If we remove one side of the cube shown in Figure [[fig:closed_box]], we would have much smaller torsional stiffness along the axis perpendicular to the removed side.
#+name: fig:closed_box
#+caption: Closed box.
[[file:./figs/closed_box.png]]
If we use triangles, we obtain high torsional stiffness as shown in Figure [[fig:torsion_stiffness_box_double_triangle]].
Frames are usually corresponding to open-boxes with have a small stiffness in torsion.
On way to reinforce it is using triangles.
A nice way to have a 1dof flexure guiding with stiff frame is shown in Figure [[fig:z_stage_triangles]].
#+name: fig:z_stage_triangles
#+caption: Box with integrated flexure guiding
[[file:./figs/z_stage_triangles.png]]
* Keynote: Mechatronic challenges in optical lithography :@hans_butler:
** Introduction
*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
** Chip manufacturing loop
In this presentation, only the exposure step is discussed (lithography).
#+name: fig:asml_chip_manufacturing_loop
#+caption: Chip manufacturing loop
[[file:./figs/asml_chip_manufacturing_loop.png]]
** Imaging process - Basics
- 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 [[fig:asml_imaging_process]].
- Wafer and mast are placed on high accuracy moving stages
#+name: fig:asml_imaging_process
#+caption: Imaging process - basics
[[file:./figs/asml_imaging_process.png]]
** From stepper to scanner
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!
#+name: fig:asml_stepper_to_scanner
#+caption: From stepper to scanner
[[file:./figs/asml_stepper_to_scanner.png]]
** Dual stage scanners
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)
#+name: fig:asml_dual_stage_scanners
#+caption: Machine based on the dual stage scanners
[[file:./figs/asml_dual_stage_scanners.png]]
** 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 [[fig:asml_hood_system]]).
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 [[fig:asml_immersion]]):
- Disturbance decoupling
- Iterative learning control
- Feed-forward control from the Wafer control signal
#+name: fig:asml_hood_system
#+caption: Hood System
[[file:./figs/asml_hood_system.png]]
#+name: fig:asml_immersion
#+caption: Control system for the "hood"
[[file:./figs/asml_immersion.png]]
** Multiple Patterning
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
** Machine layout
Each stage is controlled with 6dof lorentz short stroke actuators (Figure [[fig:asml_machine_layout_bis]]).
The magnet stage can move horizontally (due to reaction forces of the wafer stages): it asks as a balance mass.
#+name: fig:asml_machine_layout_bis
#+caption: Machine layout
[[file:./figs/asml_machine_layout_bis.png]]
** EUV Lithography
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
#+name: fig:asml_euv
#+caption: Schematic of the ASML EUV machine
[[file:./figs/asml_euv.png]]
** The future: high-NA EUV
#+name: fig:asml_na_euv
#+caption: The CD will be 8nm
[[file:./figs/asml_na_euv.png]]
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 [[fig:asml_reflection_angle]]).
#+name: fig:asml_reflection_angle
#+caption: Change of reflection of a mirror as a function of the angle of indicence
[[file:./figs/asml_reflection_angle.png]]
** Challenges for future Optical Lithography machines
*Challenges*:
- Double wafer stage acceleration
- Much bigger mirrors
- Tighter accuracy specifications despite
*Solutions*:
- Stage and mirror dynamics, high bandwidth control
- 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
* 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.
For discrete time controlled systems, there can be an additional limitation: aliased resonances which are rarely discussed.
#+name: fig:aliasing_resonances
#+caption: Example of high frequency lighlty damped resonances
[[file:./figs/aliasing_resonances.png]]
The aliasing of signals is well known (Figure [[fig:aliasing_signals]]).
However, aliasing in systems can also happens and is schematically shown in Figure [[fig:aliasing_system]].
#+name: fig:aliasing_signals
#+caption: Aliasing of Signals
[[file:./figs/aliasing_signals.png]]
#+name: fig:aliasing_system
#+caption: Aliasing of Systems
[[file:./figs/aliasing_system.png]]
The poles of the system will be aliased and their location will change in the complex plane as shown in Figure [[fig:aliasing_poles]].
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.
#+name: fig:aliasing_poles
#+caption: Aliasing of poles in the complex plane
[[file:./figs/aliasing_poles.png]]
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 [[fig:aliasing_above_nyquist]]):
- 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.
