Add some comments about what to write
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paper/paper.org
@ -48,7 +48,7 @@
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)
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#+END_SRC
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* Abstract :ignore:
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* Abstract :ignore:
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#+BEGIN_EXPORT latex
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\abstract{
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Abstract text to be done
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@ -57,32 +57,32 @@
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* Introduction
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<<sec:introduction>>
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*** Establish the importance of the research topic :ignore:
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** Establish the importance of the research topic :ignore:
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# Active Damping + Rotating System
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Controller Poles are shown by black crosses (
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\begin{tikzpicture} \node[cross out, draw=black, minimum size=1ex, line width=2pt, inner sep=0pt, outer sep=0pt] at (0, 0){}; \end{tikzpicture}
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).
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*** Applications of active damping :ignore:
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** Applications of active damping :ignore:
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# Link to previous paper / tomography
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cite:dehaeze18_sampl_stabil_for_tomog_exper
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# Such as the Nano-Active-Stabilization-System currently in development at the ESRF cite:dehaeze18_sampl_stabil_for_tomog_exper.
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*** Current active damping techniques :ignore:
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** Current active damping techniques :ignore:
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# IFF, DVF
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*** Describe a gap in the research :ignore:
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** Describe a gap in the research :ignore:
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# No literature on rotating systems => gyroscopic effects
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*** Describe the paper itself / the problem which is addressed :ignore:
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** Describe the paper itself / the problem which is addressed :ignore:
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*** Introduce Each part of the paper :ignore:
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** Introduce Each part of the paper :ignore:
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* System Under Study
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** Rotating Positioning Platform
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* Dynamics of Rotating Positioning Platforms
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** Studied Rotating Positioning Platform
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# Simplest system where gyroscopic forces can be studied
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Consider the rotating X-Y stage of Figure [[fig:rotating_xy_platform]].
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Consider the rotating X-Y stage of Figure [[fig:system]].
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# Present the system, parameters, assumptions
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@ -98,16 +98,15 @@ Consider the rotating X-Y stage of Figure [[fig:rotating_xy_platform]].
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- $F_u$, $F_v$
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- $d_u$, $d_v$
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#+name: fig:rotating_xy_platform
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#+name: fig:system
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/system.pdf]]
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#+name: fig:cedrat_xy25xs
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#+caption: Figure caption
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#+attr_latex: :width 0.5\linewidth
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[[file:figs/cedrat_xy25xs.jpg]]
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# #+name: fig:cedrat_xy25xs
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# #+caption: Figure caption
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# #+attr_latex: :width 0.5\linewidth
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# [[file:figs/cedrat_xy25xs.jpg]]
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** Equation of Motion
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The system has two degrees of freedom and is thus fully described by the generalized coordinates $u$ and $v$.
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@ -234,6 +233,14 @@ When the rotation speed is null, the coupling terms are equal to zero and the di
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When the rotation speed in not null, the resonance frequency is duplicated into two pairs of complex conjugate poles.
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As the rotation speed increases, one of the two resonant frequency goes to lower frequencies as the other one goes to higher frequencies (Figure [[fig:campbell_diagram]]).
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#+name: fig:campbell_diagram
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#+caption: Campbell Diagram
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#+attr_latex: :environment subfigure :width 0.4\linewidth :align c
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| file:figs/campbell_diagram_real.pdf | file:figs/campbell_diagram_imag.pdf |
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| <<fig:campbell_diagram_real>> Real Part | <<fig:campbell_diagram_imag>> Imaginary Part |
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#+name: fig:campbell_diagram
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#+caption: Campbell Diagram
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#+attr_latex: :scale 1
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@ -243,10 +250,16 @@ As the rotation speed increases, one of the two resonant frequency goes to lower
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The magnitude of the coupling terms are increasing with the rotation speed.
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# #+name: fig:plant_compare_rotating_speed
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# #+caption: Caption
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# #+attr_latex: :scale 1
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# [[file:figs/plant_compare_rotating_speed.pdf]]
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#+name: fig:plant_compare_rotating_speed
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#+caption: Caption
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#+attr_latex: :scale 1
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[[file:figs/plant_compare_rotating_speed.pdf]]
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#+caption: Dynamics
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#+attr_latex: :environment subfigure :width 0.45\linewidth :align c
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| file:figs/plant_compare_rotating_speed_direct.pdf | file:figs/plant_compare_rotating_speed_coupling.pdf |
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| <<fig:plant_compare_rotating_speed_direct>> Direct Terms $d_u/F_u$, $d_v/F_v$ | <<fig:plant_compare_rotating_speed_coupling>> Coupling Terms $d_v/F_u$, $d_u/F_v$ |
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* Integral Force Feedback
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** Control Schematic
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@ -291,9 +304,21 @@ Which then gives:
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G_{fc} &= \left( 2 \xi \frac{s}{\omega_0} + 1 \right) \left( 2 \frac{\Omega}{\omega_0} \frac{s}{\omega_0} \right)
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\end{align}
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** Plant Dynamics
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#+name: fig:plant_iff_compare_rotating_speed
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/plant_iff_compare_rotating_speed.pdf]]
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# Show that the low frequency gain is no longer zero
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# Explain the two real zeros => change of gain but not of phase
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# Explain physically why
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** Integral Force Feedback
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# General explanation for the Root Locus Plot
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# MIMO root locus: gain is simultaneously increased for both decentralized controllers
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@ -305,37 +330,64 @@ Which then gives:
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#+attr_latex: :scale 1
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[[file:figs/root_locus_pure_iff.pdf]]
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** Physical Interpretation
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# Physical Interpretation
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At low frequency, the gain is very large and thus no force is transmitted between the payload and the rotating stage.
