How is purely torque-sensing PAS actually implemented?

[Jeremy McCreary]

Curious as to how purely torque-sensing PAS is actually implemented in ebikes with rear hub motors?

Few details on the internet, but simple control models along these lines keep popping up: At a given PAS level p, the motor's output torque Mp will be

Mp = Xp R

where R = rider input torque at the crank, and Xp is the torque coefficient assigned to level p in software.

Based on the forces I'm feeling on a 2023 Surface 604 V Rook, this control model seems plausible.

Let X1 be the lowest non-zero torque coefficient, and Xmax the highest. Articles cite figures like X1 = 50% and Xmax = 300% without evidence. At best, these are typical settings likely to vary with make and perhaps even ebike model.

On my Rook, X1 seems to decrease as I increase the number of PAS levels from 3 to 5 to 6 to 9. But Xmax seems about the same. The Rook offers some clues as to how the Xp values between X1 and Xmax are spaced, but that's for a follow-up post.

Reality check: Is this simple control model really typical? If not, what is? Any key factors that the parameters Mp, Xp, and R fail to capture?

Assume a geared hub motor operating well within its specs.

 

[scrambler]

The basic principle is that for a max power assist you choose (MP), the torque sensor signal is used as a multiplier from zero to 100% to calculate the actual Power assistance.

So for example, in the simplest case, if you choose a max power assist of 1000W, and the torque sensor signal Tx goes from 1V / Tmin (no pressure on pedals) to 5 V / Tmax (max pressure on pedals), then then at 1V you get no assist, and at 5V you get 1000W of assist.
For the simplest linear response. the formula would look like
Px (assist power) = (Tx -Tmin) * MP / (Tmax - Tmin)
Pmin = (1-1) * 1000W / (5-1) = 0W
Pmax = (5-1) * 1000W / (5-1) = 1000W
P(50%) = (3-1) * 1000W / (5-1) = 500W

That said, depending on the type of torque sensor and controller being used, the calculation can be way more elaborate, with ease in and out curves, nonlinear response, and blending of the Cadence sensor signal...

 

[fooferdoggie]

That said, depending on the type of torque sensor and controller being used, the calculation can be way more elaborate, with ease in and out curves, nonlinear response, and blending of the Cadence sensor signal...

Plus on more mainstream bikes thats a highly guarded secret with patents on the software.

 

[AHicks]

Jeremy, the tough part about torque sensing (from a practical standpoint) is coming up with a controller that will accept a signal from a torque sensing device. Most will not....

There are 2 different fairly easy to source types of torque sensors. One is built into the main crank (sort of), the other is used to hold the axle of a hub motor.

 

[Jeremy McCreary]

Plus on more mainstream bikes thats a highly guarded secret with patents on the software.

Dang, I was hoping to avoid industrial esponiage this time.

 

[fooferdoggie]

Dang, I was hoping to avoid industrial esponiage this time.

well if you now how to hack a Bosch motor good luck (G) this why torque sensing varies form manufacture to manufacture. but its pretty complex and I bet takes al to of work to make it work well since only a few manufactures have such seamless response from the motor.

 

[Jeremy McCreary]

The basic principle is that for a max power assist you choose (MP), the torque sensor signal is used as a multiplier from zero to 100% to calculate the actual Power assistance.

So for example, in the simplest case, if you choose a max power assist of 1000W, and the torque sensor signal Tx goes from 1V / Tmin (no pressure on pedals) to 5 V / Tmax (max pressure on pedals), then then at 1V you get no assist, and at 5V you get 1000W of assist.
For the simplest linear response. the formula would look like
Px (assist power) = (Tx -Tmin) * MP / (Tmax - Tmin)
Pmin = (1-1) * 1000W / (5-1) = 0W
Pmax = (5-1) * 1000W / (5-1) = 1000W
P(50%) = (3-1) * 1000W / (5-1) = 500W

That said, depending on the type of torque sensor and controller being used, the calculation can be way more elaborate, with ease in and out curves, nonlinear response, and blending of the Cadence sensor signal...

Excellent! Where can I read more about this?

Let's see if I understand this correctly. When I select a PAS level, I'm really selecting a motor power ceiling MP. The torque sensor signal then determines what fraction of MP the motor is to deliver. The controller then manipulates voltage or current or both to make it happen?

 

[harryS]

You can buy a torque sensor from Grin ebikes at ebikes.ca. along with their Cycle Analyst display unit. The sensor installs in your bottom bracket and puts out a signal for your pedal pressure. The Cycle analyst converts that to a voltage that most hub motor controllers can recognize as a throttle voltage.
.
https://ebikes.ca/getting-started/pas-options.html
.
However, I am sure the ultimate systems would take into account how fast the pedals are spinnning, the speed of the wheel, and combine all of this into a more pleasureable pedaling experience. Not happening with the above,
.
I am fiddling with a middrive kit, made by Tong Sheng, that uses torque sensing. I didn't get it running til November, so cold weather has limited my trials. The system works, but I.m not sold on whether the added complexity is worth it,

 

[scrambler]

Let's see if I understand this correctly. When I select a PAS level, I'm really selecting a motor power ceiling MP. The torque sensor signal then determines what fraction of MP the motor is to deliver. The controller then manipulates voltage or current or both to make it happen?

A PAS level is to decide how much help you want.
The basics of a torque sensor, is to act as a multiplier of your own force, so that the help you get feels natural, like if you were superhuman.
This is why many of the torque sensing based pedal assist refer to the PAS level as an input multiplier.
If you apply a pressure of X to the pedal, the pedal assist system will multiply your effort by 2 or 3 or more depending how powerful is the motor.

