diff --git a/notes.html b/notes.html index 3433b73..9788a01 100644 --- a/notes.html +++ b/notes.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + EUSPEN @@ -30,114 +30,114 @@

Table of Contents

@@ -147,41 +147,41 @@

This report is also available as a pdf.

-
-

1 Tutorial: Design concepts for sub-micrometer positioning   @huub_janssen

+
+

1 Tutorial: Design concepts for sub-micrometer positioning   @huub_janssen

-
-

1.1 Positioning Terminology

+
+

1.1 Positioning Terminology

  • Accuracy: -Accuracy describes how close the mean result is to the reference value. (Figure 1)
    • +Accuracy describes how close the mean result is to the reference value. (Figure 1)
  • Repeatability: -Repeatability describes the variation between results. (Figure 1)
    • +Repeatability describes the variation between results. (Figure 1)
  • Resolution: -The resolution of a system is equal to the smallest incremental step that can be made (Figure 2)
    • +The resolution of a system is equal to the smallest incremental step that can be made (Figure 2)
  • Stability: The stability of a system is the maximum deviation from a constant reference value over time. -The stability is always related to the time frame taken into account. (Figure 3)
    • +The stability is always related to the time frame taken into account. (Figure 3)
-
+

position_terminology.png

Figure 1: Accuracy and Repeatability

-
+

position_resolution.png

Figure 2: Position Resolution

-
+

position_stability.png

Figure 3: Position Stability

@@ -189,11 +189,11 @@ The stability is always related to the time frame taken into account. (Figure
-
-

1.2 Principles of accuracy

+
+

1.2 Principles of accuracy

-Limited stiffness, play and friction will induce an hysteresis for a positioning system as shown in Figure 4. +Limited stiffness, play and friction will induce an hysteresis for a positioning system as shown in Figure 4.

@@ -201,7 +201,7 @@ The hysteresis can actually help estimating the play and friction present in the

-
+

stiffness_friction.png

Figure 4: Stiffness, play and Friction

@@ -217,7 +217,7 @@ Ways to make the hysteresis smaller:

-The position uncertainty of a system can be estimated as follow (Figure 5): +The position uncertainty of a system can be estimated as follow (Figure 5):

\begin{equation} \text{Position Uncertainty} = \text{play} + 2 \times \text{Virtual Play} @@ -230,7 +230,7 @@ where the virtual play can be estimated as follow: \end{equation} -
+

position_uncertainty.png

Figure 5: Hysterestis, play and virtual play

@@ -254,11 +254,11 @@ Note that it is very difficult to make a system with constant friction in practi
-
-

1.3 Case 1 - Estimate the virtual play

+
+

1.3 Case 1 - Estimate the virtual play

-Estimate the virtual play of the system in Figure 6 with following characteristics: +Estimate the virtual play of the system in Figure 6 with following characteristics:

  • Payload: \(m = 20\,kg\)
    • @@ -269,7 +269,7 @@ Estimate the virtual play of the system in Figure 6 wi
-
+

case_1.png

Figure 6: Studied system for “Case 1”

@@ -306,43 +306,43 @@ And finally:
-
-

1.4 Conventional elements for constraining DoFs

+
+

1.4 Conventional elements for constraining DoFs

There exist many conventional elements for constraining DoFs. Some of them are:

    -
  • Struts with ball joint: 1DoF constrained (Figure 7)
    • -
  • Ball bearing: 5DoF constrained (Figure 8)
    • -
  • Guide with roller bearing: 4DoF constrained (Figure 9)
    • -
  • Roller rail guide: 5DoF constrained (Figure 10)
    • +
  • Struts with ball joint: 1DoF constrained (Figure 7)
    • +
  • Ball bearing: 5DoF constrained (Figure 8)
    • +
  • Guide with roller bearing: 4DoF constrained (Figure 9)
    • +
  • Roller rail guide: 5DoF constrained (Figure 10)
-
+

ball_joint.png

Figure 7: Ball Joint

-
+

ball_bearing.png

Figure 8: Ball Bearing

-
+

roller_bearing.png

Figure 9: Roller Bearing

-
+

roller_rail_guide.png

Figure 10: Roller Rail Guide

@@ -350,19 +350,19 @@ Some of them are:
-
-

1.5 Compliant elements for constraining DoFs

+
+

1.5 Compliant elements for constraining DoFs

-
-

1.5.1 Basic leaf springs and folded leaf springs

+
+

1.5.1 Basic leaf springs and folded leaf springs

-An example of a complaint element is shown in Figure 11. +An example of a complaint element is shown in Figure 11.

-
+

compliant_1dof.png

Figure 11: Example of 1dof constrained compliant element

@@ -372,28 +372,28 @@ An example of a complaint element is shown in Figure 11
    -
  • Leaf spring: constrains 3 dof (Figure 12)
    • -
  • Folded leaf spring: constrains only 1dof (Figure 13) +
  • Leaf spring: constrains 3 dof (Figure 12)
    • +
  • Folded leaf spring: constrains only 1dof (Figure 13) These are generally used in combination with other folded leaf springs.
    • -
  • Flexure pivots: constrains 5 dofs (Figure 14)
    • +
  • Flexure pivots: constrains 5 dofs (Figure 14)
-
+

leaf_springs.png

Figure 12: Leaf springs

-
+

folded_leaf_springs.png

Figure 13: Folded Leaf springs

-
+

flexure_pivots.png

Figure 14: Flexure Pivots (5dof constrained)

@@ -401,11 +401,11 @@ These are generally used in combination with other folded leaf springs.
-
-

1.5.2 1dof Parallel Guiding

+
+

1.5.2 1dof Parallel Guiding

-Parallel guiding can be made using two leaf springs (Figure 15): +Parallel guiding can be made using two leaf springs (Figure 15):

  • 2 parallel leaf springs
    • @@ -418,26 +418,26 @@ This sag is predictible and reproducible: \delta z = 0.6 \frac{x^2}{L} \end{equation}
  • Vertical stiffness negatively affected by displacement
    • -
  • Take care of maximum buckling (Figure 16)
    • -
  • Improve buckling load and Z stiffness by reinforced mid-section (Figure 17)
    • +
  • Take care of maximum buckling (Figure 16)
    • +
  • Improve buckling load and Z stiffness by reinforced mid-section (Figure 17)
-
+

parallel_guiding.png

Figure 15: Parallel guiding

-
+

buckling.png

Figure 16: Example of bucklink

-
+

reinforced_leaf_springs.png

Figure 17: Reinforced leaf springs

@@ -445,11 +445,11 @@ This sag is predictible and reproducible:
-
-

1.5.3 Rotation Compliant Mechanism

+
+

1.5.3 Rotation Compliant Mechanism

-Figure 18 shows a rotation compliant mechanism: +Figure 18 shows a rotation compliant mechanism:

  • 3 leaf springs
    • @@ -457,7 +457,7 @@ Figure 18 shows a rotation compliant mechanism:
-
+

rotation_leaf_springs.png

Figure 18: Example of rotation stage using leaf springs

@@ -465,11 +465,11 @@ Figure 18 shows a rotation compliant mechanism:
-
-

1.5.4 Z translation

+
+

1.5.4 Z translation

-Figure 19 shows a Z translation mechanism: +Figure 19 shows a Z translation mechanism:

  • 5 struts (“needles”)
    • @@ -482,18 +482,18 @@ This parasitic rotation is however predictable.

    -
    +

    vertical_stage_compliant.png

    Figure 19: Z translation using 5 struts

    -An alternative is to use folder leaf springs (Figure 20), and this avoid the parasitic rotation. +An alternative is to use folder leaf springs (Figure 20), and this avoid the parasitic rotation.

    -
    +

    vertical_stage_leafs.png

    Figure 20: Z translation using 5 folded leaf springs

    @@ -501,22 +501,22 @@ An alternative is to use folder leaf springs (Figure 20
    -
    -

    1.5.5 X-Y-Rz Stage

    +
    +

    1.5.5 X-Y-Rz Stage

    -An X-Y-Rz stage can be done either using 3 struts (Figure 21) or using 3 folded leaf springs (Figure 22). +An X-Y-Rz stage can be done either using 3 struts (Figure 21) or using 3 folded leaf springs (Figure 22).

    -
    +

    x_y_rz_stage.png

    Figure 21: X,Y,Rz using 3 struts

    -
    +

    x_y_rz_leafs.png

    Figure 22: X,Y,Rz using 3 folded leaf springs

    @@ -524,15 +524,15 @@ An X-Y-Rz stage can be done either using 3 struts (Figure
    -
    -

    1.5.6 Compliant mechanism with only one fixed dof

    +
    +

    1.5.6 Compliant mechanism with only one fixed dof

    -The compliant mechanism shown in Figure 23 only constrain the rotation about the y-axis. +The compliant mechanism shown in Figure 23 only constrain the rotation about the y-axis.

    -
    +

    case_1_leaf_springs.png

    Figure 23: 5dof motion, only the Ry is constrained

    @@ -540,8 +540,8 @@ The compliant mechanism shown in Figure 23 only constr
    -
    -

    1.5.7 Summary

    +
    +

    1.5.7 Summary

    • compliant elements enable defined movements
      • @@ -552,26 +552,26 @@ The compliant mechanism shown in Figure 23 only constr
    -
    -

    1.5.8 Examples

    +
    +

    1.5.8 Examples

    -An example of a complex compliant mechanism is shown in Figure 24. +An example of a complex compliant mechanism is shown in Figure 24.

    -
    +

    compliant_example_1.png

    Figure 24: Design concept

    -Figure 25 shown a reinforced part to avoid buckling and improve vertical stiffness. +Figure 25 shown a reinforced part to avoid buckling and improve vertical stiffness.

    -
    +

    linear_bearing_leafs.png

    Figure 25: Use leaf springs instead of linear roller bearings

    @@ -579,11 +579,11 @@ Figure 25 shown a reinforced part to avoid buckling an
    -
    -

    1.5.9 Mechatronics positioning challenge

    +
    +

    1.5.9 Mechatronics positioning challenge

    -A X-Y-Rz stage is shown in Figure 26. +A X-Y-Rz stage is shown in Figure 26. To make this stage usable for nano-metric positioning, the following ideas where used:

      @@ -614,23 +614,23 @@ To make this stage usable for nano-metric positioning, the following ideas where
    -
    +

    xyRz_positioning_challenge.png

    Figure 26: Example of X-Y-Rz positioning stage

    - +

    -
    -

    1.5.10 Case - Play Free parallel Stage

    +
    +

    1.5.10 Case - Play Free parallel Stage

    -Figure 27 shows a parallel mechanism that should be converted to a compliant mechanism. +Figure 27 shows a parallel mechanism that should be converted to a compliant mechanism. Its characteristics are:

      @@ -643,7 +643,7 @@ Its characteristics are:
    -
    +

    play_free_parallel_stage.png

    Figure 27: Example of a parallel stage that should be converting to a compliant mechanism

    @@ -659,11 +659,11 @@ The goals are to:

-The solution is shown in Figure 28. +The solution is shown in Figure 28.

