PD2 Feedforward Control for Process Transfer Function with Damping = 0

Peter, why should I stop post calculated data? Anyone can decide to read or to skip my websites. If you won't give me your K_PID, T_I and T_D, please PLONK me.

Thanks in advance.

PS: If anyone else asks me for provable data I will set the data into a website. Please without conditions! Just ask for them.

"Zdenek Hurak" schrieb im Newsbeitrag news:f4ciar$tju$ snipped-for-privacy@ns.felk.cvut.cz...

Thanks for responding. See basics of this topic in:

Otto Föllinger, Regelungstechnik, Hüthig, ISBN 3-7785-1137-8 (He gave lectures at the University of Karlsruhe, Germany)

Otto Föllinger tried synthesis of control on an ovehead crane model. The physics and mathematics (white box) is shown on page 357 to 373. In the end he wrote that 'observers' should be avoided for practical use.

THAT MOTIVATED ME.

My approach solved this. It is just solving a set of 3 linear differential equations of 2nd order:

Though I was sure that it must work but was surprised it did without further tuning.

THE WHOLE STORY:

What I have not discussed so far is how I can get a proper process transfer function if physics is difficult or nonlinear? This problem I solved with process identification methods. If few discrete measured points are known from a step function I use least-square approximation methods (black box) using a program I have written for that purpose.

See example: Page 1

This program makes 'any nonlinear physics' linear for control synthesis and practical use! This I have tested: See page 2.

For a crane all can be derived physically. It is almost a mathematical pendulum with very low damping. For thermodynamical systems like power stations it is almost impossible to derive the differential equation analytically.

15 years ago I transfered an another topic to a university nearby and a student wrote his master thesis with the given topic. It was a success for the student (he got A) and the company I worked for at that time. The student was paid for that work by the company.

Unfortunately I haven't this opportunity any more.

It could be a topic for a master thesis. A motor driven cart, PC and any math program (e.g. MATLAB) that can solve linear differential equations would be necessary:

See necessary equipment

Note

The topic is not new but the way for finding a calculated solution may be new. It is control synthesis of feedforward (PD2), feedback (PID) control, and dynamical disturbance (Z) compensation.

JCH wrote: [...]

Thank you very much, Jan. Expressing the opition, that your examples are difficult to follow for a fresh newcomer to the discussion was not a request for a recommended literature..:-) But with all modesty, I think that I have mastered the basics of control to an acceptable level...:-)

For instance, if I just have a look at the web page

, I can see some block diagram. OK. But what is the goal of the control design here? Fastest response? Is the reference signal only considered to be a unit step? Is overshoot allowed? What are the assumptions about the disturbances? What are the limitations on control variable? What can I assume about the uncertainty in modelling? For instance, will not be the assumption of at least 10% relative error in gain at low frequencies be safer then just assuming totally accurate model?

I am interested in participating in discussion, but I have no time to dig up this information somewhere in one of your numerous previous posts.

Different people write different things...:-) Reading that observers should be avoided in engineering applications is surely an interesting information for researchers in Honeywell Prague Lab, who use Kalman filters frequently in their applications. No, just kidding, I am pretty confident that this information will not be very interesting for them.

I am not quite sure if I understand. What motivates you? Reading a book? By expressing that I am not understanding your motivation I meant that I dont understand why you are performing this public exhibition here while not showing us how you compute the controller parameters? This is what I meant by the claim that I dont believe that you are interested in feedback.

Without further tuning for the purpose of simulations? Well..:-) Thousands of papers have been written that feature the same exellency...:-) What you can perhaps try is to analyze robustness of your controller by perturbing the nominal model a bit (10% at low frequency, some phase shift, ...)

Z.

-- snip --

-- snip --

I'm just finishing up teaching a class in basic control theory for software engineers. Whenever we manage to get beyond the mechanics of squeezing polynomials until they drip out some useful information about system behavior, I'm trying to instill the notions that systems change, systems aren't linear, their models don't match your reality, and 'good' performance depends heavily on what you're designing for.

