Trajectory Tracking through Overactuation for an Optical Delay Line

Nano-positioning devices constitute the mechatronic heart of the VLTI (Very Large Telescope Interferometer) for the ESO (European Southern Observatory) astrometry instrumentation. In the context of the development of a new optical Differential Delay Line (DDL) for the VLTI, a dual-stage feedback control structure for an overactuated system is developed. In order to achieve fast nanometer accuracy over large displacements, a piezoelectric stack actuator is used for fast and fine positioning, while a permanent magnet stepper motor manages the coarse positioning. A double-parallelogram flexure with a notch-hinge mechanism (on top of which the piezo is mounted) ensures flat translation within the coarse precision specification. Because a single measurement device is used, the references for both control loops (fine and coarse) must be suitably obtained. An adequate control structure including a partial observer is designed so as to take into account the influence of the fine actuator on the position of the coarse actuator. Furthermore, a new elaborate control strategy, using the global symmetry of the optical application as a supplementary overactuation capability, enhances the overall performance. The efficiency of the control scheme is validated through simulations and experiments carried on a setup realizing the optical differential delay line. The results conclude that the desired accuracy is achieved throughout the full specified bandwidth and stroke.