Chaotic Motion and Control Algorithm Analysis of AFM-TM Microcantilever System
SONG Peijie1,2,CHU Yandong1,ZHANG Hang2,YU Rui2
1. School of Mechanical and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou,Gansu 730070, China
2. Length Measurement Institute, Gansu Institute of Metrology, Lanzhou,Gansu 730050, China
Abstract：To address the issue of measurement accuracy in atomic force microscope in tapping mode (AFM-TM ) caused by the chaotic motion of the AFM-TM cantilever beam system, this study focused on analyzing the dynamic characteristics and control algorithm of the system. Through numerical simulation, the Lyapunov index, bifurcation diagram, Poincaré cross section, and phase diagram were used to analyze the evolution of the motion characteristics of AFM-TM microcantilever beam system when the external excitation amplitude changes. The delayed feedback control and fuzzy adaptive delayed feedback were proposed to control the chaotic motion of the system. Finally, the two control algorithms were compared. The results showed that the system exhibited obvious chaotic motion characteristics when the dimensionless external excitation amplitude was within the range of values such as ［0.65,0.85］. Both the time-delay feedback control and the fuzzy adaptive time-delay feedback control could effectively pull the chaotic motion of the system back to the periodic orbit, but the fuzzy adaptive time-delay feedback was more suitable for the complex situation of the change of the AFM-TM sample. The research results provide a significant theoretical reference for selecting external excitation parameters of AFM-TM microcantilever beams, analyzing complex dynamic characteristics of nonlinear systems and controlling chaotic motion.
AZIZI A, FARD N M, MOBKI H, et al. Bifurcation behavior and stability analysis of a nano-beam subjected to electrostatic pressure ［J］. Applied and Computational Mathematics, 2018, 7(1): 1-11.
WANG H Q, LI W, LI Q, et al. Double probe atomic force microscope for linewidth measurement ［J］. Acta Metrologica Sinica, 2017, 38(z1): 18-24.
［5］
BHUSHAN B. Nanotribology and nanomechanics of mems/nems and biomems/bionems materials and devices ［J］. Microelectronic Engineering, 2007, 84(3): 387-412.
LIN Z D, GAO S T, HUANG L, et al. Design and experimental verification of positioning platform for double probe atomic force microscope ［J］. Acta Metrologica Sinica, 2020, 41(11): 1321-1326.
LU M Z, GAO S T, DU H, et al. The atomic force probe is used to measure the nano-step height sample ［J］. Acta Metrologica Sinica, 2008,29(3): 193-197.
［8］
CHEN Z Y, CHEN F Q, WANG D, et al. Tapping modes in the atomic force microscope model with Lennard-Jones force and slow-fast base motion ［J］. Chaos, Solitons & Fractals, 2021, 144(1): 2-4.
TANG Y, CAO C, ZHANG J, et al. The influence of AFM setting value on the measurement accuracy and probe life ［J］. Acta Metrologica Sinica, 2019, 40(z1): 17-22.
［12］
SUDHARSANA S A, VENKATESAN P, MURUGANANDAM M S. Suppression of extreme events and chaos in a velocity-dependent potential system with time-delay feedback ［J］. Chaos, Solitons & Fractals, 2022, 161(1): 2-4.
［13］
MIN F H, WANG Z Q. Analyze the time-delayed feedback control of chaotic Lorenz system ［J］. Control Theory & Applications, 2004, 21(2): 205-211.
［15］
RUTZEL S, LEE S I, RAMAN A. Nonlinear dynamics of atomic force-microscope probes driven in lennard-jones potentials ［J］. Proc Roy Soc Lond Ser A: Math Phys Eng Sci, 2003, 459(2036): 1925-1948.
［17］
ICHIKO M, KENTARO S, RYOSUKE K, et al. Extension of the range of profile surface roughness measurements using metrological atomic force microscope ［J］. Precision Engineering, 2019, 56(2): 321-326.
［2］
MARRESE M, CIRILLO V, GUARINO V, et al. Shortterm degradation of bi-component electrospun fibers: qualitative and quantitative evaluations via afm analysis ［J］. Journal of Functional Biomaterials, 2018, 9(2): 1-10.
［7］
BO F, YING L L, RUI L, et al. Error analysis in calculation and interpretation of AFM tip-surface interaction forces ［J］. Advances in Colloid and Interface Science, 2022, 306(1): 1-12.
［9］
KORAYEM M H, KHAKSAR H. Investigating the impact models for nanoparticles manipulation based on atomic force microscope (according to contact mechanics) ［J］. Powder Technology, 2019, 344(1): 18-19.
［16］
TSENG C S. Model reference output feedback fuzzy tracking control design for nonlinear discrete-time systems with time-delay ［J］. IEEE Transaction on Fuzzy System, 2006, 14(1): 58-70.
［18］
AHMET U. Model-reference control of chaotic systems ［J］. Chaos, Solutions and Fractals, 2007, 31(1): 712-717.
LEE W K, HYUN C H, LEE H E, et al. Model reference adaptive synchronization of T-S fuzzy discrete chaotic systems using output tracking contro1 ［J］. Chaos, Solutions and Fractals, 2007, 34(1): 1590-1598.
ZHANG W M, MENG G, ZHOU J B, et al. Nonlinear dynamics and chaos of microcantilever-based TM-AFMs with squeeze film damping effects ［J］. Sensors 2009, 9(5): 3854-3874.
2024, Vol. 45 
