PD2 Feedforward Control for Process Transfer Function with Damping = 0

To whom who is interested:
Page 1: Process transfer function with 'damping ~ 0' Page 2: PD(PID) control, PID not active
Page 3: Math Model
http://home.arcor.de/janch/janch/_control/20070608-pd2 (pid)d0/
IT WORKS!
--
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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Dear Jan
JCH wrote:

I have been following the discussion here (passively) for quite some time and register you coming up with various new theoretical ideas that you claim are superior to the existing control design schemes. And yet you have troubles to gain recognition of a single person participating in this discussion.
May I have one suggestion? Why don't you follow a more standard route to the professional recognition that you struggle for? Put your ideas down to a paper, describing the notations properly, formulating the problem clearly and unambiguosly, explaining every detail of your proposed solution, not hiding anything, and submit it to some leading journal on control theory. As you appear to offer fundamentally new concepts, I can recommend one of the following leading journals on control theory:
IEEE Transactions on Automatic Control IFAC Automatica SIAM Journal on Control and Optimization Systems and Control Letters International Journal of Robust and Nonlinear Control International Journal of Adaptive Control and Signal Processing Optimal Control Applications and Methods European Journal of Control International Journal of Control
I can assure you that your paper will receive proper and unbiased attention by people who are experts in the field and whose books you studied (hopefully) from. Alternatively, you can consider either of the two journals
IEEE Transactions on Control Systems Technology IFAC Control Engineering Practice
which are a bit more practically oriented, and yet quite mathematically rigorous.
I believe that it is the only right way. I dont find the discussion group here the best place for a just evaluation of your results (of course, you can do whatever you like, we are free people, but the question of your motivation then arises). The reason is that the forum is attended by diverse audience, including beginers. I don't find it quite fair obviate the standard fields for competition with best in the field and to offer the results to newbies. On the other hand, it is well possible that your results deserve this appreciation by the community. But you will never ever receive it here, on anonymous internet discussion forum, in contrast with having your paper published and ARCHIVED by some leading journal. That is the only way to get these fancy labels of yours like PD2, PD3 into the popular textbooks.
Finally, let me explain the reason for my passivity in the discussion so far. Just imagine that a newcomer to the discussion here goes to the above link without spending several hours by reading your previous inputs here to learn your terminology and notation. Even though my full-time profession is reading and writing control theoretic texts, I have big troubles to find a formulation of the problem, to identify assumptions, to learn how you computed the particular values. I confess that this gives me an impression that you are not really interested in feedback and therefore I am not much motivated to work hard to understand what you are actually trying to do.
All the best,
Zdenek Hurak Department of Control Engineering Faculty of Electrical Engineering Czech Technical University in Prague
PS: Please note that most probably I will not have access to internet till the next Thursday and therefore excuse my lack of responsiveness (should there be anything to respond to).
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Zdenek Hurak wrote:

<SNIP>
<SNIP>
_____ I second Zdenek Hurak's above mentioned recommendations based on what i have seen of JCH's (in Germany) comments. I have offered the odd advice when a "Question about PI control integration time" arose on 2 June. It is very important to ensure that the problems are described clearly and completely, and that the solutions are fully documented.
In my professional opinion JCH might consider taking a position in an industrial setting and work on some real live process plants. There are plenty of real problems to solve; often very simple ones. There is no shortage of control algorithms in the literature, and some of the recent ones (like BrainWave from Vancouver, BC, Canada [now owned by an Austrian company]) and the multi-variable interacting control packages show a great deal of promise, and have been accepted by many plants. These newer approaches are now possible due to the vast processing power we have access to. Simulation has its place, but must be supported by a thorough understanding of the physical limits of process plants.
In my own control engineering career (with a very large multi-national oil/chemical company) i had the opportunity to develop computer control applications that ranged from simple furnace excess O2 control to multi-variable distillation and reactor controls. To learn the control discipline properly there is nothing like designing a control application, developing the economics, getting approval from the Superintendent of Operations, training the operators in the control room, and tuning the loops properly during the commissioning phase.
There is clearly room for academic work, and i fully endorse that as well. However, we must always keep sight of the ultimate goal of the discipline; improve the performance of processes (batch and continuous) via process control that is stable, rugges, reliable, and cost effective.
The technology employed must also be matched to the region of the world in which it is utilised. It may be inadvisable to use a sophisticated gas chromatograph based control scheme in a distillation train on a Venezuelan gas processing platform. The same scheme would be fine in Canada or the USA in a similar plant. The reasons have to do with availability of qualified technical personnel and the ability of local knowledge workers to maintain complex control systems.
--
Regards / John C H (in Canada)