#+name: fig:aliasing_above_nyquist
#+caption: Aliazed resonance shown on the Bode Diagram
[[file:./figs/aliasing_above_nyquist.png]]
#+name: fig:alising_much_above_nyquist
#+caption: Higher resonance frequency
[[file:./figs/alising_much_above_nyquist.png]]
** 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 [[fig:alising_nature]])
#+name: fig:alising_nature
#+caption: Local vibration mode that will be alized
[[file:./figs/alising_nature.png]]
The proposed idea to better model aliasing resonances is to include more modes in the FEM software as shown in Figure [[fig:aliasing_modeling]] and then perform an order reduction in matlab.
#+name: fig:aliasing_modeling
#+caption: Common procedure and proposed procedure to include aliazed resonances
[[file:./figs/aliasing_modeling.png]]
** Anti aliasing filter design
*** 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:
#+caption: Magnitude, Phase and Phase delay of 3 filters
[[file:./figs/aliasing_equivalent_delay.png]]
*** 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 [[fig:aliasing_budget_phase]])
#+name: fig:aliasing_budget_phase
#+caption: Typical control loop with several phase lag / time delays
[[file:./figs/aliasing_budget_phase.png]]
The equivalent delay of each element are listed in Figure [[fig:aliasing_budget_table]].
#+name: fig:aliasing_budget_table
#+caption: Equivalent delay for all the elements of the control loop
[[file:./figs/aliasing_budget_table.png]]
*** 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 [[fig:aliasing_filter_order_bode]] and summarized in Figure [[fig:aliasing_filter_order_table]].
#+name: fig:aliasing_filter_order_bode
#+caption: Example of few Butterworth filters
[[file:./figs/aliasing_filter_order_bode.png]]
#+name: fig:aliasing_filter_order_table
#+caption: Butterworth filters
[[file:./figs/aliasing_filter_order_table.png]]
*** Reducing the phase lag
The equivalent delay of a low pass (here second order) depends on its damping, since:
\[ T_e = -2 \frac{\xi_{zi}}{\omega_{0zi}} \]
#+name: fig:aliasing_reduce_phase_lag
#+caption: Change of the phase delay with the damping of the filter
[[file:./figs/aliasing_reduce_phase_lag.png]]
** Conclusion
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
* Flexure positioning stage based on delta technology for high precision and dynamic industrial machining applications :@mikael_bianchi:
** Introduction
- *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
- *Objectives*: improve the productivity reaching high accelerations at high precision
** Design
*** Description of the Delta robot
*Technical choice*: flexure based delta robot (Figure [[fig:flexure_delta_robot]]).
- Advantages: high mechanical precision without backlash
- Disadvantage: the motion is coupled, some transformations are required from motor coordinates to machine coordinates (Figure [[fig:flexure_delta_robot_schematic]])
#+name: fig:flexure_delta_robot
#+caption: Picture of the Delta Robot
[[file:./figs/flexure_delta_robot.png]]
#+name: fig:flexure_delta_robot_schematic
#+caption: 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
[[file:./figs/flexure_delta_robot_schematic.png]]
*** 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 [[fig:flexure_equations]]).
#+name: fig:flexure_equations
#+caption: Linearized equations of the Delta Robot
[[file:./figs/flexure_equations.png]]
Then the parameters are identified from experiment (Figure [[fig:flexure_identification]]).
#+name: fig:flexure_identification
#+caption: Identification fo the transfer function from $F_1$ to $x_1$
[[file:./figs/flexure_identification.png]]
The measurement of the coupling is move complicated as shown in Figure [[fig:flexure_identification_coupling]].
#+name: fig:flexure_identification_coupling
#+caption: Problem of identifying the coupling between F1 and x2 at low frequency
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.
#+name: fig:mimo_sensitivity_functions
#+caption: Visual representation of the three systems
[[file:./figs/mimo_sensitivity_functions.png]]
** 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 [[fig:mimo_example_system]] 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.
#+name: fig:mimo_example_system
#+caption: Schematic representation of the example system
[[file:./figs/mimo_example_system.png]]
The bode plot of the MIMO system is shown in Figure [[fig:mimo_example_bode]] where we can see the resonances in the off-diagonal elements.
