Analyse et Commande de Microscope à Effet Tunnel (STM)

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Christophe Ducharme
il y a 8 ans
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1 Analyse et Commande de Microscope à Effet Tunnel (STM) Présenté par: Irfan Ahmad (Doctorant en 2 éme année) Encadré par: Alina Voda & Gildas Besançon GIPSA-lab, Département Automatique Grenoble, France 22/01/2009 1

2 Plan of Presentation Introduction System Analysis Control Problem Controller Analysis Control Simulation Results Conclusion and Perspectives 22/01/2009 2

3 Introduction Application Scanning the Surface of Material Sample with Atomic Resolution Instrument Scanning Tunneling Microscope (STM) (G. Binnig & H. Rohrer: 1980) Benzene Molecules over Gold Surface Scanning Tunneling Microscope 22/01/2009 3

4 Introduction Working of Scanning Tunneling Microscope Tunnel current (IT) introduces when distance (d) is nm Control objective: To ensure constant tunnel current (IT) Logarithmic amplification to deal with exponential nonlinearity 22/01/2009 4

0 nm Control objective: To ensure constant tunnel current (IT)

5 Introduction State of the Art «Some design criteria in scanning tunneling microscopy» [Pohl, 1986] «Analysis of scanning tunneling microscopy feedback system» [Oliva, 1995] «VSC of a piezoelectric actuator for a scanning tunneling microscope» [Bonnail, 2004] «Analysis of scanning tunneling microscopy feedback system» [Mathies, 2005] Requirement Design advanced controller techniques for scanning tunneling microscope feedback system considering robustness, high performance and noise issues. 22/01/2009 5

[Bonnail, 2004] «Analysis of scanning tunneling microscopy feedback system» [Mathies, 2005] Requirement Design advanced

6 System Analysis Simulation Model Logarithmic Non-Linearity Exponential Non-Linearity 22/01/2009 6

7 System Analysis General Approach Assumption: Linearization Neglecting dynamics of amplifiers, considering as constants Neglecting presence of noise between them First Order Linear Approximation Approach where C1, C2 and C3,.,C8 are constant terms, depending on parameters of original non -linear equations (which are defined in previous slide) 22/01/2009 7

Order Linear Approximation Approach where C1, C2 and C3,.

8 Imaginary axis System Analysis Control Design Model Open Loop Model of System Remarks Fifth order system model Critical point : Location of dominant poles of system model High controller gains can make closed loop system unstable Real axis 22/01/2009 8

point : Location of dominant poles of system model High

9 Control Problem Tracking problem Disturbance rejection problem Scan speed Closed loop bandwidth Noise Non-Lineariteis Desired Performance Specifications 22/01/2009 9

10 Controller Analysis Control Design Constraints Closed Loop Sensitivity Functions Constraint 1 Constraint 4 Constraint 2 Constraint 5 Constraint 3 Constraint 6 22/01/

11 Controller Analysis Control Design Methodology Robust digital control using pole placement with sensitivity function shaping using 2 nd order digital notch filters [Landau, 1998] Iterative procedure of selecting the dominant poles, the auxiliary poles and the fixed parts of the controller Assurance of robust stability of the closed loop system against the parameter uncertainity The 8 th order controller obtained for the system of scanning tunneling microscope The Flow chart of the iterative procedure 22/01/

and the fixed parts of the controller Assurance of robust stability of the closed loop system against the parameter uncertainity

12 Controller Analysis Control Design Methodology Robust Digital Control using Pole Placement with Sensitivity Functions Shaping using 2 nd Order Digital Notch Filter 22/01/

13 Controller Analysis Control Design Methodology Robust Digital Control using Pole Placement with Sensitivity Functions Shaping using 2 nd Order Digital Notch Filter 22/01/

14 Controller Analysis Control Design Methodology Robust Digital Control using Pole Placement with Sensitivity Functions Shaping using 2 nd Order Digital Notch Filter Bad Disturbance Rejection Bad Noise Rejection 22/01/

Functions Shaping using 2 nd Order Digital Notch Filter

15 Controller Analysis Nominal H-infinity controller design Control Design Methodology Two weighting functions designed The generalized plant P (i.e. the interconnections of the plant and the weighting functions) given by: The 11 th order controller obtained for the system of scanning tunneling microscope 22/01/

interconnections of the plant and the weighting functions) given by: The 11 th

16 Controller Analysis Control Design Methodology Nominal H-infinity Control 22/01/

17 Controller Analysis Control Design Methodology Nominal H-infinity Control 22/01/

18 Control Simulation Results RS Control with Sensitivity Function Shaping Comparison between RS Control and PID Simulation Result with and Noise Variance of 22/01/

19 Control Simulation Results H-Infinity Control Comparison between H-Infinity and PID Simulation Result with and Noise Variance of 22/01/

20 Control Simulation Results RS Control with Sensitivity Function Shaping H-Infinity Control Simulation Result with and Noise Variance of 22/01/

21 Conclusion Better performance than PID control for fast (continuous) variations in sample surface Closed-loop bandwidth 3 times better than PID control technique Perspectives Analysis with robust performance and robust stability in the presence of plant uncertainities Experimental validation of proposed control scheme 22/01/

22 THANKS 22/01/

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