A new approach to scan-trajectory design and track: AFM force measurement example

In this article, two practical issues encountered in the design and track of scan trajectories are studied: One issue is the large output oscillations occurring during the scanning, and the other one is the effect of modeling errors on trajectory tracking. Output oscillations need to be small in scanning operations, particularly for lightly damped systems, such as the piezoelectric actuators and the flexible structures. Moreover, modeling errors are ubiquitous in practical applications. The proposed approach extends the recently developed optimal scan-trajectory design and control method by introducing the prefilter design to reduce the output oscillations. Furthermore, a novel enhanced inversion-based iterative control (EIIC) algorithm is proposed. The EIIC algorithm is then integrated with the optimal scan-trajectory design method to compensate for the effect of modeling errors on the scanning. The convergence of the iterative control law is discussed, and the frequency range of the convergence is quantified. The proposed approach is illustrated by implementing it to the high-speed adhesion-force measurements using atomic force microscope. Simulation and experimental work are presented and discussed to demonstrate the efficacy of the proposed approach. The experimental results show that compared to the conventional DC-gain method, the proposed approach can reduce the tracking error by over 25 times during the force-curve measurements.