Comparison of Two Optimization-Based Controllers for Feature Tracking SPM Scanning in Dual-Stage Nanopositioners

In this paper, two control methods are investigated for motion tracking of a particular class of trajectories, termed local circular scan (LCS), defined by a non-raster scanning algorithm for scanning probe microscopes. The methods are further developed for multi-axis dual-stage nanopositioning systems. In the first method, the long-range and short-range actuators of a dual-stage system are controlled through model predictive control (MPC) and a linear quadratic tracking controller (LQT), respectively. This architecture lends itself well to applications such as LCS scanning where a distinct high-frequency, low-amplitude signal can be followed entirely by the short-range actuator (SRA) because of the actuator's high bandwidth, but is not easily extended to more generic scenarios. The second method is a discrete linear quadratic controller (LQC) with a cascading reference structure. This scheme is both more general and simpler to implement but does not take advantage of trajectory prior knowledge. Both controllers are validated through simulations on linear models of the planar axes of an experimental dual-stage system, where three planar reference trajectories are selected to evaluate the tracking performances representing different imaging scenarios. Overall, the MPC-receding LQT controller has a better tracking performance for LCS references, likely due to the dedication of the high-frequency sinusoidal components to the SRA and the a priori trajectory information used when calculating the feedforward portion of the control efforts. The MPC-receding LQT controller demonstrates about 30% improvement in the maximum and root-mean-square error over the cascading structure. Tracking is improved further when large steps in the reference signal are desired; the cascading LQC is prone to large overshoot while the MPC-receding LQT reduces the integrated error by more than 70%.