This is why torque sensing Pedal assist is very intuitive, because it responds in real time to the pressure you apply to the pedals.

BUT, the devil is in the details, depending on your cycling conditions, just multiplying your input may not provide the smoothest experience. This is why the best motors use both a torque sensor, to know how much effort you are applying, but also a cadence sensor, to know how fast you are pedaling and how fast the bike is going. All that information is fed into a program (in the controller) that tries to figure out your exact cycling conditions (gear, slope, etc...) and then estimate how must help the motor should provide.

 

[Jeremy McCreary]

https://ebikes.ca/getting-started/pas-options.html

Thanks for the helpful link! The bottom bracket torque sensors described there appear to measure both torque and cadence. From these values, the display calculates human power at the crank -- call it Wc. A programmable scaling factor S then sets Wmax, motor power at max assist, according to Wmax = S Wc.

Grin recommends setting S in the 3-4 range. Nothing on what happens at lower PAS levels, but you could always just reduce S accordingly.

In an ideal world, a control scheme like this would be called "power-sensing" rather than just "torque-sensing", but the latter is what the article uses.

My "torque sensor" is at the right rear drop-out. If it also measures cadence somehow, seems like the rather detailed online specs would have said so. Definitely no cadence sensor near the crank.

That leads me think that my Rook has pure torque-sensing.

 

[mschwett]

Thanks for the helpful link! The bottom bracket torque sensors described there appear to measure both torque and cadence. From these values, the display calculates human power at the crank -- call it Wc. A programmable scaling factor S then sets Wmax, motor power at max assist, according to Wmax = S Wc.

Grin recommends setting S in the 3-4 range. Nothing on what happens at lower PAS levels, but you could always just reduce S accordingly.

In an ideal world, a control scheme like this would be called "power-sensing" rather than just "torque-sensing", but the latter is what the article uses.

My "torque sensor" is at the right rear drop-out. If it also measures cadence somehow, seems like the rather detailed online specs would have said so. Definitely no cadence sensor near the crank.

That leads me think that my Rook has pure torque-sensing.

using input from torque by itself would lead to a very unnatural feeling experience, I’d think. there’s a huge difference between pedaling with a given torque at 10 rpm and 100rpm, and having the motor respond the same way at both speeds would be quite odd feeling. it would also disregard the natural relationship between resistance (particularly wind, but also rolling) and speed, which the combination of speed and torque (aka power) would take into account too.

 

[tomjasz]

well if you now how to hack a Bosch motor good luck (G) this why torque sensing varies form manufacture to manufacture. but its pretty complex and I bet takes al to of work to make it work well since only a few manufactures have such seamless response from the motor.

elite BS

 

[Jeremy McCreary]

using input from torque by itself would lead to a very unnatural feeling experience, I’d think. there’s a huge difference between pedaling with a given torque at 10 rpm and 100rpm, and having the motor respond the same way at both speeds would be quite odd feeling. it would also disregard the natural relationship between resistance (particularly wind, but also rolling) and speed, which the combination of speed and torque (aka power) would take into account too.

Thanks! Aside from a little surging under certain uncommon conditions, I'd rate my Rook's power delivery as quite smooth and natural-feeling. Certainly way more so than 5 bikes we tested with cadence sensors alone.

I think I read somewhere that my torque sensor just measures distortion in its own rear drop-out. Could you get crude but useful cadence info from the ripple in such a sensor's signal?

 

[Jeremy McCreary]

The basic principle is that for a max power assist you choose (MP), the torque sensor signal is used as a multiplier from zero to 100% to calculate the actual Power assistance.
...
For the simplest linear response. the formula would look like
Px (assist power) = (Tx -Tmin) * MP / (Tmax - Tmin)

Thanks for all your help. Where can I read about ebike control models like this? No problem reading engineering journals.

 

[Stefan Mikes]

The premium mid-drive motor e-bikes use from 5 to 6 sensors, so it is not only the torque control. It is not the secret these high-end e-bikes provide the most of assistance in the low speed region where assistance is the most sougth for. Now, there is different motor tuning for city and MTB scenarios. It is not that a simple formula does it all.

 

[fooferdoggie]

elite BS

yet true.

 

[mclewis1]

However, I am sure the ultimate systems would take into account how fast the pedals are spinnning, the speed of the wheel, and combine all of this into a more pleasureable pedaling experience. Not happening with the above,

The torque sensors from Grin have both pedal torque/pressure data as well as cadence (for pedal speed as well as direction). With many of their hub motors you also have the embedded speed sensor (for wheel speed). So the Cycle Analyst has all of that data for the "ultimate" system.

The so called "premium" systems aren't the only ones with all the sensors and the smarts to manage them.

 

[fooferdoggie]

The torque sensors from Grin have both pedal torque/pressure data as well as cadence (for pedal speed as well as direction). With many of their hub motors you also have the embedded speed sensor (for wheel speed). So the Cycle Analyst has all of that data for the "ultimate" system.

The so called "premium" systems aren't the only ones with all the sensors and the smarts to manage them.

no but they have refined it over many years.

 

[Stefan Mikes]

The so called "premium" systems aren't the only ones with all the sensors and the smarts to manage them.

As many sensors as Specialized or Giant e-bikes? (I am sure Bosch has all of them too).

 

[Jeremy McCreary]

I was really hoping this thread wouldn't generate into a "my bike's better than your bike" thing, or "my control system's better than yours". I just want to know how torque-sensing works at a more detailed level.

But here we go again!