I prefer to get a hold of the machinery build and point out the same things and convince them good mechanical engineers can reduce the variances and make life much easier for the control guy and more importantly the people that must keep the machine running after those that commissioned the machine have left.

How close must their models be to 'match' reality? I get a little tired of hearing about this or that system is non-linear. Nothing is perfect so why bother? When does one give up on calculating the gains and resort to tweaking gains and drinking coffee? I haven't seen anybody work out how non-linear must a system be to just ignore a linear model and use this lame excuse. Has anybody around done any analysis of where the poles and zeros move if the system parameters vary with a standard deviation of 5% or 10%? It is easy enough to do.

So what if the model doesn't match reality? One can get close enough. If not then there may be something flawed in the design and the mechanical guys should fix it. One can run many simulations where gains are calculated for the model and then test the gains against plants where the model parameters are varied as described above. So what if the system isn't linear? Linearize it! The gains may need to change as a function of the PV but that is easy enough to handle.

Take a look at the heat exchanger example on

It isn't linear yet one can calculate suitable gains almost by inspection. The model doesn't need to be that close. A second order model would be better. Better yet one could calculate how the heat exchanger gain changes as a function of temperature due to the log mean temperature difference.

BTW, if you model the system, you can figure out what parameter variations affect the model the most so you spend more effort estimating this parameter. Go back to the iterative tuning thread and the pdf file I posted a link to that showed how one uses the gradient of the evaluation routine as a function of the plant parameters. Anything one can do to estimate the system better makes the control better.

I know this is too much for basic control students but they should at least know that people solve these problems all the time. Learning the next steps will bring them back for the intermediate course.

Finally, a model or simulation can't really tell one if the system will work. It can definitely show that it will not work. Often this alone can save lots of money and at least point out where the weak spots are. I have saved people a lot of money by just proving a system will not work.

Peter Nachtwey

This info may be also quite interesting for people working in hard disk drive control. Look at your computer disk drive. If it was produced during last 5-7 years, probably it is based on observers one way or another. Many, many observers... for states and for disturbances... :-) Sure, it can be represented in other forms for different purposes, but internally... it is in state space...

--JS

Citation

Sorry for misunderstanding. The literature I recommended describes the problem in detail we dicuss. I meant the basics for topic, not theory.

The goal is designing the best possible controller that fits to the BENCHMARK SCHEME. The controller has all features that can be used. The response can be designed. If using feedforward compensation techniques you can adjust acceleration of the process value by using a filter. I defined the limits for the control variable in a range of 0.2...1. This can be

0.2...1 bar, 4...20mA, 2...10V, 0...100% etc. Simulation is done in this range. So you can set K1=K2=1, having in mind that e.g. 0.2...1 is equivalent to pressure range 0...100bar. The uncertainty in modelling is dependent from the accuracy of the process transfer function. That is generally the weak point. I have written therefore a program for finding an appropriate differential equation. That is the step to reality. The question is how accurate can I identify the process? The model is an ideal assumption that should be aimed to a certain degree if necessary and paid for.

I state: If I have an 99% accurate process transfer function then my calculation is about 99% accurate.

No, solve the task described in the book I mentioned.

Controller parameters: Make a reload and see page 2. See PID in action on page 5. Disturbance compensation (Z1Z2) is switched off. PID makes the work instead. The optimum criterion is not time dependent:

Integral[0...t] abs(e) dt => MIN

As I stated before the process transfer function is the basis. The best approach is ignore physics if too complicated and use least-square methods. Measure some points on site and find a differential equation. Nonlinearities are approximated to linear differential equations.

I have defined A1 and A2 for a 2nd order system. Use these parameters and set B1=A1 and B2=A2 (PD2). For disturbance (Z1) time compensation you can use F_open and for controller variable distubance (Z2) you must compensate the time behavior of the process using A1 and A2 parameters. For details see formulae on page 1.