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This means that at low frequency, the system is decoupled (the force sensor removed) and thus the system is unstable.
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# Introduce next two sections where either:
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# - IFF is modified to deal with this low frequency behavior
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# - physical system is modified
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* Integral Force Feedback with High Pass Filters
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** Modification of the Control Low
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# Reference to Preumont where its done
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# Explain why it is usually done and why it is done here: the problem is the high gain at low frequency => high pass filter
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** Close Loop Analysis
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** Feedback Analysis
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# Explain that now the low frequency loop gain does not reach a gain more than 1 (if g not so high)
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#+name: fig:loop_gain_modified_iff
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/loop_gain_modified_iff.pdf]]
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# Not the system can be stable for small values of g
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# Actually, the system becomes unstable for g > ...
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#+name: fig:root_locus_modified_iff
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/root_locus_modified_iff_ter.pdf]]
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[[file:figs/root_locus_modified_iff.pdf]]
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** Optimal Cut-Off Frequency
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# Controller: two parameters: gain and wi
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# Try few wi
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# Small wi seems to allow more damping to be added
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# but the gain is limited to small values
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# Trade off
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#+name: fig:root_locus_wi_modified_iff
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/root_locus_wi_modified_iff_bis.pdf]]
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[[file:figs/root_locus_wi_modified_iff.pdf]]
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# Study this trade-off
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# Explain how the figure is obtained
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# for small wi => gain limited
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# for large wi => damping limited
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# wi = 0.1 w0 is chosen
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#+name: fig:mod_iff_damping_wi
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#+caption: Figure caption
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@ -343,60 +395,101 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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[[file:figs/mod_iff_damping_wi.pdf]]
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* Integral Force Feedback with Parallel Springs
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** Stiffness in Parallel with the Force Sensor
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#+name: fig:rotating_xy_platform_springs
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# Zeros = remove force sensor
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# We want to have stable zeros => add stiffnesses in parallel
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#+name: fig:system_parallel_springs
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/rotating_xy_platform_springs.pdf]]
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[[file:figs/system_parallel_springs.pdf]]
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# Maybe add the fact that this is equivalent to amplified piezo for instance
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# Equations: sensed force
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# New parameters
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** Effect of the Parallel Stiffness on the Plant Dynamics
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# Negative Stiffness due to rotation => the stiffness should be larger than that
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# For kp < negative stiffness => real zeros
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# For kp > negative stiffness => complex conjugate zeros
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#+name: fig:plant_iff_kp
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/plant_iff_kp.pdf]]
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# Location of the zeros as a function of kp
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# Show that it is the case on the root locus
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#+name: fig:root_locus_iff_kp
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/root_locus_iff_kp.pdf]]
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# For kp > m Omega => unconditionally stable
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** Optimal Parallel Stiffness
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# Explain that we have k = ka + kp constant in order to have the same resonance
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# Large Stiffness decreases the attainable damping
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# kp = 2mOmega to 5mOmega is ok
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#+name: fig:root_locus_iff_kps
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/root_locus_iff_kps.pdf]]
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#+name: fig:root_locus_iff_kp_bis
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/root_locus_iff_kp_ter.pdf]]
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#+name: fig:root_locus_opt_gain_iff_kp
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/root_locus_opt_gain_iff_kp.pdf]]
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#+name: fig:plant_iff_compare_rotating_speed
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/plant_iff_compare_rotating_speed.pdf]]
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* Direct Velocity Feedback
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** Control Schematic
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#+name: fig:system_dvf
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/system_dvf.pdf]]
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** Equations
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** Relative Direct Velocity Feedback
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#+name: fig:root_locus_dvf
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/root_locus_dvf.pdf]]
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* Comparison of the Proposed Active Damping Techniques
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* Comparison of the Proposed Active Damping Techniques for Rotating Positioning Stages
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**
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#+name: fig:comp_root_locus
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/comp_root_locus.pdf]]
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#+name: fig:comp_compliance
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/comp_compliance.pdf]]
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#+name: fig:comp_active_damping
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#+caption: Comparison of the three proposed Active Damping Techniques
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#+attr_latex: :environment subfigure :width 0.45\linewidth :align c
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| file:figs/comp_compliance.pdf | file:figs/comp_transmissibility.pdf |
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| <<fig:comp_compliance>> Transmissibility | <<fig:comp_transmissibility>> Compliance |
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#+name: fig:comp_transmissibility
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#+caption: Figure caption
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#+attr_latex: :scale 1
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[[file:figs/comp_transmissibility.pdf]]
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# #+name: fig:comp_compliance
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# #+caption: Figure caption
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# #+attr_latex: :scale 1
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# [[file:figs/comp_compliance.pdf]]
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# #+name: fig:comp_transmissibility
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# #+caption: Figure caption
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# #+attr_latex: :scale 1
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# [[file:figs/comp_transmissibility.pdf]]
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* Conclusion
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<<sec:conclusion>>
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@ -407,5 +500,5 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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:UNNUMBERED: t
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:END:
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* Bibliography :ignore:
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* Bibliography :ignore:
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\bibliography{ref.bib}
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