A new modeling and control framework for MEMS characterization utilizing piezoresistive microcantilever sensors

This paper presents a comprehensive modeling and control framework for characterizing MEMS utilizing piezoresistive microcantilevers. These microcantilevers have recently received widespread attention due to their extreme sensitivity and simplicity in a variety of sensing applications. Most of the current studies; however, focus on a simple lumped-parameters representation rather than modeling the piezoresistive microcantilever itself. Due to the applications of the piezoresistive microcantilevers in nanoscale force sensing or non-contact atomic force microscopy with nano-Newton to pico-Newton range force measurement requirement, precise modeling of the piezoresistive microcantilevers is essential. For this, a distributed-parameters modeling is proposed and developed here to arrive at the most complete model of the piezoresistive microcantilever with tip-mass, tip-force and base movement considerations. In order to have online control and real-time sensor feedback, an inverse model of piezoresistive microcantilever is needed which utilizes the output voltage of the piezoresistive layer as well as the base motion information to predict the force acting on the microcantilever's tip. Utilizing a novel approach, an inverse modeling framework and control algorithm are then proposed for the characterization of MEMS utilizing piezoresistive microcantilevers. Following the mathematical modeling and controller design, both numerical simulations and experimental results are presented to demonstrate the accuracy of the proposed distributed-parameters modeling when compared with the previously reported lumped-parameters approach. It is shown that by utilizing the distributed-parameters model rather than lumped-parameters approach and by predicting the exact motion of each point on the microcantilever, the precision of the piezoresistive microcantilever's model is significantly enhanced.