So far all is feedforward controlled [PD2(xxx)Z1Z2]. What is necessary in addition is I, PI or PID (xxx) for doing the 'fine work', i.e. make steady state error e=0. PID parameters can be found automatically or manually using ITAE criterion or any other wished criterion. I used modified ITAE.

Yes, just one expert of the thousands:

He is the most famos and respected expert in Germany. He was tackling this problem and couldn't find a sufficient solution as he wrote in his book.

I found the solution and show it in

I repeat: If A1 and A2 is 99% accurate then all you see is about 99% accurate. Anyone who can solve the 3 differential equations (page 1) can prove that. Anything you need can be found on the mentioned website. There is nothing left.

Any better alternative concept is welcome based on the BENCHMARK TEST and disturbances already defined.

If leaving the plant I turned the parameters to a more secure adjustment.

On Thu, 14 Jun 2007 19:57:42 +0200, Zdenek Hurak proclaimed to the world:

Thank you for this and a previous post. I would like to some day discuss aspects of PID and mathematical/computer models without having to deal with the history that this subject seems to carry around here. I see other member's comments and it strikes me how different their experience is and the tools they use to do their trade. For instance, Tim W deals with solid state embedded systems that control very responsive elements compared to the tank levels and boiler controls which I learned the basics of PID on. For me models have been of limited use, but this is not true for other people. My intuitive understanding offer little to someone trying to grapple with PID. I think that models are a great teaching tool.

Sometime, I would like to discuss some of this without the thread being hijacked to serve the continuation of the debate that has been raging here.

Thanks again for your concise thoughts. They express much of what I have been feeling.

Honestly, Peter, I think that you are perhaps pushing this too far. The internet is full of texts of disputable validity. You cannot change it. You seem to underestimate the readers, though, be they even control engineering newbies. Relax, Peter. If some newbie gets allured by JCH's confusing texts, it only shows that they did not study hard and were not critical enough. That is life...:-)

Zdenek Hurak

Before you can sensibly ask a mechanical engineer to reduce a variance, you (a) have to know that the variance is likely and will take effort to reduce, and (b) understand that it can be reduced, but probably not eliminated.

One should always be aware that one is trading off the closeness to perfection of one's physical plant with it's expense; sensible tradeoffs don't include doubling the price of the whole effort with the mechanical engineering budget because the control guy is too lazy to do his job, any more than they include the control guy spending that same amount to save 10 cents of mechanical engineering.

Responsible engineering means that you look at the whole life cycle cost and minimize it -- and not spending too long doing so, because that costs money and time-to-market.

You know as well as I do -- just enough. And just how close "enough" is depends on the problem at hand.

You obviously haven't coached enough beginners. Look at the author of this whole thread. Nothing is perfect, and when we assume it is we dig big holes to fall into. You have shown in your posts that you have a deep-down appreciation for nonlinearites like actuator saturation, so don't go downplaying it now! Nothing is perfect, so you should be aware of this and take it into account!

If you're going to refer to ancient threads, resurrect the damn thing so that folks can see how you're mangling the context, please.

Perhaps because the question hasn't come up? I address this in my book, and it's a lengthly subject.

_Sometimes_ one can get close enough, but if you aren't aware that it's an issue you may never check. If you _have_ checked and you _can't_ get close enough with a linear model then you have to decide if you're going to try to compensate for the nonlinearities in your controller or if you're going to hit on the mechanical folks to change their design.

Perhaps. But if you're naively unaware that a system may possibly not be linear, or you haven't been trained to consider component variations, will you know what to ask the mechanical folks?

You contradict yourself. You've just been insisting that nonlinearities must be dealt with by banging on the mechanical engineering team.

Or are you just agreeing with me that one should do that which meets the needs and minimizes cost?

