A new multi-piezoelectric microcantilever sensor is introduced in this article for replacing laser sensors in atomic force microscopes. This microcantilever consists of multiple piezoelectric layers over its surface, and a consensus algorithm is designed to provide a robust and accurate estimation of the deflections at the tip of the microcantilever. The dynamic equation set of the microcantilever is developed first and then the consensus observer is designed. A set of Riccati equations is used to obtain the optimal gains for the observer, and the robustness of the microcantilever is considered by designing a H∞ norm constraint. A set of numerical simulations is conducted to evaluate the performance of the microcantilever. Results show that the consensus-based multi-piezoelectric microcantilever can successfully provide an accurate estimation of the deflections at the tip of the microcantilever. It is also shown that the robustness of the design can positively improve the estimation performance in the presence of noise. Additionally, a comparison with a single-layered design shows the advantages of the new sensor.
BarhenS (2008) Analytic and numerical modeling of the transient dynamics of a microcantilever sensor. Physics Letters A372(7): 947–957.
2.
DemetriouMA (2009) Natural consensus filters for second order infinite dimensional systems. Systems and Control Letters58(12): 826–833.
3.
DemetriouMA (2010) Guidance of mobile actuator-plus-sensor networks for improved control and estimation of distributed parameter systems. IEEE Transactions on Automatic Control55(7): 1570–1584.
4.
DongHWangZLamJ (2013) Distributed filtering in sensor networks with randomly occurring saturations and successive packet dropouts. International Journal of Robust and Nonlinear Control24(12): 1743–1759.
5.
FloreaCBerdichKDreuceanM (2012) Topography imaging of material surfaces using atomic force microscope. Solid State Phenomena188: 199–204.
6.
GurjarMJaliliN (2007) Toward ultra-small mass detection using adaptive self-sensing piezoelectrically driven microcantilevers. IEEE/ASME Transactions on Mechatronics12(6): 680–688.
7.
HidayatZBabuskaRDe SchutterB (2011) Observers for linear distributed-parameter systems: a survey. In: IEEE international symposium on robotic and sensors environments, Piscataway, NJ, 17–18 September, pp. 166–171. New York: IEEE.
8.
JinZMurrayRM (2004) Double-graph control strategy of multi-vehicle formations. In: IEEE conference on decision and control, Nassau, Bahamas, 14–17 December, pp. 1988–1994. New York: IEEE.
9.
KimSRatchfordDCLiX (2009) Atomic force microscope nanomanipulation with simultaneous visual guidance. ACS Nano3(10): 2989–2994.
10.
LapshinRV (2007) Automatic drift elimination in probe microscope images based on techniques of counter-scanning and topography feature recognition. Measurement Science and Technology18(3): 907–927.
11.
LewisFLVrabieDSyrmosVL (2012) Optimal Control. Hoboken, NJ: John Wiley & Sons.
12.
LewisFLZhangHHengster-MovricK (2014) Cooperative Control of Multi-Agent Systems. Berlin, Heidelberg: Springer.
13.
LiHFuM (1997) A linear matrix inequality approach to robust H∞ filtering. IEEE Transactions on Signal Processing45(9): 2338–2350.
14.
LiMTangHXRoukesML (2007) Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications. Nature Nanotechnology2(2): 114–120.
15.
LiZDuanZChenG (2010) Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint. IEEE Transactions on Circuits and Systems57(1): 213–224.
16.
LiZIshiguroH (2014) Consensus of linear multi-agent systems based on full-order observer. Journal of the Franklin Institute351(2): 1151–1160.
17.
LiangJWangZLiuX (2012) Distributed state estimation for uncertain Markov-type sensor networks with mode-dependent distributed delays. International Journal of Robust and Nonlinear Control22(3): 331–346.
18.
MahmoodiSNJaliliN (2007) Non-linear vibrations and frequency response analysis of piezoelectrically driven microcantilevers. International Journal of Non-Linear Mechanics42(4): 577–587.
19.
MahmoodiSNAfshariMJaliliN (2008) Nonlinear vibrations of piezoelectric microcantilevers for biologically-induced surface stress sensing. Communications in Nonlinear Science and Numerical Simulation13(9): 1964–1977.
