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Thomas Dehaeze 22fb3361a5 Update Content - 2022-03-15

2022-03-15 16:40:48 +01:00

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+++ title = "test Page" author = ["Dehaeze Thomas"] draft = false +++

Basics

Normal Markup

You can make words bold, italic, underlined, verbatim and code, and, if you must, ~~strike-through~~.

Here is some inline code Matlab code: [K,CL,gamma] = mixsyn(G,W1,[],W3);.

Links to Footnotes

A link to a footnote¹ and to another footnote².

Lists

Unordered List:

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Nam aliquet euismod viverra.
Phasellus turpis nisi, faucibus a orci et, faucibus fermentum ligula.

List with Tasks:

Task 1
Task 2
[-] Sub-tasks:
- Sub-task 1
- Sub-task 2

Ordered List:

In libero odio, imperdiet eget ex a, vulputate suscipit tellus.
Etiam sed leo ex.
Integer eu rutrum turpis.

Nested Lists:

Nulla facilisi.
Donec vulputate risus ut lectus bibendum, vitae fringilla odio tempus.
1. In libero odio, imperdiet eget ex a, vulputate suscipit tellus.
2. Etiam sed leo ex.
  - Nulla facilisi.
  - Donec vulputate risus ut lectus bibendum, vitae fringilla odio tempus.
3. Integer eu rutrum turpis.
Ut porta, quam id mattis feugiat, augue mauris bibendum sapien, a pulvinar mi lorem vitae nunc.
- Integer eu rutrum turpis.
  - Sed pretium mattis nibh, vel lobortis augue semper vel.

Definition List:

Lorem ipsum: dolor sit amet, consectetur adipiscing elit. Mauris laoreet sollicitudin venenatis. Duis sed consequat dolor.
Etiam feugiat: pharetra sapien et semper. Nunc ornare lacus sit amet massa auctor, vitae aliquam eros interdum. Mauris arcu ante, imperdiet vel purus ac, bibendum faucibus diam. Ut blandit nec mi at ultricies. Donec eget mattis nisl. In sed nibh felis. Cras quis convallis orci.
Sed aliquam: odio sed faucibus aliquam, arcu augue elementum justo, ut vulputate ligula sem in augue. Maecenas ante felis, pellentesque auctor semper non, eleifend quis ante. Fusce enim orci, suscipit ac dapibus et, fermentum eu tortor. Duis in facilisis ante, quis faucibus dolor. Etiam maximus lorem quis accumsan vehicula.

Maths

Here is some inline mathematics: \(z = 2\).

Unumbered equation: \[ F(x) = \int_0^x f(t) dt \]

Using the equation environment in Eq. eq:numbered.

\begin{equation} F(s) = \int_0^\infty f(t) e^{-st} dt \label{eq:numbered} \end{equation}

Using the align environment Equations eq:align_1 and 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} \\ \int_D (\nabla\cdot \mathcal{F})\,dV &=\int_{\partial D}\mathcal{F}\cdot n\, dS \label{eq:align_2} \end{align}

Verse, Quote

Below is a verse.

Great clouds overhead
Tiny black birds rise and fall
Snow covers Emacs

---AlexSchroeder

Below is a quote.

Nobody ever figures out what life is all about, and it doesn't matter. Explore the world. Nearly everything is really interesting if you go into it deeply enough.

---Richard P. Feynman

Aside

An aside block can be used as shown below.

Cras elementum ex vel orci congue porttitor. Vestibulum scelerisque gravida mattis. Suspendisse sit amet volutpat felis. Cras luctus porta lectus eget scelerisque. Cras blandit purus vel odio malesuada pellentesque. Interdum et malesuada fames ac ante ipsum primis in faucibus. Morbi eget aliquet sapien. Nunc eu elit in ligula aliquam congue dapibus eu massa. Sed accumsan hendrerit viverra. Quisque purus enim, tristique vitae porttitor eu, feugiat non ligula. Duis vitae ipsum vel quam ultricies ornare quis vitae quam. Vivamus commodo mauris non ex rutrum, sagittis facilisis metus tincidunt. Etiam vel nibh sit amet lorem auctor volutpat vel quis nulla. Quisque nec pharetra justo.

