Contrôle de position ultra-rapide d un objet nanométrique

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Ruth Wood
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1 Contrôle de position ultra-rapide d un objet nanométrique présenté par Alina VODA alina.voda@gipsa-lab.grenoble-inp.fr sur la base de la thèse de Irfan AHMAD, co-encadrée avec Gildas BESANCON plate-forme conçué et réalisée avec Sylvain BLANVILLAIN et l équipe technique du département d Automatique UNIVERSIT E DE GRENOBLE

2 meter Context 2

3 Presentation Outline Introduction Tunneling current Applications System Analysis and Control System modeling Control problem and desired performances Controller design and simulations Experimental Application and Extension Experimental setup Experimental results Conclusions and Perspectives 3

4 Introduction Distance d 3 nm 2 nm 1 nm 0 - Tip V b 10-9 Distance (m) 1,2 1 0,8 0,6 0,4 0,2 0 Tunneling Current (A) Surface 4

5 Introduction y z x V b V b 5

6 Introduction V b 6

7 Introduction Performance compromises Range Nonlinearities Stability Dynamic nonlinearities Quantization Waterbed effect Modeling errors Coupling effects Noise Precision Noise Bandwidth Study, propose and experimentally validate modern control laws in order to deal with nanopositioning issues using tunneling current. V b 7

8 System Analysis and Control System Description: V b Surface Variations z S Initial Distance d 0 d Tunneling i t i des v ref Reference Feedback Control DAC v 1 v 2 Voltage Amplifier Piezoelectric Actuator z - Current v b ADC v y v 3 Current Sensor n Noise 8

9 System Analysis and Control Voltage ampli er: Piezoelectric actuator: Tunneling current: Current sensor: 9

10 System Analysis and Control Surface Variations z S v 1 Voltage v 2 Amplifier Initial Distance Piezoelectric Actuator d 0 z - d Tunneling Current i t Current Sensor v 3 n v y v b Noise 10

11 System Analysis and Control d Tunneling Current i t Current v 3 Logarithmic v y Sensor Amplifier v b Approximate linearization around an operating point: 11

12 System Analysis and Control G(s) z S v 1 i t = 3rd order feed-forward transfer function = 1st order feedback transfer function v y = tunneling current constant n 12

13 System Analysis and Control 13

14 System Analysis and Control V b Control objectives can be expressed by means of constraints on the shape of closed-loop sensitivity functions. 14

15 System Analysis and Control z S K S o S o G S o c 1 v ref - v e K v 1 G f i t T v y G b -T G n n 15

16 System Analysis and Control 16

17 System Analysis and Control K v ref T - 1 / S v 1 R v y 17

18 System Analysis and Control 18

19 System Analysis and Control 19

20 System Analysis and Control 20

21 System Analysis and Control P(s) v ref w = z S n u = v 1 P(s) K(s) e = v e y 1 y = y 2 y 3 v ref z s n v 1 c 1 G f G n W u W t G b - i t K(s) v y W p y 1 y 2 y 3 v e 21

22 System Analysis and Control v ref y 1 y 1 y 2 y 3 W p W u W t G z S c 1 w = z S n u = v 1 P(s) K(s) y = y 2 e = v e y 3 v ref - v e K G f v 1 i t v y G b G n n 22

23 System Analysis and Control 23

24 System Analysis and Control 24

25 System Analysis and Control 25

26 Experimental Application and Extension 26

piezoelectric actuator Experimental Application and Extension [-20V - 130 V] voltage amplifier reconstruction filter v z v y v x [0-10 V] [0-10 V]

27 piezoelectric actuator Experimental Application and Extension [-20V V] voltage amplifier reconstruction filter v z v y v x [0-10 V] [0-10 V] acquisition card PCI bus current sensor anti-aliasing filter [0-10 na] [0-10 V] [0-10 V] acquisition card target PC development PC V b electrically conducting surface 27

