tdehaeze/hugo
1
0 Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Re-export everything
Deploy / deploy (push) Successful in 5s
Details

Browse Source
This commit is contained in:
tdehaeze committed 2026-10-12 14:10:30 +02:00
1 parent 665774dd08
commit 432702d1a4
40 files changed
+397 -646
Download Patch File Download Diff File Expand all files Collapse all files

No files matched your search

content/zettels/analog_to_digital_converters.md
+1 -1
View File
@@ -33,7 +33,7 @@ Let's suppose that the ADC is ideal and the only noise comes from the quantizati
Interestingly, the noise amplitude is uniformly distributed.
The quantization noise can take a value between \\(\pm q/2\\), and the probability density function is constant in this range (i.e., it’s a uniform distribution).
Since the integral of the probability density function is equal to one, its value will be \\(1/q\\) for \\(-q/2 < e < q/2\\) (Fig. [Figure 1](#figure--fig:probability-density-function-adc)).
Since the integral of the probability density function is equal to one, its value will be \\(1/q\\) for \\(-q/2 < e < q/2\\) ([Figure 1](#figure--fig:probability-density-function-adc)).
<a id="figure--fig:probability-density-function-adc"></a>
content/zettels/continuous_transfer_functions.md
+1 -1
View File
@@ -192,7 +192,7 @@ Characteristics:
- Zero at \\(\omega\_c/\sqrt{a}\\) and pole at \\(\omega\_c \sqrt{a}\\), geometrically centered on \\(\omega\_c\\)
- Unity gain at \\(\omega\_c\\), low frequency gain of \\(1/\sqrt{a}\\), high frequency gain of \\(\sqrt{a}\\)
- Maximum phase lead, obtained at \\(\omega\_c\\), equal to (Figure [Figure 8](#figure--fig:filter-lead-effect-a-phase)):
- Maximum phase lead, obtained at \\(\omega\_c\\), equal to ([Figure 8](#figure--fig:filter-lead-effect-a-phase)):
\\[ \angle H(j\omega\_c) = \tan^{-1}(\sqrt{a}) - \tan^{-1}(1/\sqrt{a}) \\]
<!--listend-->
content/zettels/decimation.md
+13 -11
View File
@@ -69,7 +69,7 @@ where \\(F\\) is the ratio of single-stage low pass filter's transition region w
F = \frac{f\_{\text{stop}} - B^\prime}{f\_{\text{stop}}}
\end{equation}
After using Eq. \ref{eq:M1opt} to determine the optimum first downsampling factor, and setting \\(M\_1\\) equal to the integer sub-multiple of \\(M\\) that is closest to \\(M\_{1,\text{opt}}\\), the second downsampling factor is:
After using Eq. \eqref{eq:M1opt} to determine the optimum first downsampling factor, and setting \\(M\_1\\) equal to the integer sub-multiple of \\(M\\) that is closest to \\(M\_{1,\text{opt}}\\), the second downsampling factor is:
\begin{equation} \label{eq:M2\_from\_M1}
M\_2 = \frac{M}{M\_1}
@@ -89,9 +89,9 @@ N = \frac{\text{Atten}}{22 (f\_{\text{stop}} - f\_{\text{pass}})} = \frac{60}{22
which is way too large for practical implementation.
To reduce the number of necessary filter taps, we can partition the decimation problem into two stages.
With \\(M = 100\\), \\(F = (2200-1800)/2200\\), Eq. \ref{eq:M1opt} yields \\(M\_{1,\text{opt}} = 26.4\\).
With \\(M = 100\\), \\(F = (2200-1800)/2200\\), Eq. \eqref{eq:M1opt} yields \\(M\_{1,\text{opt}} = 26.4\\).
The integer sub-multiple of 100 closest to \\(26.4\\) is \\(25\\), so we set \\(M\_1 = 25\\).
Next, from Eq. \ref{eq:M2\_from\_M1}, \\(M\_2 = 4\\) is found.
Next, from Eq. \eqref{eq:M2\_from\_M1}, \\(M\_2 = 4\\) is found.