Inline Task

Some text.

This is an inline task
nil

Some text.

Headlines

Second level Headline with tags @home@work

Third level Headline

Fourth level Headline

Aliquam aliquet sagittis lorem in rutrum. Cras pharetra viverra nisi, at placerat felis malesuada elementum. Donec tincidunt pharetra tincidunt. Praesent id lectus eget erat porttitor placerat non a magna. Cras non mauris ex. Morbi ut eros eu tellus egestas dapibus et et est. Aenean sollicitudin nibh enim, sed pulvinar massa iaculis sit amet. Vivamus egestas laoreet varius. Sed finibus libero nec quam tempor, eget viverra sapien fermentum. Donec dictum eleifend velit, vel elementum ex ultrices non. Vivamus mauris ex, ultrices quis sem vel, dapibus lacinia est. Praesent a sapien id diam venenatis finibus non vel justo. Cras sagittis tortor ac rutrum elementum. Maecenas luctus tempor enim, vitae suscipit quam consequat a. Phasellus feugiat congue sapien commodo cursus. Interdum et malesuada fames ac ante ipsum primis in faucibus.

Third level Headline

Fourth level Headline

Second level Headline with Schedule

Second level Headline with a priority

Second level Headline with TODO State

Vivamus egestas laoreet varius. Sed finibus libero nec quam tempor, eget viverra sapien fermentum. Donec dictum eleifend velit, vel elementum ex ultrices non. Vivamus mauris ex, ultrices quis sem vel, dapibus lacinia est. Praesent a sapien id diam venenatis finibus non vel justo.

Second level Headline with DONE State

Cras sagittis tortor ac rutrum elementum. Maecenas luctus tempor enim, vitae suscipit quam consequat a. Phasellus feugiat congue sapien commodo cursus. Interdum et malesuada fames ac ante ipsum primis in faucibus.

Third level Headline with DONE State

Cras non mauris ex. Morbi ut eros eu tellus egestas dapibus et et est. Aenean sollicitudin nibh enim, sed pulvinar massa iaculis sit amet.

Blocks

seealso block.

hint block.

definition block.

important block.

exampl block.

exercice block.

question block.

answer block.

summary block.

note block.

caution block.

warning block.

Source Blocks

Figures

  t = 0:0.01:5; % Time [s]
  x = sin(2*pi*t); % Output Voltage [V]

  figure;
  plot(t, x);
  xlabel('Time [s]'); ylabel('Voltage [V]');

{{< figure src="figs/matlab_fig_example.png" caption="Figure 1: Matlab Figure" >}}

Table Result

  x = 1:10;
  y = x.^2;

Table 1: Table caption

\(x\)	\(y = x^2\)
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100

Inline Results

Results can be automatically outputed as shown below.

  sqrt(2)

1.4142

y =
     1     4     9    16    25    36    49    64    81   100

Caption and Reference

Captions can be added to code blocks. Moreover, we can link to specific bode blocks (Listing 1 or 2).

  figure;
  [X,Y,Z] = peaks;
  contour(X,Y,Z,20)

Code Snippet 1: Code to produce a nice contour plot

{{< figure src="figs/matlab_logo.png" caption="Figure 2: Obtained Contour Plot" >}}

  A = [1 2; 3 4; 5 6; 7 8]
  [U,S,V] = svd(A)

Code Snippet 2: Code to compute the Singular Value Decomposition

A = [1 2; 3 4; 5 6; 7 8]
A =
     1     2
     3     4
     5     6
     7     8
[U,S,V] = svd(A)
U =
        -0.152483233310201         -0.82264747222566        -0.394501022283829        -0.379959133877596
        -0.349918371807964         -0.42137528768458         0.242796545704357         0.800655879510063
        -0.547353510305727       -0.0201031031435029         0.697909975442776        -0.461434357387336
         -0.74478864880349         0.381169081397575        -0.546205498863303        0.0407376117548695
S =
          14.2690954992615                         0
                         0         0.626828232417541
                         0                         0
                         0                         0
V =
        -0.641423027995072         0.767187395072177
        -0.767187395072177        -0.641423027995072

Source Blocks with Line Numbers

The Listing 3 has line numbers as the -n option was used.

