Throttle and Current Limit Theory

[safe]

Throttle and Current Limit Theory

In a controller there are two parameters that effect the behavior of the motors powerband. One parameter is the throttle which sets an absolute cap on the duty cycle, but makes no attempt to tell the controller to lower the current. The other parameter is the "Current Limit" that a controller is set to stay within so as to not overheat the motor. These two parameters have VERY different behavior.

First let me begin with a review of exactly what a throttle does. The duty cycle is the percentage of time that a pulse is allowed to remain open within the periodic cycle that the controller cycles through. The typical frequency of the controller seems to be around 20 kHz and so the period is about 20 milliseconds in length. As the throttle is reduced the duty cycle is limited so that it cannot rise above the proportion of the throttle setting. So the effect on a motor looks like the charts below. Notice how at 50% the powerband is effectively unchanged except it's basically "chopped" off from it's high rpms. At below 50% you see things really start to fall apart.

 

[safe]

The next parameter is the current limit of the controller. If you were to create a "current limit based throttle" that ONLY limited the current limit and then allowed the controller to make all the decisions about the actual duty cycle that would be delivered (since that is what the "controller" actually does) then you would see this sort of thing. Notice how in this case the efficiency actually drops away at the high rpms because it's effectively being "starved" of current.

 

[safe]

What if you combine BOTH types of limiting?

That's what we will look at now. These charts show the effect of proportionally reducing the duty cycle limit and the current limit at the same time.

 

[safe]

Analysis

I'll only make a brief comment here and then you can look at the comparision table to understand better. The bottom line is that it seems like a "good idea" to improve things by combining BOTH limiting behaviors into one throttle. "Hopefully" Fechters "Current Based Throttle" works like the combined limiting system and not just an adjustable current limit. The "Boost Control Throttle" also falls into this category of "an improvement" over the standard controller, but not the "ideal".

The "ideal" seems to be to limit BOTH duty cycle and current limit AT THE SAME TIME

Note: The "Torque" value is the "Hub Torque" at the peak power rpm which is normally where you would "feel" the power. If one is at full throttle in all three systems on a steep hill they will work the same and whatever torque is available would be used. The real value of this limiting idea is in saving energy in places where the load is small.

Check out those range numbers for flat land!

 

[TylerDurden]

How are you calculating efficiency?

Looks like you are getting higher ranges, with lower efficiency.

 

[safe]

How are you calculating efficiency?

Looks like you are getting higher ranges, with lower efficiency.

It's called "slowing down". If you ride at full throttle you use up more energy pushing wind around and there's nothing you can do about it. With a fixed gear setup you don't have the freedom to "shift gears" and move the efficiency peak around... it's ALWAYS in the same place. You lose a lot more to the wind than to the motor losses. (I should post the top speeds shouldn't I?)

Now, conversely, when you start to fiddle with the throttle you can change your speed and improve your range. The "trick" here is that with slow speed riding there are a variety of ways that the motor can react to the partial throttle.

So rather than me restating everything, go back through the "lesson" and think in terms of squeezing the maximum out of the bike in an "economy mode" setting.

The startling result is that BOTH duty cycle limiting and current limiting need to be done AT THE SAME TIME in order to squeeze the maximum amount of energy out of the motor.

The results are very impressive.... (and I think this forms the basis of what Fechter is calling his "Current Based Throttle"... at least I HOPE he's using BOTH )

Okay, here's the top speeds that are attained for each type... so there might be an argument for using the current limit only option in that you can get higher top speeds while using less energy than standard. It seems that ANYTHING is better than standard.

 

[TylerDurden]

Jeepers I'm confused...

How can 79% efficiency result in a range of 45.5

But 73% efficiency result in a range of 105.4


Greater than double the range, but 9% less efficient

:?

 

[safe]

Philosphically

When you go back over this stuff it's as though there are two dimensions:

The X-axis is controlled by the duty cycle.
The Y-axis is controlled by the current limit.

So in the default situation the throttle only effects the X-axis. A "current limit" throttle would only effect the Y-axis. Finally a combined throttle would effect BOTH the X-axis and the Y-axis at the same time.

It preserves the geometry of the powerband... which might be why it appears to produce better results than either of the one dimensional alternatives. (including standard)

 

[safe]

How can 79% efficiency result in a range of 45.5
But 73% efficiency result in a range of 105.4

Greater than double the range, but 9% less efficient
:?

But look at the speed difference.

22 mph in the "combined" verses 37.9 mph for the "current limit" solution.

That's twice the speed...

 

[safe]

Okay how about this for a mind blower...

Look at the value for "current limit" at 25 Amps... you get a speed of 37.9 mph and a range of 45.5 miles.

Now look at the value for the "combined" at 50% throttle and 50% amps and you get 45.9 mph and 55.1 mile range.

So the comparisions are complex... you are actually getting a more responsive (more sensitive) throttle with the "combined" solution. The "standard" throttle is "dead to the world" in many situations unable to provide much more than "on" or (within the remaining half throttle) some degree of control.

This is very interesting stuff...

 

[TylerDurden]

But look at the speed difference.

22 mph in the "combined" verses 37.9 mph for the "current limit" solution.

That's twice the speed...

Ja, ok I got that.

Where the hell are those efficiency numbers coming from?


Don't gimmie the 'ol "LOOK at this hand over here!" jazz...

 

[safe]

Where the hell are those efficiency numbers coming from?

Just open the spreadsheet and enter the numbers for throttle and amps ("Main") and watch what happens... (look in the "Power Peak" area) And you might open up "Chart1" and watch things change at the same time.

 

[TylerDurden]

Oy vey.