The first low pass filter has a pass-band cutoff frequency of \\(1.8\\,kHz\\) and its stop-band is \\(400/25 - 1.8 = 14.2\\,kHz\\) ([Figure 4](#figure--fig:decimation-two-stage-example) (d)).
The second low pass filter has a pass-band cutoff frequency of \\(1.8\\,kHz\\) and its stop-band is \\(4-1.8 = 2.2\\,kHz\\).
@@ -116,16 +116,18 @@ There are two **practical issues** to consider for two-stage decimation:
In order to cope with the second issue, an efficient decimation filter implementation scheme called _polyphase decomposition_ can be used.
<summary>The advantages of two stage decimation, over single-stage decimation are:
<div class="sum">
<ul class="org-ul">
<li>an overall reduction in computation workload</li>
<li>reduced signal and filter coefficient data storage</li>
<li>simpler filter designs</li>
<li>a decrease in the ill effects of finite binary-work-length filter coefficients</li>
</ul>
The advantages of two stage decimation, over single-stage decimation are:
These advantages become more pronounced as the overall desired decimation factor \(M\) becomes larger.</summary>
- an overall reduction in computation workload
- reduced signal and filter coefficient data storage
- simpler filter designs
- a decrease in the ill effects of finite binary-work-length filter coefficients
These advantages become more pronounced as the overall desired decimation factor \\(M\\) becomes larger.
</div>
### References: {#references}
content/zettels/decoupled_control.md
+1 -1
View File
@@ -36,7 +36,7 @@ It is equal to the inverse of the mass matrix (diagonal when evaluated at the Co
\bm{G}\_{\\{CoM\\}}(s) = \frac{\bm{\mathcal{X}}\_{\\{CoM\\}}}{\bm{\mathcal{F}}\_{\\{CoM\\}}} \approx \frac{1}{s^2} \bm{M}^{-1}
\end{equation}
To work at the CoM, the plant is pre- and post-multiplied by the Jacobian matrices as shown in Figure [Figure 1](#figure--fig:detail-control-decoupling-control-jacobian):
To work at the CoM, the plant is pre- and post-multiplied by the Jacobian matrices as shown in [Figure 1](#figure--fig:detail-control-decoupling-control-jacobian):
\begin{equation}
\bm{G}\_{\\{CoM\\}}(s) = \bm{J}\_{\\{CoM\\}}^{-1} \\, \bm{G}\_{\\{\mathcal{L}\\}}(s) \\, \bm{J}\_{\\{CoM\\}}^{-\intercal}
content/zettels/eddy_current_damping.md
+1 -1
View File
@@ -40,7 +40,7 @@ with:
\\(C\_0 = 1\\) corresponds to a conductor with conductivity \\(\sigma\\) inside a uniform magnetic field and conductivity infinite outside this field.
A typical value of \\(C\_0\\) is about 0.25-0.4 for a conductor plate with area 2 to 5 times that of the magnetic field.
From \ref{eq:damping\_formula}, we see that the damping coefficient is proportional to:
From \eqref{eq:damping\_formula}, we see that the damping coefficient is proportional to:
- the square of the magnetic flux density \\(B\\). Therefore it is very important to have large magnetic field strengh
- the thickness \\(t\\) of the conductor. However due to **skin depth effect**, the benefit of increasing the thickness is limited.
content/zettels/feedforward_control.md
+6 -12
View File
@@ -11,14 +11,12 @@ Tags
Depending on the physical system to be controlled, several feedforward controllers can be used:
- [Rigid body feedforward](#org-target--sec-rigid-body-feedforward)
- [Fourth order feedforward](#org-target--sec-fourth-order-feedforward)
- [Model based feedforward](#org-target--sec-model-based-feedforward)
- [Rigid body feedforward](#sec:rigid_body_feedforward)
- [Fourth order feedforward](#sec:fourth_order_feedforward)
- [Model based feedforward](#sec:model_based_feedforward)
## Rigid Body Feedforward {#rigid-body-feedforward}
<span class="org-target" id="org-target--sec-rigid-body-feedforward"></span>
## Rigid Body Feedforward {#sec:rigid_body_feedforward}
Second order trajectory planning: the acceleration and velocity can be bound to wanted values.