Specific lines of codes can be referenced. For instance, the code used to specify the wanted the vertical label is on line 4.

{{< highlight matlab "linenos=table, linenostart=1, anchorlinenos=true, lineanchors=org-coderef--967846" >}} figure; plot(t, x) xlabel('Time [s]'); ylabel('Output [V]'); {{< /highlight >}}

Code Snippet 3: Specify Labels

Numbering can be continued by using +n option as shown below.



5
6
7
8


  figure;
  plot(t, u)
  xlabel('Time [s]');
  ylabel('Input [V]');

Images

Normal Image

Figure 3 shows the results of the Tikz code of listing 4.

  \begin{tikzpicture}

    % Blocs
    \node[block={2.0cm}{2.0cm}] (P) {$P$};
    \node[block={1.5cm}{1.5cm}, below=0.7 of P] (K) {$K$};

    % Input and outputs coordinates
    \coordinate[] (inputw)  at ($(P.south west)!0.75!(P.north west)$);
    \coordinate[] (inputu)  at ($(P.south west)!0.25!(P.north west)$);
    \coordinate[] (outputz) at ($(P.south east)!0.75!(P.north east)$);
    \coordinate[] (outputv) at ($(P.south east)!0.25!(P.north east)$);

    % Connections and labels
    \draw[<-] (inputw) node[above left, align=right]{(weighted)\\exogenous inputs\\$w$} -- ++(-1.5, 0);
    \draw[<-] (inputu) -- ++(-0.8, 0) |- node[left, near start, align=right]{control signals\\$u$} (K.west);

    \draw[->] (outputz) node[above right, align=left]{(weighted)\\exogenous outputs\\$z$} -- ++(1.5, 0);
    \draw[->] (outputv) -- ++(0.8, 0) |- node[right, near start, align=left]{sensed output\\$v$} (K.east);
  \end{tikzpicture}

Code Snippet 4: Tikz code that is used to generate Figure 3

{{< figure src="figs/general_control_names.png" caption="Figure 3: General Control Configuration" >}}

#+name: fig:general_control_names
#+caption: General Control Configuration
[[file:figs/general_control_names.png]]

Wrap Image

{{< figure src="figs/general_control_names.png" caption="Figure 4: General Control Configuration" >}}

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Pellentesque non semper turpis. Proin tristique ipsum at mauris viverra efficitur. Maecenas semper urna vitae hendrerit consectetur. Vivamus id odio et lectus pretium hendrerit ac in libero. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia curae; Pellentesque gravida, nibh vitae euismod mollis, dolor justo hendrerit mauris, sed dapibus velit magna ut purus. Mauris sagittis ligula in ante congue, vel rhoncus velit rutrum. In pulvinar elit nibh, a sodales enim iaculis sed. Maecenas et eleifend libero, vel congue urna. Praesent sit amet ornare lacus, nec maximus lectus.

Fusce blandit mauris dui, sed lobortis sapien tincidunt ac. Maecenas vitae molestie mi. Ut sodales euismod mauris, vitae finibus orci sagittis a. Quisque fringilla ante mi, vel aliquet est mollis in. Nam rutrum, nibh vitae tincidunt ultrices, quam urna efficitur ipsum, eget tristique lorem purus vitae metus. Maecenas dictum varius eros. Sed aliquam quis tortor in ultricies. Suspendisse imperdiet, mi eget mattis porta, felis quam gravida mi, malesuada venenatis dui dui a libero. Duis in lorem eget elit fermentum accumsan. Cras consequat eros vehicula, laoreet neque nec, tincidunt odio. Phasellus eu arcu lacus. Aliquam vel sollicitudin ipsum, sed iaculis risus. In pulvinar purus libero, quis vestibulum ex lacinia vel. Ut imperdiet ut erat non vulputate.

