Microcantilever-Based Force Tracking With Applications to High-Resolution Imaging and Nanomanipulation

This paper presents the development and implementation of a robust nonlinear control framework for piezoresistive nanomechanical-cantilever (NMC)-based force tracking with applications to high-resolution imaging and nanomanipulation. Among many nanoscale force sensing platforms, NMC is an attractive approach to measure and apply forces at this scale when compared with other previously reported configurations utilizing complicated MEMS devices or inconvenient-to-handle nanowires and nanotubes. More specifically, a piezoresistive layer is utilized here to measure nanoscale forces at the NMC's tip instead of bulky laser-based feedback that is commonly used in atomic force microscopy. Excluding the laser from the sensing loop offers a compact, inexpensive, and portable yet precise nanoscale force sensing platform. In order to track a predefined force trajectory at the NMC's tip, there is a need to model the piezoresistive NMC and design appropriate controller to move its base to provide the desired force. In previous publications of the authors, a new distributed-parameter modeling framework has been proposed to precisely predict the force acting on the microcantilever's tip. In contrast to this approach and in an effort to ease the follow-up controller development, the NMC-based force sensor is modeled here as a lumped-parameter system. However, replacing the NMC with a linear mass-spring-damper trio creates a variety of uncertainties and unmodeled dynamics that need to be addressed for a precise force sensor's readout. Moreover, the very slow response of NMC's piezoresistive layer to force variations at the NMC's tip makes the tracking problem even more challenging. For this, a modified robust controller, built around sliding mode control strategy and augmented with a perturbation estimation module, is proposed to overcome these roadblocks. Extensive numerical simulations and experimental results are presented to demonstrate the stability and performance characteristics of the designed controller. It is shown that utilizing the proposed controller instead of the commonly used proportional-integral-derivative controller can significantly enhance the controller's stability and performance characteristics and, ultimately, the imaging resolution and manipulation accuracy needed at this scale.