Using "measured" MOT_THST_EXPO: What improvement can one expect?

ArduCopter
24

Hi Olliw42,

I am happy that you found the problem. It looks like you included your junk measurements at the lower end in the data fit though and that is probably why you are still getting the wrong result. (in the context of a real tune)

It is worth noting that my numbers are based on just the first sweep too as I was doing a quick calculation. If I use all the data and the remove all values below my Min PWM setting I get:
Min PWM : 0
test : Expo : 0.99985 , Zero Throttle : 0.034106 , Max_Thrust : 0.87124
Min PWM : 0.05
test : Expo : 0.99985 , Zero Throttle : 0.034106 , Max_Thrust : 0.87124
Min PWM : 0.1
test : Expo : 0.99985 , Zero Throttle : 0.034106 , Max_Thrust : 0.87124
Min PWM : 0.15
test : Expo : 0.99985 , Zero Throttle : 0.034106 , Max_Thrust : 0.87124
Min PWM : 0.2
test : Expo : 0.72572 , Zero Throttle : 0.14802 , Max_Thrust : 0.86822
Min PWM : 0.25
test : Expo : 0.6265 , Zero Throttle : 0.18258 , Max_Thrust : 0.86504
Min PWM : 0.3
test : Expo : 0.72258 , Zero Throttle : 0.14755 , Max_Thrust : 0.86744
Min PWM : 0.35
test : Expo : 0.87766 , Zero Throttle : 0.083542 , Max_Thrust : 0.86909
Min PWM : 0.4
test : Expo : 0.99973 , Zero Throttle : 0.028075 , Max_Thrust : 0.86911

MOT_THST_EXPO is not intended to be a way to characterise the motor, it is a variable used to linearise the thrust in over the used range, a sensible and simple way. If used properly it does a good job. Like many things it is easy to use incorrectly.

Yes, as we implement it, it was never intended to be a figure of merit to compare drive systems. It’s sole purpose is linearise the thrust characteristics for the purposes of maintaining a good tune over the throttle range.

Looking at your data it appears like your ESC’s are not operating reliably below 0.2. Using only data above 0.2 I get an EXPO of 0.6265. If I adjust the minimum throttle to 0.2 I would need to adjust the expo to 0.54157 if I wanted to make it perfect based on your data.

A final note on the application. The goal of MOT_THST_EXPO is to ensure the gain of the PID loops remain reasonably constant throughout the throttle range. That means it is not the thrust fit that is really important, it is the slope of the thrust fit.

This has been demonstrated to work extremely well in practice. As you can see using your data, you can get reasonable results with a range of parameters, depending on the throttle range your aircraft works in and how tight your tune is. Compared to the majority of pilots, my aircraft cover a significantly greater throttle range and I have much higher expectations of tune quality. As such I go to much greater effort to ensure I get the most out of my aircraft.

For the vast majority of pilots a value of 0.65 combined with a simple autotune will make them very happy.

25

I have left the “noise” at small pwms in the fit, since it’s not reasonable that the current is zero there. These noisy data have the effect of giving some small current in average in this region and to “bend” up the fit a bit yielding a more realistic result.
Cutting out parts, as you do in somewhat arbitrarily setting min and max is IMHO not appropriate. As you mentioned, explained, demonstrated, and agreed to, the value of EXPO is much dependent on the choice of min/max. Thus, it must be determined in accordance to what min/max values are actually used by ArduPilot. Otherwise it’s an arbitrary number generator, of no use for setting ArduPilot’s EXPO parameter. In fact, I see a bit of a bias in your reasoning, it seems that you kind of like some values better than others and rather prefer to move your min/max around to get there. I argue the other way around.
Glad to hear that you agree that the value of EXPO has no meaning, in the sense of a characteristic value. I totally understand that this is not what is needed here, you just needed some analytical expression, and your choice is perfectly fine. It’s more that I was a bit surprised to realize it’s true nature, since exponents are usually used to characterize the thrust of propellors, and I’m kind of used to think about exponents in terms of a characteristic value. In other words, the MOT_THST_EXPO could be derived from a more fundamental description of the thrust curve which typically would be characterized by a characteristic exponent.
As was concluded already in the above, the large majority of us don’t really need to worry about getting EXPO really perfect, only if it gets extreme one may want to act. But it’s probably good to have a relatively simple method at hand to identify that. And reassuring to know that one is not totally of the mark if one finds it to be normal.
:slight_smile:

cheers, Olli

BTW, I think it would bit a bit of a stretch to claim that the KISS 32A ESCs do not operate reliably below 0.2. I guess you rather would want to discuss that with Felix/Flyduino, not me :smiley: The current measurement however, as I’ve pointed out earlier, indeed doesn’t look reliable here; I’ve brought this already to Felix’s attention.