@@ -36,9 +34,7 @@ F\_{ff} = m a + c v
\end{equation}
## Fourth Order Feedforward {#fourth-order-feedforward}
<span class="org-target" id="org-target--sec-fourth-order-feedforward"></span>
## Fourth Order Feedforward {#sec:fourth_order_feedforward}
The main advantage of "fourth order feedforward" is that it takes into account the flexibility in the system (one resonance between the actuation point and the measurement point, see [Figure 2](#figure--fig:feedforward-double-mass-system)).
This can lead to better results than second order trajectory planning as demonstrated [here](https://www.20sim.com/control-engineering/snap-feedforward/).
@@ -110,9 +106,7 @@ The same architecture shown in [Figure 3](#figure--fig:feedforward-fourth-order-
In order to implement a fourth order trajectory, look at [this](https://www.mathworks.com/matlabcentral/fileexchange/16352-advanced-setpoints-for-motion-systems) nice implementation in Simulink of fourth-order trajectory planning (see also (<a href="#citeproc_bib_item_1">Lambrechts, Boerlage, and Steinbuch 2004</a>)).
## Model Based Feedforward Control for Second Order resonance plant {#model-based-feedforward-control-for-second-order-resonance-plant}
<span class="org-target" id="org-target--sec-model-based-feedforward"></span>
## Model Based Feedforward Control for Second Order resonance plant {#sec:model_based_feedforward}
See (<a href="#citeproc_bib_item_2">Schmidt, Schitter, and Rankers 2020</a>) (Section 4.2.1).
content/zettels/inertial_sensors.md
+1 -1
View File
@@ -37,7 +37,7 @@ Wireless Accelerometers
- <https://micromega-dynamics.com/products/recovib/miniature-vibration-recorder/>
Several commercial accelerometers are compared in Table [Figure 2](#figure--fig:characteristics-accelerometers) (see (<a href="#citeproc_bib_item_1">Collette et al. 2011</a>)).
Several commercial accelerometers are compared in [Figure 2](#figure--fig:characteristics-accelerometers) (see (<a href="#citeproc_bib_item_1">Collette et al. 2011</a>)).
<a id="figure--fig:characteristics-accelerometers"></a>
content/zettels/jacobian.md
+1 -1
View File
@@ -67,7 +67,7 @@ The Jacobian matrix links the joint variable velocities to the moving platform l
with \\(\bm{q} = \left[ q\_1, q\_2, \ldots, q\_m \right]^T\\) the vector of actuated joint coordinates (linear displacement of an actuator prismatic joint or angular rotation of an actuated revolute joint) and \\(\bm{\mathcal{X}} = \left[ x\_1, x\_2, \ldots, x\_n \right]^T\\) the vector of moving platform motion variables (position or orientation).
From equation \ref{eq:velocity\_loop\_closure}, we have:
From equation \eqref{eq:velocity\_loop\_closure}, we have:
\begin{equation}
\bm{J} = \begin{bmatrix}
content/zettels/stewart_platforms.md
+22 -50
View File
@@ -35,9 +35,7 @@ Tags
| ID16a | ESRF | Piezo (PI) |
## Built Stewart PLatforms {#built-stewart-platforms}
<span class="org-target" id="org-target--sec-built"></span>
## Built Stewart PLatforms {#sec:built}
**Actuators**:
@@ -58,9 +56,7 @@ Tags
- External Metrology
### Short Stroke {#short-stroke}
<span class="org-target" id="org-target--sec-built-short-stroke"></span>
### Short Stroke {#sec:built_short_stroke}
| University | Figure | Configuration | Joints | Actuators | Sensors | Application | Link to bibliography |
|----------------|---------------------------------------------|-------------------|-------------|--------------------------|------------------------------------------------------------|------------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
@@ -171,9 +167,7 @@ Tags
{{< figure src="/ox-hugo/stewart_ulb_vc.jpg" caption="<span class='figure-number'>Figure 21: </span>ULB - Voice Coil <&hanieh03_activ_stewar>" >}}
### Long Stroke {#long-stroke}
<span class="org-target" id="org-target--sec-built-long-stroke"></span>
### Long Stroke {#sec:built_long_stroke}
| University | Figure | Configuration | Joints | Actuators | Sensors | Link to bibliography |
