoffmann eMail aktuell: snipped-for-privacy@nospam.arcornews.de
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You mean if the cart doesn't move instantly with infinite gain?. Well duh. At least you now acknowledge that the cart can't move instantly from point to point but you website doesn't reflect that.

I don't know why you persist in this non sense. On page 6 you claim that a PID can't control your system. I proved in a previous thread I can beat your control with a simple PID. How can you ignore that? This is unbelievable.
Peter Nachtwey
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<cited: Completion of Controller Synthesis, 1. July 2007>

http://home.arcor.de/janch/janch/_control/20070613-pd2 (pid)z1z2/
Why should I bother? I proved what I wanted to. You won't meet me half way by answering any questions. As Tim says, "your receiver is broken" you don't listen or don't understand. You are on your own.
</cited>
Did you consider '2 sudden disturbances'? No, you didn't bother!
See Page 6, Fig.2 (z1, z2) red arrows: http://home.arcor.de/janch/janch/_control/20070613-pd2 (pid)z1z2/
You didn't consider disturbances (z) as I did. Don't compare unless you have the same basis for that!
--
Regards/Gre http://home.arcor.de/janch/janch/menue.htm
Jan C. Hoffmann eMail aktuell: snipped-for-privacy@nospam.arcornews.de
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You don't even know what a disturbance is! http://www.engr.uconn.edu/control/pdf/isa04-1.pdf See the pretty picture. I told you that your example of a disturbance is wrong but you just ignored me. Notice that your disturbance look more like a bias or offset to the set point as your 'disturbances' are inputs into the controller. Disturbances affect the process so should be summed afterwards depending on where the disturbance occurs not inputs to the controller.
I have already demonstrated how well my PID can respond to step changes in the set point in my basic example. In any case my example PID will always have a critically damped response as long a the control output isn't in saturation. Since I know what the characteristic equation is I can predict exactly how long it will take to get into the set point within 1% no matter what the disturbance is as long as the controller doesn't saturate the control output. If you can't see that then you have a problem and yes my PIDs response will be better than yours since you rely less on proper tuning and more on your input filter or feed forwards.
Your PIDs wanders all over the place,,,,,still. The problem isn't with the PID, the problem is with the person tuning it. Haven't you figured out what you have done wrong in the last month? Twice I showed how I can solve for gains. Once symbolically and another time using Ackermann's method. Twice you have ignored my examples and persist in your nonsense. When one has perfect information about the model there is no excuse for poorly tuned systems. You just want to make the PID look bad for some reason.
JCH, you are misleading others like User. I told this newsgroup that this sort of thing would happen.
User, if you want to understand more then goto http://www.controlguru.com if you are a process type.
Otherwise look at my posts where there are links to .pdf files on my FTP site. You can learn a lot without having to buy a book. Get a math package. I have Mathcad and Scilab. At least get Scilab. It is free.
Peter Nachtwey
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Why summed afterwards? z1 and z2 are (external) input signals that are processed and then summed to v2! All is in one unit as shown in Fig.2.
Look to Page 1, Equation 2 (controller functions):
http://home.arcor.de/janch/janch/_control/20070613-pd2 (pid)z1z2/
4 components are 'summed' to a total controller function v2:
- PD2 (u transfer function for feedforward 2nd order) - PID (PID controller function for feedback) - z2 (signal, direct and for Z2) - Z2 (- z2 transfer function 2nd order!)
Then z1 and z1*F_open are 'summed' to a total process model K1*v2 (Equation 1). Nothing is missing!
The simulation if using all control functions is shown in Page 2.
--
Regards/Gre http://home.arcor.de/janch/janch/menue.htm
Jan C. Hoffmann eMail aktuell: snipped-for-privacy@nospam.arcornews.de
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Boen S. Liong wrote:

"Adaptive" is just another way to say "automatic trial and error".

"Trial and error" is short for "make a change, observe the result, and from that observation decide on a new change that is likely to be better."

Tuning a system by observing its behavior and with a range of tuning adjustments is a way to deduce its transfer function. "Poke it and see how it wiggles" is a valuable analysis tool.

That's an invalid syllogism. It make no sense for me to claim that a car is useless because it might be unstable.
...
Jerry
--
Engineering is the art of making what you want from things you can get.
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Thanks Jerry for making clarification. Sorry, I miss it. But I will totally disagree with on the last part.
The car is designed to be conttrolable. Remember Wright brothers who are the first to discover aircraft controller. Without Wright Brothers, aircraft was useless because it is a control had not been found. It had been proven useless, until it is proven useful.
I merely copy from a book that states what you call invalid syllogism. I still believe it holds that in general an uncontrollable unstable system is useless. Of course you can still make some exception. The point is how to make it controllable. Furthermore make it observer. That's modern control engineering is all about if u are talking in that frame.
If u want to invent something new, then it would take more than one statement about false or proven.
BTW, u make false assumption by assuming a car is useless. Prove: See above.
- Boen S. Liong


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On Thu, 09 Aug 2007 04:45:33 -0700, Boen S. Liong wrote: (top posting fixed)

