I'm newbie so I might understand more

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

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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.

That can work.

How does it simplify things more than what I have shown?

Yes, those are problems. I don't think the technique I used would work unless the crane moved in simple x, y and z directions. Overhead cranes to that.

OK, how do you do that? How would you improve my state space model?

I am sure there are systems like that. There are systems that use cameras too. So what would you do with it? JCH assumed he had perfect position feed back and that the crane position would go instantly to a position proportional to the control voltage. How would you improve on what JCH did?

Peter Nachtwey

"Boen S. Liong" schrieb im Newsbeitrag news: snipped-for-privacy@e9g2000prf.googlegroups.com... 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

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

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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

"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

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.

Did you consider '2 sudden disturbances'? No, you didn't bother!

See Page 6, Fig.2 (z1, z2) red arrows:

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tackling '2 sudden disturbances', Fig.2 red arrows.

arrows:

You don't even know what a disturbance is!

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

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

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):

- 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

The simulation if using all control functions is shown in Page 2.

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. Li> >

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.

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

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?

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

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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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