#+name: fig:general_control_names
#+caption: General Control Configuration
#+attr_html: :float wrap-left
#+attr_latex: :float wrap
[[file:figs/general_control_names.png]]

{{< figure src="figs/general_control_names.png" caption="Figure 5: General Control Configuration" >}}

Sub Images

Link to subfigure 2.

#+name: fig:subfigure
#+caption: Subfigure Caption
#+attr_latex: :environment subfigure :width 0.49\linewidth :align c
| file:figs/general_control_names.png                | file:figs/general_control_names.png                |
| <<fig:general_control_names_1>> sub figure caption | <<fig:general_control_names_2>> sub figure caption |

Table 2: Subfigure Caption


sub figure caption	sub figure caption

Tables

Table 3 shows a table with some mathematics inside.

Table 3: A Simple table with included math

\(N\)	\(N^2\)	\(N^3\)	\(N^4\)	\(\sqrt n\)	\(\sqrt[4]N\)
1	1	1	1	1	1
2	4	8	16	1.4142136	1.1892071
3	9	27	81	1.7320508	1.3160740

Table 4: Table without Head

	1	2	3	4	5
1	1	2	3	4	5
2	2	4	6	8	10
3	3	6	9	12	15
4	4	8	12	16	20
5	5	10	15	20	25

Table 5: Table with multiples groups

	Classical Control	Modern Control	Robust Control
Date	1930-	1960-	1980-
Tools	Transfer Functions	State Space formulation	Disk margin
	Nyquist Plots	Riccati Equations	Systems and Signals Norms (\(\mathcal{H}_\infty\), \(\mathcal{H}_2\) Norms)
	Bode Plots		Closed Loop Transfer Functions
	Phase and Gain margins		Weighting Functions
Control Architectures	Proportional, Integral, Derivative	Full State Feedback	General Control Configuration
	Leads, Lags	LQR, LQG
		Kalman Filters
Advantages	Study Stability	Automatic Synthesis	Automatic Synthesis
	Simple	MIMO	MIMO
	Natural	Optimization Problem	Optimization Problem
			Guaranteed Robustness
			Easy specification of performances
Disadvantages	Manual Method	No Guaranteed Robustness	Required knowledge of specific tools
	Only SISO	Difficult Rejection of Perturbations	Need a reasonably good model of the system

Details

Below is some content hidden until you click the bar.

Hiden Part

Almost anything can be put here for instance this table below.

Table 6: A Simple table with included math

\(N\)	\(N^2\)	\(N^3\)	\(N^4\)	\(\sqrt n\)	\(\sqrt[4]N\)
1	1	1	1	1	1
2	4	8	16	1.4142136	1.1892071
3	9	27	81	1.7320508	1.3160740

This details blocks can even be put in other blocks are shown below.

Answer

It is approximately 12,742 km

What is the approximate diameter of the earth?

Answer

It is approximately 12,742 km

Videos

Bibliography

A long foot note. Lorem ipsum dolor sit amet, consectetur adipiscing elit. With a reference to Figure 3. ↩︎
An other footnote. ↩︎

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Basics

Normal Markup

Links to Footnotes

Lists

Links

Maths

Verse, Quote

Aside

Inline Task

Headlines

Second level Headline with tags @home@work

Third level Headline

Fourth level Headline

Third level Headline

Fourth level Headline

Second level Headline with Schedule

Second level Headline with a priority

Second level Headline with TODO State

Second level Headline with DONE State

Third level Headline with DONE State

Blocks

Source Blocks

Figures

Table Result

Inline Results

Caption and Reference

Source Blocks with Line Numbers

Images

Normal Image

Wrap Image

Sub Images

Tables

Details

Videos

Bibliography

25 KiB

Raw Blame History