It's done every day, in industrial settings the world over. You slap in a controller, you play with the settings for the gains, and if the result is good enough you walk away. Alternately, you push the "autotune" button, the controller plays with the gains for you, and you walk away.
Note that this approach only works if your needs don't approach what the system would be capable of if it were 'properly' tuned, but often the advantages gained from even a less-than-perfectly-tuned controller are more than enough for the job.
As an intermediate step between having no transfer function and having an explicit, accurate transfer function, you can measure the frequency response of a system and use that for your design. Frequency domain design methods have been with us for decades, they're well known by anyone with gray hair, they work pretty darn well for many kinds of systems, and IMHO the measurement of frequency response gives a more accurate characterization of many systems than the measurement of it's step response.
I would be remiss (and Peter would point it out) if I didn't mention that a frequency domain approach doesn't work for _all_ systems: it is most useful where your system doesn't have any nonlinearities such as backlash or friction that make it's high-frequency behavior unpredictable, and there are some systems where a swept-sine response measurement would be prohibitively expensive.
For systems where swept-sine measurement is a no-go, a step (or other simple time-domain response) measurement followed by an ARMA transfer function fit is probably best -- but the data that you collect has a very poor signal/noise ratio at the higher frequencies, which means that your transfer function is guaranteed to be inaccurate up there, which in turn means that you must restrict your control system bandwidth to a figure that may well be lower than what you could otherwise reliably achieve with frequency domain techniques.

You can measure the response + noise, then you can use that measurement to estimate the transfer function. You'll never get a perfect representation, which is why it's called an 'estimate'.
This measurement works even if the system isn't observable -- you get a reasonable estimate of the end-to-end transfer function, you just don't get an estimate of the internal, unobservable dynamics. If these dynamics are stable and well behaved then it doesn't matter if you don't see them.

By testing for observability. See Kalaith, "Linear Systems".

I very much doubt that even 1/10th of 1% of the control loops in the world get analyzed for their robustness during their design -- even in terms of gain and phase margins. Yet they work, because they are designed so that their tuning falls way short of any dangerous instability, or because they are attached to equipment where instability can either be tolerated or where it can be detected and the equipment shut down.
--
Tim Wescott
Control systems and communications consulting
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I see. The autotune is an adaptive controller. It follows certain algorithm in the microprocessor. Even though it is not mentioned explicitly, it implies to find the optimal control for certain processes with regards to the algorithm. Different algorithm yields different control.
And not forget about constraints.
If u have read the book of Kailath, that presents view from theoretical, methodological dan practical side of a control. Then u should agree with me and I agree with u.
But for the sake of arguments. Designing an optimal control and meeting certain constraints cannot be done by trial and error. Because there are infinite feasible solution, and more then one optimal solution.
Heuristic method is good and practical. I won't argue about it. But I will argue the method needed or used to solve a control problem. Different mehtod, algorithm produce different results. As long as it satisfies certain criteria, then the control is good.
Boen S. Liong

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On Sun, 19 Aug 2007 20:26:42 -0700, Boen S. Liong wrote: (top posting fixed)

Optimal control methods tends to design controllers with very high gains, that will get an ideal plant onto target lickety-split, and will make any target that doesn't match the model oscillate even faster.
Robust control methods extend optimal control to find the "best" controller with the unknowns taken into account -- but you have to know what the unknowns are, and parametrize them carefully. This can take an exorbitant amount of time unless you absolutely need the absolute best possible safe control rule.
So for the less than absolutely critical loops, and for the ones with large numbers of poorly understood unknowns, one finds oneself using heuristics, or a combination of heuristics and older formal design techniques.
--
Tim Wescott
Control systems and communications consulting
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Not if the control output costs are factored into equation to be optimized. I have some Mathcad worksheets that show this. I am not home where I can post this but there is already a simular worksheet on my FTP site. ftp://ftp.deltacompsys.com/public/PDF/ITAE0.pdf All I need to do is add a term that include u to the eval in minITAE.
Peter Nachtwey
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On Tue, 21 Aug 2007 15:13:48 -0700, pnachtwey wrote:

If the cost function you're using isn't the actual cost of control then it's not optimal control anymore -- it's just a hack to coerce a formerly 'optimal' control algorithm into producing something that's got stability characteristics that are some poorly defined version of 'better' than optimal control without.
If you want it to be robust, why not use robust design techniques, with a semi-realistic characterization of the plant's variability?
--
Tim Wescott
Control systems and communications consulting
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Thanks, Wescott and Peter N. I see there are a lot to be taken into consideration here. It's not merely designing a so called "optimal control" and defining "control cost J".
What do you think about Algebraic Ricatti Equation (ARE)? I have a lot of interest in it.
- Boen S. Liong

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This sums it all up. Designing the cost function is an art. So do you think that all those people that use linear quadratic control are hackers? What do you do when there are more poles than gains?

I hope you have seen by now that I prefer to vary the model parameters using a Mathcad rnorm function to see how the calculated gain for the ideal model will respond to variances.
Peter Nachtwey
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z1 and z2 can be of any type.
E.g. step function in page 2: z1=-0.1 and z2=+0.1 http://home.arcor.de/janch/janch/_control/20070613-pd2 (pid)z1z2/
--
Regards/Gre http://home.arcor.de/janch/janch/menue.htm
Jan C. Hoffmann eMail aktuell: snipped-for-privacy@nospam.arcornews.de
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