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tdehaeze committed 2020-12-04 23:54:53 +01:00
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@@ -17,7 +17,7 @@
#+BIND: org-latex-image-default-width ""
#+LaTeX_CLASS: scrreprt
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12]
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
#+LaTeX_HEADER_EXTRA: \input{preamble.tex}
#+CSL_STYLE: ieee.csl
@@ -50,7 +50,7 @@
* LaTeX Config :noexport:
#+begin_src emacs-lisp :tangle no
(setq org-latex-default-table-environment "tabular")
(setq org-latex-tables-booktabs nil)
(setq org-latex-tables-booktabs t)
#+end_src
#+begin_src latex :tangle preamble.tex
@@ -210,7 +210,6 @@ Therefore, for more advanced discussion, please have a look at the recommended r
When possible, Matlab scripts used for the example/exercises are provided such that you can easily test them on your computer.
The general structure of this document is as follows:
- A short introduction to /model based control/ is given in Section [[sec:model_based_control]]
- Classical /open/ loop shaping method is presented in Section [[sec:open_loop_shaping]].
@@ -316,7 +315,7 @@ Note that in parallel, there have been numerous other developments, including no
#+name: tab:comparison_control_methods
#+caption: Table summurazing the main differences between classical, modern and robust control
#+attr_latex: :environment tabularx :booktabs t :width \linewidth :align lccc
#+attr_latex: :environment tabularx :width \linewidth :align lccc
| <l> | <c> | <c> | <c> |
| | *Classical Control* | *Modern Control* | *Robust Control* |
|---------------+---------------------+--------------------------+-------------------------------|
@@ -468,17 +467,19 @@ The notations used on Figure [[fig:mech_sys_1dof_inertial_contr]] are listed and
#+name: tab:example_notations
#+caption: Example system variables
#+attr_latex: :environment tabularx :booktabs t :width \linewidth :align cXcc
#+attr_latex: :environment tabularx :width \linewidth :align cXcc
| *Notation* | *Description* | *Value* | *Unit* |
|--------------------+----------------------------------------------------------------+----------------+-----------|
| $m$ | Payload's mass to position / isolate | $10$ | [kg] |
| $k$ | Stiffness of the suspension system | $10^6$ | [N/m] |
| $c$ | Damping coefficient of the suspension system | $400$ | [N/(m/s)] |
|--------------------+----------------------------------------------------------------+----------------+-----------|
| $y$ | Payload absolute displacement (measured by an inertial sensor) | | [m] |
| $d$ | Ground displacement, it acts as a disturbance | | [m] |
| $u$ | Actuator force | | [N] |
| $r$ | Wanted position of the mass (the reference) | | [m] |
| $\epsilon = r - y$ | Position error | | [m] |
|--------------------+----------------------------------------------------------------+----------------+-----------|
| $K$ | Feedback controller | to be designed | [N/m] |
#+begin_exercice
@@ -563,12 +564,13 @@ The Bode plots of $G(s)$ and $G_d(s)$ are shown in Figures [[fig:bode_plot_examp
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-9, 1e-5]);
ax2 = nexttile;
hold on;
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G, freqs, 'Hz')))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
yticks(-360:90:360); ylim([-270, 90]);
yticks(-360:90:360); ylim([-200, 20]);
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
linkaxes([ax1,ax2],'x');
@@ -576,7 +578,7 @@ The Bode plots of $G(s)$ and $G_d(s)$ are shown in Figures [[fig:bode_plot_examp
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/bode_plot_example_afm.pdf', 'width', 'wide', 'height', 'normal');
exportFig('figs/bode_plot_example_afm.pdf', 'width', 'wide', 'height', 'tall');
#+end_src
#+name: fig:bode_plot_example_afm
@@ -845,7 +847,7 @@ Such shape corresponds to the typical wanted Loop gain Shape shown in Figure [[f
#+name: tab:open_loop_shaping_specifications
#+caption: Wanted Loop Shape corresponding to each specification
#+attr_latex: :environment tabularx :booktabs t :width \linewidth :align lXX