20.
ManalisSRMinneSCQuateCF (1996) Atomic force microscopy for high speed imaging using cantilevers with an integrated actuator and sensor. Applied Physics Letters68(6): 871–873.
21.
MarinelloFBarianiPCarmignatoS (2009) Geometrical modelling of scanning probe microscopes and characterization of errors. Measurement Science and Technology20(8): 084013.
22.
MeyerGAmerNM (1990) Optical-beam-deflection atomic force microscopy: the NaCl (001) surface. Applied Physics Letters56(21): 2100–2101.
23.
Olfati-SaberRMurrayRM (2003) Consensus protocols for networks of dynamic agents. In: Proceedings of American control conference, Denver, CO, 4–6 June, pp. 951–956. New York: IEEE.
24.
Olfati-SaberRMurrayRM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control49(9): 1520–1533.
OmidiEKorayemAHKorayemMH (2013) Sensitivity analysis of nanoparticles pushing manipulation by AFM in a robust controlled process. Precision Engineering37(3): 658–670.
27.
OrunBNecipogluSBasdoganC (2009) State feedback control for adjusting the dynamic behavior of a piezoactuated bimorph atomic force microscopy probe. Review of Scientific Instruments80(6): 063701 (7 pp.).
28.
PatanM (2012) Optimal Sensor Networks Scheduling in Identification of Distributed Parameter Systems. Berlin, Heidelberg: Springer.
29.
RogersBManningLJonesM (2003) Mercury vapor detection with a self-sensing, resonating piezoelectric cantilever. Review of Scientific Instruments74(11): 4899–4901.
30.
RogersBManningLSulchekT (2004) Improving tapping mode atomic force microscopy with piezoelectric cantilevers. Ultramicroscopy100(3): 267–276.
31.
SahooDRAgarwalPSalapakaMV (2007) Transient force atomic force microscopy: a new nano-interrogation method. In: Proceedings of American control conference, Piscataway, NJ, 9–13 July, pp. 2135–2140. New York: IEEE.
32.
SahooDRDeTSalapakaMV (2005) Observer based imaging methods for atomic force microscopy. In: IEEE conference on decision and control, Seville, 12–15 December, pp. 1185–1190. New York: IEEE.
33.
SahooDRSebastianASalapakaMV (2003) Transient-signal-based sample-detection in atomic force microscopy. Applied Physics Letters83(26): 5521–5523.
34.
SahooDRSebastianASalapakaMV (2005) Harnessing the transient signals in atomic force microscopy. International Journal of Robust and Nonlinear Control15(16): 805–820.
SchaumAMorenoJAFridmanE (2013) Matrix inequality-based observer design for a class of distributed transport-reaction systems. International Journal of Robust and Nonlinear Control24(16): 2213–2230.
37.
ShibataTUnnoKMakinoE (2002) Characterization of sputtered ZnO thin film as sensor and actuator for diamond AFM probe. Sensors and Actuators A: Physical102(1): 106–113.
38.
ShishkinEIShurVYMiethO (2006) Kinetics of the local polarization switching in stoichiometric LiTaO3 under electric field applied using the tip of scanning probe microscope. Ferroelectrics340(1): 129–136.
39.
UosakiKKoinumaM (1993) Atomic imaging of an InSe single-crystal surface with atomic force microscope. Journal of Applied Physics74(3): 1675–1678.
40.
Van Der WeideDWAgrawalVNeuzilP (1998) Micromachined SFM probes for high-frequency electric and magnetic fields. In: Proceedings of materials research society symposium, Boston, MA, 1–4 December, vol. 500, pp. 21–27. Warrendale, PA: Materials Research Society.
41.
VillarrubiaJS (1997) Algorithms for scanned probe microscope image simulation, surface reconstruction, and tip estimation. Journal of Research of the National Institute of Standards and Technology102(4): 425–454.
42.
ZhangWMengGLiH (2006) Adaptive vibration control of micro-cantilever beam with piezoelectric actuator in MEMS. International Journal of Advanced Manufacturing Technology28(3–4): 321–327.