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I'm just a bit stunned that so much analysis would be carried out on such simple systems. Where I come from the control engineer wouldn't even get to hear about these sorts of things. Any competent instrument tech would have it tuned and working fine by morning tea time. Use it as an exercise for one of the apprentices.
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Bruce Varley wrote: <snip>

_____ Exactly. Properly trained instrument technologists with some decent field experience should be able to solve a great percentage of the problems in the plant, especially tuning issues.
--
Regards / JCH

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jch wrote:

Ditto, but remember there's a lot of servo systems out there, too. Many of them that have never been close to a chemical plant since they were little plastic pellets waiting to be sold.
--

Tim Wescott
Wescott Design Services
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Thanks for responding. See basics of this topic in:
Otto Fllinger, Regelungstechnik, Hthig, ISBN 3-7785-1137-8 (He gave lectures at the University of Karlsruhe, Germany)
Otto Fllinger 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:
http://home.arcor.de/janch/janch/_control/20070608-pd2 (pid)d0/
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 http://home.arcor.de/janch/janch/_control/20070611-systemident /
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 http://www.mast.queensu.ca/~dtyner/ControlLab/single-pendulum.mpg
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.
--
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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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 http://home.arcor.de/janch/janch/_control/20070613-pd2 (pid)z1z2/ , 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.
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On Thu, 14 Jun 2007 19:57:42 +0200, Zdenek Hurak wrote:

-- 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.
--
Tim Wescott
Control systems and communications consulting
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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 www.controlguru.com. 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
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snipped-for-privacy@gmail.com wrote:

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.
--

Tim Wescott
Wescott Design Services
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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
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snipped-for-privacy@gmail.com wrote:

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.
--

Tim Wescott
Wescott Design Services
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Zdenek Hurak wrote:

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
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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 and B2 (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 http://home.arcor.de/janch/janch/_control/20070613-pd2 (pid)z1z2/
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.
--
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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On Thu, 14 Jun 2007 19:57:42 +0200, Zdenek Hurak

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.
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On Jun 15, 8:00 am, Paul M <PaulMatWiredogdotcom> wrote:

The www.controlguru.com 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 www.conttrolguru.com 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 http://groups.google.com/group/sci.engr.control/browse_frm/thread/d11d0963eaa46b65/43d61036dda8ded8?lnk=gst&q=tuned&rnum=4&hl=en#43d61036dda8ded8 Poor 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
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What is your definition of damping = 0? I don't see how you figure the damping factor is zero given A1 is not 0.

That works on paper but what do you do when the model isn't exact?

So what is the relationship between K1 and K2? I have said before you should need a target generator and feed forwards for something so simple.

Ship it! Just kidding. Seriously, it only works on your website.
Again, there is no educational value to your website because you don't show how you calculate your solutions.
I think you should play a little game. I think you should vary the model using a standard deviation of 10% after you have calculated the gains and feed forwards. I do. This test lets you know how robust your solutions really are. Feed forwards are great but if they are off by 10% the PID must correct the control output by 10% to get the output to the true value.
Another test. Quantize your double precision floating point numbers to 3 decimal places to represent the the fact that AtoD converters quantize the feed back values.
Peter Nachtwey
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[...]

It works on my computer, not paper.
Show your alternative! The same conditions, please. Process tranfer function: v1 + A1*v1' + A2*v1'' = v2
A1 = 6.324E-05 A2 = 0.001
w scheme as shown in http://home.arcor.de/janch/janch/_control/20070608-pd2 (pid)d0/
--
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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As usually you didn't answer my question about how you figure the damping = 0?
Peter Nachtwey
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