|----------------|------------------------------------------|---------------|--------------|-------------------------|--------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
@@ -199,20 +193,16 @@ Tags
{{< figure src="/ox-hugo/stewart_czech.jpg" caption="<span class='figure-number'>Figure 25: </span>Stewart platform from Brno University (Czech) <&brezina08_ni_labview_matlab_simmec_stewar_platf_desig>" >}}
## Articles - Design Related {#articles-design-related}
## Articles - Design Related {#sec:design}
<span class="org-target" id="org-target--sec-design"></span>
- Flexible joints (Section )
- Specific geometry to have good decoupling properties (Section )
- Alternative architectures for 6DoF parallel mechanisms (Section )
- Workspace (Section )
- Modelling (Section )
- Flexible joints (Section [Flexures](#sec:design_flexure))
- Specific geometry to have good decoupling properties (Section [Decoupling](#sec:design_decoupling))
- Alternative architectures for 6DoF parallel mechanisms (Section [Alternative Architectures](#sec:design_architecture))
- Workspace (Section [Workspace](#sec:design_workspace))
- Modelling (Section [Modelling](#sec:design_modelling))
### Flexures {#flexures}
<span class="org-target" id="org-target--sec-design-flexure"></span>
### Flexures {#sec:design_flexure}
From (<a href="#citeproc_bib_item_31">Hauge and Campbell 2004</a>):
@@ -223,9 +213,7 @@ From (<a href="#citeproc_bib_item_31">Hauge and Campbell 2004</a>):
| Effect of flexures | (<a href="#citeproc_bib_item_46">McInroy 2002</a>) |
### Decoupling {#decoupling}
<span class="org-target" id="org-target--sec-design-decoupling"></span>
### Decoupling {#sec:design_decoupling}
| Main Object | Link to bibliography |
|------------------------------------|---------------------------------------------------------------|
@@ -233,9 +221,7 @@ From (<a href="#citeproc_bib_item_31">Hauge and Campbell 2004</a>):
| | (<a href="#citeproc_bib_item_4">Afzali-Far 2016</a>) |
### Alternative Architectures {#alternative-architectures}
<span class="org-target" id="org-target--sec-design-architecture"></span>
### Alternative Architectures {#sec:design_architecture}
| Figure | Link to bibliography |
|------------------------------------------|----------------------------------------------------------------------------------------------------------------------------|
@@ -250,9 +236,7 @@ From (<a href="#citeproc_bib_item_31">Hauge and Campbell 2004</a>):
{{< figure src="/ox-hugo/stewart_dong07.jpg" caption="<span class='figure-number'>Figure 26: </span><&dong07_desig_precis_compl_paral_posit>" >}}
### Workspace {#workspace}
<span class="org-target" id="org-target--sec-design-workspace"></span>
### Workspace {#sec:design_workspace}
| Main Object | Link to bibliography |
|------------------------------------------------------|----------------------------------------------------------------|
@@ -262,9 +246,7 @@ From (<a href="#citeproc_bib_item_31">Hauge and Campbell 2004</a>):
| Orientation Workspace | (<a href="#citeproc_bib_item_37">Jiang and Gosselin 2009b</a>) |
### Modelling {#modelling}
<span class="org-target" id="org-target--sec-design-modelling"></span>
### Modelling {#sec:design_modelling}
#### Multi Body {#multi-body}
@@ -276,25 +258,21 @@ From (<a href="#citeproc_bib_item_31">Hauge and Campbell 2004</a>):
#### Lumped {#lumped}
## Control {#control}
<span class="org-target" id="org-target--sec-control"></span>
## Control {#sec:control}
Different control objectives:
- Vibration Control (Section )
- Position Control (Section )
- Vibration Control (Section [Vibration Control and Active Damping](#sec:control_isolation))
- Position Control (Section [Position Control](#sec:control_position))
Sometimes, the two objectives are simultaneous, in that case multiple sensors needs to be combined in the control architecture (Section ).
