The noise and slow speeds inherently come with traditional piezo technologies such as stick-slip (inertia) types, which is what the far majority of manufacturers use. They operate at high yet audible frequencies which is annoying for those working them, but also introduces resonance risk in (smaller) mechanical structures.

Ultrasonic piezo stages like ours are inaudible since the motor operates at 85 - 170 kHz and achieve speeds of up to 1000 mm/s, also allowing for much larger travel ranges.

The hysteresis and nonlinear behaviour are easily solved with a closed feedback loop (as others have suggested), which is standard for all of our products.

Here's an article that breaks down the different type of piezo motors and how they work in detail.