ICA  Vol.4 No.3 , August 2013
Constant Force Feedback Controller Design Using PID-Like Fuzzy Technique for Tapping Mode Atomic Force Microscopes
Abstract: A novel constant force feedback mechanism based on fuzzy logic for tapping mode Atomic Force Microscopes (AFM) is proposed in this paper. A mathematical model for characterizing the cantilever-sample interaction subsystem which is nonlinear and contains large uncertainty is first developed. Then, a PID-like fuzzy controller, combing a PD-like fuzzy controller and a PI controller, is designed to regulate the controller efforts and schedule the applied voltage of the Z-axis of the piezoelectric tube scanner to maintain a constant tip-sample interaction force during sample-scanning. Using the PID-like fuzzy controller allows the cantilever tip to track sample surface rapidly and accurately even though the topography of the surface is arbitrary and not given in advance. This rapid tracking response facilitates us to observe samples with high aspect ratio micro structures accurately and quickly. Besides, the overshoot which will result in tip crash in commercial AFMs with a traditional PID controller could be avoided. Additionally, the controller efforts can be intelligently scheduled by using the fuzzy logic. Thus, continuous manual gain-tuning by trial and error such as those in commercial AFMs is alleviated. In final, computer simulations and experimental verifications are provided to demonstrate the effectiveness and confirm the validity of the proposed controller.
Cite this paper: Y. Wang, "Constant Force Feedback Controller Design Using PID-Like Fuzzy Technique for Tapping Mode Atomic Force Microscopes," Intelligent Control and Automation, Vol. 4 No. 3, 2013, pp. 263-279. doi: 10.4236/ica.2013.43031.

[1]   G. Binnig, C. Quate and Ch. Gerber, “Atomic Force Mi croscope,” Physical Review Letter, Vol. 56, No. 9, 1986, pp. 930-933. doi:10.1103/PhysRevLett.56.930

[2]   F. J. Giessibl, “Advances of Atomic Force Microscopy,” Reviews of Modern Physics, Vol. 75, No. 3, 2003, pp. 949-983. doi:10.1103/RevModPhys.75.949

[3]   A. Sebastian, D. R. Sahoo and M. V. Salapaka, “An Ob server Based Sample Detection Scheme for Atomic Force Microscopy,” Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, 9-12 December 2003, pp. 2132-2137.

[4]   S. B. Anderson, “An Algorithm for Boundary Tracking in AFM,” Proceedings of the 2006 IEEE American Control Conference, Minneapolis, 14-16 June 2006, pp. 508-513.

[5]   N. A. Burnham, A. J. Kulik, G. Gremaud and G. A. D. Briggs, “Nanosubharmonic: The Dynamics of Small Non linear Contacts,” Physical Review Letter, Vol. 74, 1995, pp. 5092-5059. doi:10.1103/PhysRevLett.74.5092

[6]   M. Ashhab, M. V. Salapaka, M. Dahleh and I. Mezic, “Control of Chaos in Atomic Force Microscopes,” Pro ceedings of the 1997 American Control Conference, Al buquerque, 4-6 June 1997, pp. 196-202.

[7]   F. M. Battiston, M. Bammerlin, C. Loppacher, R. Luthi, E. Meyer and H. J. Guntherodt, “Fuzzy Controlled Feed back Applied to a Combined Scanning Tunneling and Force Microscope,” Applied Physics Letters, Vol. 72, No. 25, 1998, pp. 25-27. doi:10.1063/1.120635

[8]   S. H. Hsu and L. C. Fu, “Robust Output High-Gain Feed back Controllers for the Atomic Force Microscope Under High Data Sampling Rate,” Proceedings of the 1999 IEEE International Conference on Control Applications, Hawaii, 22-27 August 1999, pp. 1626-1631.

[9]   A. Sebastian, M. V. Salapaka and J. P. Cleveland, “Ro bust Control Approach to Atomic Force Microscopy,” Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, 9-12 December 2003, pp. 3443-3445.

[10]   R. Vazquez, F. J. Rubio-Sierra and R. W. Stark, “Transfer Function Analysis of a Surface Coupled Atomic Force Microscope Cantilever System,” Proceedings of the 2006 American Control Conference, Minneapolis, 14-16 June 2006, pp. 532-537. doi:10.1109/ACC.2006.1655411

[11]   Y. Wu, Q. Zou and C. Su, “A Current Cycle Feedback Iterative Learning Control Approach to AFM Imaging,” Proceedings of the 2008 American Control Conference, Seattle, 11-13 June 2008, pp. 2040-2045.

[12]   A. Sebastian, A. Gannepalli and M. V. Salapaka, “A Re view of the Systems Approach to the Analysis of Dy namic-Mode Atomic Force Microscopy,” IEEE Transac tions on Control Systems Technology, Vol. 15, No. 5, 2007, pp. 952-959. doi:10.1109/TCST.2007.902959

[13]   L. X. Wang, “A Course in Fuzzy Systems and Control,” Prentice Hall, Upper Saddle River, 1997.

[14]   C. C. Lee, “Fuzzy Logic in Control System: Fuzzy Logic Controller, Part I and Part II,” IEEE Transactions on Sys tems, Man and Cybernetics, Vol. 20, No. 2, 1990, pp. 404-435. doi:10.1109/21.52551

[15]   C. W. Tao and J. S. Taur, “Flexible Complexity Reduced PID-Like Fuzzy Controllers,” IEEE Transactions on Sys tems, Man and Cybernetics, Part B: Cybernetics, Vol. 30, No. 4, 2000, pp. 510-516. doi:10.1109/3477.865168

[16]   A. V. Topalov and O. Kaynak, “Online Learning in Adap tive Neurocontrol Schemes with a Sliding Mode Algo rithm,” IEEE Transactions on Systems, Man and Cyber netics, Part B: Cybernetics, Vol. 31, No. 3, 2001, pp. 445-450. doi:10.1109/3477.931542

[17]   P. Pivonka, “Comparative Analysis of Fuzzy PI/PD/PID Controller Based on Classical PID Controller Approach,” Proceedings of the 2002 IEEE World Congress on Com putational Intelligence, Honolulu, 12-17 May 2002, pp. 541-546.

[18]   R. K. Mudi and N. K. Pal, “A Self-Tuning Fuzzy PI Con troller,” Fuzzy Sets and Systems, Vol. 115, No. 2, 2000, pp. 327-328. doi:10.1016/S0165-0114(98)00147-X

[19]   Y. Zhao and E. G. Collins, “Fuzzy PI Control Design for an Industrial Weigh Belt Feeder,” IEEE Transactions on Fuzzy Systems, Vol. 11, No. 3, 2003, pp. 311-319. doi:10.1109/TFUZZ.2003.812686

[20]   “AD637 High Precision, Wideband RMS-to-DC Con verter,” Analog Devices, Inc., Norwood, 2007.

[21]   W. Z. Qiao and M. Mizumoto, “PID Type Fuzzy Con troller and Parameters Adaptive Method,” Fuzzy Sets and Systems, Vol. 78, No. 1, 1996, pp. 23-35.

[22]   “DT300 Series User’s Manual,” Data Translation, Inc., Marlboro, 2010.