For high speed (but lower precision) you would normally use an open-loop solution, i.e. no feedback. You drive a voice coil by giving a voltage. The higher the voltage, the larger the deflection. Within a limited range, the voice coil is almost linear.

Besides HDD heads, you may also look at loudspeakers. They are built for higher frequencies than a normal HDD head, which allows you quicker movement of the laser beam. Using two voice coils can give you two-dimensional deflection of the beam.