-
+

play_free_parallel_stage_solution.png

Figure 28: Case Solution

@@ -672,12 +672,12 @@ The solution is shown in Figure 28.
-
-

1.6 Thin plate design

+
+

1.6 Thin plate design

-
-

1.6.1 Thin plate in torsion

+
+

1.6.1 Thin plate in torsion

Thin plates are very important for compliant mechanisms. @@ -710,7 +710,7 @@ where \(A\) is the area of the cross section.

-
+

thin_plate_torsion.png

Figure 29: A plate under torsion

@@ -718,8 +718,8 @@ where \(A\) is the area of the cross section.
-
-

1.6.2 Difference between open and close profile

+
+

1.6.2 Difference between open and close profile

The close profile has much more torsional stiffness than the open profile. @@ -730,7 +730,7 @@ Just by opening the tube, we have a much smaller torsional stiffness (but almost

-
+

open_close_profil_torsion_stiffness.png

Figure 30: Stiffness comparison open and closed tube (torsion)

@@ -739,22 +739,22 @@ Just by opening the tube, we have a much smaller torsional stiffness (but almost

We have similar behavior with an open/closed box. -If we remove one side of the cube shown in Figure 31, we would have much smaller torsional stiffness along the axis perpendicular to the removed side. +If we remove one side of the cube shown in Figure 31, we would have much smaller torsional stiffness along the axis perpendicular to the removed side.

-
+

closed_box.png

Figure 31: Closed box.

-If we use triangles, we obtain high torsional stiffness as shown in Figure 32. +If we use triangles, we obtain high torsional stiffness as shown in Figure 32.

-
+

torsion_stiffness_box_double_triangle.png

Figure 32: Open box (double triangle)

@@ -766,11 +766,11 @@ On way to reinforce it is using triangles.

-A nice way to have a 1dof flexure guiding with stiff frame is shown in Figure 33. +A nice way to have a 1dof flexure guiding with stiff frame is shown in Figure 33.

-
+

z_stage_triangles.png

Figure 33: Box with integrated flexure guiding

@@ -780,12 +780,16 @@ A nice way to have a 1dof flexure guiding with stiff frame is shown in Figure
-
-

2 Keynote: Mechatronic challenges in optical lithography   @hans_butler

+
+

2 Keynote: Mechatronic challenges in optical lithography   @hans_butler

+

+ +

-
-

2.1 Introduction

+ +
+

2.1 Introduction

Question: in chip manufacturing, how do developments in optical lithography impact the mechatronic design? @@ -803,15 +807,15 @@ Main developments:

-
-

2.2 Chip manufacturing loop

+
+

2.2 Chip manufacturing loop

In this presentation, only the exposure step is discussed (lithography).

-
+

asml_chip_manufacturing_loop.png

Figure 34: Chip manufacturing loop

@@ -819,19 +823,19 @@ In this presentation, only the exposure step is discussed (lithography).
-
-

2.3 Imaging process - Basics

+
+

2.3 Imaging process - Basics

-
+

asml_imaging_process.png

Figure 35: Imaging process - basics

@@ -839,8 +843,8 @@ This will induce a sinusoidal wave on the wafer as shown in Figure -

2.4 From stepper to scanner

+
+

2.4 From stepper to scanner

Before, one chip was illumating at a time, but people wanted to make bigger chips. @@ -853,7 +857,7 @@ This implied many requirements in dynamics and accuracy!

-
+

asml_stepper_to_scanner.png

Figure 36: From stepper to scanner

@@ -861,8 +865,8 @@ This implied many requirements in dynamics and accuracy!
-
-

2.5 Dual stage scanners

+
+

2.5 Dual stage scanners

Both the reticle stage and wafer stage are moving. @@ -887,7 +891,7 @@ Which are solved by: -

+

asml_dual_stage_scanners.png

Figure 37: Machine based on the dual stage scanners

@@ -895,20 +899,20 @@ Which are solved by:
-
-

2.6 Immersion technology

+
+

2.6 Immersion technology

Water is used between the lens and the wafer to increase the “NA” and thus decreasing the “critical dimension”.

-The “hood” is there to prevent any bubble to enter the illumination area (Figure 38). +The “hood” is there to prevent any bubble to enter the illumination area (Figure 38). The position of the “hood” is actively control to follow the wafer stage (that can move in z direction and tilt).

-Three solutions are used for the positioning control of the “hood” system (Figure 39): +Three solutions are used for the positioning control of the “hood” system (Figure 39):

  • Disturbance decoupling
    • @@ -917,14 +921,14 @@ Three solutions are used for the positioning control of the “hood” s
-
+

asml_hood_system.png

Figure 38: Hood System

-
+

asml_immersion.png

Figure 39: Control system for the “hood”

@@ -932,8 +936,8 @@ Three solutions are used for the positioning control of the “hood” s
-
-

2.7 Multiple Patterning

+
+

2.7 Multiple Patterning

The multiple patterning approach adds few mechatronics challenges: @@ -953,16 +957,16 @@ This was solved by:

-
-

2.8 Machine layout

+
+

2.8 Machine layout

-Each stage is controlled with 6dof lorentz short stroke actuators (Figure 40). +Each stage is controlled with 6dof lorentz short stroke actuators (Figure 40). The magnet stage can move horizontally (due to reaction forces of the wafer stages): it asks as a balance mass.

-
+

asml_machine_layout_bis.png

Figure 40: Machine layout

@@ -970,8 +974,8 @@ The magnet stage can move horizontally (due to reaction forces of the wafer stag
-
-

2.9 EUV Lithography

+
+

2.9 EUV Lithography

Vacuum is required which implies: @@ -999,7 +1003,7 @@ Wafer stage: -

+

asml_euv.png

Figure 41: Schematic of the ASML EUV machine

@@ -1007,22 +1011,22 @@ Wafer stage:
-
-

2.10 The future: high-NA EUV

+
+

2.10 The future: high-NA EUV

-
+

asml_na_euv.png

Figure 42: The CD will be 8nm

-In order to do so, high “opening” of the optics is required which is very challenges because the reflectiveness of mirror is decreasing as high angle of incidence (Figure 43). +In order to do so, high “opening” of the optics is required which is very challenges because the reflectiveness of mirror is decreasing as high angle of incidence (Figure 43).

-
+

asml_reflection_angle.png

Figure 43: Change of reflection of a mirror as a function of the angle of indicence

@@ -1030,8 +1034,8 @@ In order to do so, high “opening” of the optics is required which is
-
-

2.11 Challenges for future Optical Lithography machines

+
+

2.11 Challenges for future Optical Lithography machines

Challenges: @@ -1053,8 +1057,8 @@ In order to do so, high “opening” of the optics is required which is

-
-

2.12 Conclusion

+
+

2.12 Conclusion

The conclusions are: @@ -1075,14 +1079,494 @@ The conclusions are:

-
-

3 Designing anti-aliasing-filters for control loops of mechatronic systems regarding the rejection of aliased resonances   @ulrich_schonhoff

+
+

3 Keynote: High precision mechatronic approaches for advanced nanopositioning and nanomeasuring technologies   @eberhard_manske

+

+ +

-
-

3.1 The phenomenon of aliasing of resonances

+ +
+

3.1 Coordinate Measurement Machines (CMM)

+Examples of Nano Coordinate Measuring Machines are shown in Figure 44. +

+ + +
+

prec_cmm.png +

+

Figure 44: Example of Coordinate Measuring Machines

+
+
+
+ +
+

3.2 Difference between CMM and nano-CMM

+
+

+With classical CMM, the Abbe-principle is not fulfilled in the x and y directions (Figure 45). +

+ +

+The Abbe error can be determined with: +

+\begin{equation} + \Delta l_{x,y,z} = l_{x,y,z} \sin \Delta \phi_{x,y,z} +\end{equation} + +

+Even with the best spindle: \(l_{x,y} = 100 mm\) and \(\Delta \phi = 2 \text{arcsec}\), we obtain an error of: +

+\begin{equation} + \Delta l = 0.1 \mu m +\end{equation} +

+which is not compatible with nano-meter precisions. +

+ +

+Then, the classical CMM will not work for nano precision +

+ + +
+

prec_cmm_nano_cmm.png +

+

Figure 45: Schematic of a CMM

+
+
+
+ +
+

3.3 How to do nano-CMM

+
+

+High precision mechatronic approaches are required for advanced nano-positionign and nano-measuring technologies: +

+
    +
  • High precision measurement concept
    • +
  • High precision measurement systems
    • +
  • High precision nano-sensors
    • +
+

+Combined with: +

+
    +
  • Advanced automatic control
    • +
  • Advanced measuring strategies
    • +
+
+
+ +
+

3.4 Concept - Minimization of the Abbe Error

+
+

+In order to minimize the Abbe error, the measuring “lines” should have a common point of intersection (Figure 46). +

+ +

+The 3D-realization of Abbe-principle is as follows: +

+
    +
  • 3 interferometers: cartesian coordinate system
    • +
  • probe located as the intersection point of the interferometers
    • +
+ + +
+

prec_nano_cmm_concept.png +

+

Figure 46: Error minimal measuring principle

+
+
+
+ +
+

3.5 Minimization of residual Abbe error

+
+

+Still some residual Abbe error can happen as shown in Figure 47 due to both a change of angle and change of position. +

+ + +
+

prec_abbe_min.png +

+

Figure 47: Residual Abbe error

+
+
+
+ +
+

3.6 Compare of long travel guiding systems

+
+

+In order to have the Abbe error compatible with nano-meter precision, the precision of the spindle should be less and one arcsec which is not easily feasible with air bearing of precision roller bearing technologies as shown in Figure 48. +

+ + +
+

prec_comp_guid.png +

+

Figure 48: Characteristics of guidings

+
+
+
+ +
+

3.7 Extended 6 DoF Abbe comparator principle

+
+

+The solution used was to measure in real time the angles of the frame using autocollimators as shown in Figure 49 and then to minimize this tilt by close loop operation with additional actuators. +

+ +

+The angular measurement error and control is less than \(0.05 \text{arcses}\) which make the residual Abbe error: +

+\begin{equation} + \Delta l < 0.05\,nm +\end{equation} + +

+Without an error-minimal approach, nano-meter precision cannot be achieved in large areas. +

+ + +
+

prec_6dof_abbe.png +

+

Figure 49: Use of additional autocollimator and actuators for Abbe minimization

+
+
+
+ +
+

3.8 Practical Realisation

+
+

+A practical realization of the Extended 6 DoF Abbe comparator principle is shown in Figure 50. +

+ + +
+

prec_practical_6dof.png +

+

Figure 50: Practical Realization of the

+
+
+
+ +
+

3.9 Tilt Compensation

+
+

+To measure compensate for any tilt, two solutions are proposed: +

+
    +
  1. Use a zero point angular auto-collimator (Figure 51) +
      +
    • Resolution: 0.005 arcsec
      • +
    • Stability (1h): < 0.05 arcsec
      • +
    2. +
  2. 6 DoF laser interferoemter (Figure 52) +
      +
    • Resolution: 0.00002 arcsec
      • +
    • Stability (1h): < 0.00005 arcsec
      • +
    3. +
+ + +
+

prec_tilt_corection.png +

+

Figure 51: Auto-Collimator

+
+ + +
+

prec_tilt_corection_bis.png +

+

Figure 52: 6 Interferometers to measure tilts

+
+
+
+ +
+

3.10 Comparison of long travail guiding systems - Bis

+
+

+Now, if we actively compensate the tilts are shown previously, we can fulfill the requirements as shown in Figure 53. +