Yea, so that was my point, too -- why the vehemence?

That's a good point, although I would argue that modeling and simulation can give you a pretty darn good idea of how _likely_ it is that a system will work, or at least tell you what sub-systems need to be investigated more before you build the whole thing.

The

site has plenty of information for process control. You can find the formulas for calculating the PI or PID gains there if you can determine the plant gain, time constant(s) and dead time. There is instruction there on how to determine the plant parameters too. You should be able to get close with little trial and error very quickly. After reading all the material there you should be able to see things in a different way. There are equations that directly relate the PID gains to the plant parameters. This makes one think, should I be tweaking gains or tweaking the plant model when a gain needs to be changed?

What you should realize is that given one knows tha plant parameters the gains can be calculated. The examples on

use direct synthesis which I can explain or you might try asking the control guru guys on how the gain equations are derived. It isn't that difficult. I use pole and zero placement to provide the desired response I want. For motion control applications I think this more robust than direct synthesis. Tim has expressed his opinion about pole placement. I think 'yuk' described it. I haven't figured out how Tim computes his PID gains except that he uses a swept sinewave to generate a Bode plot. You see even those of us that do very fast embedded control have different techniques.

Both direct synthesis and pole placement require that the parameters of the plant be identified. It is this identification that is the real challenge. This is what the Bestune, Expertunes and Control Stations are really offering is the system identification. This also the heart of the auto tuning for motion controllers.

Yes, but math is the same. Boiler controllers are a different issue and are much more complicated than a simple PID. I am a motion control person now but once an engineer in a power plant and the steam generator control was more than just a PID because there are multiple inputs.

Yes, once a few years ago I caught a person telling another how to tweak a PID knowing nothing about the system. I made a series of Excel work sheets of different types of plants and I challenged the people on the forum to tune them. The point was to show how each system is different. One size does not fit all.

The newsgroup has history. There seems to be two camps. There are those that think gains are calculated and

Tom got no help. He didn't even post a follow up. There was no intelligent life here. Shame. Pole placement and direct synthesis have been around for a long time.

Peter Nachtwey

Why is it that I can leave JCH's post alone for a couple days and no one can find the flaws? I think he is fooling more than the rookies. You and I may be very familiar with differential equations but I bet most that visit this newsgroup are not. I think JCH has math skills but doesn't know how to use them. What JCH is proposing will not come close to working in reality. JCH's examples are that bad. I will wait one more day. What is wrong with JCH's laser measurement system? Is a natural frequency of about 5 Hz realistic or is 0.5 Hz a more realistic example? Us JCH's system controllable at 5 Hz. If the natural frequency in JCH's examples are reduced by a factor of 10 what does that do to the gains? What does that do to the control output?

Peter Nachtwey

We teach about 300 people a year on how to tune motion controllers. We try to teach them to know the difference between those systems that can be tuned and those that will be difficult or impossible.

There are too many threads that stated that PID gains are tuned and not calculated. I am hoping you don't agree. Even if the system is not perfect you can adjust the gains on-the-fly to match the current conditions. For instance, a hydraulic actuator can be moving a swing arm or charger for a veneer lathe. This kind of system will not be linear but gains can be calculated as a function of the angle.

That bothers me. I have seen many posts on this news group say PID gains are tuned not caclulated. Long ago wondered what would happen if the system wasn't linear or the plant gains did change. I found that response changed but not that much. Certainly not enough to dismiss calculating gains.

I am not contradicting myself. Sometimes the non-linear swing arm can't be avoided. However, the non-linear valves can be. It costs a little more for a linear valve but it reduces the time to startup the system and to keep it working. That saves money. One can compensate for many things but then only few well trained engineers can maintain the system because the auto tuning systems will not do the job.

Peter Nachtwey

I didn't specify the time scale. It can be milliseconds, seconds, minutes, houres, etc. It can also be 3 seconds, 1/1.1223 minutes.

