servo system and transfer function etc.

[misterT]

They replace (s La + Ra) with (Ra). Well, that's fine in some cases, but we are not really comparing La to Ra, but need to compare (s La) to Ra, which includes frequency.

They are not comparing sLa to Ra. They are just removing the pole (sLa + Ra). When you remove a pole, you must make sure that you do not change the steady state response (static gain). Thats why they replace the pole (sLa + Ra) with just Ra and not with 1. (they set La=0)

There are no strict rules or methods when you can or can not remove a pole.. if you want the model to be as accurate as possible, then you do not remove any poles. If you want to make the model simpler (reduse it to second or first order model). Then you remove the "fastest pole" first. Usually transfer functions are reduced to second order because it is relatively easy to design controllers etc. for second and first order systems.

 

[steveB]

They are not comparing sLa to Ra. They are just removing the pole (sLa + Ra). When you remove a pole, you must make sure that you do not change the steady state response (static gain). Thats why they replace the pole (sLa + Ra) with just Ra and not with 1. (they set La=0)

How, do you know what their logic is? They make almost no explanation other than "when La is small it can be neglected"

We are saying essentially the same thing. If you look at their transfer function just before they derive eqn. 3-120, it is not in a simple pole-zero form. So, they have not clearly identified the pole locations. Hence, we can also say they are simply saying sLa+Ra is about equal to Ra in the frequency range we are interested in. There is more than one way to look at it. But, it all amounts to the same thing. A pole is removed and if La is small enough, it is a pole that we don't care about because it is at sufficiently high frequency to not impact anything we typically care about in a control problem. In fact, it's sometimes out of the bandwidth of our control system.

 

[misterT]

How, do you know what their logic is? They make almost no explanation other than "when La is small it can be neglected"

The only logic there is that if you neglect the La, the error to the model is very small. And it is better to work with simpler model.

 

[steveB]

The only logic there is that if you neglect the La, the error to the model is very small. And it is better to work with simpler model.

Agreed.

But, it is incorrect for you to say "They are just removing the pole (sLa + Ra)", when (sLa+Ra) is not even a pole in the system.

Why add false logic to their simple logic? That's the point of my response. At least my logical conclusion of what they did and said follows ... uh, logic.

 

[misterT]

But, it is incorrect for you to say "They are just removing the pole (sLa + Ra)", when (sLa+Ra) is not even a pole in the system.

Replacing (sLa + Ra) with Ra removes a pole from the system.

 

[steveB]

Replacing (sLa + Ra) with Ra removes a pole from the system.

Of course it does. We agree again.

 

[MrAl]

Hi again,


This is not an issue to be determined by one single reference (that 'book'). Stating that "the inductance is small so it can be ignored" is a very common way to explain this phenomenon withing having to take the time to go into detail about why this was said. If we look at better written books i am totally certain that we will see them comparing the time constant of R and L to the time constant of J and f, and i have absolutely no doubt whatsoever about this because this is a time tested and fairly well known concept.

Just to show how confident i am about this, if someone brought to this thread 2000 references by authors from around the world that stated otherwise i would reject each and every one of them. However i know that wont happen because there's no decent author on this subject who knows their subject well that would ever try to refute the time constant comparison.

I am sure that if we were to look in some decent books we could find this explained better, and that they would definitely make a time constant comparison.

Another way to look at this is if someone told us about four variables that represented four quantities that influence some physical process in the lab, we probably could not predict the outcome of any experiment with that process by knowing only two of those quantities. So if they only tell us what two of the quantities are we are stuck. Stuck unless we can find an equation that proves that the two missing variables are dependent on the two that we do know and by also knowing the law of the process we can work this out. We also realize that initially the process depends on all four variables, but we might want to show that somehow using that process we can show that the two unknown variables are dependent on the other two, or are superfluous so are not needed at all to show the outcome of ANY experiment.

So if someone could show an equation that proves that J and f do not need to be known in order to predict the output of the motor but only L and R are sufficient, then i would be more convinced to take another look. But from past experience with motors i know this can not happen except in the strictest setting where we are only dealing with one motor from one manufacturer and there are already constraints on what the values of J and f can be. But because J and f also depend on the system, we'd even have to restrict our results to that of a single system even though another system had the very same motor in it. And systems vary by extremes...compare a watch movement to a garbage compactor.

