Loop-shaping H ∞-control of a 2-DOF piezoelectric-stack actuated platform for nanoscale positioning

Piezoelectric-stack actuated platforms are utilized in many nanopositioning applications. Their performance is limited by their low-frequency resonance due to the mechanical construction as well as piezoelectric nonlinear effects. We propose a hybrid control scheme comprising a loop-shaping H∞ controller and an inversion-based feedforward control scheme, capable of delivering accurate nanopositioning performance at relatively high speeds, upto 40 Hz. It is shown that the implemented control strategy is robust in the presence of uncertainty in resonance frequency due to loading. It is also shown that by employing charge actuation on the fast axis and integral tracking control on the slow axis, accurate raster scans can be obtained. Experimental results that show resonance damping, integral tracking action as well as the robustness of the implemented control scheme to resonance frequency uncertainty are presented. Finally, raster scans recorded at 10 Hz, 20 Hz and 40 Hz are presented to show the achievable positioning performance.