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 varieties of 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 which is commonly used in Atomic Force Microscopy (AFM). 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-parameters 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-parameters 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 read-out. 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 new controller is proposed to overcome these roadblocks. Using extensive numerical simulations and experimental results it is shown that utilizing the proposed controller instead of the commonly used PID controller can significantly enhance the controller’s stability and performance characteristics, and ultimately the imaging resolution and manipulation accuracy needed at this scale.
A constant-speed penetrometer for high-resolution snow stratigraphy