 

[misterT]

Mr Al, when you design a PCB, do you ignore the resistance and inductance of the traces (most of the time)? Do you ignore the current leakage, parasitic inductance and resistance of capacitors? Do you compare some values and check if it is ok to ignore them.. or do you just use your common sense and deside to ignore them because you know that they do not affect the perfomance practically at all.. you ignore them because you want to keep things simple.

Ignoring the inductance La is just common sense. Just like ignoring parasitics in passive components in electronics.. Of course there are cases when you can't ignore them, but you pretty much know when it is ok to ignore them.

To ignore or not to ignore. It comes down to one question "do you want your model to be as perfect as possible, or will you tolerate certain error to make your model simpler and easier to work with". How much error you can tolerate in your model is up to the designer and the specs of the system. I do not see how any author can give a definitive rule when you can or can not ignore something.

This is not about solving an unknow parameter with insufficient parameters. This is about building a mathematical model of a physical system. You always ignore hundreds of things without proving "why". It is just common sense. You use intuition, creativity etc. to build a mathematical model of a complex system. You ignore the static friction, but you keep the dynamic friction etc. It is an art at best.

EDIT: MrAl, I read your post again and I am little confused.. are we saying the same thing, or the opposite?

 

[steveB]

This is not an issue to be determined by one single reference (that 'book'). Stating that "the inductance is small so it can be ignored" is a very common way to explain this phenomenon withing having to take the time to go into detail about why this was said. If we look at better written books i am totally certain that we will see them comparing the time constant of R and L to the time constant of J and f, and i have absolutely no doubt whatsoever about this because this is a time tested and fairly well known concept.

MrAl,

I still don't see a big issue. No one here is arguing against the time constant viewpoint, but one always needs to be careful to go carefully through the analysis to make sure that viewpoint holds up in the particular problem you are solving. The book chooses a different way of looking at it, but it's not clear to me that doing so creates any particular issues. If La is small, then τ=La/Ra is small, and it makes sense that the electrical time constant is fast compared to the mechanical time constant. If the mechanical time constant is indeed slow, then this should hold up for a simplified analysis. If the mechanical time constant is fast, then perhaps you dont' want to neglect La. In that case you have two fast time constants and you have to potential to implement a fast controller if you want to. A fast controller with a fast motor may very well require keeping all poles in the analysis. The book's highly simplified approach does not seem to contradict this, as far as I can tell.

Can you give a particular example, with all value specified that you feel reveals a flaw in the way the book approaches the problem? Perhaps with an example, the issues will be more obvious to me.

EDIT: I'll reiterate what MisterT said. I am also confused on exactly what you are trying to say.

 

[The Electrician]

Hi,

Just to add a little here to a good post already here by MisterT...

The units of Torque would be kilogram meters not Newton meters if working in SI units. The energy is in Newton meters.

Are you sure about this?

https://en.wikipedia.org/wiki/Newton_metre

Maybe the SI unit of torque should be the "meter-newton", for reasons similar to the use of the English name "pound-foot" for torque:

https://en.wikipedia.org/wiki/Pound-foot_(torque)

 

[steveB]

Are you sure about this?

https://en.wikipedia.org/wiki/Newton_metre

Maybe the SI unit of torque should be the "meter-newton", for reasons similar to the use of the English name "pound-foot" for torque:

https://en.wikipedia.org/wiki/Pound-foot_(torque)

TheElectrician,

Of course, you are correct. Torque is defined as force acting on a lever arm distance. Hence it is always force times distance which is Newton-meters (Nm), in SI units. However, there is a good reason not to call it a meter-Newton because we would tend to abbreviate this as mN which looks like milliNewtons, and would be confusing.

 

[The Electrician]

TheElectrician,

Of course, you are correct. Torque is defined as force acting on a lever arm distance. Hence it is always force times distance which is Newton-meters (Nm), in SI units. However, there is a good reason not to call it a meter-Newton because we would tend to abbreviate this as mN which looks like milliNewtons, and would be confusing.

That's now how it would be abbreviated; it would be m-N.

