Precision tracking of driving wave forms for inertial reaction devices

Inertial reaction devices (also referred to as impact drive, or slip-stick devices) enable nano/micro resolution positioning over macroscopic ranges. Such positioning devices are characterized by the displacement of a mass by utilizing stick-slip phenomena between the mass and the device's actuators. The displacement of the actuator (i.e., the driving wave form) is chosen such that the mass sticks to the actuator and is displaced with the actuator during the first tracking phase, and the mass slips with respect to the actuator during the second retrace phase during which the actuator's position is reset. However, as the driving wave form's frequency is increased to operate an inertial-reaction device at high speed, induced mechanical vibrations prevent accurate actuator positioning and thereby, limit the maximum achievable operating speed. In this article, the actuator dynamics is modeled and iteratively inverted to find the input that compensates for the induced mechanical vibrations. This inversion-based input allows the actuator to track high-frequency driving wave forms without exciting mechanical vibrations, and thereby, allows the inertial reaction device to operate at higher operating speeds. The method is applied to a rotational inertial-reaction device, and experimental results show that the use of the inversion-based iterative approach enables tracking of the desired wave form at an order-of-magnitude higher frequency.