Towards Microcantilever-based Force Sensing and Manipulation: Modeling,Control Development and Implementation

Abstract

This paper presents a distributed-parameters-based modeling framework for piezoresistive microcantilever (MC)-based force sensors used in a variety of cantilever-based nanomanipulation processes. Current modeling practices call for a simple lumped-parameters approach rather than modeling the piezoresistive MC itself. Owing to the widespread applications of such MCs in nanoscale force sensing or non-contact atomic force microscopy with nano-Newton to pico-Newton force measurement requirements, precise modeling of the piezoresistive MCs is essential. Instead of the previously used lumped-parameters modeling, a distributed-parameters modeling framework is proposed and developed here to arrive at the most complete model of the piezoresistive MC including tip-mass, tip-force and base movement considerations. In order to have online control and real-time sensor feedback, a closed-form model of the piezoresistive MC, which expresses the MC's piezoresistive output voltage as a function of tip force and base motion, is highly desirable. Along this line of reasoning, a closed-form model for the piezoresistive MC is presented. Following mathematical modeling, both numerical simulations and experimental results are presented to demonstrate the accuracy of the proposed distributed-parameters model when compared with the previously reported lumped-parameters modeling approach. Utilizing the developed model, a modified robust controller with perturbation estimation is adopted to target the problem of slow imaging acquisition and manipulation at the nanoscale. It is shown that the proposed controller can stabilize such nanomanipulation process in less than a second. Experimental results are presented to demonstrate the stability and performance characteristics of the designed controller. Such modeling and control development could pave the way for MC-based nanomanipulation and nanopositioning.

Keywords

force sensing manipulation and control at the nanoscale distributed-parameters modeling piezoresistive microantilever

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