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
meter Context 2
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
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) 10-9 30 25 20 15 10 5 0 Surface 4
Introduction y z x V b V b 5
Introduction V b 6
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
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
System Analysis and Control Voltage ampli er: Piezoelectric actuator: Tunneling current: Current sensor: 9
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
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
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
System Analysis and Control 13
System Analysis and Control V b Control objectives can be expressed by means of constraints on the shape of closed-loop sensitivity functions. 14
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
System Analysis and Control 16
System Analysis and Control K v ref T - 1 / S v 1 R v y 17
System Analysis and Control 18
System Analysis and Control 19
System Analysis and Control 20
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
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
System Analysis and Control 23
System Analysis and Control 24
System Analysis and Control 25
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] 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
Experimental Application and Extension 28
Experimental Application and Extension 29
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
Experimental Application and Extension 31
Experimental Application and Extension Sensitivity Functions validation with Templates Template for sensitivity function Sensitivity obtained with controller Sensitivity obtained with PI controller 32
Experimental Application and Extension 33
Experimental Application and Extension 34
Experimental Application and Extension 35
Experimental Application and Extension 36
Experimental Application and Extension 37
Experimental Application and Extension Comparison of power spectral densities of tunneling current with different reference values 38
Experimental Application and Extension 39
Experimental Application and Extension Voltage Amplifier Horizontal (x) Dynamics of Piezoelectric Actuator u h v 1h z h v h Capacitive Sensor 40
Experimental Application and Extension 41
Experimental Application and Extension 42
Experimental Application and Extension 43
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
Experimental Application and Extension 45
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
Experimental Application and Extension 47
Experimental Application and Extension 48
Experimental Application and Extension 49
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
Experimental Application and Extension 51
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
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
Thank you for your attention! 54