 

[MrAl]

Hello again,


misterT:
No i agree with you i am pretty sure i agree fully with you, that the
inductance can be 'ignored', but my test for the significance of the
inductor is to compare the time constant of the R and L with the
time constant of the J and f (f is friction in many texts).
You are saying the poles are the determining factor, and i agree with
that too because the time constants and the poles are closely related.
What i do not agree with i will spell out a little more to Steve because
he is the one that disagrees here.

Steve:
Yes but now your changing your stand. You said that we can compare
R and wL and now you are including the 'mechanical time constant'
which is what i had been arguing in favor of. I see now that you realize
that your R and wL needs something to be compared to, it can not be
held alone by itself in order to determine anything. But still 'w' in
the wL does not make sense even so.

I myself am saying that you can ignore inductance for a couple different reasons
but the best reason is if the time constant of the L and R is smaller than
the time constant of J and f (f friction). That is the best possible way
to test the significance of the inductor and it has to be the best because
it covers ANY values of L, R, J, and f, while other shortcut views can
not cover all cases. Also, i am sure you will find this in control books.
But let me say also that the other methods are often quoted in order to
save time and not have to go into this much detail, and they leave it up
to the reader to find out why. So this gives us a list of methods in the
order of most preferred to least preferred:
1. L,R time constant vs J,f time constant.
2. L vs J.
3. L vs R (or wL vs R).
4. L alone.

Explanation in reverse order:
4. L alone is often quoted to make it short and quick, assming the reader knows why or doesnt care why.
3. L vs R, when it is assumed that the inertia of the system is huge compared to L.
2. A slightly better view in an attempt to convey that the inertia is also important.
1. The ultimate test: works in EVERY conceivable system.

So there you have it. #1 works in every conceivable system while the other views are shortcuts which
will turn up the wrong answer in some contexts. That's why it is best to teach that the time constant
comparison is the best method, and that will be reflected in the best books for sale in most cases.

Another test could go as follows...

I give you three inductances and resistances and you tell me if the inductance is significant
or insignificant in each case:
Case1: 0.1H and 10 ohms
Case2: 0.01H and 10 ohms
Case3: 0.001H and 10 ohms
All you have to do is determine for these three cases if the inductance is significant or not.
You will soon discover that by looking only at the R and L or R and wL that nothing definite
can be established unless we happen to be lucky and have a system with large enough inertia
friction time RELATIVE to R and L time.

I dont see why you wish to hold this book as the Bible on motors anyway.
I am not saying that you are drawing an incorrect 'logical' conclusion based on the text, i am
suggesting that any logical conclusion that comes out of that one text alone can not be sufficient.
We need to look elsewhere because the information in the book is given too quick, without
explanation. So on the one hand you say that that the book does not give enough information,
yet you are more than willing to use that limited information to reach a conclusion. While myself
on the other hand draw information from better texts on the subject which make it more clear
as well as experience with these kinds of mechanical problems.
You can look all over the web and im sure you'll find a huge number of texts that simply state the
same thing that this book does, also without sufficient explanation. But all that means is they
did not want to take the time to explain it as well as i did and misterT did.


Electrician:
No i am not sure how that got there. The SI unit of torgue is the newton meter. A better
wording would have been that Kg meter *could have* been used. Units of newton meter are
definitely more convenient.

 

[misterT]

Ok, MrAl. I think I understand your point.. I hope. There are many ways/reasons to justify why we neglect a parameter (sorry bad english). We can use intuition, "common sense", experience, ignorance etc. But if you are serious about the design, you should use mathematics and actually compare time constants and understand the effect that ignoring a parameter has to your model. Example: The people who design hard drives can't ignore parameters to simplify their model just like that (without doing the math).. it is too high performance device. And pushing the performance of HDD to the extremes is high priority. I think this thread is slowly going into "philosophy of science"

 

[steveB]

MrAl,

I think you misunderstood what my stand was from the beginning. I reread my own post #12 and I feel that that post does not contradict what you and MisterT have been saying.

Of course R and wL need something to compare to. Otherwise, how do know what frequencies are relevant to judge if wL is small compared to R. You have to look at the full system and the application and do a lot of thinking to know the relevant bandwidth (frequencies) to consider in a design. A key thing I was trying to explain to PG was how La is ignored in the analysis of the book. The book arrives at eqn. 3.120 very quickly based on a very simple idea that La is small. But I wanted to stress that you can't judge if La is small without knowing the frequency range that is relevant; - a point which the book neglected to mention. Knowing the frequency range is not always easy in general, and really goes even beyond what you have mentioned too. I would never want to suggest to any engineer or student to take too narrow a view of the system when judging what approximations to make. So, if anything I've said seemed to suggest that, then let's kill that notion now.