28 Experimental Application and Extension 28

29 Experimental Application and Extension 29

30 Experimental Application and Extension v ref z S Surface Variations v e v 1 d 0 v Initial Distance d Tunnel i ref t Current v 1 Voltage v Piezoelectric Controller DAC 2 z - - v e Amplifier Actuator v b ADC v y v 3 Current Sensor v y n Noise 30

31 Experimental Application and Extension 31

32 Experimental Application and Extension Sensitivity Functions validation with Templates Template for sensitivity function Sensitivity obtained with controller Sensitivity obtained with PI controller 32

33 Experimental Application and Extension 33

34 Experimental Application and Extension 34

35 Experimental Application and Extension 35

36 Experimental Application and Extension 36

37 Experimental Application and Extension 37

38 Experimental Application and Extension Comparison of power spectral densities of tunneling current with different reference values 38

39 Experimental Application and Extension 39

40 Experimental Application and Extension Voltage Amplifier Horizontal (x) Dynamics of Piezoelectric Actuator u h v 1h z h v h Capacitive Sensor 40

41 Experimental Application and Extension 41

42 Experimental Application and Extension 42

43 Experimental Application and Extension 43

44 Experimental Application and Extension Closed loop reference tracking with controller designed by pole placement with sensitivity function shaping for the horizontal movement of the piezoelectric actuator with compensation of hysteresis phenomenon. 44

45 Experimental Application and Extension 45

46 Experimental Application and Extension Complete Plant hv ref - v eh Horizontal Control u h v 1h Horizontal (x) Dynamics z h Capacitive Sensor v h z h Voltage Amplifier Piezoelectric Actuator Cross-Coupling Dynamics vv ref - v ev Vertical Control u v v 1v Vertical (z) Dynamics z v - z c d Tunnel Current i t Current Sensor v 2v v v Surface Variations z S Noise n 46

47 Experimental Application and Extension 47

48 Experimental Application and Extension 48

49 Experimental Application and Extension 49

50 Experimental Application and Extension Complete Plant hv ref - v eh u h v 1h Horizontal (x) Dynamics z h Capacitive Sensor v h z h MIMO Controller Voltage Amplifier Piezoelectric Actuator Cross-Coupling Dynamics vv ref - v ev u v v 1v Vertical (z) Dynamics z v z c - d Tunnel Current i t Current Sensor v 2v v v Surface Variations z S Noise n 50

51 Experimental Application and Extension 51

52 Conclusions A dynamic modeling corresponding to the considered system of tunneling current has been proposed. Two robust control techniques, firstly pole placement with sensitivity function shaping method and then mixed-sensitivity H approach, have been used and a comparison with the more conventionally used classical PI controller has been performed. The experimental validation (at ambient atmosphere) of the proposed control schemes, while working at nanometer scale, has been performed. A Linear Quadratic Regulator (LQR) approach has been analyzed in simulation for the MIMO control of the plant having horizontal, vertical and cross coupling dynamics in order to resolve coupling caused positioning errors. 52

53 Perspectives Modifications in the hardware can be made in order to achieve large closed-loop bandwidth by increasing the bandwidth of the voltage amplifier. The exact reason of the peak at low frequency during PSD analysis is not determined yet which needs to be identified to further enhance the performance. Exact model of cross-coupling dynamics needs to be identified. The experimentally observed hysteresis and creep phenomenon needs to be modeled and then compensated in order to enhance the tracking performance. The further analysis of the performance of the tunneling current measurement system can be performed with an oscillating sample surface. The impact of a better tunneling current measurement can be analyzed in various other applications, and for instance when using tunneling current as a displacement sensor. 53

54 Thank you for your attention! 54

Robust H Control of a Scanning Tunneling Microscope under Parametric Uncertainties

2010 American Control Conference Marriott Waterfront, Baltimore, MD, USA June 30-July 02, 2010 FrC08.6 Robust H Control of a Scanning Tunneling Microscope under Parametric Uncertainties Irfan Ahmad, Alina