Robust Adaptive Tracking Control of a 3D Vertical Motion System for Nanometer Precision Applications

Abstract

In this paper we address the modeling and tracking control problem of an overactuated lift and tilt vertical nanopositioning system. We derive a model based on the rigid body dynamics which adequately describes the first resonance mode of each motion axis. This model is validated with measured data in the frequency domain to illustrate that it adequately reflects the real behavior. We further device an abstract model for the derivation of advanced control strategies. By virtue of the single axis model, three SISO controllers are implemented. The control strategy is accomplished comprising a nominal feedforward and LQG-type controller plus an L1 adaptive augmentation with output feedback. The baseline (or nominal) controller features sufficiently high bandwidth for the mere stabilization, decoupling, and disturbance rejection, while the L1 adaptive component plays a central role for recovering the nominal closed-loop dynamics in the presence of parametric uncertainties w.r.t. the input gain which are quite difficult to handle in the nominal design. The effectiveness and robustness of the proposed control strategy is verified via real-time experiments featuring subnanometer and nanoradian tracking errors which seem to be fully-dominated by the measurement noise.