Torque is measured by the controller to deliver the proportional assist power. I can't figure out how the cadence is used? Please share your know how.
In the Turbo PAS Specialized uses in its mid-drives, the primary control on motor power is rider power Pr measured at the crank with a dedicated power sensor.
True cadence (not just yes-no pedal rotation detection) enters this PAS both directly and indirectly. The indirect route comes via Pr according to
Pr = k C Qr,
where Pr is in W, C is cadence in RPM, Qr is rider torque in N m, and k is a unit conversion constant.
But Specialized explicitly states that the PAS also relies on wheel speed and direct cadence sensors. This data likely adds finesse to the primary power-sensing scheme — especially in transient situations like starting out.
You can explore the basic operation of this PAS with the interactive graphical model I presented in much more detail here:
For our more math-minded Specialized mid-drive riders, here's an interactive graphical model of your bike's tunable power-sensing pedal assist system -- hereafter, just "PAS". The model doesn't cover complex PAS responses to transient events like starting out or approaching PAS cut-off speed...
forums.electricbikereview.com
As I noted in your earlier thread on this subject, I have many miles on a power-sensing Specialized Vado SL mid-drive and 2 different torque-sensing hub-drives.
The hub-drives' torque-sensing implementations are quite good. Yes, both have slight lags starting out. And both surge very slightly with pedal position in certain uncommon situations. But motor power delivery is proportional and very natural overall.
The SL's power delivery, on the otherhand, is absolutely flawless in all situations — and even more natural. This is an easily observed fact, not theory.
So, time to accept reality: Rider power and true cadence sensors can be used to very good effect in an ebike PAS. A purely torque-sensing PAS can work quite well, but better-performing solutions already exist.