Add notes about optimal nano-hexapod / add bib

index.org

@@ -759,39 +759,143 @@ This model will be used in the next sections to help the design of the nano-hexa
 <<sec:nano_hexapod_design>>
 
 ** Introduction                                                      :ignore:
-
 As explain before, the nano-hexapod properties (mass, stiffness, architecture, ...) will influence:
-- the plant dynamics $G$
-- the effect of disturbances $G_d$
+- the effect of disturbances $G_d$ (important for the rejection of disturbances)
+- the plant dynamics $G$ (important for the control robustness properties)
 
-We which here to choose the nano-hexapod properties such that:
-- has an easy
-- minimize the
-- minimize $|G_d|$
+Thus, we here wish to find the optimal nano-hexapod properties such that:
+- the effect of disturbances is minimized
+- the plant uncertainty due to a change of payload mass and experimental conditions is minimized
+
+The study presented here only consider changes in the nano-hexapod *stiffness*.
+The nano-hexapod mass cannot be change too much, and will anyway be negligible compare to the metrology reflector and the payload masses.
+The choice of the nano-hexapod architecture (e.g. orientations of the actuators and implementation of sensors) will be further studied in accord with the control architecture.
 
 ** Optimal Stiffness to reduce the effect of disturbances
+The nano-hexapod stiffness have a large influence on the sensibility to disturbance (the norm of $G_d$).
 
-** Optimal Stiffness
-The goal is to design a system that is *robust*.
+For instance, it is quite obvious that a stiff nano-hexapod is better than a soft one when it comes to direct forces applied to the sample such as cable forces.
 
