- 1 FEMTO-ST and SAMMI group activities - 2 Observer techniques applied to piezocantilevers - 3 Self sensing of piezocantilevers

Transcription

1 Talk 1: Observer techniques appied to the control of piezoelectric microactuators Micky RAKOTONDRABE, Cédric Clévy, Ioan Alexandru Ivan and Nicolas Chaillet, FEMTO-ST (Besançon, France) - 1 FEMTO-ST and SAMMI group activities - 2 Observer techniques applied to piezocantilevers - 3 Self sensing of piezocantilevers micropads - FP7-PEOPLE IEF 1

2 Talk 1: Observer techniques appied to the control of piezoelectric microactuators Micky RAKOTONDRABE, Cédric Clévy, Ioan Alexandru Ivan and Nicolas Chaillet, FEMTO-ST (Besançon, France) - 1 FEMTO-ST and SAMMI group activities - 2 Observer techniques applied to piezocantilevers - 3 Self sensing of piezocantilevers 2

3 About FEMTO-ST Institute The roots of our activity comes from Watchmakers industry in Besançon area & Automotive industry in Belfort area. Belfort Besançon - A wide range of technical competencies in ENGINEERING SCIENCES - A MULTIDISCIPLINARY research institute - A high level MICROFABRICATION TECHNOLOGY facility - A culture of INNOVATION : from basic research to industrial partnership. 500 staff people. 28 M annual overall budget including 10 M operational budget 6 research departments 6 main application fields 1 microfabrication center. About 250 running research contracts 3

4 TIME & FREQUENCY OPTICS MICRO NANO SCIENCES & SYSTEMS Research Departments - High-stability oscillators - Acousto-electronics and piezoelectricity - Time-frequency metrology - Photonics and telecommunications - Nano-optics - Optoelectronics - Non-linear optics - Biophotonics 19 % 20 % 9 % - Micro and nano-instrumentation - Nanosciences - Micro & Nano-acoustics - Multiphysical Microsystems - Micro, Nanomaterials and surfaces AUTOMATIC CONTROL & MICRO-MECHATRONIC SYSTEMS (AS2M) 13 % - Automatic control - Microrobotics - Micromechatronics - Micromanipulation and micro-assembly - E-maintenance and design activity guidance 24 % 15 % APPLIED MECHANICS ENERGY & MULTIPHYSICAL SYSTEMS - Energy metrology and modelling - Energy system design - Radio protection and medical physics - Mechanical properties of materials - Structural dynamics - Material forming and microfabrication - Surface microanalysis 4

5 SAMMI Group Automated Systems for Micromanipulation and Microassembly General objectives (1) Create microrobots and microrobotic cells for flexible micromanipulation and microassembly Because of the growing number of microproducts to assemble, efficient and reliable micromanipulation systems are required Micro-assembly 5

6 SAMMI Group Automated Systems for Micromanipulation and Microassembly General objectives (2) Control complex microsystems MEMS = specific paradigms for control science Microgripper from Femto-tools (FT G100) Nanotweezer from LIMMS 1 mm 6

7 SAMMI Group Automated Systems for Micromanipulation and Microassembly Main addressed scientific issues on control in the SAMMI group/ FEMTO-ST Modelling and control of: - micro-actuators: SMA, MSMA, piezo, thermal - microrobots: stick slip actuation, digital MEMS, - discrete distributed systems: smart surface - continuous distributed systems - assembly microfactories: calibration, information data modelling and management Need of measurement (sensors, observers)

8 Talk 1: Observer techniques appied to the control of piezoelectric microactuators Micky RAKOTONDRABE, Cédric Clévy, Ioan Alexandru Ivan and Nicolas Chaillet, FEMTO-ST (Besançon, France) - 1 FEMTO-ST and SAMMI group activities - 2 Observer techniques applied to piezocantilevers - 3 Self sensing of piezocantilevers 8

9 2 Observer techniques applied to piezocantilevers A - Context - Position control of one cantilever, - Force control of the second cantilever 9

