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Towards the mechanical and control- -oriented oriented Towards the - - PowerPoint PPT Presentation

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Control issues in the micro/nano nano- -world, ICRA09, world, ICRA09, May 17 2009 May 17 2009 Control issues in the micro/ Towards the mechanical and control- -oriented oriented Towards the mechanical and control optimization of

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Towards the mechanical and control Towards the mechanical and control-

  • oriented
  • riented
  • ptimization of
  • ptimization of micromechatronic

micromechatronic systems systems for robust control for robust control

Control issues in the micro/ Control issues in the micro/nano nano-

  • world, ICRA09,

world, ICRA09, May 17 2009 May 17 2009

Mathieu Grossard, Nicolas Chaillet, Mehdi Mathieu Grossard, Nicolas Chaillet, Mehdi Boukallel Boukallel, Arnaud Hubert, Christine , Arnaud Hubert, Christine Rotinat Rotinat-

  • Libersa

Libersa

Institut femto Institut femto-

  • st, UMR CNRS 6174, Besan

st, UMR CNRS 6174, Besanç çon

  • n

Automatic Automatic Control and Control and Micro Micro-

  • Mechatronic

Mechatronic Systems Systems Department Department

CEA List, Fontenay CEA List, Fontenay-

  • aux

aux-

  • Roses

Roses

Interactive Interactive Robotics Robotics Unit Unit

ensmm DTSI / Interactive Robotics Unit

mathieu.grossard@cea.fr mathieu.grossard@cea.fr

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Integration in micromechatronics

Micromechatronic interdisciplinary scientific area microrobotic : one application domain Evolution to the concept of adaptronics functional elements of a classic regulation process into one single system functional integration Concept of « Smart structure » Intégration

  • 1. General introduction
  • Actuator

Actuator Sensor Sensor Regulator Regulator Mechanical Mechanical structure structure

Active Active material material I n t e g r a t i

  • n

I n t e g r a t i

  • n

Integration Integration Placement Placement Placement Placement

  • !
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Design specificities of microrobots

Mechatronic design

flexible mechanisms

avantage of monolithic structures

  • fabrication,
  • simplified maintenance

no backlash

actuation and sensing functions

weak encumbrance but high resolution active material technologies

Control of microrobots

scale effects

difficulties of obtaining dynamic model difficulties of sensor integration environment influence and variability

non-linear behavior of active materials

Multidisciplinary design

complex specifications non-intuitive design

[Huang 06] [Nah 07] Piezoelectric actuator [Agnus 02] [Shacklock 05]

  • 1. General introduction
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Analysis and synthesis approach

"#

  • $!
  • %!&
  • '# #
  • %

!

  • 1. General introduction
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Positioning towards the problem (1/2)

Development of an optimal synthesis method : FlexIn

design of 2D monolithic flexible structures with integrated actuation choice of the piezoelectric actuation

good performances in the micromechatronic sense

resolution, force, bandwidth, …

electromechanical behavior known

  • mixte FE formulation

control by voltage known prototyping process

(" ("

[Bernardoni 04]

  • Fo1

Fo2

  • 1. General introduction
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Integration of the dynamic part in the method

description through a dynamical model

prediction of the frequency response function

new criteria

  • rientation of the frequency response function
  • 1. General introduction

Positioning towards the problem (2/2)

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Plan

  • 1. Building blocks method
  • 2. Optimal synthesis of active structures under FlexIn
  • 3. Optimal synthesis with dynamic considerations
  • 4. Design and control of a micro-actuator prototype

5

  • 5. Conclusion and perspectives
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General approach

Flexible structures design with FlexIn

curvilinear curvilinear representation representation of the

  • f the

structures structures Cutting Cutting out

  • ut into

into elementary elementary building blocks : building blocks :

elementary building block actuator boundary conditions contacts fixed nodes boundary conditions mechanical output

[Bernardoni 04] Actuator movement internal contacts Fixed nodes Mechanical output

CAD CAD representation representation

  • 1. Building-block method

2mm

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Design domain decomposition Elementary flexible blocks library

36 blocks topologies multiple and coupled DOF

Optimal design

Pareto front validation prototyping

Building blocks method

)*+#++,

! " #

  • .