That doesn't explain WHY.

It is highly unlikely that any system can double its effective range at lesser efficiency.

What is the efficiency calculation BASED ON?

 

[safe]

It is highly unlikely that any system can double its effective range at lesser efficiency.

At half the speed... most definitely. Speed is the biggest consumer of energy on a bike. If you go 22 mph you consume roughly 525 Watts. At 37.9 mph you are consuming roughly 900 Watts. So the losses from the motor become trivial compared to the aerodynamic losses.

You don't seem to be grasping the significance of what this means yet. A low current limit still allows higher speeds, but at lower torque. But when you do the opposite and reduce the duty cycle then you CAN'T get to the high speeds even if you still have good torque.

My "discovery" is that if you limit BOTH at the same time you can retain a powerband of a more "normal" shape.

For the time being (until you understand this better) just get your mind off of the efficiency value. (we can come back to that later)

 

[TylerDurden]

For the time being (until you understand this better) just get your mind off of the efficiency value. (we can come back to that later)

Until all the numbers look reasonable, all the numbers are suspect...


8)

 

[safe]

I was too lazy to do the full lookup by hand on the first pass, so I was just using the peak power number which is slightly different than the actual.

This is not really even related to the issue though...

The "big concept" is the two dimensions of limiting of the motor... the X-axis is the duty cycle and the Y-axis is the current limit.

Depending on how you gear the bike it can sometimes never even reach the peak rpm on the flat. The idea being than on a slight downhill you could go even faster... so the top speed could be into the 70 mph range on this bike. So since the peak efficiency is later than the peak power there is a small difference even on this motor.

Okay... I'm going to do the "hard lookup" so give me a minute...

 

[xyster]

My "discovery" is that if you limit BOTH at the same time you can retain a powerband of a more "normal" shape.

Assuming only a single gear: what happens on an incline where the "PWM effect", as you call it, is most critical to climbing up a hill, and a lower current limit proportionately reduces the torque available for climbing up that hill?

 

[safe]

In order to really prove this one way or the other I'm going to need more time.

Visually you can see that things are happening in interesting ways, but the actual proof is going to take some digging. I basically have to discover EXACTLY all the parameters that go into the RANGE number across all the slices and it's like dealing with a Rubik's Cube of data. (things like wind resistance need to be dealt with properly because they are a big part of the overall efficiency picture)

For now just look at the graphs... and ponder what might be going on...

 

[jackatfsi]

I think safe might just be on to something here !

 

[TylerDurden]

Let's not be hasty...

It's mighty easy to have a fundamental flaw in a cell's formula that gives you wonderful results. (It mighta happened here before!)

It might not be wise to spend a lot of time looking at erroneous data.

Until safe can explain how he is calculating efficiency, all other calculations are an open question.

8)

 

[safe]

Down the Rabbit Hole

Sometimes the "answers" are more complicated than you first think.

What are we really doing when we limit the current? Well, we are telling the controller at what times and at what amounts to give out energy to the motor based on the only mechanism it has which is the duty cycle.

So let's LOOK at the duty cycle... if that's the focal point of controller behavior that's where to look. The first chart is the duty cycle behavior at full throttle. The second chart shows the various throttle / current limit configurations and the effects on the powerband.

Look specifically at the RED line (50% throttle - 100 amps) verses the GRAY line. (50% throttle - 50 amps) At the "peak rpm" for those two curves they become the SAME, but at other areas below the peak the values are different. So it's difficult to really get an accurate calculation that compares the two because at what rpm do you want to compare?

If you take "peak power" this tends to be LOWER in the powerband and you see a difference. If you take "top speed" you tend to get the same result.

So there ARE DIFFERENCES, but I'm going to have to figure out metrics that people can feel comfortable about thinking about.

So it just gets curiouser and curiouser... :wink:

 

[safe]

This will likely only add fuel to the confusion but here goes.

This table compares the results of being at the various throttle settings with the various current limiting themes. As you can see by comparing the numbers you often trade off things like torque for range when you switch types.

It's complex enough that you have to sit back and go "hmmmmmm"... :wink:

 

[safe]

Conclusions

The "standard" throttle produces the maximum torque at low throttle settings. The "current limit" throttle flattens the powerband and allows high rpms while reducing the current "cost" to get there. The "combined" throttle produces a very linear peak powerband torque which would translate into a near one-to-one relationship between throttle and speed.

Looks like with the "current limit" throttle you can effectively "invert" the powerband from a low torque with high rpm at low throttle all the way up to the full throttle setting. (which is universally the same) Such a throttle might "freak people out" because it acts in such a non-intuitive way, but it might be pretty good for hub motors since you can add more "dimensions" to your fixed gear.

The "combined" throttle also can get all the torque that all the others can get at full throttle, but it's best feature is that there is a linear relationship of torque and speed. This would "feel right" and would produce the most consistent range results. Also for HILL CLIMBING on moderate slopes there is some advantage to the "combined" solution. The "combined" effectively is the "compromise" between the EXTREMES of the "standard" verses the "current limit" solution. (moderation in all things?)

The "winner" might actually be the "current limit" throttle after all. The highest range is actually with this type and it also achieves the highest top speed.

 

[Matt Gruber]

u make me feel quite proud,
since i have this control
for 1 year.
not automatic, like u desire,
but quite effective nontheless

 

[safe]

Which type have you implemented?

Are you doing "current limiting"?

Or are you doing the "combined" concept of BOTH "current limiting" and "duty cycle limiting" (so it's linear) at the same time?

There are many "flavors" of limiting systems after all...

(there's also simple static throttle limiting like "Boost Control" which is a whole other category)