+ +

+Measurement and control technology to minimize Abbe errors to achieve: +

+
    +
  • sub-nanometer precision
    • +
  • smaller moving mass
    • +
  • better dynamics
    • +
+ + +
+

prec_comp_guid_bis.png +

+

Figure 53: Characteristics of the tilt compensation system

+
+
+
+ +
+

3.11 Drive concept

+
+

+Usually, in order to achieve a large range over small resolution, each axis of motion is a combination of a coarse motion and a fine motion stage. +The coarse motion stage generally consist of a stepper motor while the fine motion is a piezoelectric actuator. +

+ +

+The approach here is to use an homogenous drive concept for increase dynamics (Figure 54). +

+ +

+Only one linear voice coil actuator is used which with large moving range and sub-nanometer resolution can be achieve at one time. +

+ + +
+

prec_drive_concept.png +

+

Figure 54: Voice Coil Actuator

+
+
+
+ + +
+

3.12 NPMM-200 with extended measuring volume

+
+

+The NPMM-200 machine can be seen in Figure 55. +

+ +

+Characteristics: +

+
    +
  • Measuring range: 200 mm x 200 mm x 25 mm
    • +
  • Resolution: 20 pm
    • +
  • Abbe comparator principle
    • +
  • 6 laser interferometers
    • +
  • Active angular compensation
    • +
  • Position uncertainty < 4 nm
    • +
  • Measuring uncertainty up to 30 nm
    • +
+ + +
+

prec_mechanics.png +

+

Figure 55: Picture of the NPMM-200

+
+ +

+The NPMM-200 actually operates inside a Vacuum chamber as shown in Figure 56. +

+ + +
+

prec_vacuum_cham.png +

+

Figure 56: Vacuum chamber used

+
+
+
+ +
+

3.13 measurement capability

+
+

+Some step responses are shown in Figure 57 and show the nano-metric precision of the machine. +

+ + +
+

prec_results_meas.png +

+

Figure 57: Sub nano-meter position accuracy

+
+ +

+Picometer steps can even be achieved as shown in Figure 58. +

+ + +
+

prec_results_pico.png +

+

Figure 58: Picometer level control

+
+
+
+ +
+

3.14 Extension of the measuring range (700mm)

+
+

+If the measuring range is to be increase, there are some limits of the moving stage principle: +

+
    +
  • large moving masses (~300kg)
    • +
  • powerful drive systems required
    • +
  • nano-meter position capability problematic
    • +
  • large heat dissipation in the system
    • +
  • dynamics and dynamic deformation
    • +
+ +

+The proposed solution is to use inverse dynamic concept for minimization of moving masses. +

+
+
+ +
+

3.15 Inverse kinematic concept - Tetrahedrical concept

+
+

+The proposed concept is shown in Figure 59: +

+
    +
  • mirrors and object to be measured are fixed
    • +
  • probe and interferometer heads are moved
    • +
  • laser beams virtually intersect in the probe tip
    • +
  • Tetrahedrical measuring volume
    • +
+ +

+This fulfills the Abbe principe but: +

+
    +
  • large construction space
    • +
  • difficult guide and drive concept
    • +
+ + +
+

prec_inverse_kin.png +

+

Figure 59: Tetrahedrical concept

+
+
+
+ +
+

3.16 Inverse kinematic concept - Scanning probe principle

+
+

+An other concept, the scanning probe principle is shown in Figure 60: +

+
    +
  • cuboidal measuring volume
    • +
  • Fixed x-y-z mirrors
    • +
  • moving measuring head
    • +
  • guide and drive system outside measuring volume
    • +
+ + +
+

prec_inverse_kin_scan.png +

+

Figure 60: Scanning probe principle

+
+
+
+ +
+

3.17 Inverse kinematic concept - Compact measuring head

+
+

+In order to minimize the moving mass, compact measuring heads have been developed. +The goal was to make a lightweight measuring head (<1kg) +

+ +

+The interferometer used are fiber coupled laser interferometers with a mass of 37g (Figure 61). +

+ + +
+

prec_interferometers.png +

+

Figure 61: Micro Interferometers

+
+ +

+The concept is shown in Figure 62: +

+
    +
  • 6dof interferometers are used
    • +
  • one micro-probe
    • +
  • the total mass of the head is less than 1kg
    • +
+ +

+There is some abbe offset between measurement axis of probe and of interferometer but Abbe error compensation by closed loop control of angular deviations is used. +

+ + +
+

prec_inverse_meas_head.png +

+
+
+
+ +
+

3.18 Inverse kinematic concept - Scanning probe principle

+
+

+As shown in Figure 63, the abbe error can be compensated from the two top interferometers as: +\[ \text{for } l_x = a: \quad \Delta l_{\text{Abbe}} = \Delta l_{\text{int}} \] +Thus the tilt and Abbe errors can be compensated for with sub-nm resolution. +

+ + +
+

prec_abbe_compensation.png +

+

Figure 63: Use of the interferometers to compensate for the Abbe errors

+
+
+
+ +
+

3.19 Conclusion

+
+

+Proposed approaches to push the nano-positioning and nano-measuring technology: +

+
    +
  • Measurement and control technology to minimize Abbe errors
    • +
  • Homogeneous drive concept for increased dynamics
    • +
  • Inverse kinematic concept for minimization of moving mass
    • +
  • Abbe-error compensation by closed loop control of angular deviations
    • +
+
+
+
+ +
+

4 Designing anti-aliasing-filters for control loops of mechatronic systems regarding the rejection of aliased resonances   @ulrich_schonhoff

+
+
+
+

4.1 The phenomenon of aliasing of resonances

+
+

Weakly damped flexible modes of the mechanism can limit the performance of motion control systems.

@@ -1091,36 +1575,36 @@ For discrete time controlled systems, there can be an additional limitation: ali

-
+

aliasing_resonances.png

-

Figure 44: Example of high frequency lighlty damped resonances

+

Figure 64: Example of high frequency lighlty damped resonances

-The aliasing of signals is well known (Figure 45). +The aliasing of signals is well known (Figure 65).

-However, aliasing in systems can also happens and is schematically shown in Figure 46. +However, aliasing in systems can also happens and is schematically shown in Figure 66.

-
+

aliasing_signals.png

-

Figure 45: Aliasing of Signals

+

Figure 65: Aliasing of Signals

-
+

aliasing_system.png

-

Figure 46: Aliasing of Systems

+

Figure 66: Aliasing of Systems

-The poles of the system will be aliased and their location will change in the complex plane as shown in Figure 47. +The poles of the system will be aliased and their location will change in the complex plane as shown in Figure 67.

@@ -1136,10 +1620,10 @@ Therefore, the damping of the aliased resonances are foreseen to have larger dam

-
+

aliasing_poles.png

-

Figure 47: Aliasing of poles in the complex plane

+

Figure 67: Aliasing of poles in the complex plane

@@ -1151,7 +1635,7 @@ Let’s consider two systems with a resonance:

-Then looking at the same systems in the digital domain, one can see thathen the resonance is above the Nyquist frequency (Figure 48): +Then looking at the same systems in the digital domain, one can see thathen the resonance is above the Nyquist frequency (Figure 68):

  • the resonance mirrors
    • @@ -1163,84 +1647,84 @@ Therefore, when identifying a low damped resonance, it could be that it comes fo

    -
    +

    aliasing_above_nyquist.png

    -

    Figure 48: Aliazed resonance shown on the Bode Diagram

    +

    Figure 68: Aliazed resonance shown on the Bode Diagram

    -
    +

    alising_much_above_nyquist.png

    -

    Figure 49: Higher resonance frequency

    +

    Figure 69: Higher resonance frequency

    -
    -

    3.2 Nature, Modelling and Mitigation of potentially aliasing resonances

    -
    +
    +

    4.2 Nature, Modelling and Mitigation of potentially aliasing resonances

    +

    -The aliased modes can for instance comes from local modes in the actuators that are lightly damped and at high frequency (Figure 50) +The aliased modes can for instance comes from local modes in the actuators that are lightly damped and at high frequency (Figure 70)

    -
    +

    alising_nature.png

    -

    Figure 50: Local vibration mode that will be alized

    +

    Figure 70: Local vibration mode that will be alized

    -The proposed idea to better model aliasing resonances is to include more modes in the FEM software as shown in Figure 51 and then perform an order reduction in matlab. +The proposed idea to better model aliasing resonances is to include more modes in the FEM software as shown in Figure 71 and then perform an order reduction in matlab.

    -
    +

    aliasing_modeling.png

    -

    Figure 51: Common procedure and proposed procedure to include aliazed resonances

    +

    Figure 71: Common procedure and proposed procedure to include aliazed resonances

    -
    -

    3.3 Anti aliasing filter design

    -
    +
    +

    4.3 Anti aliasing filter design

    +
    -
    -

    3.3.1 Introduction

    -
    +
    +

    4.3.1 Introduction

    +
    • Anti-aliasing filtering can be used to reject aliasing of resonances and to maintain the stability of the control loop
    • However, its phase lag deteriorates the control loop performances:
        -
      • phase margin decreases (Figure 52)
        • -
      • sensitivity peak increases (Figure 53)
        • +
      • phase margin decreases (Figure 72)
        • +
      • sensitivity peak increases (Figure 73)
    • Thus, the anti-aliasing filter should be targeted at sufficient rejection at least possible phase lag
    -
    +

    alising_filter_introduction.png

    -

    Figure 52: Example of the effect of aliased resonance on the open-loop

    +

    Figure 72: Example of the effect of aliased resonance on the open-loop

    -
    +

    aliasing_sensitivity_effect.png

    -

    Figure 53: Example of the effect of aliased resonance on sensitivity function

    +

    Figure 73: Example of the effect of aliased resonance on sensitivity function

    -
    -

    3.3.2 Concept of equivalent delay

    -
    +
    +

    4.3.2 Concept of equivalent delay

    +

    Concept:

    @@ -1263,7 +1747,7 @@ Similarly, \(\omega_{0zi}\) is the natural frequency \(\xi_{zi}\) is the damping

-Examples (Figure 54): +Examples (Figure 74):

  • First order low pass filter: @@ -1275,86 +1759,86 @@ Similarly, \(\omega_{0zi}\) is the natural frequency \(\xi_{zi}\) is the damping
-
+

aliasing_equivalent_delay.png

-

Figure 54: Magnitude, Phase and Phase delay of 3 filters

+

Figure 74: Magnitude, Phase and Phase delay of 3 filters

-
-

3.3.3 Budgeting of phase lag

-
+
+

4.3.3 Budgeting of phase lag

+

-The budgeting of the phase lag is done by expressing the phase lag of each element by a time delay (Figure 55) +The budgeting of the phase lag is done by expressing the phase lag of each element by a time delay (Figure 75)

-
+

aliasing_budget_phase.png

-

Figure 55: Typical control loop with several phase lag / time delays

+

Figure 75: Typical control loop with several phase lag / time delays

-The equivalent delay of each element are listed in Figure 56. +The equivalent delay of each element are listed in Figure 76.