-Thus, we have to identify the sources of uncertainty and try to minimize them.
+A complete study of the optimal nano-hexapod stiffness for the minimization of disturbance sensibility [[https://tdehaeze.github.io/nass-simscape/optimal_stiffness_disturbances.html][here]] and summarized below.
+
+
+
+The sensibility to the spindle vibration as a function of the nano-hexapod stiffness is shown in Figure [[fig:opt_stiff_sensitivity_Frz]] (similar curves are obtained for translation stage vibrations).
+It is shown that a softer nano-hexapod it better to filter out stage vibrations.
+More precisely, is start to filters the vibration at the first suspension mode of the payload on top of the nano-hexapod.
+
+#+name: fig:opt_stiff_sensitivity_Frz
+#+caption: Sensitivity to Spindle vertical motion error to the vertical error position of the sample
+[[file:figs/opt_stiff_sensitivity_Frz.png]]
+
+
+The sensibilities to ground motion in the Y and Z directions are shown in Figure [[fig:opt_stiff_sensitivity_Dw]].
+We can see that above the suspension mode of the nano-hexapod, the norm of the transmissibility is close to one until the suspension mode of the granite.
+
+It will be further suggested that using soft mounts for the granite can greatly improve the sensibility to ground motion.
+
+#+name: fig:opt_stiff_sensitivity_Dw
+#+caption: Sensitivity to Ground motion to the position error of the sample
+[[file:figs/opt_stiff_sensitivity_Dw.png]]
+
+
+
+Then, we take the Power Spectral Density of all the sources of disturbances as identified in Section [[sec:identification_disturbances]], and we compute what would be the Power Spectral Density of the vertical motion error for all the considered nano-hexapod stiffnesses (Figure [[fig:opt_stiff_psd_dz_tot]]).
+
+We can see that the most important change is in the frequency range 30Hz to 300Hz where a stiffness smaller than $10^5\,[N/m]$ greatly reduces the sensibility to disturbances.
+
+#+name: fig:opt_stiff_psd_dz_tot
+#+caption: Amplitude Spectral Density of the Sample vertical position error due to Vertical vibration of the Spindle for multiple nano-hexapod stiffnesses
+[[file:figs/opt_stiff_psd_dz_tot.png]]
+
+
+If we look at the Cumulative amplitude spectrum of the vertical error motion in Figure [[fig:opt_stiff_cas_dz_tot]], we can observe that a soft hexapod ($k < 10^5 - 10^6\,[N/m]$) helps reducing the high frequency disturbances, and thus a smaller control bandwidth will suffice to obtain the wanted performance.
+
+#+name: fig:opt_stiff_cas_dz_tot
+#+caption: Cumulative Amplitude Spectrum of the Sample vertical position error due to all considered perturbations for multiple nano-hexapod stiffnesses
+[[file:figs/opt_stiff_cas_dz_tot.png]]
+
+** Optimal Stiffness to reduce the plant uncertainty
+*** Introduction                                                    :ignore:
+One of the primary design goal is to obtain a system that is *robust* to all changes in the system.
+To design a robust system, we have to identify the sources of uncertainty and try to minimize them.
+
+The uncertainty in the system can be caused by:
+- A change in the *Support's compliance* (complete analysis [[https://tdehaeze.github.io/nass-simscape/uncertainty_support.html][here]]): if the micro-station dynamics is changing due to the change of parts or just because of aging effects, the feedback system should remains stable and the obtained performance should not change.
+- A change in the *Payload mass/dynamics* (complete analysis [[https://tdehaeze.github.io/nass-simscape/uncertainty_payload.html][here]]).
+- A change of *experimental condition* such as the micro-station's pose or the spindle rotation (complete analysis [[https://tdehaeze.github.io/nass-simscape/uncertainty_experiment.html][here]])
+
+
+All these uncertainties will limit the attainable bandwidth and hence the performances.
+
+
+Fortunately, the nano-hexapod stiffness have an influence on the dynamical uncertainty induced by the above effects and we wish here to determine the optimal nano-hexapod stiffness.
+
+Separate studies has been conducted to see how the support's compliance appears in
+
+*** Effect of Payload
+:PROPERTIES:
+:UNNUMBERED: t
+:END:
+
+#+name: fig:opt_stiffness_payload_mass_fz_dz
+#+caption: Dynamics from $\mathcal{F}_z$ to $\mathcal{X}_z$ for varying payload mass, both for a soft nano-hexapod and a stiff nano-hexapod
+[[file:figs/opt_stiffness_payload_mass_fz_dz.png]]
+
+#+name: fig:opt_stiffness_payload_freq_fz_dz
+#+caption: Dynamics from $\mathcal{F}_z$ to $\mathcal{X}_z$ for varying payload resonance frequency, both for a soft nano-hexapod and a stiff nano-hexapod
+[[file:figs/opt_stiffness_payload_freq_fz_dz.png]]
+
+*** Effect of Micro-Station Compliance
+:PROPERTIES:
+:UNNUMBERED: t
+:END:
+
+#+name: fig:opt_stiffness_micro_station_fx_dx
+#+caption: Change of dynamics from force $\mathcal{F}_x$ to displacement $\mathcal{X}_x$ due to the micro-station compliance
+[[file:figs/opt_stiffness_micro_station_fx_dx.png]]
+
+
+
+*** Effect of Spindle Rotating Speed
+:PROPERTIES:
+:UNNUMBERED: t
+:END:
+
+#+name: fig:opt_stiffness_wz_fx_dx
+#+caption: Change of dynamics from force $\mathcal{F}_x$ to displacement $\mathcal{X}_x$ for a spindle rotation speed from 0rpm to 60rpm
+[[file:figs/opt_stiffness_wz_fx_dx.png]]
+
+
+*** Total Uncertainty
+:PROPERTIES:
+:UNNUMBERED: t
+:END:
+
+#+name: fig:opt_stiffness_plant_dynamics_task_space
+#+caption: Variability of the dynamics from $\bm{\mathcal{F}}_x$ to $\bm{\mathcal{X}}_x$ with varying nano-hexapod stiffness
+[[file:figs/opt_stiffness_plant_dynamics_task_space.gif]]
+
+
+#+begin_important
+The leg stiffness should be at higher than $k = 10^4\,[N/m]$ such that the main resonance frequency does not shift too much when rotating.
+#+end_important
+
+
+#+begin_important
+It is usually a good idea to maximize the mass, damping and stiffness of the isolation platform in order to be less sensible to the payload dynamics.
+The best thing to do is to have a stiff isolation platform.
+
+
+The dynamics of the nano-hexapod is not affected by the micro-station dynamics (compliance) when the stiffness of the legs is less than $10^6\,[N/m]$. When the nano-hexapod is stiff ($k > 10^7\,[N/m]$), the compliance of the micro-station appears in the primary plant.
+#+end_important
 
-Uncertainty in the system can be caused by:
-- Effect of Support Compliance: https://tdehaeze.github.io/nass-simscape/uncertainty_support.html
-- Effect of Payload Dynamics: https://tdehaeze.github.io/nass-simscape/uncertainty_payload.html
-- Effect of experimental condition (micro-station pose, spindle rotation): https://tdehaeze.github.io/nass-simscape/uncertainty_experiment.html
 
-All these uncertainty will limit the maximum attainable bandwidth.
 