10 2 Observer techniques applied to piezocantilevers A - Context Force Maniplation Force + - d Deflection: - Modeling, - Control, - Measurement/estimation Manipulation force: - Modeling, - Control, - Measurement/estimation 10

11 2 Observer techniques applied to piezocantilevers B - Deflection measurement and control Disturbance: - force, temperature variation, - nonlinearity, uncertainty reference controller U d d piezocantilever - Frequential controller (H-inf, PID, RST ) [CASE07] [IROS07] [ieeetcst09] 11

12 2 Observer techniques applied to piezocantilevers B - Deflection measurement and control Disturbance: - force, temperature variation, - nonlinearity, uncertainty reference controller U d d piezocantilever Estimate state ˆX Luenberger/ Kalman dxˆ dt Observer ( ˆ) = AXˆ + BU + K d d o [Haddab, PhD00] - State-Space domain (LQ, modal control, pole assignment) 12

13 2 Observer techniques applied to piezocantilevers B - Deflection measurement and control Disturbance: - force, temperature variation, - strongly nonlinearity, uncertainty reference controller compensator U d d piezocantilever Linearization of the nonlinearity (hysteresis and creep) [ifacwc08] [ieeetasea] 13

14 2 Observer techniques applied to piezocantilevers C - Force measurement and control F + - d Information on the force: from the deflection 14

15 2 Observer techniques applied to piezocantilevers C - Force measurement and control reference controller F U d d estimator ˆF piezocantilever 15

16 2 Observer techniques applied to piezocantilevers C - Force measurement and control F Luenberger state observer [Haddab, PhD00] U d d + - K o piezocantilever B + A C E ˆd ˆF d d 0 d v a b 0 v k U dt = + F F 0 d d = ( 1 0 0) v F - Do not account nonlinearities (hysteresis and creep) - Needs to impose dynamics dˆ dˆ 0 K1 d ˆ 0 ˆ v = a b v k U K2 d d dt + + Fˆ Fˆ 0 K 3 dˆ dˆ = ( 1 0 0) vˆ Fˆ dˆ Fˆ = ( 0 0 1) vˆ Fˆ ( ˆ) 16

17 2 Observer techniques applied to piezocantilevers C - Force measurement and control F U d d Open-loop estimation [AIM07] piezocantilever - Do not account uncertainties - Direct inversion of dynamics ( ) ( ) ( ) ( ) d = Γ U D s + C s U + s D s F r p 1 Fˆ = d ( U ) D( s) Cr ( s) U s D( s) Γ + p 17

18 2 Observer techniques applied to piezocantilevers C - Force measurement and control F Unknown Input Observer (UIO) [ICRA09] U d d piezocantilever state ˆX force ˆF F estimator estimator dx = A X + Γ ( u, d ) + B F dt d = C X dxˆ = AXˆ + Γ u d + B F + K d d dt dˆ = CXˆ (, ). ˆ ( ˆ) ˆ ˆ dd ˆ dx F = F1 d + F2 + G1 X + G2 + G3Γ u, d dt dt ( ) 18

19 2 Observer techniques applied to piezocantilevers D Limitation of using sensors - Accurate and high bandwidth sensors (optical sensors ): expensive large sizes (not convenient for packaged systems) 19

20 2 Observer techniques applied to piezocantilevers D Limitation of using sensors - Embeddable sensors (strain gauge sensors): noisy fragile [Haddab et al, IFAC-Mech09] 20

21 Talk 1: Observer techniques appied to the control of piezoelectric microactuators Micky RAKOTONDRABE, Cédric Clévy, Ioan Alexandru Ivan and Nicolas Chaillet, FEMTO-ST (Besançon, France) - 1 FEMTO-ST and SAMMI group activities - 2 Observer techniques applied to piezocantilevers - 3 Self sensing of piezocantilevers 3.1 Quasi-static free displacement self-sensing 3.2 Dynamic displacement self-sensing 3.3 Combined Force / displacement self-sensing 21