-
+

aliasing_budget_table.png

-

Figure 56: Equivalent delay for all the elements of the control loop

+

Figure 76: Equivalent delay for all the elements of the control loop

-
-

3.3.4 Selecting the filter order

-
+
+

4.3.4 Selecting the filter order

+

The filter order can be chosen depending on the frequency of the resonance. -Some example of Butterworth filters are shown in Figure 57 and summarized in Figure 58. +Some example of Butterworth filters are shown in Figure 77 and summarized in Figure 78.

-
+

aliasing_filter_order_bode.png

-

Figure 57: Example of few Butterworth filters

+

Figure 77: Example of few Butterworth filters

-
+

aliasing_filter_order_table.png

-

Figure 58: Butterworth filters

+

Figure 78: Butterworth filters

-
-

3.3.5 Reducing the phase lag

-
+
+

4.3.5 Reducing the phase lag

+

The equivalent delay of a low pass (here second order) depends on its damping, since: \[ T_e = -2 \frac{\xi_{zi}}{\omega_{0zi}} \]

-
+

aliasing_reduce_phase_lag.png

-

Figure 59: Change of the phase delay with the damping of the filter

+

Figure 79: Change of the phase delay with the damping of the filter

-
-

3.4 Conclusion

-
+
+

4.4 Conclusion

+

The phenomenon of aliasing of resonances:

@@ -1388,13 +1872,13 @@ Anti-aliasing filter design:
-
-

4 Flexure positioning stage based on delta technology for high precision and dynamic industrial machining applications   @mikael_bianchi

-
+
+

5 Flexure positioning stage based on delta technology for high precision and dynamic industrial machining applications   @mikael_bianchi

+
-
-

4.1 Introduction

-
+
+

5.1 Introduction

+
  • Goal: flexure positioning stage to do high precision and high dynamic/acceleration positioning. The control architecture should be as simple as possible.
    • @@ -1406,83 +1890,83 @@ The control architecture should be as simple as possible.
-
-

4.2 Design

-
+
+

5.2 Design

+
-
-

4.2.1 Description of the Delta robot

-
+
+

5.2.1 Description of the Delta robot

+

-Technical choice: flexure based delta robot (Figure 60). +Technical choice: flexure based delta robot (Figure 80).

  • Advantages: high mechanical precision without backlash
    • -
  • Disadvantage: the motion is coupled, some transformations are required from motor coordinates to machine coordinates (Figure 61)
    • +
  • Disadvantage: the motion is coupled, some transformations are required from motor coordinates to machine coordinates (Figure 81)
-
+

flexure_delta_robot.png

-

Figure 60: Picture of the Delta Robot

+

Figure 80: Picture of the Delta Robot

-
+

flexure_delta_robot_schematic.png

-

Figure 61: x1, x2 x3 are the motor positions. f1,f2 f3 are the force motors. x,y,z are the position of the final point in cartesian coordinates

+

Figure 81: x1, x2 x3 are the motor positions. f1,f2 f3 are the force motors. x,y,z are the position of the final point in cartesian coordinates

-
-

4.2.2 Modelling and validation of the delta robot

-
+
+

5.2.2 Modelling and validation of the delta robot

+

Lagrange equations are used to model the dynamics of the delta robot. The motor positions are used as the general coordinate system.

-The system is then linearized around the working point (Figure 62). +The system is then linearized around the working point (Figure 82).

-
+

flexure_equations.png

-

Figure 62: Linearized equations of the Delta Robot

+

Figure 82: Linearized equations of the Delta Robot

-Then the parameters are identified from experiment (Figure 63). +Then the parameters are identified from experiment (Figure 83).

-
+

flexure_identification.png

-

Figure 63: Identification fo the transfer function from \(F_1\) to \(x_1\)

+

Figure 83: Identification fo the transfer function from \(F_1\) to \(x_1\)

-The measurement of the coupling is move complicated as shown in Figure 64. +The measurement of the coupling is move complicated as shown in Figure 84.

-
+

flexure_identification_coupling.png

-

Figure 64: Problem of identifying the coupling between F1 and x2 at low frequency

+

Figure 84: Problem of identifying the coupling between F1 and x2 at low frequency

-
-

4.2.3 Control design for high trajectory tracking

-
+
+

5.2.3 Control design for high trajectory tracking

+

Control requirements:

@@ -1494,19 +1978,19 @@ Control requirements: -
+

flexure_control_concept.png

-

Figure 65: Control concept used for the Delta robot

+

Figure 85: Control concept used for the Delta robot

-
-

4.2.4 Electronic board

-
+
+

5.2.4 Electronic board

+

-A 3 axis servo control board as been developed (Figure 66) which includes: +A 3 axis servo control board as been developed (Figure 86) which includes:

  • identification algorithm of the coupled system integrated in the board
    • @@ -1520,71 +2004,71 @@ A 3 axis servo control board as been developed (Figure 66<
-
-

4.3 Results

-
+
+

5.3 Results

+
-
-

4.3.1 Current control

-
+
+

5.3.1 Current control

+

-Step response of the current control loop is shown in Figure 66. +Step response of the current control loop is shown in Figure 86.

-
+

flexure_current_control_results.png

-

Figure 66: Step response for the current control loop

+

Figure 86: Step response for the current control loop

-
-

4.3.2 Trajectory tracking: results with laser interferometer and encoder

-
+
+

5.3.2 Trajectory tracking: results with laser interferometer and encoder

+

-XY renishaw interferometers used to verify the performance of the system (Figure 67). +XY renishaw interferometers used to verify the performance of the system (Figure 87).

-
+

flexure_sensors.png

-

Figure 67: Experimental setup to verify the performances of the system

+

Figure 87: Experimental setup to verify the performances of the system

-Some results are shown in Figures 68, 69 and 70. +Some results are shown in Figures 88, 89 and 90.

-
+

flexure_results.png

-

Figure 68: Circuit motion results and point to point motion results

+

Figure 88: Circuit motion results and point to point motion results

-
+

flexure_steps.png

-

Figure 69: Step response of the system

+

Figure 89: Step response of the system

-
+

flexure_dynamics_errors.png

-

Figure 70: Measured dynamical errors

+

Figure 90: Measured dynamical errors

-
-

4.4 Conclusion

-
+
+

5.4 Conclusion

+

As a conclusion, here are the identified conditions for precise and high dynamic positioning:

@@ -1602,19 +2086,19 @@ Resonances at mid frequencies are an issue for further improvements.
-
-

5 Multivariable performance analysis of position-controlled payloads with flexible eigenmodes   @luca_mettenleiter

-
+
+

6 Multivariable performance analysis of position-controlled payloads with flexible eigenmodes   @luca_mettenleiter

+
-
-

5.1 Motivation

-
+
+

6.1 Motivation

+

Flexible eigenmodes are present in every system component and leads to::

    -
  • controller bandwidth limitation (Figure 71)
    • -
  • additional cross-coupling in the system behavior (Figure 72)
    • +
  • controller bandwidth limitation (Figure 91)
    • +
  • additional cross-coupling in the system behavior (Figure 92)

@@ -1622,37 +2106,37 @@ Flexible eigenmodes are present in every system component and leads to::

-
+

mimo_flexible_modes.png

-

Figure 71: Limitation of the control bandwidth due to flexible eigenmodes

+

Figure 91: Limitation of the control bandwidth due to flexible eigenmodes

-
+

mimo_flexible_modes_coupling.png

-

Figure 72: Coupling due to flexible eigenmodes

+

Figure 92: Coupling due to flexible eigenmodes

-In order to estimate the performances of a system, the sensitivity function can be used (Figure 73). +In order to estimate the performances of a system, the sensitivity function can be used (Figure 93).

-
+

mimo_sensitivity_performance.png

-

Figure 73: Bode plot of a typical Sensitivity function

+

Figure 93: Bode plot of a typical Sensitivity function

-
-

5.2 Performance analysis with different sensitivity functions

-
+
+

6.2 Performance analysis with different sensitivity functions

+

-There are different way to analyse the sensitivity function base on different plants (Figure 74): +There are different way to analyse the sensitivity function base on different plants (Figure 94):

  1. the full system (complicated): @@ -1669,19 +2153,19 @@ One loop is closed at a time, and the coupling effects are taken into account.

    -
    +

    mimo_sensitivity_functions.png

    -

    Figure 74: Visual representation of the three systems

    +

    Figure 94: Visual representation of the three systems

-
-

5.3 Example system

-
+
+

6.3 Example system

+

-In order to compare the use of the three systems to estimate the performances of a MIMO system, the system shown in Figure 75 is used. +In order to compare the use of the three systems to estimate the performances of a MIMO system, the system shown in Figure 95 is used. The 4 top masses are used to represent a payload that will add coupling in the system due to its resonances.

@@ -1690,44 +2174,44 @@ A diagonal PID controller is used.

-
+

mimo_example_system.png

-

Figure 75: Schematic representation of the example system

+

Figure 95: Schematic representation of the example system

-The bode plot of the MIMO system is shown in Figure 76 where we can see the resonances in the off-diagonal elements. +The bode plot of the MIMO system is shown in Figure 96 where we can see the resonances in the off-diagonal elements.

-
+

mimo_example_bode.png

-

Figure 76: Bode plot of the full MIMO system

+

Figure 96: Bode plot of the full MIMO system

-In Figure 77 is shown that the sensitivity function computed from the SISO system is not correct. +In Figure 97 is shown that the sensitivity function computed from the SISO system is not correct. Whereas for the “interaction method” system, it is correct and almost match the full system sensibility. However, as expected, the off-diagonal sensibilities are not modelled.

-
+

mimo_example_sensitivity.png

-

Figure 77: Bode plots of sensitivity functions

+

Figure 97: Bode plots of sensitivity functions

-
-

5.4 Conclusion

-
+
+

6.4 Conclusion

+

-The conclusion are the following and summarized in Figure 78: +The conclusion are the following and summarized in Figure 98:

-
-

6 High-precision motion system design by topology optimization considering additive manufacturing   @arnoud_delissen

-
+
+

7 High-precision motion system design by topology optimization considering additive manufacturing   @arnoud_delissen

+
-
-

6.1 Introduction

-
+
+

7.1 Introduction

+

The goal of this project is to perform a topology optimization of a 6dof magnetic levitated stage suitable for vacuum.

-For the current system (Figure 79), the bandwidth is limited by the short-stroke dynamics (eigenfrequencies). +For the current system (Figure 99), the bandwidth is limited by the short-stroke dynamics (eigenfrequencies).

@@ -1770,104 +2254,104 @@ The goal here is to make the eigen-frequency higher as this will allow more band

-
+

mimoopt_6dof_stage.png

-

Figure 79: Schematic of the 6dof levitating stage

+

Figure 99: Schematic of the 6dof levitating stage

-
-

6.2 Case

-
+
+

7.2 Case

+

-More precisely, the goal is to automatically maximize the three eigen-frequencies of the system shown in Figure 80. +More precisely, the goal is to automatically maximize the three eigen-frequencies of the system shown in Figure 100.

-
+

mimoopt_case.png

-

Figure 80: System to be optimized

+

Figure 100: System to be optimized

-
-

6.3 Manufacturing process

-
+
+

7.3 Manufacturing process

+

The manufacturing process must be embedded in the optimization such that the obtained design is producible. -The process is shown in Figure 81. +The process is shown in Figure 101.

