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Exploiting global dynamics of a noncontact atomic force microcantilever to enhance its dynamical robustness via numerical control. (English) Zbl 1343.34150

34H20 Bifurcation control of ordinary differential equations
37M20 Computational methods for bifurcation problems in dynamical systems
34C23 Bifurcation theory for ordinary differential equations
Full Text: DOI
[1] Bahrami, A. & Nayfeh, A. [2012] ” On the dynamics of tapping mode atomic force microscope probes,” Nonlin. Dyn.70, 1605-1617. genRefLink(16, ’S0218127416300184BIB001’, ’10.1007%252Fs11071-012-0560-6’); genRefLink(128, ’S0218127416300184BIB001’, ’000310088300055’);
[2] Hornstein, S. & Gottlieb, O. [2008] ” Nonlinear dynamics, stability and control of the scan process in noncontacting atomic force microscopy,” Nonlin. Dyn.54, 93-122. genRefLink(16, ’S0218127416300184BIB002’, ’10.1007%252Fs11071-008-9335-5’); genRefLink(128, ’S0218127416300184BIB002’, ’000258657600008’);
[3] Hornstein, S. & Gottlieb, O. [2012] ” Nonlinear multimode dynamics and internal resonances of the scan process in noncontacting atomic force microscopy,” J. Appl. Phys.112, 074314. genRefLink(16, ’S0218127416300184BIB003’, ’10.1063%252F1.4754814’);
[4] Hu, Q.-Q. & Chen, L.-Q. [2008] ” Bifurcation and chaos of atomic-force-microscope,” Chaos Solit. Fract.36, 740-745. genRefLink(16, ’S0218127416300184BIB004’, ’10.1016%252Fj.chaos.2006.07.004’); genRefLink(128, ’S0218127416300184BIB004’, ’000252642100030’);
[5] Kirrou, I. & Belhaq, M. [2015] ” Control of bistability in non-contact mode atomic force microscopy using modulated time delay,” Nonlin. Dyn.81, 607-619. genRefLink(16, ’S0218127416300184BIB005’, ’10.1007%252Fs11071-015-2014-4’); genRefLink(128, ’S0218127416300184BIB005’, ’000355919700046’);
[6] Kuiper, S., VandenHof, P. & Schitter, G. [2013] ” Integrated design of the feedback controller and topography estimator for atomic force microscopy,” Contr. Eng. Pract.21, 1110-1120. genRefLink(16, ’S0218127416300184BIB006’, ’10.1016%252Fj.conengprac.2013.03.006’); genRefLink(128, ’S0218127416300184BIB006’, ’000320827600011’);
[7] Lee, S. & Howell, S. [2003] ” Nonlinear dynamic perspectives on dynamic force microscopy,” Ultramicroscopy97, 185-198. genRefLink(16, ’S0218127416300184BIB007’, ’10.1016%252FS0304-3991%252803%252900043-3’); genRefLink(128, ’S0218127416300184BIB007’, ’000183783200022’);
[8] Lenci, S. & Rega, G. [2003a] ” Optimal control of homoclinic bifurcation: Theoretical treatment and practical reduction of safe basin erosion in the Helmholtz oscillator,” J. Vibr. Contr.9, 281-315. genRefLink(16, ’S0218127416300184BIB008’, ’10.1177%252F107754603030753’); genRefLink(128, ’S0218127416300184BIB008’, ’000181457000003’); · Zbl 1156.70314
[9] Lenci, S. & Rega, G. [2003b] ” Optimal control of nonregular dynamics in a Duffing oscillator,” Nonlin. Dyn.33, 71-86. genRefLink(16, ’S0218127416300184BIB009’, ’10.1023%252FA%253A1025509014101’); genRefLink(128, ’S0218127416300184BIB009’, ’000185124700005’); · Zbl 1038.70019
[10] Lenci, S. & Rega, G. [2003c] ” Optimal numerical control of single-well to cross-well chaos transition in mechanical systems,” Chaos Solit. Fract.15, 173-186. genRefLink(16, ’S0218127416300184BIB010’, ’10.1016%252FS0960-0779%252802%252900116-9’); genRefLink(128, ’S0218127416300184BIB010’, ’000178334300017’); · Zbl 1058.70027
[11] Lenci, S. & Rega, G. [2004] ” A unified control framework of the non-regular dynamics of mechanical oscillators,” J. Sound Vibr.278, 1051-1080. genRefLink(16, ’S0218127416300184BIB011’, ’10.1016%252Fj.jsv.2003.12.010’); genRefLink(128, ’S0218127416300184BIB011’, ’000225048600018’); · Zbl 1236.70050
[12] Lenci, S. & Rega, G. [2005] ” Heteroclinic bifurcations and optimal control in the nonlinear rocking dynamics of generic and slender rigid blocks,” Int. J. Bifurcation and Chaos15, 1901-1918. [Abstract] genRefLink(128, ’S0218127416300184BIB012’, ’000231464100005’); · Zbl 1092.70519
[13] Lenci, S. & Rega, G. [2006] ” Control of pull-in dynamics in a nonlinear thermoelastic electrically actuated microbeam,” J. Micromech. Microeng.16, 390-401. genRefLink(16, ’S0218127416300184BIB013’, ’10.1088%252F0960-1317%252F16%252F2%252F025’); genRefLink(128, ’S0218127416300184BIB013’, ’000235674000025’);