26

Obviously bad data does not give a better results. It is either repeatedly going back into restart mode or it is blatantly bad data. In either case you are just adding noise and messing up your fit over the good data.

There is nothing abetary about cutting out the data I chose to cut out. I chose that point assuming the ESC is still going in and out of start mode there. You don’t want the controllers to have to deal with that as it increases the load on the ESC and increases the chances of sync loss.

Given that you are not actually measuring the thrust curve here and I can’t actually tell if the motor is stuttering or if it is a bad current measurement this is just an exercise to demonstrate to other users how to approach the problem.

Statements like this make me wonder if you actually understand why we are doing this at all or if you are simply having fun trying to get a rise out of me. If you don’t understand I am happy to try to explain it to you in simpler terms. (see what I did there)

%%%%
For the benefit of others
-The process is define the minimum thrust level that will result in reliable operation of the esc/motors. To do this you need to get the motor/esc on a thrust stand and do step increases from minimum throttle to mid and max throttle. This defines the MOT_SPIN_MIN. You should also consider your ESC settings to ensure reliable operation during these tests.
-Then plot your thrust curve and check for a flat spot at the top of the ESC throttle range. If you have this set MOT_SPIN_MAX to take it out.
-Finally you set MOT_THST_EXPO to get the best fit of your thrust curve between MOT_SPIN_MIN and MOT_SPIN_MAX. There are some instances where there is an unusual thrust curve that this simple equation does not fit well to, often caused by over powering the prop. In that case you need to consider where in the thrust curve you will be operating generally and consider choosing a curve that does not increase the gain of your pid loops over the throttle point where you do your tuning.

For most people this isn’t necessary unless you are working with a wide range of take off weight, or are building a racing aircraft (think of it as TPA for racers).
%%%

Yeh I called it EXPO because I thought people would relate to it through the EXPO function in their Tx. The equation is based on physical reality of propeller thrust vs voltage drive with some loss. That is why the single value approach works well. Thankfully the same equation can be still used when starting from a non-zero minimum thrust.

Oh, you do like to cause trouble don’t you :slight_smile:

27

first, I don’t treat anyone just for the sake of it. And, honestly, it’s exactly the other way around. Statements like this make me wonder if you actually understand what you are doing here, and what is wrong with your number gaming and why it is wrong. Also, I think I have explained this now through arguments at least three times. It’s clear that you don’t see the fallacy you are trapping into here, and it is sad that you are not willing to assume for a second that the arguments I presented could have a merit, which they have, and give the arguments a thought. I would recommend looking up the phrase I’ve used twice in the above, but I assume it would not be perceived as a well intentioned recommendation, so I better don’t.

Oh, you do like to cause trouble don’t you

I do have opinions, and I have clearcut arguments leading to these opinions. If you consider this as like to cause troubles, then you’re free to do so, but I really don’t have to worry about or should take serious such an interpretation.

Anyway. the relevant conclusion has been drawn now twice, and the question raised in the title been answered.

good luck
Olli

28

Hi Olliw42,

Sorry for offending you Olliw. I assumed that you were aware of the condescending way you talked and that you were just playfully trolling a little so I played a little myself.

You came to the thread with some interesting work that may have some value if we can establish that the results are representative of the thrust curves on the problem propeller examples. Thank you for that!

I pointed out a mistake and where you made it. You then spent a bunch of time arguing that you didn’t make the mistake I pointed out or that it was my fault in some way. You finally worked out your initial mistake and corrected it. Thank you for that!

I then corrected you on your interpretation that the value was meant to be more than a single value interpolation factor for measured data over the used range. You continue to make demeaning statements about the usefulness of the approach that would suggest to users that have not taken the time to understand the math that the MOT_THST_EXPO factor is not important or worse does nothing useful at all. That doesn’t help anybody and calls into question if you actually understand the application/purpose or if you just understand the math.

You also directly claim that I am biased towards specific values rather than use a specific engineering approach to the problem at hand. You then ignore that approach when it is described and demonstrated to you. Quite frankly this is blatantly offensive to an engineer.

Yes, your approach has potential but without comparison to measured thrust data, especially problem combinations, we can’t tell.

Finally you suggest that I was:

And you insinuate that I was criticizing

I assumed that the smiley face meant you knew what you were saying was both completly inaccurate and inappropriate it is so I responded in kind under the assumption you were joking around. Unfortunately it appears that you are unaware of how inappropriate you can be in your replies or you apply different standards to others than apply to yourself. I don’t know which and I don’t particularly care.