-
+

mimoopt_process.png

-

Figure 81: Manufacturing process

+

Figure 101: Manufacturing process

-
-

6.4 Topology optimization

-
+
+

7.4 Topology optimization

+

Problem: for a given volume, maximize the eigen-frequencies of the system.

-To do so, the system is discretized into small elements (Figure 82). +To do so, the system is discretized into small elements (Figure 102). Then, a Finite Element Analysis is performed to compute the eigen-frequencies of the system. Finally, for each element, the “gradient is computed” and we determine if material should be added or removed.

-This is done in 3D. The individual 1mm x 1mm x 1mm elements are shown in Figure 82. +This is done in 3D. The individual 1mm x 1mm x 1mm elements are shown in Figure 102. The number of elements is 1 million (=> 15 minutes per iteration to compute the 3 eigen-frequencies).

-
+

mimoopt_3d_opti.png

-

Figure 82: Results of the topology optimization and zoom to see individual elements

+

Figure 102: Results of the topology optimization and zoom to see individual elements

-
-

6.5 Performance Comparison

-
+
+

7.5 Performance Comparison

+

-The obtained mass and eigen-frequencies of the optimized system and the solid equivalents are compared in Figure 83. +The obtained mass and eigen-frequencies of the optimized system and the solid equivalents are compared in Figure 103.

-
+

mimoopt_performance.png

-

Figure 83: Comparison of the obtained performances

+

Figure 103: Comparison of the obtained performances

-Identification on the realized system shown that the obtained eigen-frequencies are very closed to the estimated ones (Figure 84). +Identification on the realized system shown that the obtained eigen-frequencies are very closed to the estimated ones (Figure 104).

-
+

mimoopt_frf_identification.png

-

Figure 84: Results very close to simulation (~1% for the eigen frequencies)

+

Figure 104: Results very close to simulation (~1% for the eigen frequencies)

-
-

6.6 Conclusion

-
+
+

7.6 Conclusion

+
  • Increase in performance (~2x) compared to solid designs
  • A design is obtained in ~ 1 day
    • @@ -1878,13 +2362,13 @@ Identification on the realized system shown that the obtained eigen-frequencies
-
-

7 A multivariable experiment design framework for accurate FRF identification of complex systems   @nic_dirkx

-
+
+

8 A multivariable experiment design framework for accurate FRF identification of complex systems   @nic_dirkx

+
-
-

7.1 Introduction

-
+
+

8.1 Introduction

+

Goal: Need for higher quality FRF models that are used to:

@@ -1900,7 +2384,7 @@ High quality FRFs requires careful design of excitation \(w\).

-Typical experimental identification of the FRFs is shown in Figure 85. +Typical experimental identification of the FRFs is shown in Figure 105.

@@ -1912,10 +2396,10 @@ The design trade-off is: -

+

frf_introduction.png

-

Figure 85: schematic of the identification of the FRF

+

Figure 105: schematic of the identification of the FRF

@@ -1941,14 +2425,14 @@ For MIMO systems:

-
-

7.2 Role of directions and constrains in multivariable excitation design

-
+
+

8.2 Role of directions and constrains in multivariable excitation design

+

The classical way to estimate MIMO FRFs is the following:

    -
  • First start with one direction and increase the gain until constrains is attained (Figure 86)
    • +
  • First start with one direction and increase the gain until constrains is attained (Figure 106)
  • Do the same with the second input
@@ -1957,34 +2441,34 @@ This lead to non-optimal FRFs estimation.

-
+

frf_direction_excitation.png

-

Figure 86: Example of a SISO approach to identify MIMO FRFs

+

Figure 106: Example of a SISO approach to identify MIMO FRFs

-When having a MIMO approach and choosing both the direction and gain of the excitation inputs, we can obtained much better FRFs uncertainty while still fulfilling the constraints (Figure 87). +When having a MIMO approach and choosing both the direction and gain of the excitation inputs, we can obtained much better FRFs uncertainty while still fulfilling the constraints (Figure 107).

-
+

frf_mimo.png

-

Figure 87: Example of the MIMO approach that gives much better FRFs

+

Figure 107: Example of the MIMO approach that gives much better FRFs

-
-

7.3 Solving the optimization problem

-
+
+

8.3 Solving the optimization problem

+

The optimization problem is to minimize the model uncertainty by choosing the design variables which are the magnitude and direction of the inputs \(w\).

-The optimization is a two step process as shown in Figure 88: +The optimization is a two step process as shown in Figure 108:

  1. first identification without optimization that allows to have data to run the optimization process
    2. @@ -2001,17 +2485,17 @@ In this work, two algorithms are proposed and not further detailed here.

    -
    +

    frf_optimization_steps.png

    -

    Figure 88: Two step optimization process

    +

    Figure 108: Two step optimization process

-
-

7.4 Experimental validation

-
+
+

8.4 Experimental validation

+

Experimental identification of a 7x8 MIMO plant was performed in for different cases:

@@ -2023,34 +2507,34 @@ Experimental identification of a 7x8 MIMO plant was performed in for different c

-The obtained FRFs are shown in Figure 89. +The obtained FRFs are shown in Figure 109.

-
+

frf_experiment.png

-

Figure 89: Obtained MIMO FRFs

+

Figure 109: Obtained MIMO FRFs

-A comparison of one of the obtained FRFs is shown in Figure 90. +A comparison of one of the obtained FRFs is shown in Figure 110. It is quite clear that the MIMO approach can give much lower FRF uncertainty. The RR proposed algorithm is giving the best results

-
+

frf_experiment_optimized.png

-

Figure 90: Example of one of the obtained FRF

+

Figure 110: Example of one of the obtained FRF

-
-

7.5 Conclusion

-
+
+

8.5 Conclusion

+
  • The uncertainty of the obtained FRF are obtained by doing several experimental identification with a deterministic input signal. The FRF are computed multiple times, and the spread of the results at each frequency represents this uncertainty.
    • @@ -2063,495 +2547,19 @@ The FRF are computed multiple times, and the spread of the results at each frequ
-
-

8 Keynote: High precision mechatronic approaches for advanced nanopositioning and nanomeasuring technologies   @eberhard_manske

-
-
-
-

8.1 Coordinate Measurement Machines (CMM)

-
-

-Examples of Nano Coordinate Measuring Machines are shown in Figure 91. -

- - -
-

prec_cmm.png -

-

Figure 91: Example of Coordinate Measuring Machines

-
-
-
- -
-

8.2 Difference between CMM and nano-CMM

-
-

-With classical CMM, the Abbe-principle is not fulfilled in the x and y directions (Figure 92). -

- -

-The Abbe error can be determined with: -

-\begin{equation} - \Delta l_{x,y,z} = l_{x,y,z} \sin \Delta \phi_{x,y,z} -\end{equation} - -

-Even with the best spindle: \(l_{x,y} = 100 mm\) and \(\Delta \phi = 2 \text{arcsec}\), we obtain an error of: -

-\begin{equation} - \Delta l = 0.1 \mu m -\end{equation} -

-which is not compatible with nano-meter precisions. -

- -

-Then, the classical CMM will not work for nano precision -

- - -
-

prec_cmm_nano_cmm.png -

-

Figure 92: Schematic of a CMM

-
-
-
- -
-

8.3 How to do nano-CMM

-
-

-High precision mechatronic approaches are required for advanced nano-positionign and nano-measuring technologies: -

-
    -
  • High precision measurement concept
    • -
  • High precision measurement systems
    • -
  • High precision nano-sensors
    • -
-

-Combined with: -

-
    -
  • Advanced automatic control
    • -
  • Advanced measuring strategies
    • -
-
-
- -
-

8.4 Concept - Minimization of the Abbe Error

-
-

-In order to minimize the Abbe error, the measuring “lines” should have a common point of intersection (Figure 93). -

- -

-The 3D-realization of Abbe-principle is as follows: -

-
    -
  • 3 interferometers: cartesian coordinate system
    • -
  • probe located as the intersection point of the interferometers
    • -
- - -
-

prec_nano_cmm_concept.png -

-

Figure 93: Error minimal measuring principle

-
-
-
- -
-

8.5 Minimization of residual Abbe error

-
-

-Still some residual Abbe error can happen as shown in Figure 94 due to both a change of angle and change of position. -

- - -
-

prec_abbe_min.png -

-

Figure 94: Residual Abbe error

-
-
-
- -
-

8.6 Compare of long travel guiding systems

-
-

-In order to have the Abbe error compatible with nano-meter precision, the precision of the spindle should be less and one arcsec which is not easily feasible with air bearing of precision roller bearing technologies as shown in Figure 95. -

- - -
-

prec_comp_guid.png -

-

Figure 95: Characteristics of guidings

-
-
-
- -
-

8.7 Extended 6 DoF Abbe comparator principle

-
-

-The solution used was to measure in real time the angles of the frame using autocollimators as shown in Figure 96 and then to minimize this tilt by close loop operation with additional actuators. -

- -

-The angular measurement error and control is less than \(0.05 \text{arcses}\) which make the residual Abbe error: -

-\begin{equation} - \Delta l < 0.05\,nm -\end{equation} - -

-Without an error-minimal approach, nano-meter precision cannot be achieved in large areas. -

- - -
-

prec_6dof_abbe.png -

-

Figure 96: Use of additional autocollimator and actuators for Abbe minimization

-
-
-
- -
-

8.8 Practical Realisation

-
-

-A practical realization of the Extended 6 DoF Abbe comparator principle is shown in Figure 97. -

- - -
-

prec_practical_6dof.png -

-

Figure 97: Practical Realization of the

-
-
-
- -
-

8.9 Tilt Compensation

-
-

-To measure compensate for any tilt, two solutions are proposed: -

-
    -
  1. Use a zero point angular auto-collimator (Figure 98) -
      -
    • Resolution: 0.005 arcsec
      • -
    • Stability (1h): < 0.05 arcsec
      • -
    2. -
  2. 6 DoF laser interferoemter (Figure 99) -
      -
    • Resolution: 0.00002 arcsec
      • -
    • Stability (1h): < 0.00005 arcsec
      • -
    3. -
- - -
-

prec_tilt_corection.png -

-

Figure 98: Auto-Collimator

-
- - -
-

prec_tilt_corection_bis.png -

-

Figure 99: 6 Interferometers to measure tilts

-
-
-
- -
-

8.10 Comparison of long travail guiding systems - Bis

-
-

-Now, if we actively compensate the tilts are shown previously, we can fulfill the requirements as shown in Figure 100. -

- -

-Measurement and control technology to minimize Abbe errors to achieve: -

-
    -
  • sub-nanometer precision
    • -
  • smaller moving mass
    • -
  • better dynamics
    • -
- - -
-

prec_comp_guid_bis.png -

-

Figure 100: Characteristics of the tilt compensation system

-
-
-
- -
-

8.11 Drive concept

-
-

-Usually, in order to achieve a large range over small resolution, each axis of motion is a combination of a coarse motion and a fine motion stage. -The coarse motion stage generally consist of a stepper motor while the fine motion is a piezoelectric actuator. -

- -

-The approach here is to use an homogenous drive concept for increase dynamics (Figure 101). -

- -

-Only one linear voice coil actuator is used which with large moving range and sub-nanometer resolution can be achieve at one time. -

