+
6 Save
The PSD of the disturbance force are now saved for further noise budgeting when control is applied (the mat file is accessible here).
@@ -536,7 +545,7 @@ save(
Author: Dehaeze Thomas
-Created: 2019-11-04 lun. 15:53
+Created: 2019-11-04 lun. 15:56
Validate
diff --git a/disturbances/index.org b/disturbances/index.org
index e97d420..1f5537b 100644
--- a/disturbances/index.org
+++ b/disturbances/index.org
@@ -44,12 +44,124 @@
* Introduction :ignore:
The goal here is to extract the Power Spectral Density of the sources of perturbation.
-The sources of perturbations are:
-- Ground Motion
-- Parasitic forces applied in the system when scanning with the Translation Stage and the Spindle.
+The sources of perturbations are (schematically shown in figure [[fig:uniaxial-model-micro-station]]):
+- $D_w$: Ground Motion
+- Parasitic forces applied in the system when scanning with the Translation Stage and the Spindle ($F_{rz}$ and $F_{ty}$).
These forces can be due to imperfect guiding for instance.
-Because we cannot measure directly the perturbation forces, we have the measure the effect of those perturbations on the system (in terms of velocity for instance using geophones) and then, using a model, compute the forces that induced such velocity.
+Because we cannot measure directly the perturbation forces, we have the measure the effect of those perturbations on the system (in terms of velocity for instance using geophones, $D$ on figure [[fig:uniaxial-model-micro-station]]) and then, using a model, compute the forces that induced such velocity.
+
+
+#+begin_src latex :file uniaxial-model-micro-station.pdf :post pdf2svg(file=*this*, ext="png") :exports results
+ \begin{tikzpicture}
+ % ====================
+ % Parameters
+ % ====================
+ \def\massw{2.2} % Width of the masses
+ \def\massh{0.8} % Height of the masses
+ \def\spaceh{1.2} % Height of the springs/dampers
+ \def\dispw{0.4} % Width of the dashed line for the displacement
+ \def\disph{0.3} % Height of the arrow for the displacements
+ \def\bracs{0.05} % Brace spacing vertically
+ \def\brach{-12pt} % Brace shift horizontaly
+ \def\fsensh{0.2} % Height of the force sensor
+ \def\velsize{0.2} % Size of the velocity sensor
+ % ====================
+
+
+ % ====================
+ % Ground
+ % ====================
+ \draw (-0.5*\massw, 0) -- (0.5*\massw, 0);
+ \draw[dashed] (0.5*\massw, 0) -- ++(1, 0);
+ \draw[->, dasehd] (0.5*\massw+0.8, 0) -- ++(0, 0.5) node[right]{$D_{w}$};
+ % ====================
+
+
+ % ====================
+ % Marble
+ \begin{scope}[shift={(0, 0)}]
+ % Mass
+ \draw[fill=white] (-0.5*\massw, \spaceh) rectangle (0.5*\massw, \spaceh+\massh) node[pos=0.5]{$m_{m}$};
+
+ % Spring, Damper, and Actuator
+ \draw[spring] (-0.4*\massw, 0) -- (-0.4*\massw, \spaceh) node[midway, left=0.1]{$k_{m}$};
+ \draw[damper] (0, 0) -- ( 0, \spaceh) node[midway, left=0.2]{$c_{m}$};
+
+ % Legend
+ \draw[decorate, decoration={brace, amplitude=8pt}, xshift=\brach] %
+ (-0.5*\massw, \bracs) -- (-0.5*\massw, \spaceh+\massh-\bracs) node[midway,rotate=90,anchor=south,yshift=10pt]{Marble};