-Fortunately, the nano-hexapod stiffness have an influence on the dynamical uncertainty induced by the above effects.
 
 Determination of the optimal stiffness based on all the effects:
 - https://tdehaeze.github.io/nass-simscape/uncertainty_optimal_stiffness.html
 
-#+begin_conclusion
-
-#+end_conclusion
-
 
 The main performance limitation are payload variability
 #+begin_question
@@ -799,27 +903,14 @@ The main performance limitation are payload variability
   The first resonance frequency of the sample will limit the performance.
 #+end_question
 
-
-The nano-hexapod stiffness will also change the sensibility to disturbances.
-
-Effect of Nano-hexapod stiffness on the Sensibility to disturbances: https://tdehaeze.github.io/nass-simscape/optimal_stiffness_disturbances.html
-
 #+begin_conclusion
 
 #+end_conclusion
 
-** Sensors to be included
+It is preferred that *one* controller is working for all the payloads.
+If not possible, the alternative would be to develop an adaptive controller that depends on the payload mass/inertia.
 
-Ways to damp:
-- Force Sensor
-- Relative Velocity Sensors
-- Inertial Sensor
-
-
-
-https://tdehaeze.github.io/rotating-frame/index.html
-
-Sensors to be included:
+** Conclusion
 
 
 * Robust Control Architecture
@@ -829,15 +920,38 @@ Sensors to be included:
 https://tdehaeze.github.io/nass-simscape/optimal_stiffness_control.html
 
 
+** Active Damping and Sensors to be included
+Ways to damp:
+- Force Sensor
+- Relative Velocity Sensors
+- Inertial Sensor
+
+
+https://tdehaeze.github.io/rotating-frame/index.html
+
+Sensors to be included:
+
+** Motion Control
+
 ** Simulation of Tomography Experiments
 <<sec:tomography_experiment>>
 
+#+name: fig:opt_stiff_hac_dvf_L_psd_disp_error
+#+caption: Amplitude Spectral Density of the position error in Open Loop and with the HAC-LAC controller
+[[file:figs/opt_stiff_hac_dvf_L_psd_disp_error.png]]
+
+#+name: fig:opt_stiff_hac_dvf_L_cas_disp_error
+#+caption: Cumulative Amplitude Spectrum of the position error in Open Loop and with the HAC-LAC controller
+[[file:figs/opt_stiff_hac_dvf_L_cas_disp_error.png]]
+
+#+name: fig:opt_stiff_hac_dvf_L_pos_error
+#+caption: Position Error of the sample during a tomography experiment when no control is applied and with the HAC-DVF control architecture
+[[file:figs/opt_stiff_hac_dvf_L_pos_error.png]]
+
 #+name: fig:closed_loop_sim_zoom
-#+caption: Figure caption
+#+caption: Tomography Experiment using the Simscape Model in Closed Loop with the HAC-LAC Control - Zoom on the sample's position (the full vertical scale is $\approx 10 \mu m$)
 [[file:figs/closed_loop_sim_zoom.gif]]
 
-
-
 ** Conclusion
 * Further notes
 Soft granite
@@ -849,3 +963,6 @@ Common metrology frame for the nano-focusing optics and the measurement of the s
 Cable forces?
 
 Slip-Ring noise?
+* Bibliography                                                        :ignore:
+bibliographystyle:unsrt
+bibliography:ref.bib

ref.bib

@@ -0,0 +1,20 @@
+@book{schmidt14_desig_high_perfor_mechat_revis_edition,
+  author = {Schmidt, R Munnig and Schitter, Georg and Rankers, Adrian},
+  title = {The Design of High Performance Mechatronics - 2nd Revised Edition},
+  year = {2014},
+  publisher = {Ios Press},
+  tags = {favorite},
+}
+
+@article{oomen18_advan_motion_contr_precis_mechat,
+  author = {Tom Oomen},
+  title = {Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems},
+  journal = {IEEJ Journal of Industry Applications},
+  volume = {7},
+  number = {2},
+  pages = {127-140},
+  year = {2018},
+  doi = {10.1541/ieejjia.7.127},
+  url = {https://doi.org/10.1541/ieejjia.7.127},
+  tags = {favorite},
+}