Why are you saying that I hold the book as a bible? That is a ridiculous thing to say. How can one page from a student's text book be considered a bible by any reasonable person? I've spent the last 7 years doing advanced motor control on induction, PM and SRM motors. Trust me when I say that I understand that there is a lot to doing a proper analysis and judging where approximations can be made. Also, I can give a few examples where comparing time constants would give the wrong answer about making the approximations. It is too bold to say your #1 comparison works in EVERY conceivable case. There is no way that book, or anything said in this thread can do justice to the full complexity of motor control design. I was simply trying to help PG get over one stumbling block in his studies, and that requires using the excerpt from the book he provided.

To show just how much you misunderstood me, look at what you asked me.

"I give you three inductances and resistances and you tell me if the inductance is significant
or insignificant in each case:
Case1: 0.1H and 10 ohms
Case2: 0.01H and 10 ohms
Case3: 0.001H and 10 ohms
All you have to do is determine for these three cases if the inductance is significant or not."

After I explained the importance of using frequency when comparing R and wL, you give me no insight to judge what frequencies are relevant. How can isolated values for R and L tell me anything about the system to make a judgment about frequency? No, we need all information about the system and the application to decide if eqn. 3.120 from the book might be a simplification we can make in our design. We arrive at eqn. 3.120 in a very simple way, but judging if eqn. 3.120 can be used is a different matter entirely.

 

[PG1995]

Thank you very much, everyone.

The reason that I'm not following this thread closely being that I'm busy with the exams and once I'm free I will read all the posts carefully and try to absorb as much information as I could. For the time being, I have only memorized the fact that La can be ignored. So, please don't mind and don't think that I'm not responding out of carelessness. I appreciate your help; and thanks a lot for your time.

Regards
PG

 

[MrAl]

MrAl,

I think you misunderstood what my stand was from the beginning. I reread my own post #12 and I feel that that post does not contradict what you and MisterT have been saying.

Of course R and wL need something to compare to. Otherwise, how do know what frequencies are relevant to judge if wL is small compared to R. You have to look at the full system and the application and do a lot of thinking to know the relevant bandwidth (frequencies) to consider in a design. A key thing I was trying to explain to PG was how La is ignored in the analysis of the book. The book arrives at eqn. 3.120 very quickly based on a very simple idea that La is small. But I wanted to stress that you can't judge if La is small without knowing the frequency range that is relevant; - a point which the book neglected to mention. Knowing the frequency range is not always easy in general, and really goes even beyond what you have mentioned too. I would never want to suggest to any engineer or student to take too narrow a view of the system when judging what approximations to make. So, if anything I've said seemed to suggest that, then let's kill that notion now.

Why are you saying that I hold the book as a bible? That is a ridiculous thing to say. How can one page from a student's text book be considered a bible by any reasonable person? I've spent the last 7 years doing advanced motor control on induction, PM and SRM motors. Trust me when I say that I understand that there is a lot to doing a proper analysis and judging where approximations can be made. Also, I can give a few examples where comparing time constants would give the wrong answer about making the approximations. It is too bold to say your #1 comparison works in EVERY conceivable case. There is no way that book, or anything said in this thread can do justice to the full complexity of motor control design. I was simply trying to help PG get over one stumbling block in his studies, and that requires using the excerpt from the book he provided.

To show just how much you misunderstood me, look at what you asked me.

"I give you three inductances and resistances and you tell me if the inductance is significant
or insignificant in each case:
Case1: 0.1H and 10 ohms
Case2: 0.01H and 10 ohms
Case3: 0.001H and 10 ohms
All you have to do is determine for these three cases if the inductance is significant or not."

After I explained the importance of using frequency when comparing R and wL, you give me no insight to judge what frequencies are relevant. How can isolated values for R and L tell me anything about the system to make a judgment about frequency? No, we need all information about the system and the application to decide if eqn. 3.120 from the book might be a simplification we can make in our design. We arrive at eqn. 3.120 in a very simple way, but judging if eqn. 3.120 can be used is a different matter entirely.