The distance could be inches, meters, kilometers, etc. Can you find such specifications?

Look at

Tell me where you find a dimension (unit). I wouldn't mind if using 1 pet for 3.5564 seconds and 1 tim for 12.4325 inches. Then read distance in tims, velocity 1 tim/pet and acceleration in tims/pet^2.

Example

1 tim/pet^2 = 12.4325inches/(3.5564 seconds)^2 = 0.982963212809897inches/second

It's convenient to me to tackle such problems as I do. Just the basis must be known.

ABOUT GAINS: I refer for definitions to page 1

e = u - v1 v2_PID = K_PID * (e + 1/T_i * Integral e*dt + T_D*e')

If u=const then e' = - v1'. But u is not constant!

v1 range is 0.2...1 (0.8=100%) and v2 range is 0.2...1 (0.8=100%). If an optimization procedure calculates gain K_PID = 1.65 on the basis 0.2...1 then K_PID = 100%/60.6%

The MAX. controller value can be 100% or 1 for internal value. The MIN. controller value can be 0% or 0.2 for internal value.

If distance transmitter range is 0 to 10 meters then 0.2...1 equals e.g.

4...20 mA and the P-Band of controller is 6.06 meter or 60.6%.

If controller output is moved 10% then 6.06% process value is moved/changed (not regarding integral and derivative action).

Basically one cannot ignore the life point (0.2, 4mA, 2V etc.). You can get into trouble ignoring that in simulating and in practice. Ranges e.g. -10...0...+10V should be transformed e.g. into 0.2...1 or 4...20mA, etc. That is industrial standard and should be used if algebraically processing signals or computer values.

...

Because most people just don't read them any more?

Jerry

"JCH" schrieb im Newsbeitrag news:46752933$0$6397$ snipped-for-privacy@newsspool2.arcor-online.net...

Sorry, should be

That's OK. I think everyone is beyond caring now.

Peter Nachtwey

"Peter Nachtwey" schrieb im Newsbeitrag news:_pKdneBbDJhC5-jbnZ2dnUVZ snipped-for-privacy@comcast.com...

Yes, I know. You find many faults where no fault can be found. I think you are a little bit exaggerating. At least my solver works.

SOLVER TEST

Task and solution:

My solver test for comparing: I was interested. Don't waste your time my solver is ok.

Good. I try to do the same thing. Often just leaving people with the knowledge that there _are_ untunable loops is better than nothing at all

-- that's generally where I start.

I've said this before, I guess I have to say it again: for a system that clearly doesn't need to be pushed anywhere near the limits of stability, a 'casual' tuning approach where you tune by experiment should work just fine. Furthermore, if someone knows _nothing_ about control systems then a casual tuning approach is the only one available

-- and often _any_ closed loop is better than none. For a system that's not safety critical (and I suspect I run into many more of these than you do) I don't think it's a bad thing for people to get their feet wet in control with a casual approach.

Me? With a few exceptions I calculate gains, often from measured frequency response data. The only times I _don't_ calculate gains are when I have a plant that's not at all challenging and goals that are known to be extremely modest in comparison to the plant capabilities, or when I have a plant that I'm planning on measuring, and which needs to be in closed loop for the measurement to be good -- then I'll tune it enough to get it to behave, and take my measurements.

A motor with friction sees an effective gain change of (finite number)/0 if you don't drive it right -- that's more than 10%. Ditto for a motor that's driven right but run through a gear train with significant backlash. These are things that are often not practical to correct by whipping the mechanical designers, so you must deal with them at the control systems level.

Even when one does deal with the issues (and they are well-known and solvable issues) one still has to accept that when the design work is done there will be some residual errors and sometimes significant changes in apparent loop bandwidth as targets are approached.

In the world that I work one cannot lean on auto tuning controllers -- if the tuning that it has coming out of the design phase isn't right then it's broken.

I think we agree on when to ask for mechanical changes.