+
+ % Displacements
+ \draw[dashed] (0.5*\massw, \spaceh+\massh) -- ++(2*\dispw, 0) coordinate(xm) -- ++(2.2*\dispw, 0) coordinate(dbot);
+ \end{scope}
+ % ====================
+
+
+ % ====================
+ % Ty
+ \begin{scope}[shift={(0, \spaceh+\massh)}]
+ % Mass
+ \draw[fill=white] (-0.5*\massw, \spaceh) rectangle (0.5*\massw, \spaceh+\massh) node[pos=0.5]{$m_{t}$};
+
+ % Spring, Damper, and Actuator
+ \draw[spring] (-0.4*\massw, 0) -- (-0.4*\massw, \spaceh) node[midway, left=0.1]{$k_{t}$};
+ \draw[damper] (0, 0) -- ( 0, \spaceh) node[midway, left=0.2]{$c_{t}$};
+ \draw[actuator={0.45}{0.2}] ( 0.4*\massw, 0) -- ( 0.4*\massw, \spaceh) node[midway, right=0.1](ft){$F_{ty}$};
+
+ % Legend
+ \draw[decorate, decoration={brace, amplitude=8pt}, xshift=\brach] %
+ (-0.5*\massw, \bracs) -- (-0.5*\massw, \spaceh+\massh-\bracs) node[midway,rotate=90,anchor=south,yshift=10pt]{Ty};
+ \end{scope}
+ % ====================
+
+
+ % ====================
+ % Rz
+ \begin{scope}[shift={(0, 2*(\spaceh+\massh))}]
+ % Mass
+ \draw[fill=white] (-0.5*\massw, \spaceh) rectangle (0.5*\massw, \spaceh+\massh) node[pos=0.5]{$m_{z}$};
+
+ % Spring, Damper, and Actuator
+ \draw[spring] (-0.4*\massw, 0) -- (-0.4*\massw, \spaceh) node[midway, left=0.1]{$k_{z}$};
+ \draw[damper] (0, 0) -- ( 0, \spaceh) node[midway, left=0.2]{$c_{z}$};
+ \draw[actuator] ( 0.4*\massw, 0) -- ( 0.4*\massw, \spaceh) node[midway, right=0.1](F){$F_{rz}$};
+
+ % Legend
+ \draw[decorate, decoration={brace, amplitude=8pt}, xshift=\brach] %
+ (-0.5*\massw, \bracs) -- (-0.5*\massw, \spaceh+\massh-\bracs) node[midway,rotate=90,anchor=south,yshift=10pt]{Rz};
+ \end{scope}
+ % ====================
+
+
+ % ====================
+ % Hexapod
+ \begin{scope}[shift={(0, 3*(\spaceh+\massh))}]
+ % Mass
+ \draw[fill=white] (-0.5*\massw, \spaceh) rectangle (0.5*\massw, \spaceh+\massh) node[pos=0.5]{$m_{h}$};
+
+ % Spring, Damper, and Actuator
+ \draw[spring] (-0.4*\massw, 0) -- (-0.4*\massw, \spaceh) node[midway, left=0.1]{$k_{h}$};
+ \draw[damper] (0, 0) -- ( 0, \spaceh) node[midway, left=0.2]{$c_{h}$};
+
+ % Displacements
+ \draw[dashed] (0.5*\massw, \spaceh+\massh) -- ++(2*\dispw, 0) coordinate(xs) -- ++(2.2*\dispw, 0) coordinate(dtop);
+
+ % Legend
+ \draw[decorate, decoration={brace, amplitude=8pt}, xshift=\brach] %
+ (-0.5*\massw, \bracs) -- (-0.5*\massw, \spaceh+\massh-\bracs) node[midway,rotate=90,anchor=south,yshift=10pt]{Hexapod};
+ \end{scope}
+ % ====================
+
+ \draw[<->] ($(dbot)+(-0.3,0)$) --node[midway, right]{$D$} ($(dtop)+(-0.3,0)$);
+ \end{tikzpicture}
+#+end_src
+
+#+name: fig:uniaxial-model-micro-station
+#+caption: Schematic of the Micro Station and the sources of disturbance
+#+RESULTS:
+[[file:figs/uniaxial-model-micro-station.png]]
+
This file is divided in the following sections:
- Section [[sec:identification]]: transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup
diff --git a/figs/uniaxial-model-micro-station.png b/figs/uniaxial-model-micro-station.png
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