Hello Steve,


From your statements:

However, my thought was to compare ωL and R which have the same units. We can see in the text that they arrive at eqn. 3.120 by neglecting sL compared to R. Then, they lump parameters together to get a simple expression. I think this is the easiest way to understand the neglecting of inductance in this case. This is what I mentioned above, and I'm not sure why you didn't understand it.

It may very well be that La and R are not enough to look at to see if La can be neglected. However, this is what the book is doing, and my quick look at it didn't reveal a case where La can be neglected if R is small compared to sLa. However, if you have identified another case where R is small and La can still be neglected, then that's fine. You have looked at this in more detail than I have, and I trust your analysis over my lack of analysis.

You have agreed with the book in it's simplicity, now you say you dont agree with the book.
You have debated over what point then all this time if suddenly you agree with me and misterT completely now?

In engineering we look for the best ways to understand.

"After i explained the importance of frequency when comparing R and wL, you give me no insight to judge what frequencies are relevant".

From that statement you find another relevance. But "I" can not give you that value. The only way you can get that is by knowing other parts of the system, which i have already explained. The 'frequency' you refer to can be 0 to whatever. And it's not the frequency anyway that matters.

You said you can compare R to wL and make a determination. I said you can not do that. You said you can do that knowing the frequency, i said you can not know the frequency, but it doesnt help anyway.

For example, 100 Hz. What does that even mean in this context? Explain what you do next.

 

[steveB]

PG,

No problem. Please take your time and deal with first things first.

MrAl,

On your last post, I really feel you are not understanding my points and misrepresenting what I'm saying. I'll have to conclude that I've done a very poor job of communicating. I apologize for not being more clear. Let's just forget my opinions on this matter. They are clearly not useful.

I'll address this one comment in some more detail.

I dont see why you wish to hold this book as the Bible on motors anyway.
I am not saying that you are drawing an incorrect 'logical' conclusion based on the text, i am
suggesting that any logical conclusion that comes out of that one text alone can not be sufficient.
We need to look elsewhere because the information in the book is given too quick, without
explanation. So on the one hand you say that that the book does not give enough information,
yet you are more than willing to use that limited information to reach a conclusion.

Let me be clear that I don't think this book is a Bible, or even of any particular practical use at all. It merely is useful for introducing students into the very basic ideas of a motor control problem.

To say that "any logical conclusion that comes out of the text is not sufficient" is a gross understatement. However, I was not trying to reach a conclusion, but to provide an explanation and a viewpoint to aid in the book's goal to "introduce".

I find it confusing why you highlight a few issues of the book, but ignore so many others.

What about the assumption of linear friction, when many systems have static friction and nonlinear windage effects? It's much harder to make comparisons with the mechanical time constant then. Currently I'm working with two systems used in military applications. One has static friction which is huge and dominates over linear friction. The other deliberately uses windage for cooling and has highly nonlinear viscous friction. This last motor has an inertia well over 1000 kgm^2, with mechanical time constant dependent on operating point (if you linearize the equations), but typically well over 100 seconds. Yet, the L/R is below 1 s. In this case, we can't ignore inductance (because of control requirements) despite the > 1000 factor difference in time constants.

I'm also working on an application with a synchronous reluctance motor for flywheel application. Even though inductance is small for this SRM (τ<0.1s) and even though the inertial is large with tiny friction (τ> 100000s - it is a flywheel after all!), we had to include inductance in the analysis because it is a high speed flywheel (30,000 to 100,000 rpm is expected in these cases), and a speed controller analysis is useless without considering inductance.

What about the crazy assumption that the controller is a simple K1 gain factor. Wow, we have an infinite bandwidth controller with arbitrary gain! I'd like to buy one of those for my next project. Seriously, we know that even an analog controller has a bandwidth limit and we might want to reduce the bandwidth deliberately. We also know that a PI control is more typical in motor control applications. We also know that digital control is more likely nowadays, and typical sample times often place a bandwidth limit lower than we might like.

I can go on and on with criticisms of the book, but think about this last issue from a stability viewpoint. If we use a realistic controller, we will have more poles and zeros in the analysis, and a stability analysis will probably require consideration of the pole related with inductance, if we decide to implement fast current control and speed control on the motor. It is issues like this that force many of us who design in these applications to consider a "frequency" perspective typical in a classical control analysis approach.