#+attr_latex: :environment tabularx :width \linewidth :align lXX
| | *Specification* | *Corresponding Loop Shape* |
|--------------+----------------------------------------+------------------------------------------|
| *Dist. Rej.* | Highest possible rejection below 1Hz | Slope of -40dB/dec at low frequency |
@@ -967,7 +969,7 @@ Let's finally compare the obtained stability margins of the $\mathcal{H}_\infty$
#+name: tab:open_loop_shaping_compare
#+caption: Comparison of the characteristics obtained with the two methods
#+attr_latex: :environment tabularx :booktabs t :width \linewidth :align Xcc
#+attr_latex: :environment tabularx :width \linewidth :align Xcc
#+RESULTS:
| *Specifications* | *Manual Method* | *$\mathcal{H}_\infty$ Method* |
|-----------------------------+-----------------+-------------------------------|
@@ -1108,7 +1110,7 @@ A practical example about how to derive the generalized plant for a classical co
#+name: tab:notation_general
#+caption: Notations for the general configuration
#+attr_latex: :environment tabularx :booktabs t :width 0.8\linewidth :align cX :float nil
#+attr_latex: :environment tabularx :width 0.8\linewidth :align cX :float nil
| *Notation* | *Meaning* |
|------------+----------------------------------------------------|
| $P$ | Generalized plant model |
@@ -1329,7 +1331,7 @@ These are summarized in Table [[tab:spec_closed_loop_tf]].
#+name: tab:spec_closed_loop_tf
#+caption: Typical Specification and associated closed-loop transfer function
#+attr_latex: :environment tabularx :booktabs t :width 0.8\linewidth :align Xl
#+attr_latex: :environment tabularx :width 0.8\linewidth :align Xl
| *Specification* | *CL Transfer Function* |
|--------------------------------+-----------------------------------------------|
| Reference Tracking | From $r$ to $\epsilon$ |
@@ -1409,7 +1411,7 @@ The comparison of the sensitivity functions shapes and their effect on the step
#+name: tab:compare_sensitivity_shapes
#+caption: Comparison of the sensitivity function shape and the corresponding step response for the three controller variations
#+attr_latex: :environment tabularx :booktabs t :width 0.9\linewidth :align lXX
#+attr_latex: :environment tabularx :width 0.9\linewidth :align lXX
| *Controller* | *Sensitivity Function Shape* | *Change of the Step Response* |
|--------------+----------------------------------------------------+----------------------------------|
| $K_1(s)$ | Larger bandwidth $\omega_b$ | Faster rise time |
@@ -1817,7 +1819,7 @@ And we now understand why setting an upper bound on the magnitude of $S$ is gene
#+name: tab:specification_modern
#+caption: Typical Specifications and corresponding wanted norms of open and closed loop tansfer functions
#+attr_latex: :environment tabularx :booktabs t :width 0.9\linewidth :align lXX
#+attr_latex: :environment tabularx :width 0.9\linewidth :align lXX
| | *Open-Loop Shaping* | *Closed-Loop Shaping* |
|-----------------------------+---------------------+--------------------------------------------|
| Reference Tracking | $L$ large | $S$ small |
@@ -2244,7 +2246,7 @@ When multiple closed-loop transfer function are shaped at the same time, it is r
#+name: tab:usual_shaping_gang_four
#+caption: Typical specifications and corresponding shaping of the /Gang of four/
#+attr_latex: :environment tabularx :booktabs t :width 0.9\linewidth :align llX
#+attr_latex: :environment tabularx :width 0.9\linewidth :align llX
| <l> | <c> | <l> |
| *Specifications* | *TF* | *Wanted shape* |
|-------------------------------+------+------------------------------------------------|
@@ -3029,7 +3031,7 @@ In such case, we want to shape $S$, $GS$ and $T$.
#+name: tab:ex_specification_shapes
#+caption: Control Specifications and associated wanted shape of the closed-loop transfer functions
#+attr_latex: :environment tabularx :booktabs t :width 0.7\linewidth :align llX
#+attr_latex: :environment tabularx :width 0.7\linewidth :align llX
| <l> | <c> | <l> |
| *Specification* | *TF* | *Wanted Shape* |
|--------------------------+-----------+------------------------------------|