David said:
The same as I'd hope to gain in theory but with relaxed expectations
due to the non-ideal nature of reality...i.e to significantly reduce
the error in the position of or pressure created by the driver -
thereby reducing distortion.
You would need to invent a new device, something faster than light FTL. Your
driving signal is a couple of milliseconds ahead, because of the highpass
characteristic of the speaker. Whatever you do has to be done before. It
only works for the higher frequencies, at the resonance the phase shift is
already +90° leaving little stability margin and without differentiation no
way to pump in any real power. The amp will ad a significant phase shift at
these low frequencies, as will your sensor interface.
The speaker characteristic is of second order, whereas a PID can only
compensate a first order slope and give you max. 45° margin more.
But you could maybe develop a non-linear model for a DSP, glue an
accelerometer on the dustcap and thus determine the pulse response for
different input levels and then apply an inverse model to the input signal.
If you use adaptive filters, you could make up for thermal effects, there is
a lot to imagine.
And then the distortion is mostly because the cone is bending, you need
laser interferometry for that. And it is intrinsic to the speaker
construction.
I like this time-warp predistortion idea, and you do not need a contact
sensor, but can do it with a mike, soundcard and existing programs.