Hopefully you can see that there is a lot of detail I withhold when trying to help PG because too much will overload him. The experience you and I have amassed over decades of work can't be instantly transmitted to a student. We have to judiciously temper what we say, or it is too overwhelming.

 

[MrAl]

Hello again Steve,


Yes it is hard to get these points across i agree. But all the variables i have used appear in the book, no more come from outside except the fact that i have seen this before and know what good books say.
The book refers to a certain number of variables, and that is all that we need to understand the point of the book. Bringing in new variables such as disturbance torque is OUTSIDE the realm of the book, but conversing over the variables that were mentioned in the book is valid in determining what the book would have said if they took more time. And if you were to create a list of preferred methods even with more outside variables, the time constant comparison technique would still be above that of purely R and L alone in any way. It would be such that the new variables taken into account would merely be above just R,L and J,f at that point, because obviously a new variable of significance needs to be looked at and that trumps anything that does not that take into account, again this is obvious. And when we seek to understand something we do not attempt to make the problem more difficult we try to make it more simple. In other words, we dont add more variables and then exclaim, "See, nothing works!". For example, did we take into account relativistic effects yet We dont take into account sticking friction because the book does not talk about that at all, and this is more typical too of other books which have a goal to convey other more basic information.

A more light view of this would be to examine the song i think from the late 1960's, the Ode to Billy Joe. Billy Joe was a fictional character invented by the song author. But after the song became a huge huge success, many people began to question why Billy Joe jumped off the 'famous' bridge and killed himself. I think they questioned this because all of the places mention in the song were real life objects located in Mississippi, but Billie Joe was fictional or may have been an old wives tale. But anyway there were various theories that came up about why he killed himself, yet there was no clear cut reason for this. But still people went on and on taking the smallest clues from the song to build a case upon.
Now the point is if we create a theory, it may or may not be right, and we have no way to prove it. But if it was a historical fact, then we could perhaps look in other references to find out the real truth. The truth is not given in the song, but if a record was noted by the local sheriff for example then we would know for sure. But the details are not to be found within the song, so we have to look elsewhere. If we take artistic liberty then there is a chance we will be wrong, but if we look at other references there is almost no change we would be wrong.

But anyway, rather than go on and on about this, i propose that we present a list to PG. A list of preferred methods of determining whether or not the inductance is significant or not. The list could be presented in order of what it takes into account and why it is better than the lower grade method.
We can still talk about this, but it will be much easier to discuss then and the result will help PG rather than make him wade though a mountain of text

Here is the list i propose we start with. Your job then is to reorder the list if you would like to.
Note that f is quoted as b0 in the book itself. Consider this task fuzzy logic.

1. Compare the time constant of R and L with the time constant of J and f.
2. Compare just L with J.
3. Compare wL with R (am still not clear how you would determine a value for w)
4. Compare L with R.
5. Think about L alone.

Note i am still not clear how you would determine a value for w because it's hard to say what frequency is good for a system when it may operate in several basic modes.

The reason i rank #1 as such is because it works in EVERY case that the book works for, and the book was the original subject of the question. I did not include the 'poles' explanation because that is the same as the time constant explanation.

So anyway, you can reorganize that list if you dont agree with it, or add to it, or make some elements have the same rank (such as R and L vs wL and R might both be ranked #2 or #3 or whatever. I think this will show me more about how you are thinking about this.

BTW i do value your views and opinions on these topics as usual.

Perhaps you would like to see an analysis of the system.

Also, maybe you would prefer to read a reference from a better book?

 

[steveB]

As I said, let's forget about my opinion on this matter. It's not leading down a productive path.

I would propose to remove #3 from the list altogether. PG didn't understand the concept and you don't understand how I would estimate frequency. If you don't understand my viewpoint, then surely no one else will. Hence, I failed in my goal to communicate my idea.

I could try harder, but I already put in more time than i should have given my other responsibilities. I'm not trying to debate that my view is best or that other ways are flawed. I'm not trying to present a practical method to do anything.

I just thought I could provide an idea that might help PG understand better, but I was wrong.

A list of 4 should be more than sufficient for PG, once he comes back to this problem.