#+name: fig:mimo_example_bode
#+caption: Bode plot of the full MIMO system
[[file:./figs/mimo_example_bode.png]]
In Figure [[fig:mimo_example_sensitivity]] 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.
#+name: fig:mimo_example_sensitivity
#+caption: Bode plots of sensitivity functions
[[file:./figs/mimo_example_sensitivity.png]]
** Conclusion
The conclusion are the following and summarized in Figure [[fig:mimo_results]]:
- 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
#+name: fig:mimo_results
#+caption: Comparison of the three methods to deal with a MIMO system
[[file:./figs/mimo_results.png]]
* High-precision motion system design by topology optimization considering additive manufacturing :@arnoud_delissen:
** 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 [[fig:mimoopt_6dof_stage]]), 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.
#+name: fig:mimoopt_6dof_stage
#+caption: Schematic of the 6dof levitating stage
[[file:./figs/mimoopt_6dof_stage.png]]
** Case
More precisely, the goal is to automatically maximize the three eigen-frequencies of the system shown in Figure [[fig:mimoopt_case]].
#+name: fig:mimoopt_case
#+caption: System to be optimized
[[file:./figs/mimoopt_case.png]]
** Manufacturing process
The manufacturing process must be embedded in the optimization such that the obtained design is producible.
The process is shown in Figure [[fig:mimoopt_process]].
#+name: fig:mimoopt_process
#+caption: Manufacturing process
[[file:./figs/mimoopt_process.png]]
** 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 [[fig:mimoopt_3d_opti]]).
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 [[fig:mimoopt_3d_opti]].
The number of elements is 1 million (=> 15 minutes per iteration to compute the 3 eigen-frequencies).
#+name: fig:mimoopt_3d_opti
#+caption: Results of the topology optimization and zoom to see individual elements
[[file:./figs/mimoopt_3d_opti.png]]
** Performance Comparison
The obtained mass and eigen-frequencies of the optimized system and the solid equivalents are compared in Figure [[fig:mimoopt_performance]].
#+name: fig:mimoopt_performance
#+caption: Comparison of the obtained performances
[[file:./figs/mimoopt_performance.png]]
Identification on the realized system shown that the obtained eigen-frequencies are very closed to the estimated ones (Figure [[fig:mimoopt_frf_identification]]).
#+name: fig:mimoopt_frf_identification
#+caption: Results very close to simulation (~1% for the eigen frequencies)
[[file:./figs/mimoopt_frf_identification.png]]
** Conclusion
- 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
* A multivariable experiment design framework for accurate FRF identification of complex systems :@nic_dirkx:
** Introduction
*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 [[fig:frf_introduction]].
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)
#+name: fig:frf_introduction
#+caption: schematic of the identification of the FRF
[[file:./figs/frf_introduction.png]]
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
** 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 [[fig:frf_direction_excitation]])
- Do the same with the second input
This lead to non-optimal FRFs estimation.
#+name: fig:frf_direction_excitation
#+caption: Example of a SISO approach to identify MIMO FRFs
[[file:./figs/frf_direction_excitation.png]]
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 [[fig:frf_mimo]]).
#+name: fig:frf_mimo
#+caption: Example of the MIMO approach that gives much better FRFs
[[file:./figs/frf_mimo.png]]
** 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 [[fig:frf_optimization_steps]]:
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.
#+name: fig:frf_optimization_steps
#+caption: Two step optimization process
[[file:./figs/frf_optimization_steps.png]]
** Experimental validation
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 [[fig:frf_experiment]].
#+name: fig:frf_experiment
#+caption: Obtained MIMO FRFs
[[file:./figs/frf_experiment.png]]
A comparison of one of the obtained FRFs is shown in Figure [[fig:frf_experiment_optimized]].
It is quite clear that the MIMO approach can give much lower FRF uncertainty.
The RR proposed algorithm is giving the best results
#+name: fig:frf_experiment_optimized
#+caption: Example of one of the obtained FRF
[[file:./figs/frf_experiment_optimized.png]]
** 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.
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:
[[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
[[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
[[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
[[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
[[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
[[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]])
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
[[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
[[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.
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
[[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:
This projects focuses on reducing the control delay times of a magnetic bearing shown in Figure [[fig:magn_bear_intro]].