[14] Lu, H., Fang, Y., Ren, X. & Zhang, X. [2015] ” Improved direct inverse tracking control of a piezoelectric tube scanner for high-speed AFM imaging,” Mechatronics31, 189-195. genRefLink(16, ’S0218127416300184BIB014’, ’10.1016%252Fj.mechatronics.2015.08.006’); genRefLink(128, ’S0218127416300184BIB014’, ’000367772000021’);
[15] Molenaar, R., Prangsma, J. C., van der Werf, K. O., Bennink, M. L., Blum, C. & Subramaniam, V. [2015] ” Microcantilever based distance control between a probe and a surface,” Rev. Sci. Instrum.86, 063706. genRefLink(16, ’S0218127416300184BIB015’, ’10.1063%252F1.4922885’);
[16] Morita, S., Giessibl, F. & Wiesendanger, R. [2009] Noncontact Atomic Force Microscopy, Vol. 2 (Springer, Berlin, Heidelberg). genRefLink(16, ’S0218127416300184BIB016’, ’10.1007%252F978-3-642-01495-6’);
[17] Nozaki, R., Balthazar, J., Tusset, A., de Pontes, B. J. & Bueno, Á. [2013] ” Nonlinear control system applied to Atomic Force Microscope including parametric errors,” J. Contr. Autom. Electr. Syst.24, 223-231. genRefLink(16, ’S0218127416300184BIB017’, ’10.1007%252Fs40313-013-0034-1’);
[18] Nusse, H. & Yorke, J. [1994] Dynamics: Numerical Explorations, Applied Mathematical Sciences (Book 101) (Springer, US). genRefLink(16, ’S0218127416300184BIB018’, ’10.1007%252F978-1-4684-0231-5’); · Zbl 0805.58007
[19] Rega, G. & Lenci, S. [2008] ” Dynamical integrity and control of nonlinear mechanical oscillators,” J. Vibr. Contr.14, 159-179. genRefLink(16, ’S0218127416300184BIB019’, ’10.1177%252F1077546307079403’); genRefLink(128, ’S0218127416300184BIB019’, ’000252947600008’);
[20] Rega, G. & Settimi, V. [2013] ” Bifurcation, response scenarios and dynamic integrity in a single-mode model of noncontact atomic force microscopy,” Nonlin. Dyn.73, 101-123. genRefLink(16, ’S0218127416300184BIB020’, ’10.1007%252Fs11071-013-0771-5’); genRefLink(128, ’S0218127416300184BIB020’, ’000320954900009’);
[21] Rega, G. & Lenci, S. [2015] ” A global dynamics perspective for system safety from macro- to nanomechanics: Analysis, control, and design engineering,” Appl. Mech. Rev.67, 050802. genRefLink(16, ’S0218127416300184BIB021’, ’10.1115%252F1.4031705’);
[22] Settimi, V., Gottlieb, O. & Rega, G. [2015] ” Asymptotic analysis of a noncontact AFM microcantilever sensor with external feedback control,” Nonlin. Dyn.79, 2675-2698. genRefLink(16, ’S0218127416300184BIB022’, ’10.1007%252Fs11071-014-1840-0’); genRefLink(128, ’S0218127416300184BIB022’, ’000350863600034’); · Zbl 1331.93074
[23] Settimi, V., Rega, G. & Lenci, S. [2016] ” Analytical control of homoclinic bifurcation of the hilltop saddle in a noncontact atomic force microcantilever,” Procedia IUTAM19, 19-26. genRefLink(16, ’S0218127416300184BIB023’, ’10.1016%252Fj.piutam.2016.03.005’);
[24] Settimi, V. & Rega, G. [2016a] ” Global dynamics and integrity in noncontacting Atomic Force Microscopy with feedback control,” Nonlin. Dyn., doi: [10.1007/s11071-016-2620-9] , in press. · Zbl 1343.34150
[25] Settimi, V. & Rega, G. [2016b] ” Influence of a locally-tailored external feedback control on the overall dynamics of a noncontact AFM model,” Int. J. Nonlin. Mech.80, 144-159. genRefLink(16, ’S0218127416300184BIB025’, ’10.1016%252Fj.ijnonlinmec.2015.05.010’); genRefLink(128, ’S0218127416300184BIB025’, ’000371556000014’);
[26] Stirling, J. [2014] ” Control theory for scanning probe microscopy revisited,” Beilstein J. Nanotechnol.5, 337-345. genRefLink(16, ’S0218127416300184BIB026’, ’10.3762%252Fbjnano.5.38’); genRefLink(128, ’S0218127416300184BIB026’, ’000333299300001’);
[27] Wang, Y., Wan, J., Hu, X., Xu, L., Wu, S. & Hu, X. [2015] ” A rate adaptive control method for improving the imaging speed of atomic force microscopy,” Ultramicroscopy155, 49-54. genRefLink(16, ’S0218127416300184BIB027’, ’10.1016%252Fj.ultramic.2015.04.004’); genRefLink(128, ’S0218127416300184BIB027’, ’000355211900006’);
[28] Zhang, Y. & Zhao, Y. [2007] ” Nonlinear dynamics of atomic force microscopy with intermittent contact,” Chaos Solit. Fract.34, 1021-1024. genRefLink(16, ’S0218127416300184BIB028’, ’10.1016%252Fj.chaos.2006.03.125’); genRefLink(128, ’S0218127416300184BIB028’, ’000247525100001’);
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