So I think I can summarise what we agree on:

  • For the purposes at hand MOT_THST_EXPO is a factor used to line fit the thrust curve of the esc/motor/propeller thrust curve.
  • When calculating a line fit it should be done over the data within the range that you are using in practise. As such it is prudent to discard data outside of that range to achieve the best line fit possible.
  • Finally a user doing this should understand how to shift and scale the axis of normalised input vs thrust to ensure the MOT_THST_EXPO is correct when it is applied to in ArduCopter.
1 Like
29

MOT_THST_EXPO could maybe be autotuned (or post-tuned from log) ? What about measuring performance at different levels by setting throttle demand to a few different levels, then compare power*voltage or vertical acceleration produced at the different levels.

1 Like
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According to prop physics correct expo value should be 0.67 (2/3) for static thrust of ideal prop. That is very close match to recommended 0.65 setting!
Variable prop and motor losses, ESC design and other factors make that number differ from theoretical value.

31

According to prop physics correct expo value should be 0.67 (2/3) for static thrust of ideal prop.

Where did you get 0.67 from?

33

“Where did you get 0.67 from?”

From aerodynamic control volume approach, for example actuator disc theory. This is example:
https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node86.html
See there “11.7.3 Actuator Disk Theory” section. If we take expression for Power (closer to the end of section 11.7.3) , set u0=0 (static thrust), simplify and express Thrust through Power, I think we will get T=const*P^(2/3) for ideal (no loss) system.
If we assume that ESC-motor power is proportional to PWM input, then ideal thrust curve expo is (2/3).
I measured battery side of esc when I did my thrust curve, current draw was proportional to control signal, voltage close to constant. So in that case supply Power = cont * PWM approximately.

Edit: I was wrong: checked my records, current draw was closer to PWM^2

34

image

This equation? if you set U0 = 0 you get power = inf?

edit: rather I mean you get power = zero but you cant solve for T?

35

Yes, this equation, but you have to open brackets and simplify it first, before you set U0=0, this way you get rid of U0 in some terms, and then other terms will go to zero with U0=0
Basically only first term with T/(AdiscU0^2pho/2) will stay in play

36

Wolfram seems to think there is no solution

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It can be easily expanded and simplified on piece of paper. But let’s try wolfram at different angle, set ones to zeros, since they get multiplied by U0=0 anyway, like this:
p = 1/2 * U0 * T * [(T/(AU0^2rho/2) + 0)^1/2 +0] solve for T

I can’t figure out how to copy link to solution :slight_smile:

Edit:
I think this is proper wolfram input:
Limit [1/2 * U0 * T * [(T/(A * U0^2 * rho/2) + 1)^1/2 +1], U0->0]

38

Yeh, this is not correct. It is closer to RPM is proportional to PWM.

39

What is the status here?
Is there a working script that is verified to produce correct expo value?
If the script were a mavproxy plugin - one could automagically fetch/configure correct parameters needed to run the test.
I had trouble getting Flame80A -driven octaquad to behave well under all conditions, with 0.8 or so expo - and suspect this parameter is a major reason…

40

Hi guys, I have check the file “ArduPilot Motor Thrust Fit.xlsx” and studied the formula of Normalized Thrust. Does it just depend on the voltage drop over higher PWM pulse (say 21.72V at 1000us and 21.52V at 2000us) or it also vary if we supply higher voltage (6S, 7S…)

I just want to understand the formula (any research or theory behind?) so, could you please verify this @Leonardthall?

Thanks in advance.

41

Hi, is it possible for you to upload that MATLAB script here. It seems to have been lost and I am not able to find it. Thanks

42

Hi all
very interesting thread. Maybe I missed it but would it not make sense to have a table where everybody buts his measured/tested MOT_THST_EXPO values in with all the measurements?
I would be interested in the following setups:
7inch HQ triblade - 1800kV Xing -Holybro Tekko32 Metal F4
7inch HQ triblade - 1500kV Xing -Holybro Tekko32 Metal F4
T-Motor Carbon P18*6.1 - T-Motor Antigravity MN5008 KV340 - APD 80F3

43

There is this discussion and there’s a table Tridge has to save the new data. I’m tracking it too, in case we can improve the motor thrust expo calculation in the Initial Parameters.
I think it’s on hold while some improvements are being made but I believe the script is totally safe to run, you just need quite some altitude.

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Thanks Shawn
I saw that thread but thought its on hold. You think I could try the script with my overpowered 7"?
I will put ATC_THR_MIX_MAN to 0.2 to be on the safe side. Any other parameter to look at before running it?