Sometimes, the two objectives are simultaneous, in that case multiple sensors needs to be combined in the control architecture (Section [Multi Sensor Control](#sec:control_multi_sensor)).
Stewart platform, being 6DoF parallel mechanisms, have a coupled dynamics.
In order to ease the control design, decoupling is generally required.
Several approaches can be used (Section ).
### Vibration Control and Active Damping {#vibration-control-and-active-damping}
<span class="org-target" id="org-target--sec-control-isolation"></span>
### Vibration Control and Active Damping {#sec:control_isolation}
From (<a href="#citeproc_bib_item_31">Hauge and Campbell 2004</a>):
@@ -348,9 +326,7 @@ From (<a href="#citeproc_bib_item_31">Hauge and Campbell 2004</a>):
| Shangai | Piezoelectric | Force Sensor + Accelerometer | Vibration isolation, HAC-LAC (IFF + FxLMS) | Dynamic Model + Vibration Control | (<a href="#citeproc_bib_item_76">Wang et al. 2016</a>) |
### Position Control {#position-control}
<span class="org-target" id="org-target--sec-control-position"></span>
### Position Control {#sec:control_position}
Here, the objective is to _position_ the mobile platform with respect to an external metrology or internal metrology.
@@ -380,9 +356,7 @@ From: (<a href="#citeproc_bib_item_80">Yang et al. 2019</a>):
> The idea is to synthesize the control force that can compensate the parasitic bending and torsional torques of the flexible joints and simultaneously achieve diagonalization of the matrices M, C and K.
### Multi Sensor Control {#multi-sensor-control}
<span class="org-target" id="org-target--sec-control-multi-sensor"></span>
### Multi Sensor Control {#sec:control_multi_sensor}
Improvement by the use of several sensors:
@@ -478,9 +452,7 @@ From (<a href="#citeproc_bib_item_68">Thayer et al. 2002</a>):
| Harbin (China) | Voice Coil | Accelerometers | MIMO H-Infinity, active damping | (<a href="#citeproc_bib_item_38">Jiao et al. 2018</a>) |
### Long Stroke Stewart Platforms {#long-stroke-stewart-platforms}
<span class="org-target" id="org-target--sec-control-long-stroke"></span>
### Long Stroke Stewart Platforms {#sec:control_long_stroke}
| Link to bibliography | University | Actuators | Sensors | Control | Main Object |
|-------------------------------------------------------------------------------------------------------------------------------------------------|----------------|------------------------|------------------|--------------------------------------------------|--------------------------------------------|
content/zettels/system_identification.md
+2 -4
View File
@@ -23,7 +23,7 @@ The system is represented in [Figure 1](#figure--fig:siso-identification-schemat
The goal of system identification is to compute the transfer function \\(G\\) from known excitation signal \\(u\\) and from a measure of \\(y\_m\\).
There are different ways of obtaining a model \\(G\\) of the system summarized in Table [Table 1](#table--tab:system-identification-model-types).
There are different ways of obtaining a model \\(G\\) of the system summarized in [Table 1](#table--tab:system-identification-model-types).
For mechatronics systems, _frequency domain identification_ is the norm.
<a id="table--tab:system-identification-model-types"></a>
@@ -161,9 +161,7 @@ When the complete \\(GS\\) and \\(S\\) matrices are identified, the plan estimat
\\[ \hat{\bm{G}}(j\omega) = \bm{GS}(j\omega) \bm{S\_i}^{-1}(j\omega) \\]
## Design of the Excitation Signal {#design-of-the-excitation-signal}
<span class="org-target" id="org-target--sec-system-identification-excitation-signal"></span>
## Design of the Excitation Signal {#sec:system_identification_excitation_signal}
### Introduction {#introduction}
content/zettels/temperature_sensors.md
+6 -12
View File
@@ -14,16 +14,14 @@ Tags
There are mainly three main types of temperature sensors:
- [Thermocouples](#org-target--sec-temperature-sensor-thermocouple) with are based on the Seebeck effect
- [RTD](#org-target--sec-temperature-sensor-rtd) (Resistance Temperature Detectors): made of pure metals (Pt, Ni or Cu)
- [Thermocouples](#sec:temperature_sensor_thermocouple) with are based on the Seebeck effect
- [RTD](#sec:temperature_sensor_rtd) (Resistance Temperature Detectors): made of pure metals (Pt, Ni or Cu)
They are all PTC (Positive Temperature Coefficient): PT100, PT1000, Ni100, Ni1000, ...