$

/

Fo1 Fo2 Front de Pareto: solutions de rang 1 bb ab

bloc : assemblage de poutres élémentaires

b1 b2 b3 b4 a1 a2 # %"

  • #

# ) 0,

  • 1. Building-block method
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Plan

  • 1. Building blocks method
  • 2. Optimal synthesis of active structures under FlexIn
  • 3. Optimal synthesis with dynamic considerations
  • 4. Design and control of a micro-actuator prototype

5

  • 5. Conclusion and perspectives
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Implementation of an active library

Active blocks of various topologies

actuation mode distributed planar actuation controlled by electric voltage Up

U Up

p

U Up

p

  • 2. Optimal synthesis of active structures under FlexIn

Bloc 14 Bloc 3 Bloc 4 Bloc 5 Bloc 9 Bloc 11 Bloc 10 Bloc 12 Bloc 13 Bloc 15 Bloc 16 Bloc 29 Bloc 31 Bloc 30 Bloc 32 Bloc 33 Bloc 34 Bloc 35 Bloc 2 Bloc 3 Bloc 1 Bloc 4 Bloc 5 Bloc 6 Bloc 7 Bloc 8 Bloc 9 Bloc 10 Bloc 11 Bloc 12 Bloc 13 Bloc 15 Bloc 14 Bloc 16 Bloc 17 Bloc 19 Bloc 20 Bloc 18 Bloc 21 Bloc 22 Bloc 23 Bloc 24 Bloc 26 Bloc 27 Bloc 25 Bloc 28 Bloc 29 Bloc 30 Bloc 31 Bloc 32 Bloc 33 Bloc 35 Bloc 34 Bloc 36 Bloc 36

Passive blocks Active blocks

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Implementation under FlexIn

Elementary active blocks

Assembly of elementary piezoelectric beam

Code of a complete structure

monolithic structure : assembly of active and passive blocks active/passive topologies

Integer matrix active / passive topologies

1 1 3 3 3 3 5 5 6 6 12 12 33 33

PZT blocks

  • 2. Optimal synthesis of active structures under FlexIn
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Plan

  • 1. Building blocks method
  • 2. Optimal synthesis of active structures under FlexIn
  • 3. Optimal synthesis with dynamic considerations
  • 4. Design and control of a micro-actuator prototype

5

  • 5. Conclusion and perspectives
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Implementation of the dynamic part

Second order dynamic model

transfer matrix : modal expansion input/ouput frequency reponse simulation

t p g i i g 2 2 i 1 i i i

s 2ξ ω s ω

=

= + +

∑

F Q Q E y u

  • 3. Optimal synthesis with dynamic considerations
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identification of flexible structures

Reduction of the number of dominant modes

1 ## #0# #

# %(

##

)#,

&

  • # )

# ,

# #

  • &

& # # # #

  • +

+ ! !

  • 3. Optimal synthesis with dynamic considerations
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Reduction in the modal base

Moore method expressed directly in the diagonal modal base characterization of the joint controllability/observability degree

Expression of the numeric criteria 1

k

choice of the number k of dominant modes

maximization of control authority of the k first modes minimization of modes out of the bandwidth

graphical interpretation by using ║. ║∞ norm (SISO)

ω )#/, #)#',"*

2# * ω* '#&#

  • #

3* #

2## # #

  • Identification of flexible structures
  • 3. Optimal synthesis with dynamic considerations

1 1 1 k i k i N i i k

J σ σ

= = +

= ∑

∑

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Control of flexible structures

  • Analysis of frequential properties of flexible structures

## # # .

)! # 0,

& # # (4#

Variability of system parameters (poles, zeros,…) " 5)# #+! 06,

1# 7

  • *
  • 3. Optimal synthesis with dynamic considerations
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  • Influence of the feedback gain g
  • feedback scheme for control
  • trajectory of poles in closed-loop
  • pole/zero alternating properties

stability loops in closed-loop

  • Expression of the numerical critria J2

k’

  • criteria expressed from the modal expansion of the

input/output transfer

  • choice of the number k’ of considered modes for the

alternating poles/zeros

  • +
  • 8),
  • %

2

  • #

"

