EUSPEN

• Accuracy: Accuracy describes how close the mean result is to the reference value. (Figure 1)
• Repeatability: 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)
• 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)

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

The hysteresis can actually help estimating the play and friction present in the system.

Ways to make the hysteresis smaller:

• avoid play (=> use compliant elements)
• minimize friction
• use high stiffness

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} \end{equation}

where the virtual play can be estimated as follow:

\begin{equation} \text{Virtual Play} = \frac{\text{Friction Force}}{\text{Actuator Stiffness}} = \frac{F_w}{c} \end{equation}

When considering dynamics, the goal is to make the first resonance frequency much higher than the frequency of the wanted motion. Thus, the general recommendation is then to minimize mass and to increase stiffness.

Moreover, we generally want things to be predictable:

• constant, preferably no friction. Note that it is very difficult to make a system with constant friction in practice, so better make a system with no friction.
• no play
• high stiffness
• low pass

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

• Payload: \(m = 20\,kg\)
• Friction coefficient in drive direction: \(f = 0.05\)
• Table stroke: \(L = 300\,mm\)
• Screw spindle inner diameter: \(d = 8\, mm\)
• Spindle Material: Stainless steel

First the friction force can be calculated as the vertical mass times the friction coefficient:

\begin{equation} F_w = (mg) f \end{equation}

Then, the axial stiffness of the screw spindle is computed:

\begin{equation} c = \frac{A}{L} E \end{equation}

with:

• \(A = \pi d^2\) is the screw section area
• \(L = 300\,mm\) is the screw length
• \(E\) is the Young modulus of stainless steel

And finally:

\begin{equation} \text{Virtual Play} = \frac{F_w}{c} \approx 0.6\,\mu m \end{equation}

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)

Question: in chip manufacturing, how do developments in optical lithography impact the mechatronic design?

Main developments:

• Scanning & dual stage scanning
• Immersion
• Multiple patterning
• Extreme ultra violet lithography

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

• An illuminator provides light at constant wavelength \(\lambda\)
• The pattern on the reticle diffracts the light into order
• At least +/-1st orders need to be captures. This will induce a sinusoidal wave on the wafer as shown in Figure 35.
• Wafer and mast are placed on high accuracy moving stages

Before, one chip was illumating at a time, but people wanted to make bigger chips. However, if was difficult to make larger lenses.

The solution was to use a scanner, were both the mask and wafer are on moving stages. This implied many requirements in dynamics and accuracy!

Both the reticle stage and wafer stage are moving. In order to have the same throughput, higher stage accelerations are required.

This implies some mechatronics challenges:

• higher stage acceleration
• higher accuracy
• interaction between stages

Which are solved by:

• Larger forces => balance masses
• Stage dynamical design for high bandwidth control
• Control coupling between stages (one control system can act as a disturbance to another controlled system => feedforward)

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 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):

• Disturbance decoupling
• Iterative learning control
• Feed-forward control from the Wafer control signal

The multiple patterning approach adds few mechatronics challenges:

• Position accuracy limited to ~4nm due to interferoemter position measurement (variation of temperature/pressure of air)
• Stage swap is complex and time-consuming

This was solved by:

• Using encoder instead of interferometers
• Use long stroke motor: h-stage => new wafer stage concept

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.

Vacuum is required which implies:

• no bearings
• no cooling

All the optics are reflective:

• extremely accurately polished
• challenge: keep mirrors optimally positioned

Wafer stage:

• Move at high speed and accelerations
• Challenge: in vaccum
• Solved by: machanically suspended balance mass, and interferoemter position meaured can be used because it is in vacuum now

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).

Challenges:

• Double wafer stage acceleration
• Much bigger mirrors
• Tighter accuracy specifications despite

Solutions:

• Stage and mirror dynamics, high bandwidth control
• Dynamics architecture: improved isolation, multiple isolate sets
• Heating compensation

The conclusions are:

• Lithographic tools are the main enabler for over shrinking device sizes
• New (optical) requirements lead to new mechatronic challenges:
  • Larger fields / better imaging: from stepping to scanning
  • Larger wafer size: dual stage scanners
  • Immersion: wafer stage & hood control
  • Multiple patterning: planar motors and encoder technology
  • EUV: all-vacuum stages
  • High-NA EUV: new optics, much larger accelerations

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

For discrete time controlled systems, there can be an additional limitation: aliased resonances which are rarely discussed.

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

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

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

More precisely:

• the imaginary parts of the poles mirror about the Nyquist frequency
• the real parts of the poles remain equal

Therefore, the damping of the aliased resonances are foreseen to have larger dampings.

Let’s consider two systems with a resonance:

1. below the Nyquist frequency (blue dashed)
2. above the Nyquist frequency (green dashed)

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

• the resonance mirrors
• the damping is increased

Therefore, when identifying a low damped resonance, it could be that it comes form a high frequency low damped resonance.