#+name: fig:magn_bear_intro
#+caption: 6 DoF Position System - Concept
[[file:./figs/magn_bear_intro.png]]
Active magnetic bearings are unstable systems and require active control.
However, the active control of magnet forces leads to a control delay that limits the performances (stiffness) of the bearing.
Typical contributors to the control delay time are shown in Figure [[fig:magn_bear_delay]].
#+name: fig:magn_bear_delay
#+caption: Typical Contributors to control delay time
[[file:./figs/magn_bear_delay.png]]
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 [[fig:magn_bear_distur]]).
The steps to reduce the control delay time are:
1. Eliminate BUSS-communication by merging position and current controller
2. Reduce cycle time by using rapid prototyping system
3. Reduce delay in PWM driver by using high PWM frequencies with SiC driver
#+name: fig:magn_bear_distur
#+caption: The effect of control delay on stiffness
[[file:./figs/magn_bear_distur.png]]
Therefore, the position and current control have been merged into one controller (Figure [[fig:magn_controller]]).
#+name: fig:magn_controller
#+caption: Controller for position and current
[[file:./figs/magn_controller.png]]
A dSpace rapid prototyping system is used for fast position and current control.
Characteristics of the used elements are shown in Figure [[fig:magn_bear_setup]].
#+name: fig:magn_bear_setup
#+caption: Setup for reduced delay times
[[file:./figs/magn_bear_setup.png]]
Differences between the previous PWM controller and the new SiC controller are shown in Figure [[fig:magn_bear_results]].
The delay time is almost completely eliminated.
#+name: fig:magn_bear_results
#+caption: Reduction of delay in PWM Driver
[[file:./figs/magn_bear_results.png]]
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 [[fig:magn_bear_conclusion]].
#+name: fig:magn_bear_conclusion
#+caption: Next Steps
[[file:./figs/magn_bear_conclusion.png]]
* Digital twins in control: From fault detection to predictive maintenance in precision mechatronics :@koen_classens:
** 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 [[fig:twins_motivation]]).
#+name: fig:twins_motivation
#+caption: Typical of of models in a mechatronic system
[[file:./figs/twins_motivation.png]]
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 [[fig:twing_fdi]]).
#+name: fig:twing_fdi
#+caption: FDI is using the model of the plant
[[file:./figs/twing_fdi.png]]
** Predictive Maintenance
Classical maintenance happens when the system is not working anymore as shown in Figure [[fig:twins_predictive_maintenance]].
#+name: fig:twins_predictive_maintenance
#+caption: Maintenance done when a failure is appearing
[[file:./figs/twins_predictive_maintenance.png]]
It is possible to perform some preventive maintenance before a failure happens, but this is still not optimal.
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
** Null-space based FDI
The goal is to applied a decentralized Fault Detection on the system shown in Figure [[fig:twings_fdi_test]] to detect actuator faults at $J_1$.
This should take into account the control loop, interaction in the system and be FRF based.
#+name: fig:twings_fdi_test
#+caption: Test System
[[file:./figs/twings_fdi_test.png]]
The architecture to estimate faults in the system is shown in Figure [[fig:twins_null_space_fdi]].
The goal is to design $Q_u$ and $Q_y$ such that $\epsilon$ is a representation of faults in the system.
#+name: fig:twins_null_space_fdi
#+caption: Residual Generator
[[file:./figs/twins_null_space_fdi.png]]
When a fault happens (Figure [[fig:twins_results_fdi]]), 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 $\epsilon$.
#+name: fig:twins_results_fdi
#+caption: Simulation Results
[[file:./figs/twins_results_fdi.png]]
*Procedure*:
- Additive faults
- Closed-loop
- Interaction
- start from identification
** Roadmap from fault detection to predictive maintenance
The proposed system can detect faults in the system (Figure [[fig:twins_roadmap]]).
This proof of principle should now be applied on industrial systems.
Moreover, from the fault detection, predictive maintenance should be performed (Figure [[fig:twins_roadmap]]).
#+name: fig:twins_roadmap
#+caption: From proof of principle to industrial application
[[file:./figs/twins_roadmap.png]]
#+name: fig:twins_roadmap_bis
#+caption: From fault detection to predictive maintenance