- - -
-

prec_drive_concept.png -

-

Figure 101: Voice Coil Actuator

-
-
-
- - -
-

8.12 NPMM-200 with extended measuring volume

-
-

-The NPMM-200 machine can be seen in Figure 102. -

- -

-Characteristics: -

-
    -
  • Measuring range: 200 mm x 200 mm x 25 mm
    • -
  • Resolution: 20 pm
    • -
  • Abbe comparator principle
    • -
  • 6 laser interferometers
    • -
  • Active angular compensation
    • -
  • Position uncertainty < 4 nm
    • -
  • Measuring uncertainty up to 30 nm
    • -
- - -
-

prec_mechanics.png -

-

Figure 102: Picture of the NPMM-200

-
- -

-The NPMM-200 actually operates inside a Vacuum chamber as shown in Figure 103. -

- - -
-

prec_vacuum_cham.png -

-

Figure 103: Vacuum chamber used

-
-
-
- -
-

8.13 measurement capability

-
-

-Some step responses are shown in Figure 104 and show the nano-metric precision of the machine. -

- - -
-

prec_results_meas.png -

-

Figure 104: Sub nano-meter position accuracy

-
- -

-Picometer steps can even be achieved as shown in Figure 105. -

- - -
-

prec_results_pico.png -

-

Figure 105: Picometer level control

-
-
-
- -
-

8.14 Extension of the measuring range (700mm)

-
-

-If the measuring range is to be increase, there are some limits of the moving stage principle: -

-
    -
  • large moving masses (~300kg)
    • -
  • powerful drive systems required
    • -
  • nano-meter position capability problematic
    • -
  • large heat dissipation in the system
    • -
  • dynamics and dynamic deformation
    • -
- -

-The proposed solution is to use inverse dynamic concept for minimization of moving masses. -

-
-
- -
-

8.15 Inverse kinematic concept - Tetrahedrical concept

-
-

-The proposed concept is shown in Figure 106: -

-
    -
  • mirrors and object to be measured are fixed
    • -
  • probe and interferometer heads are moved
    • -
  • laser beams virtually intersect in the probe tip
    • -
  • Tetrahedrical measuring volume
    • -
- -

-This fulfills the Abbe principe but: -

-
    -
  • large construction space
    • -
  • difficult guide and drive concept
    • -
- - -
-

prec_inverse_kin.png -

-

Figure 106: Tetrahedrical concept

-
-
-
- -
-

8.16 Inverse kinematic concept - Scanning probe principle

-
-

-An other concept, the scanning probe principle is shown in Figure 107: -

-
    -
  • cuboidal measuring volume
    • -
  • Fixed x-y-z mirrors
    • -
  • moving measuring head
    • -
  • guide and drive system outside measuring volume
    • -
- - -
-

prec_inverse_kin_scan.png -

-

Figure 107: Scanning probe principle

-
-
-
- -
-

8.17 Inverse kinematic concept - Compact measuring head

-
-

-In order to minimize the moving mass, compact measuring heads have been developed. -The goal was to make a lightweight measuring head (<1kg) -

- -

-The interferometer used are fiber coupled laser interferometers with a mass of 37g (Figure 108). -

- - -
-

prec_interferometers.png -

-

Figure 108: Micro Interferometers

-
- -

-The concept is shown in Figure 109: -

-
    -
  • 6dof interferometers are used
    • -
  • one micro-probe
    • -
  • the total mass of the head is less than 1kg
    • -
- -

-There is some abbe offset between measurement axis of probe and of interferometer but Abbe error compensation by closed loop control of angular deviations is used. -

- - -
-

prec_inverse_meas_head.png -

-
-
-
- -
-

8.18 Inverse kinematic concept - Scanning probe principle

-
-

-As shown in Figure 110, the abbe error can be compensated from the two top interferometers as: -\[ \text{for } l_x = a: \quad \Delta l_{\text{Abbe}} = \Delta l_{\text{int}} \] -Thus the tilt and Abbe errors can be compensated for with sub-nm resolution. -

- - -
-

prec_abbe_compensation.png -

-

Figure 110: Use of the interferometers to compensate for the Abbe errors

-
-
-
- -
-

8.19 Conclusion

-
-

-Proposed approaches to push the nano-positioning and nano-measuring technology: -

-
    -
  • Measurement and control technology to minimize Abbe errors
    • -
  • Homogeneous drive concept for increased dynamics
    • -
  • Inverse kinematic concept for minimization of moving mass
    • -
  • Abbe-error compensation by closed loop control of angular deviations
    • -
-
-
-
- -
-

9 Reducing control delay times to enhance dynamic stiffness of magnetic bearings   @jan_philipp_schmidtmann

+
+

9 Reducing control delay times to enhance dynamic stiffness of magnetic bearings   @jan_philipp_schmidtmann

-
-

9.1 Introduction

+
+

9.1 Introduction

-This projects focuses on reducing the control delay times of a magnetic bearing shown in Figure 111. +This projects focuses on reducing the control delay times of a magnetic bearing shown in Figure 111.

-
+

magn_bear_intro.png

Figure 111: 6 DoF Position System - Concept

@@ -2564,22 +2572,22 @@ However, the active control of magnet forces leads to a control delay that limit
-
-

9.2 Time Delay Reduction

+
+

9.2 Time Delay Reduction

-Typical contributors to the control delay time are shown in Figure 112. +Typical contributors to the control delay time are shown in Figure 112.

-
+

magn_bear_delay.png

Figure 112: Typical Contributors to control delay time

-The reduction of the control time delay will increase the dynamic stiffness of the bearing as well as decrease the effects of external disturbances and hence improve the positioning errors (Figure 113). +The reduction of the control time delay will increase the dynamic stiffness of the bearing as well as decrease the effects of external disturbances and hence improve the positioning errors (Figure 113).

@@ -2592,7 +2600,7 @@ The steps to reduce the control delay time are: -

+

magn_bear_distur.png

Figure 113: The effect of control delay on stiffness

@@ -2600,15 +2608,15 @@ The steps to reduce the control delay time are:
-
-

9.3 Practical Realization

+
+

9.3 Practical Realization

-Therefore, the position and current control have been merged into one controller (Figure 114). +Therefore, the position and current control have been merged into one controller (Figure 114).

-
+

magn_controller.png

Figure 114: Controller for position and current

@@ -2616,11 +2624,11 @@ Therefore, the position and current control have been merged into one controller

A dSpace rapid prototyping system is used for fast position and current control. -Characteristics of the used elements are shown in Figure 115. +Characteristics of the used elements are shown in Figure 115.

-
+

magn_bear_setup.png

Figure 115: Setup for reduced delay times

@@ -2628,16 +2636,16 @@ Characteristics of the used elements are shown in Figure 1
-
-

9.4 Results

+
+

9.4 Results

-Differences between the previous PWM controller and the new SiC controller are shown in Figure 116. +Differences between the previous PWM controller and the new SiC controller are shown in Figure 116. The delay time is almost completely eliminated.

-
+

magn_bear_results.png

Figure 116: Reduction of delay in PWM Driver

@@ -2645,16 +2653,16 @@ The delay time is almost completely eliminated.
-
-

9.5 Conclusion

+
+

9.5 Conclusion

Due to all the performed modifications, the control delay time could be reduced by 80%. -The next steps for this project are shown in Figure 117. +The next steps for this project are shown in Figure 117.

-
+

magn_bear_conclusion.png

Figure 117: Next Steps

@@ -2663,20 +2671,20 @@ The next steps for this project are shown in Figure 117
-
-

10 Digital twins in control: From fault detection to predictive maintenance in precision mechatronics   @koen_classens

+
+

10 Digital twins in control: From fault detection to predictive maintenance in precision mechatronics   @koen_classens

-
-

10.1 Motivation

+
+

10.1 Motivation

Models are usually for the control design part that can be either physical models (FEM, first principle) or data-driven models. -However, these models are usually not used after control system is implemented (Figure 118). +However, these models are usually not used after control system is implemented (Figure 118).

-
+

twins_motivation.png

Figure 118: Typical of of models in a mechatronic system

@@ -2684,11 +2692,11 @@ However, these models are usually not used after control system is implemented (

Here, the models are exploited to monitor the system and predict future possible failures in the system. -Use models as digital twin for fault detection and Isolation for predictive maintenance in precision mechatronics (Figure 119). +Use models as digital twin for fault detection and Isolation for predictive maintenance in precision mechatronics (Figure 119).

-
+

twing_fdi.png

Figure 119: FDI is using the model of the plant

@@ -2696,15 +2704,15 @@ Use models as digital twin for fault detection and Isolation for predictive m
-
-

10.2 Predictive Maintenance

+
+

10.2 Predictive Maintenance

-Classical maintenance happens when the system is not working anymore as shown in Figure 120. +Classical maintenance happens when the system is not working anymore as shown in Figure 120.

-
+

twins_predictive_maintenance.png

Figure 120: Maintenance done when a failure is appearing

@@ -2715,7 +2723,7 @@ It is possible to perform some preventive maintenance before a failure happens,

-
+

twins_predictive_maintenance_bis.png

Figure 121: Preventive Maintenance

@@ -2727,7 +2735,7 @@ This will minimize the down time of the machine.

-
+

twins_predictive_maintenance_ter.png

Figure 122: Predictive maintenance

@@ -2735,8 +2743,8 @@ This will minimize the down time of the machine.
-
-

10.3 Objectives

+
+

10.3 Objectives

The main objective is to develop a system monitoring approach for precision mechatronic systems, exploiting prior information (models) and integrating posterior information (real-time measured data). @@ -2754,39 +2762,39 @@ Even though state of the art system monitoring are already in used in aerospace,

-
-

10.4 Null-space based FDI

+
+

10.4 Null-space based FDI

-The goal is to applied a decentralized Fault Detection on the system shown in Figure 123 to detect actuator faults at \(J_1\). +The goal is to applied a decentralized Fault Detection on the system shown in Figure 123 to detect actuator faults at \(J_1\). This should take into account the control loop, interaction in the system and be FRF based.

-
+

twings_fdi_test.png

Figure 123: Test System

-The architecture to estimate faults in the system is shown in Figure 124. +The architecture to estimate faults in the system is shown in Figure 124. The goal is to design \(Q_u\) and \(Q_y\) such that \(\epsilon\) is a representation of faults in the system.

-
+

twins_null_space_fdi.png

Figure 124: Residual Generator

-When a fault happens (Figure 125), the outputs signals are not changing that much (because of feedback), however the system is able to find that there is a problem using the residual \(\epsilon\). +When a fault happens (Figure 125), the outputs signals are not changing that much (because of feedback), however the system is able to find that there is a problem using the residual \(\epsilon\).

-
+

twins_results_fdi.png

Figure 125: Simulation Results

@@ -2804,24 +2812,24 @@ When a fault happens (Figure 125), the outputs signals
-
-

10.5 Roadmap from fault detection to predictive maintenance

+
+

10.5 Roadmap from fault detection to predictive maintenance

-The proposed system can detect faults in the system (Figure 126). +The proposed system can detect faults in the system (Figure 126). This proof of principle should now be applied on industrial systems. -Moreover, from the fault detection, predictive maintenance should be performed (Figure 126). +Moreover, from the fault detection, predictive maintenance should be performed (Figure 126).