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

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 phenomenon of aliasing of resonances:

• Aliasing of resonances is an issue in discrete-time controlled mechatronic systems and can limit the performance and even render the closed loop system unstable
• Resonances above the Nyquist Frequency appear aliased at mirrored frequency for the discrete-time controller
• Aliased resonances show increased damping compared to the original resonances
• To find out if a resonance is an aliased one or not, change the sampling frequency and see if the frequency of the resonance is changing or not

Nature, modelling and mitigation of potentially aliasing resonances:

• The origin are typically local resonances of the sensor and actuator components
• Careful modelling and selecting dominant modes above the Nyquist frequency is commended

Anti-aliasing filter design:

• Anti-Aliasing filter design is the trade-off between rejection and phase-lag
• The concept of equivalent delay allows to budget and design the phase lag
• The order selection of anti alising-filter based on the required rejection is shown
• Several approaches to reduce overall phase lag are presented

• Goal: flexure positioning stage to do high precision and high dynamic/acceleration positioning. The control architecture should be as simple as possible.
• Application: micromachinign for fabrication of 3d structures
• Possible field: watch industry, electronics, optics, …
• Possible technologies: laser, milling, electro discharge machine
• Objectives: improve the productivity reaching high accelerations at high precision

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

• Mechanics without backlash and resonances in higher frequency
• Feedforward with correct parameters
• High bandwidth position control and precise encoder
• Low noise current sensors and high bandwidth current control

Resonances at mid frequencies are an issue for further improvements.

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)

=> can lead to stability problems

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

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

1. the full system (complicated): \[ L_{full} = \begin{bmatrix}L_{11} & L_{12} \\ L_{21} & L_{22} \end{bmatrix} \]
2. the diagonal system (ignoring interaction) \[ L_{diag} = \begin{bmatrix}L_{11} & 0 \\ 0 & L_{22} \end{bmatrix} \]
3. the loop interaction system (the one proposed here) \[ L^{LI} = \begin{bmatrix}L_1^{LI} & 0 \\ 0 & L_2^{LI} \end{bmatrix} \]

The loop interaction methods created a SISO system that also represents the coupling in the system. One loop is closed at a time, and the coupling effects are taken into account.

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. The 4 top masses are used to represent a payload that will add coupling in the system due to its resonances.

A diagonal PID controller is used.

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

In Figure 77 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.

The conclusion are the following and summarized in Figure 78:

• Choice of suitable analysis method is key concept in mechatronics engineering
• Various methods for analysis of multivariable systems available:
  • Full system always delivers reliable information, but much analysis effort
  • Loop interaction method delivers reliable information, only if the system is weakly or symmetrically coupled
  • Diagonal system delivers unreliable information, as it does not take multivariable character into account

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).

The goal here is to make the eigen-frequency higher as this will allow more bandwidth.

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

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

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

To do so, the system is discretized into small elements (Figure 82). 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. The number of elements is 1 million (=> 15 minutes per iteration to compute the 3 eigen-frequencies).

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

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

• Increase in performance (~2x) compared to solid designs
• A design is obtained in ~ 1 day
• Practical constraints are incorporated in the optimization
• The method is validated in practice by a demonstrator

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

• Controller design
• Observer design
• System diagnostics
• Parametric modelling

High quality FRFs requires careful design of excitation \(w\).

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

The design trade-off is:

• Maximize input gain to minimize FRF uncertainty
• Bounded signal \(u\) and \(y\) to remain within operating limited (actuator/amplifier power limitations and limited move ranges)

For SISO systems:

• Only the frequency size of the excitation signal should be optimized

For MIMO systems:

• the gains and directions should be frequency wise optimized

Objective:

• establish optimal experiment design framework that optimize the excitation signal to obtain MIMO FRFs with low uncertainty

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)
• Do the same with the second input

This lead to non-optimal FRFs estimation.

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).

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:

1. first identification without optimization that allows to have data to run the optimization process
2. second identification with optimized input direction and gain

The problem with this optimization problem is that it is not convex in general and has a log of design variables. There is no general methods to solve this problem, a dedicated algorithm is required.

In this work, two algorithms are proposed and not further detailed here.

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

1. non optimized SISO approach (grey)
2. optimized SISO approach (blue)
3. optimized MIMO approach using SSDR (first algorithm proposed) (green)
4. optimized MIMO approach using RR (second algorithm proposed) (red)

The obtained FRFs are shown in Figure 89.

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

• 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.
• Exploiting directionality in excitation design enables significant FRF quality improvement
• Multivariable design involves hard non-convex optimization problem
• Computationally tractable design framework for large scale MIMO systems established
• Near global optimal quality achieved on wafer stage setup using RR algorithm

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

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

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

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

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

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.

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.

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

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. 6 DoF laser interferoemter (Figure 99)
   • Resolution: 0.00002 arcsec
   • Stability (1h): < 0.00005 arcsec

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

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.

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

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

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

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

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.

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

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

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).

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.

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.

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

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).

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).

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

It is possible to perform some preventive maintenance before a failure happens, but this is still not optimal.

The idea here is to predict when the failure will happen in order to only do maintenance only when really necessary. This will minimize the down time of the machine.

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).

Even though state of the art system monitoring are already in used in aerospace, process industry and automotive, there are few specificity for mechatronic systems:

• Control loops
• Large-scale MIMO systems (interaction)
• Accurate models: Frequency Response Functions

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.

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.

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 \(\epsilon\).

Procedure:

• Additive faults
• Closed-loop
• Interaction
• start from identification

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).