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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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References

Abramovitch, D.Y. , Anderson, A.B. , Pao, L.Y. and Schitter, G. (2007). A tutorial on the mechanics dynamics and control of atomic force microscopes. Proceedings of the 2007 American Control Conference, New York, 11-13 July.

Binnig, G. , Gerber, Ch. , Stoll, E. , Albrecht, T.R. and Quate, C.F. (1987). Atomic resolution with atomic force microscope . Europhysics Letters, 3(12): 1281-1286.

Boisen, A. , Thaysen, J. , Jensenius, H. and Hansen, O. (2000). Environmental sensors based on micromachined cantilevers with integrated read-out. Ultramicroscopy, 82(1): 11-16.

Chen, G.Y. , Thundat, T. , Wachter, E.A. and Warmack, R.J. (1995). Adsorption-induced surface stress and its effects on resonance frequency of microcantilevers. Journal of Applied Physics, 77(8): 3618.

Chu Duc, T. , Creemer, J.F. and Sarro, P.M. (2007). Piezoresistive cantilever beam for force sensing in two dimensions. IEEE Sensors Journal, 7(1): 96-104.

Datskos, P. and Sauers, I. , (1999). Detection of 2-mercaptoethanol using gold-coated micromachined cantilevers. Sensors and Actuators, B: Chemical , 61(1-3): 75- 82.

Fritz, J. , Baller, M.K. , Lang, H.P. , Rothuizen, H. , Vettiger, P. , Meyer, E. , Guentherodt, H.J. , Gerber, Ch. and Gimzewski, J.K. (2000). Translating biomolecular recognition into nanomechanics . Science, 288(5464): 316-318.

Harley, J.A. and Kenny, T.W. (1999). High-sensitivity piezoresistive cantilevers under 1000 angstroms thick. Applied Physics Letters, 75(2): 289.

Jalili, N. , Dadfarnia, M. and Dawson, D. (2004). A fresh insight into the microcantilever-sample interaction problem in non-contact atomic force microscopy. ASME Transactions Journal of Dynamic Systems, Measurement and Control, 126(2): 327-335.

10.

Saeidpourazar, R. and Jalili, N. (2006). Modeling and observer-based robust tracking control of a nano/micromanipulator for nanofiber grasping applications. Proceedings of the 2006 ASME International Mechanical Engineering Congress and Exposition (IMECE2006), Chicago, IL, 5-10 November.

11.

Saeidpourazar, R. and Jalili, N. (2008a). Nano-robotic manipulation using a RRP nanomanipulator: part A--Mathematical modeling and development of a robust adaptive driving mechanism. Journal of Applied Mathematics and Computation , DOI: 10.1016/j.amc.2008.05.079.

12.

Saeidpourazar, R. and Jalili, N. (2008b). Nano-robotic manipulation using a RRP nanomanipulator: part B--Robust control of manipulator's tip using fused visual servoing and force sensor feedbacks. Journal of Applied Mathematics and Computation, DOI: 10.1016/j.amc.2008.05.078.

13.

Saeidpourazar, R. and Jalili, N. (2008c). Microcantilever-based force tracking with applications to high-resolution imaging and nanomanipulation. IEEE Transactions on Industrial Electronics, 55(11): 1-11.

14.

Saeidpourazar, R. and Jalili, N. (2008d). Towards fused vision and force robust feedback control of nanoroboticbased manipulation and grasping. Mechatronics , DOI:10.1016/j.mechatronics.2008.05.014.

15.

Sepaniak, M. , Datskos, P. , Lavrik, N. and Tipple, C. (2002). Microcantilever transducers: a new approach in sensor technology. Analytical Chemistry, 74(21): 568A-575A.

16.

Slotine, J.J. (1984). Sliding controller design for nonlinear system . International Journal of Control, 40: 421-434.

17.

Thaysen, J. , Marie, R. and Boisen, A. (2001). Cantilever-based bio-chemical sensor integrated in a microliquid handling system. Proceedings of the IEEE Micro Electro Mechanical Systems (MEMS), pp. 401-404.

18.

Utkin, V.I. (1977). Variable structure system with sliding modes. IEEE Transactions on Automatic Control, 22: 212- 222.

19.

Yang, M. , Zhang, X. and Ozkan, C. (2003). Modeling and optimal design of high sensitivity piezoresistive microcantilevers for biosensing applications. Proceedings of the 2003 Nanotechnology Conference and Trade Show (Nanotech 2003), Vol. 1, pp. 360-363.

20.

Yang, S.M. and Yin, T.I. (2007). Design and analysis of piezoresistive microcantilever for surface stress measurement in biochemical sensor. Sensors and Actuators, B: Chemical, 120(2): 736-744.

21.

Yang, S.M. , Yin, T.I. and Chang, C. (2007). Development of a double-microcantilever for surface stress measurement in microsensors. Sensors and Actuators, B: Chemical, 121(2): 545-551.

22.

Yin, T.I. and Yang, S.M. (2005). Double-microcantilever design for surface stress measurement in biosensors. Proceedings of SPIE, 5763: 333-344.

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

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