22 3. Self-Sensing of Piezoelectric Actuators 3.1 Quasi-static free displacement self-sensing Q Q= σdx 1 dx 2 = αδ A F ext = 0 2 4whε = 33 d 31 E S 3d 31L 4s11ε 33 F ext 0 L Q= 3e 31s11 h = βf + C V ext Free displacement 1 + P 2 2 in F ext ε 33 4Lw + h δ = Force/Displacement V in = 22

23 Sensorless method Observer may be further used in a closed loop control 23

24 Dosch, 1992 Electronic circuits Current integrators. Direct charge conv. Pang, 2006 Resistive divider Cui, 2006 Impedance (dynamic) 24

25 Q = C R Vin +αδ Quasi-static free displacement self-sensing OBSERVER CR αδ + Q Vout = Vin C C 1 V t in( ) 1 dt i C R C C QDA ( Vin, t) CR δest = Vout + V α α α 1 1 V t dt in( ) ibias( t) dt R α α FP FP DA BIAS ( t) dt in 25

26 Identification des parametres Self-Sensing Connus: C et C R Inconnus: α, i BIAS, R FP et Q DA F ext =0 Etapes: 1) Courant polarisation i BIAS : Vin=0 taux de variation Vout 2) Resistance de fuite R FP : echelon Vin 0 derive Vout apres >1000 s. 3) Coeff. de deplacement α [C/m]: echelon Vin ou signal sinusoidal α = ( CV + C Vin )/δ out R 26

27 Identification parametres Self-Sensing - suite 27

28 Identification parametres Self-Sensing - suite 4) Absorption dielectrique Q DA identification fonction de transfer de premier ordre. δ est = δ est δ δ est = * ( s) Q ( s) V ( s) DA in Q * DA ( s) = Q DA α ( s) = k * s τs + 1 * k s = k s /α 28

29 Resultats Self-Sensing en deplacement Matlab Simulink: alpha=-10.05e-9; C=47e-9; Cr=8.2e-9; Rfp=0.435e12; ibias=-1.7e-12; tau=57; ks=3.02e8; 29

30 Resultats Self-Sensing en deplacement sans compensation erreur 2.75 µm compensation R FP erreur 1.05 µm compensation R FP et Q DA : erreur 0.38 µm 0.55% 30

31 Resultats Self-Sensing en deplacement self-sensing Triangulation laser sensor (Keyence) Laser Interferometer (SIOS) self-sensing Noise measurement 16.7 nm (RMS) Keyence 2 nm (RMS) self-sensing (temperature isolated) 0.55 nm (RMS) SIOS 31

32 Resultats Self-Sensing en deplacement Unimorph cantilever ~1µm/ 0 C Self-sensing Error due to ambient temperature variations Bimorph cantilever ~0.2µm/ 0 C 32

33 3. Self-Sensing of Piezoelectric Actuators 3.2 Dynamic displacement self-sensing Static (low frequency) Self Sensing and required dynamic self-sensing intended to superpose real (externally measured) displacement. Figure 5. Bloc-scheme of the dynamic part of the estimator. Principle scheme of the dynamic self-sensing technique. Dynamic Estimator Reverse Multiplivcative form 33

34 Result with static self-sensing (step input of 20V). Result with dynamic self-sensing. 34

35 Step response of the closed-loop system. Settling time : 30 ms Dynamic error: 5% Complete short and long term response of the closed-loop system. 35

36 3. Self-Sensing of Piezoelectric Actuators 3.3 Combined Force / Displacement self-sensing C CR 1 Fest = Vout + Vin Vin ( t) dt β β R β i ( t) dt F ( s) V F ( s) V β β β BIAS C in H in FP Force and displacement observation δ est = δ free _ est F est / k Z Hysteresis Model a) The play operator; b) Prandtl-Ishlinskii (PI) hysteresis model. F C V ( s) = V creep in ( s) = ( s) a Creep TF Model s s + a + b s s + a + b s s + a + b s s + a + b

37 37

38 .a) Measured and estimated force. b) Absolute error (force). a) Applied input signal b) Measured and estimated tip displacement. c) Absolute error (displacement) 38

39 - 1 FEMTO-ST and SAMMI group activities - 2 Observer techniques applied to piezocantilevers - 3 Self sensing of piezocantilevers THANK YOU! 39