The preferred embodiments of the present invention are directed to high bandwidth positioning systems such as fast tool servos (FTS). The applications of this invention include, for example, diamond turning of mold with structured surface for mass production of films for brightness enhancement and controlled reflectivity, diamond turning of molds for contact lens and micro-optical positioning devices. Preferred embodiments of the fast tool servo can have a closed-loop bandwidth of approximately 20±5 kHz, with acceleration of up to approximately 1000 G or more. The resolution or position error is approximately 1 nm root mean square (RMS). In a preferred embodiment, the full stroke of 50 μm can be achieved up tol kHz operation.