-
+

twins_roadmap.png

Figure 126: From proof of principle to industrial application

-
+

twins_roadmap_bis.png

Figure 127: From fault detection to predictive maintenance

@@ -2832,7 +2840,7 @@ Moreover, from the fault detection, predictive maintenance should be performed (

Author: Dehaeze Thomas

-

Created: 2020-11-20 ven. 09:48

+

Created: 2020-11-25 mer. 11:37

diff --git a/notes.org b/notes.org index 8dd6215..af37ae3 100644 --- a/notes.org +++ b/notes.org @@ -443,6 +443,9 @@ A nice way to have a 1dof flexure guiding with stiff frame is shown in Figure [[ [[file:./figs/z_stage_triangles.png]] * Keynote: Mechatronic challenges in optical lithography :@hans_butler: + +yt:DF8GrWlMwEE + ** Introduction *Question*: in chip manufacturing, how do developments in optical lithography impact the mechatronic design? @@ -605,6 +608,280 @@ The conclusions are: - EUV: all-vacuum stages - High-NA EUV: new optics, much larger accelerations +* Keynote: High precision mechatronic approaches for advanced nanopositioning and nanomeasuring technologies :@eberhard_manske: + +yt:6hSWI1wtjfo + +** Coordinate Measurement Machines (CMM) + +Examples of Nano Coordinate Measuring Machines are shown in Figure [[fig:prec_cmm]]. + +#+name: fig:prec_cmm +#+caption: Example of Coordinate Measuring Machines +#+attr_latex: :width \linewidth +[[file:./figs/prec_cmm.png]] + +** Difference between CMM and nano-CMM +With classical CMM, the Abbe-principle is not fulfilled in the x and y directions (Figure [[fig:prec_cmm_nano_cmm]]). + +The Abbe error can be determined with: +\begin{equation} + \Delta l_{x,y,z} = l_{x,y,z} \sin \Delta \phi_{x,y,z} +\end{equation} + +Even with the best spindle: $l_{x,y} = 100 mm$ and $\Delta \phi = 2 \text{arcsec}$, we obtain an error of: +\begin{equation} + \Delta l = 0.1 \mu m +\end{equation} +which is not compatible with nano-meter precisions. + +Then, the classical CMM will not work for nano precision + +#+name: fig:prec_cmm_nano_cmm +#+caption: Schematic of a CMM +#+attr_latex: :scale 0.5 +[[file:./figs/prec_cmm_nano_cmm.png]] + +** How to do nano-CMM + +High precision mechatronic approaches are required for advanced nano-positionign and nano-measuring technologies: +- High precision measurement concept +- High precision measurement systems +- High precision nano-sensors +Combined with: +- Advanced automatic control +- Advanced measuring strategies + +** Concept - Minimization of the Abbe Error + +In order to minimize the Abbe error, the measuring "lines" should have a common point of intersection (Figure [[fig:prec_nano_cmm_concept]]). + +The 3D-realization of Abbe-principle is as follows: +- 3 interferometers: cartesian coordinate system +- probe located as the intersection point of the interferometers + +#+name: fig:prec_nano_cmm_concept +#+caption: Error minimal measuring principle +#+attr_latex: :scale 0.5 +[[file:./figs/prec_nano_cmm_concept.png]] + +** Minimization of residual Abbe error + +Still some residual Abbe error can happen as shown in Figure [[fig:prec_abbe_min]] due to both a change of angle and change of position. + +#+name: fig:prec_abbe_min +#+caption: Residual Abbe error +#+attr_latex: :width \linewidth +[[file:./figs/prec_abbe_min.png]] + +** Compare of long travel guiding systems + +In order to have the Abbe error compatible with nano-meter precision, the precision of the spindle should be less and one arcsec which is not easily feasible with air bearing of precision roller bearing technologies as shown in Figure [[fig:prec_comp_guid]]. + +#+name: fig:prec_comp_guid +#+caption: Characteristics of guidings +#+attr_latex: :scale 0.5 +[[file:./figs/prec_comp_guid.png]] + +** Extended 6 DoF Abbe comparator principle + +The solution used was to measure in real time the angles of the frame using autocollimators as shown in Figure [[fig:prec_6dof_abbe]] and then to minimize this tilt by close loop operation with additional actuators. + +The angular measurement error and control is less than $0.05 \text{arcses}$ which make the residual Abbe error: +\begin{equation} + \Delta l < 0.05\,nm +\end{equation} + +Without an error-minimal approach, nano-meter precision cannot be achieved in large areas. + +#+name: fig:prec_6dof_abbe +#+caption: Use of additional autocollimator and actuators for Abbe minimization +#+attr_latex: :width \linewidth +[[file:./figs/prec_6dof_abbe.png]] + +** Practical Realisation + +A practical realization of the Extended 6 DoF Abbe comparator principle is shown in Figure [[fig:prec_practical_6dof]]. + +#+name: fig:prec_practical_6dof +#+caption: Practical Realization of the +#+attr_latex: :width \linewidth +[[file:./figs/prec_practical_6dof.png]] + +** Tilt Compensation + +To measure compensate for any tilt, two solutions are proposed: +1. Use a zero point angular auto-collimator (Figure [[fig:prec_tilt_corection]]) + - Resolution: 0.005 arcsec + - Stability (1h): < 0.05 arcsec +2. 6 DoF laser interferoemter (Figure [[fig:prec_tilt_corection_bis]]) + - Resolution: 0.00002 arcsec + - Stability (1h): < 0.00005 arcsec + +#+name: fig:prec_tilt_corection +#+caption: Auto-Collimator +#+attr_latex: :scale 0.5 +[[file:./figs/prec_tilt_corection.png]] + +#+name: fig:prec_tilt_corection_bis +#+caption: 6 Interferometers to measure tilts +#+attr_latex: :scale 0.5 +[[file:./figs/prec_tilt_corection_bis.png]] + +** Comparison of long travail guiding systems - Bis + +Now, if we actively compensate the tilts are shown previously, we can fulfill the requirements as shown in Figure [[fig:prec_comp_guid_bis]]. + +*Measurement and control technology to minimize Abbe errors to achieve*: +- sub-nanometer precision +- smaller moving mass +- better dynamics + +#+name: fig:prec_comp_guid_bis +#+caption: Characteristics of the tilt compensation system +#+attr_latex: :width \linewidth +[[file:./figs/prec_comp_guid_bis.png]] + +** Drive concept + +Usually, in order to achieve a large range over small resolution, each axis of motion is a combination of a coarse motion and a fine motion stage. +The coarse motion stage generally consist of a stepper motor while the fine motion is a piezoelectric actuator. + +The approach here is to use an *homogenous drive concept for increase dynamics* (Figure [[fig:prec_drive_concept]]). + +Only one linear voice coil actuator is used which with large moving range and sub-nanometer resolution can be achieve at one time. + +#+name: fig:prec_drive_concept +#+caption: Voice Coil Actuator +#+attr_latex: :scale 0.5 +[[file:./figs/prec_drive_concept.png]] + + +** NPMM-200 with extended measuring volume + +The NPMM-200 machine can be seen in Figure [[fig:prec_mechanics]]. + +Characteristics: +- Measuring range: 200 mm x 200 mm x 25 mm +- Resolution: 20 pm +- Abbe comparator principle +- 6 laser interferometers +- Active angular compensation +- Position uncertainty < 4 nm +- Measuring uncertainty up to 30 nm + +#+name: fig:prec_mechanics +#+caption: Picture of the NPMM-200 +#+attr_latex: :width \linewidth +[[file:./figs/prec_mechanics.png]] + +The NPMM-200 actually operates inside a Vacuum chamber as shown in Figure [[fig:prec_vacuum_cham]]. + +#+name: fig:prec_vacuum_cham +#+caption: Vacuum chamber used +#+attr_latex: :scale 0.5 +[[file:./figs/prec_vacuum_cham.png]] + +** measurement capability + +Some step responses are shown in Figure [[fig:prec_results_meas]] and show the nano-metric precision of the machine. + +#+name: fig:prec_results_meas +#+caption: Sub nano-meter position accuracy +#+attr_latex: :width \linewidth +[[file:./figs/prec_results_meas.png]] + +Picometer steps can even be achieved as shown in Figure [[fig:prec_results_pico]]. + +#+name: fig:prec_results_pico +#+caption: Picometer level control +#+attr_latex: :width 0.6\linewidth +[[file:./figs/prec_results_pico.png]] + +** Extension of the measuring range (700mm) + +If the measuring range is to be increase, there are some limits of the moving stage principle: +- large moving masses (~300kg) +- powerful drive systems required +- nano-meter position capability problematic +- large heat dissipation in the system +- dynamics and dynamic deformation + +The proposed solution is to use *inverse dynamic concept for minimization of moving masses*. + +** Inverse kinematic concept - Tetrahedrical concept + +The proposed concept is shown in Figure [[fig:prec_inverse_kin]]: +- mirrors and object to be measured are fixed +- probe and interferometer heads are moved +- laser beams virtually intersect in the probe tip +- Tetrahedrical measuring volume + +This fulfills the Abbe principe but: +- large construction space +- difficult guide and drive concept + +#+name: fig:prec_inverse_kin +#+caption: Tetrahedrical concept +#+attr_latex: :scale 0.5 +[[file:./figs/prec_inverse_kin.png]] + +** Inverse kinematic concept - Scanning probe principle + +An other concept, the scanning probe principle is shown in Figure [[fig:prec_inverse_kin_scan]]: +- cuboidal measuring volume +- Fixed x-y-z mirrors +- moving measuring head +- guide and drive system outside measuring volume + +#+name: fig:prec_inverse_kin_scan +#+caption: Scanning probe principle +#+attr_latex: :scale 0.5 +[[file:./figs/prec_inverse_kin_scan.png]] + +** Inverse kinematic concept - Compact measuring head + +In order to minimize the moving mass, compact measuring heads have been developed. +The goal was to make a lightweight measuring head (<1kg) + +The interferometer used are fiber coupled laser interferometers with a mass of 37g (Figure [[fig:prec_interferometers]]). + +#+name: fig:prec_interferometers +#+caption: Micro Interferometers +#+attr_latex: :scale 0.5 +[[file:./figs/prec_interferometers.png]] + +The concept is shown in Figure [[fig:prec_inverse_meas_head]]: +- 6dof interferometers are used +- one micro-probe +- the total mass of the head is less than 1kg + +There is some abbe offset between measurement axis of probe and of interferometer but *Abbe error compensation by closed loop control of angular deviations* is used. + +#+name: fig:prec_inverse_meas_head +#+caption: +#+attr_latex: :scale 0.5 +[[file:./figs/prec_inverse_meas_head.png]] + +** Inverse kinematic concept - Scanning probe principle + +As shown in Figure [[fig:prec_abbe_compensation]], the abbe error can be compensated from the two top interferometers as: +\[ \text{for } l_x = a: \quad \Delta l_{\text{Abbe}} = \Delta l_{\text{int}} \] +Thus the tilt and Abbe errors can be compensated for with sub-nm resolution. + +#+name: fig:prec_abbe_compensation +#+caption: Use of the interferometers to compensate for the Abbe errors +#+attr_latex: :scale 0.5 +[[file:./figs/prec_abbe_compensation.png]] + +** Conclusion + +Proposed approaches to push the nano-positioning and nano-measuring technology: +- Measurement and control technology to minimize Abbe errors +- Homogeneous drive concept for increased dynamics +- Inverse kinematic concept for