diff --git a/disturbances/index.html b/disturbances/index.html index 430a719..c1ee126 100644 --- a/disturbances/index.html +++ b/disturbances/index.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Identification of the disturbances @@ -280,12 +280,12 @@ for the JavaScript code in this tag.

Table of Contents

@@ -295,34 +295,43 @@ The goal here is to extract the Power Spectral Density of the sources of perturb

-The sources of perturbations are: +The sources of perturbations are (schematically shown in figure 1):

-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 1) and then, using a model, compute the forces that induced such velocity.

+ + +
+

uniaxial-model-micro-station.png +

+

Figure 1: Schematic of the Micro Station and the sources of disturbance

+
+ +

This file is divided in the following sections:

-
-

1 Identification

+
+

1 Identification

- +

@@ -363,43 +372,43 @@ G.OutputName = {

-
-

2 Sensitivity to Disturbances

+
+

2 Sensitivity to Disturbances

- +

-
+

sensitivity_dist_gm.png

-

Figure 1: Sensitivity to Ground Motion (png, pdf)

+

Figure 2: Sensitivity to Ground Motion (png, pdf)

-
+

sensitivity_dist_fty.png

-

Figure 2: Sensitivity to vertical forces applied by the Ty stage (png, pdf)

+

Figure 3: Sensitivity to vertical forces applied by the Ty stage (png, pdf)

-
+

sensitivity_dist_frz.png

-

Figure 3: Sensitivity to vertical forces applied by the Rz stage (png, pdf)

+

Figure 4: Sensitivity to vertical forces applied by the Rz stage (png, pdf)

-
-

3 Power Spectral Density of the effect of the disturbances

+
+

3 Power Spectral Density of the effect of the disturbances

- + The PSD of the relative velocity between the hexapod and the marble in \([(m/s)^2/Hz]\) are loaded for the following sources of disturbance:

    @@ -428,46 +437,46 @@ We now compute the relative velocity between the hexapod and the granite due to

-The Power Spectral Density of the relative motion/velocity of the hexapod with respect to the granite are shown in figures 4 and 5. +The Power Spectral Density of the relative motion/velocity of the hexapod with respect to the granite are shown in figures 5 and 6.

-The Cumulative Amplitude Spectrum of the relative motion is shown in figure 6. +The Cumulative Amplitude Spectrum of the relative motion is shown in figure 7.

-
+

dist_effect_relative_velocity.png

-

Figure 4: Amplitude Spectral Density of the relative velocity of the hexapod with respect to the granite due to different sources of perturbation (png, pdf)

+

Figure 5: Amplitude Spectral Density of the relative velocity of the hexapod with respect to the granite due to different sources of perturbation (png, pdf)

-
+

dist_effect_relative_motion.png

-

Figure 5: Amplitude Spectral Density of the relative displacement of the hexapod with respect to the granite due to different sources of perturbation (png, pdf)

+

Figure 6: Amplitude Spectral Density of the relative displacement of the hexapod with respect to the granite due to different sources of perturbation (png, pdf)

-
+

dist_effect_relative_motion_cas.png

-

Figure 6: Cumulative Amplitude Spectrum of the relative motion due to different sources of perturbation (png, pdf)

+

Figure 7: Cumulative Amplitude Spectrum of the relative motion due to different sources of perturbation (png, pdf)

-
-

4 Compute the Power Spectral Density of the disturbance force

+
+

4 Compute the Power Spectral Density of the disturbance force

- +

-Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section 2) and from the measured PSD of the relative motion (section 3), we can compute the PSD of the disturbance force. +Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section 2) and from the measured PSD of the relative motion (section 3), we can compute the PSD of the disturbance force.

@@ -477,19 +486,19 @@ tyz.psd_f = tyz.pxz_ty_r./abs +

dist_force_psd.png

-

Figure 7: Amplitude Spectral Density of the disturbance force (png, pdf)

+

Figure 8: Amplitude Spectral Density of the disturbance force (png, pdf)

-
-

5 Noise Budget

+
+

5 Noise Budget

- +

@@ -498,24 +507,24 @@ We should verify that this is coherent with the measurements.

-
+

psd_effect_dist_verif.png

-

Figure 8: Computed Effect of the disturbances on the relative displacement hexapod/granite (png, pdf)

+

Figure 9: Computed Effect of the disturbances on the relative displacement hexapod/granite (png, pdf)

-
+

cas_computed_relative_displacement.png

-

Figure 9: CAS of the total Relative Displacement due to all considered sources of perturbation (png, pdf)

+

Figure 10: CAS of the total Relative Displacement due to all considered sources of perturbation (png, pdf)

-
-

6 Save

+
+

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 new file mode 100644 index 0000000..6afcd8a Binary files /dev/null and b/figs/uniaxial-model-micro-station.png differ