"

&'→(∞

ω )#/, # )#',

/0

  • 3. Optimal synthesis with dynamic considerations

Control of flexible structures

( )

' ' 2 1 k k i i

J sign R

=

=∑

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Plan

  • 1. Building blocks method
  • 2. Optimal synthesis of active structures under FlexIn
  • 3. Optimal synthesis with dynamic considerations
  • 4. Design and control of a micro-actuator prototype

5

  • 5. Conclusion and perspectives
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Design of a monolithic microgripper

Multi-criteria optimisation

  • mechanical in static mode
  • Blocking force F
  • Free deflection δ
  • control-oriented 1

2 et 2 2

  • Optimisation parameters
  • 1 ≤ N active blocks ≤ 4
  • Up = 200V
  • 1 ≤ N fixed nodes ≤ 3

PZT PIC151 20mm 20mm

electrode

  • 4. Design and control of a micro-actuator prototype
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Selection of a pseudo-optimal solution

Pareto fronts

2

  • 5 #)(",
  • #
  • #
  • 9#

9 Free deflection δ in µm (Up=200V) Blocking force in N ║J1

2 ║

J2

2

  • 4. Design and control of a micro-actuator prototype
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Experimental set-up

Piezoelectric prototype Set-up

  • PC + Labview

L a s e r s e n s

  • r

Controlled micro-actuator Anti-aliasing filter Tension amplifier

fe=20kHz

  • 4. Design and control of a micro-actuator prototype

X Y

δfree=±10,69µm Fblocking=840mN Tension Vp=±100V X Y

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Quasi-static hysteresis

Model of the Hd hysteresis

Validation of the separation principle

Oscillating dynamic (4th order)

Hysteresis Hysteresis H Hd

d

U δ

1 interest

  • 4. Design and control of a micro-actuator prototype

δ

Static Static hysteresis hysteresis H Hs

s

Oscillating Oscillating part part D D

U

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HAC/LAC control

Double feedback loop

LAC corrector

damping of the first mode Positive Position Feedback corrector Sytnhesis using Root Locus

HAC corrector

tracking frequency synthesis from the pre- compensated system using Hl

performances

TR5%=9.9ms Interesting stability margins

  • Mg>16dB
  • Mφ>78°

LAC corrector (PPF) Tracking response HL(s) +

  • δc

e HAC δ U α0D(s)F(s) system Hl(s) LAC + +

  • 4. Design and control of a micro-actuator prototype
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Performances comparisons

Similar performances

settling time stability margins

Interest of HAC/LAC approach

Reduced order of corrector (order 4)

corrector H∞

  • rder 13

corrector RST

  • rder 9

More direct synthesis

Interest of proposed criteria

Time (s) Déflection (µm)

RST HAC/LAC H∞

  • 4. Design and control of a micro-actuator prototype
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Plan

  • 1. Building blocks method
  • 2. Optimal synthesis of active structures under FlexIn
  • 3. Optimal synthesis with dynamic considerations
  • 4. Design and control of a micro-actuator prototype

5

  • 5. Conclusion and perspectives
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Conclusion

Developement of a new method for the optimal design

elementary building blocks activated by piezoelectric effect Interest of the dynamic part and the modal authority control

Optimal synthesis of a new monolithic microgripper

Use of our method on a simple case Identification and control of the prototype Several robust control techniques tested

New tool of multidisciplinary optimal design taking into account simultaneously mechanical and control-oriented aspects

  • 6. Conclusion and perspectives
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Towards the mechanical and control Towards the mechanical and control-

  • oriented optimization of
  • riented optimization of

micromechatronic micromechatronic systems for robust control systems for robust control

Control issues in the micro/ Control issues in the micro/nano nano-

  • world, ICRA09,

world, ICRA09, May 17 2009 May 17 2009

Mathieu Grossard, Nicolas Chaillet, Mehdi Mathieu Grossard, Nicolas Chaillet, Mehdi Boukallel Boukallel, Arnaud Hubert , Arnaud Hubert Institut femto Institut femto-

  • st / CEA List

st / CEA List

ensmm DTSI / Interactive Robotics Unit