minimization of moving mass +- Abbe-error compensation by closed loop control of angular deviations + * Designing anti-aliasing-filters for control loops of mechatronic systems regarding the rejection of aliased resonances :@ulrich_schonhoff: ** The phenomenon of aliasing of resonances Weakly damped flexible modes of the mechanism can limit the performance of motion control systems. @@ -1164,277 +1441,6 @@ The RR proposed algorithm is giving the best results - Computationally tractable design framework for large scale MIMO systems established - Near global optimal quality achieved on wafer stage setup using RR algorithm -* Keynote: High precision mechatronic approaches for advanced nanopositioning and nanomeasuring technologies :@eberhard_manske: -** Coordinate Measurement Machines (CMM) - -Examples of Nano Coordinate Measuring Machines are shown in Figure [[fig:prec_cmm]]. - -#+name: fig:prec_cmm -#+caption: Example of Coordinate Measuring Machines -#+attr_latex: :width \linewidth -[[file:./figs/prec_cmm.png]] - -** Difference between CMM and nano-CMM -With classical CMM, the Abbe-principle is not fulfilled in the x and y directions (Figure [[fig:prec_cmm_nano_cmm]]). - -The Abbe error can be determined with: -\begin{equation} - \Delta l_{x,y,z} = l_{x,y,z} \sin \Delta \phi_{x,y,z} -\end{equation} - -Even with the best spindle: $l_{x,y} = 100 mm$ and $\Delta \phi = 2 \text{arcsec}$, we obtain an error of: -\begin{equation} - \Delta l = 0.1 \mu m -\end{equation} -which is not compatible with nano-meter precisions. - -Then, the classical CMM will not work for nano precision - -#+name: fig:prec_cmm_nano_cmm -#+caption: Schematic of a CMM -#+attr_latex: :scale 0.5 -[[file:./figs/prec_cmm_nano_cmm.png]] - -** How to do nano-CMM - -High precision mechatronic approaches are required for advanced nano-positionign and nano-measuring technologies: -- High precision measurement concept -- High precision measurement systems -- High precision nano-sensors -Combined with: -- Advanced automatic control -- Advanced measuring strategies - -** Concept - Minimization of the Abbe Error - -In order to minimize the Abbe error, the measuring "lines" should have a common point of intersection (Figure [[fig:prec_nano_cmm_concept]]). - -The 3D-realization of Abbe-principle is as follows: -- 3 interferometers: cartesian coordinate system -- probe located as the intersection point of the interferometers - -#+name: fig:prec_nano_cmm_concept -#+caption: Error minimal measuring principle -#+attr_latex: :scale 0.5 -[[file:./figs/prec_nano_cmm_concept.png]] - -** Minimization of residual Abbe error - -Still some residual Abbe error can happen as shown in Figure [[fig:prec_abbe_min]] due to both a change of angle and change of position. - -#+name: fig:prec_abbe_min -#+caption: Residual Abbe error -#+attr_latex: :width \linewidth -[[file:./figs/prec_abbe_min.png]] - -** Compare of long travel guiding systems - -In order to have the Abbe error compatible with nano-meter precision, the precision of the spindle should be less and one arcsec which is not easily feasible with air bearing of precision roller bearing technologies as shown in Figure [[fig:prec_comp_guid]]. - -#+name: fig:prec_comp_guid -#+caption: Characteristics of guidings -#+attr_latex: :scale 0.5 -[[file:./figs/prec_comp_guid.png]] - -** Extended 6 DoF Abbe comparator principle - -The solution used was to measure in real time the angles of the frame using autocollimators as shown in Figure [[fig:prec_6dof_abbe]] and then to minimize this tilt by close loop operation with additional actuators. - -The angular measurement error and control is less than $0.05 \text{arcses}$ which make the residual Abbe error: -\begin{equation} - \Delta l < 0.05\,nm -\end{equation} - -Without an error-minimal approach, nano-meter precision cannot be achieved in large areas. - -#+name: fig:prec_6dof_abbe -#+caption: Use of additional autocollimator and actuators for Abbe minimization -#+attr_latex: :width \linewidth -[[file:./figs/prec_6dof_abbe.png]] - -** Practical Realisation - -A practical realization of the Extended 6 DoF Abbe comparator principle is shown in Figure [[fig:prec_practical_6dof]]. - -#+name: fig:prec_practical_6dof -#+caption: Practical Realization of the -#+attr_latex: :width \linewidth -[[file:./figs/prec_practical_6dof.png]] - -** Tilt Compensation - -To measure compensate for any tilt, two solutions are proposed: -1. Use a zero point angular auto-collimator (Figure [[fig:prec_tilt_corection]]) - - Resolution: 0.005 arcsec - - Stability (1h): < 0.05 arcsec -2. 6 DoF laser interferoemter (Figure [[fig:prec_tilt_corection_bis]]) - - Resolution: 0.00002 arcsec - - Stability (1h): < 0.00005 arcsec - -#+name: fig:prec_tilt_corection -#+caption: Auto-Collimator -#+attr_latex: :scale 0.5 -[[file:./figs/prec_tilt_corection.png]] - -#+name: fig:prec_tilt_corection_bis -#+caption: 6 Interferometers to measure tilts -#+attr_latex: :scale 0.5 -[[file:./figs/prec_tilt_corection_bis.png]] - -** Comparison of long travail guiding systems - Bis - -Now, if we actively compensate the tilts are shown previously, we can fulfill the requirements as shown in Figure [[fig:prec_comp_guid_bis]]. - -*Measurement and control technology to minimize Abbe errors to achieve*: -- sub-nanometer precision -- smaller moving mass -- better dynamics - -#+name: fig:prec_comp_guid_bis -#+caption: Characteristics of the tilt compensation system -#+attr_latex: :width \linewidth -[[file:./figs/prec_comp_guid_bis.png]] - -** Drive concept - -Usually, in order to achieve a large range over small resolution, each axis of motion is a combination of a coarse motion and a fine motion stage. -The coarse motion stage generally consist of a stepper motor while the fine motion is a piezoelectric actuator. - -The approach here is to use an *homogenous drive concept for increase dynamics* (Figure [[fig:prec_drive_concept]]). - -Only one linear voice coil actuator is used which with large moving range and sub-nanometer resolution can be achieve at one time. - -#+name: fig:prec_drive_concept -#+caption: Voice Coil Actuator -#+attr_latex: :scale 0.5 -[[file:./figs/prec_drive_concept.png]] - - -** NPMM-200 with extended measuring volume - -The NPMM-200 machine can be seen in Figure [[fig:prec_mechanics]]. - -Characteristics: -- Measuring range: 200 mm x 200 mm x 25 mm -- Resolution: 20 pm -- Abbe comparator principle -- 6 laser interferometers -- Active angular compensation -- Position uncertainty < 4 nm -- Measuring uncertainty up to 30 nm - -#+name: fig:prec_mechanics -#+caption: Picture of the NPMM-200 -#+attr_latex: :width \linewidth -[[file:./figs/prec_mechanics.png]] - -The NPMM-200 actually operates inside a Vacuum chamber as shown in Figure [[fig:prec_vacuum_cham]]. - -#+name: fig:prec_vacuum_cham -#+caption: Vacuum chamber used -#+attr_latex: :scale 0.5 -[[file:./figs/prec_vacuum_cham.png]] - -** measurement capability - -Some step responses are shown in Figure [[fig:prec_results_meas]] and show the nano-metric precision of the machine. - -#+name: fig:prec_results_meas -#+caption: Sub nano-meter position accuracy -#+attr_latex: :width \linewidth -[[file:./figs/prec_results_meas.png]] - -Picometer steps can even be achieved as shown in Figure [[fig:prec_results_pico]]. - -#+name: fig:prec_results_pico -#+caption: Picometer level control -#+attr_latex: :width 0.6\linewidth -[[file:./figs/prec_results_pico.png]] - -** Extension of the measuring range (700mm) - -If the measuring range is to be increase, there are some limits of the moving stage principle: -- large moving masses (~300kg) -- powerful drive systems required -- nano-meter position capability problematic -- large heat dissipation in the system -- dynamics and dynamic deformation - -The proposed solution is to use *inverse dynamic concept for minimization of moving masses*. - -** Inverse kinematic concept - Tetrahedrical concept - -The proposed concept is shown in Figure [[fig:prec_inverse_kin]]: -- mirrors and object to be measured are fixed -- probe and interferometer heads are moved -- laser beams virtually intersect in the probe tip -- Tetrahedrical measuring volume - -This fulfills the Abbe principe but: -- large construction space -- difficult guide and drive concept - -#+name: fig:prec_inverse_kin -#+caption: Tetrahedrical concept -#+attr_latex: :scale 0.5 -[[file:./figs/prec_inverse_kin.png]] - -** Inverse kinematic concept - Scanning probe principle - -An other concept, the scanning probe principle is shown in Figure [[fig:prec_inverse_kin_scan]]: -- cuboidal measuring volume -- Fixed x-y-z mirrors -- moving measuring head -- guide and drive system outside measuring volume - -#+name: fig:prec_inverse_kin_scan -#+caption: Scanning probe principle -#+attr_latex: :scale 0.5 -[[file:./figs/prec_inverse_kin_scan.png]] - -** Inverse kinematic concept - Compact measuring head - -In order to minimize the moving mass, compact measuring heads have been developed. -The goal was to make a lightweight measuring head (<1kg) - -The interferometer used are fiber coupled laser interferometers with a mass of 37g (Figure [[fig:prec_interferometers]]). - -#+name: fig:prec_interferometers -#+caption: Micro Interferometers -#+attr_latex: :scale 0.5 -[[file:./figs/prec_interferometers.png]] - -The concept is shown in Figure [[fig:prec_inverse_meas_head]]: -- 6dof interferometers are used -- one micro-probe -- the total mass of the head is less than 1kg - -There is some abbe offset between measurement axis of probe and of interferometer but *Abbe error compensation by closed loop control of angular deviations* is used. - -#+name: fig:prec_inverse_meas_head -#+caption: -#+attr_latex: :scale 0.5 -[[file:./figs/prec_inverse_meas_head.png]] - -** Inverse kinematic concept - Scanning probe principle - -As shown in Figure [[fig:prec_abbe_compensation]], the abbe error can be compensated from the two top interferometers as: -\[ \text{for } l_x = a: \quad \Delta l_{\text{Abbe}} = \Delta l_{\text{int}} \] -Thus the tilt and Abbe errors can be compensated for with sub-nm resolution. - -#+name: fig:prec_abbe_compensation -#+caption: Use of the interferometers to compensate for the Abbe errors -#+attr_latex: :scale 0.5 -[[file:./figs/prec_abbe_compensation.png]] - -** Conclusion - -Proposed approaches to push the nano-positioning and nano-measuring technology: -- Measurement and control technology to minimize Abbe errors -- Homogeneous drive concept for increased dynamics -- Inverse kinematic concept for minimization of moving mass -- Abbe-error compensation by closed loop control of angular deviations - * Reducing control delay times to enhance dynamic stiffness of magnetic bearings :@jan_philipp_schmidtmann: ** Introduction This projects focuses on reducing the control delay times of a magnetic bearing shown in Figure [[fig:magn_bear_intro]].