- [Thermistor](#org-target--sec-temperature-sensor-thermistor): made of metal oxide mixtures (semiconductor materials).
- [Thermistor](#sec:temperature_sensor_thermistor): made of metal oxide mixtures (semiconductor materials).
They typically have a NTC (Negative Temperature Coefficient).
### Thermocouple {#thermocouple}
<span class="org-target" id="org-target--sec-temperature-sensor-thermocouple"></span>
### Thermocouple {#sec:temperature_sensor_thermocouple}
#### Working Principle {#working-principle}
@@ -101,9 +99,7 @@ Disadvantages:
- Uncertainty about 0.1K, not feasible to reach mK
### RTD {#rtd}
<span class="org-target" id="org-target--sec-temperature-sensor-rtd"></span>
### RTD {#sec:temperature_sensor_rtd}
Sensitivity of PT100 is typically around .
@@ -123,9 +119,7 @@ Disadvantages:
This corresponds to approximately 0.1 degree of self heating in "still" air
### Thermistor {#thermistor}
<span class="org-target" id="org-target--sec-temperature-sensor-thermistor"></span>
### Thermistor {#sec:temperature_sensor_thermistor}
Sensitivity of NTC is .
content/zettels/test.md
+6 -8
View File
@@ -82,8 +82,8 @@ Here is a list of links to:
- [Table 2](#table--tab:table-with-equations)
- Listing [Code Snippet 1](#code-snippet--lst:matlab-figure)
- Specific [line of code](#org-coderef--967846-4)
- Equation \ref{eq:numbered}
- Section
- Equation \eqref{eq:numbered}
- Section [Headlines](#sec:headlines)
- Bibliographic Reference (<a href="#citeproc_bib_item_3">Stanisic and Legrand 2014</a>), and (<a href="#citeproc_bib_item_2">Schulte and Davison 2011</a>; <a href="#citeproc_bib_item_1">Dominik 2010</a>; <a href="#citeproc_bib_item_3">Stanisic and Legrand 2014</a>)
@@ -94,14 +94,14 @@ Here is some inline mathematics: \\(z = 2\\).
Unumbered equation:
\\[ F(x) = \int\_0^x f(t) dt \\]
Using the `equation` environment in Eq. \ref{eq:numbered}.
Using the `equation` environment in Eq. \eqref{eq:numbered}.
\begin{equation}
\label{eq:numbered}
F(s) = \int\_0^\infty f(t) e^{-st} dt
\end{equation}
Using the `align` environment Equations \ref{eq:align\_1} and \ref{eq:align\_2}.
Using the `align` environment Equations \eqref{eq:align\_1} and \eqref{eq:align\_2}.
\begin{align}
\mathcal{F}(a) &= \frac{1}{2\pi i}\oint\_\gamma \frac{f(z)}{z - a}\\,dz \label{eq:align\_1} \\\\
@@ -157,9 +157,7 @@ Some text.
Some text.
## Headlines {#headlines}
<span class="org-target" id="org-target--sec-headlines"></span>
## Headlines {#sec:headlines}
### Second level Headline with tags <span class="tag"><span class="_home">@home</span><span class="_work">@work</span></span> {#second-level-headline-with-tags}
@@ -465,7 +463,7 @@ Numbering can be continued by using `+n` option as shown below.
```
<div class="src-block-caption">
<span class="src-block-number"><a href="#code-snippet--lst:tikz-test-general-control-names">Code Snippet 4</a>:</span>
Tikz code that is used to generate <a href="#orgd87d21e">5</a>
Tikz code that is used to generate <a href="#org7b171b1">5</a>
</div>
<a id="figure--fig:test-general-control-names"></a>