Update figures (half width)

matlab/index.org

@@ -23,6 +23,10 @@
 #+LATEX_CLASS: cleanreport
 #+LATEX_CLASS_OPTIONS: [tocnp, minted, secbreak]
 
+#+LATEX_HEADER_EXTRA: \usepackage[cache=false]{minted}
+#+LATEX_HEADER_EXTRA: \usemintedstyle{autumn}
+#+LATEX_HEADER_EXTRA: \setminted[matlab]{linenos=true, breaklines=true, tabsize=4, fontsize=\scriptsize, autogobble=true}
+
 #+LATEX_HEADER: \newcommand{\authorFirstName}{Thomas}
 #+LATEX_HEADER: \newcommand{\authorLastName}{Dehaeze}
 #+LATEX_HEADER: \newcommand{\authorEmail}{dehaeze.thomas@gmail.com}
@@ -72,12 +76,15 @@ In this example, the measured quantity $x$ is the velocity of an object.
 #+attr_latex: :environment tabular :align clc
 #+attr_latex: :center t :booktabs t :float t
 | *Notation*       | *Meaning*                         | *Unit*                    |
-|---------------+---------------------------------+---------|
+|------------------+-----------------------------------+---------------------------|
 | $x$              | Physical measured quantity        | $[m/s]$                   |
 | $\tilde{n}_i$    | White noise with unitary PSD      |                           |
 | $n_i$            | Shaped noise                      | $[m/s]$                   |
 | $v_i$            | Sensor output measurement         | $[V]$                     |
 | $\hat{x}_i$      | Estimate of $x$ from the sensor   | $[m/s]$                   |
+| $\Phi_n(\omega)$ | Power Spectral Density of $n$     | $[\frac{(m/s)^2}{Hz}]$    |
+| $\phi_n(\omega)$ | Amplitude Spectral Density of $n$ | $[\frac{m/s}{\sqrt{Hz}}]$ |
+| $\sigma_n$       | Root Mean Square Value of $n$     | $[m/s\ rms]$              |
 
 #+name: tab:sensor_dynamical_blocks
 #+caption: Description of Systems in Figure [[fig:sensor_model_noise_uncertainty]]
@@ -144,8 +151,8 @@ Both sensor dynamics in $[\frac{V}{m/s}]$ are shown in Figure [[fig:sensors_nomi
   plot(freqs, abs(squeeze(freqresp(G1, freqs, 'Hz'))), '-', 'DisplayName', '$G_1(j\omega)$');
   plot(freqs, abs(squeeze(freqresp(G2, freqs, 'Hz'))), '-', 'DisplayName', '$G_2(j\omega)$');
   set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-  ylabel('Magnitude $[\frac{V}{m/s}]$'); set(gca, 'XTickLabel',[]);
+  ylabel('Magnitude $\left[\frac{V}{m/s}\right]$'); set(gca, 'XTickLabel',[]);
-  legend('location', 'northeast');
+  legend('location', 'northeast', 'FontSize', 8);
   hold off;
 
   % Phase
@@ -163,7 +170,7 @@ Both sensor dynamics in $[\frac{V}{m/s}]$ are shown in Figure [[fig:sensors_nomi
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/sensors_nominal_dynamics.pdf', 'width', 'full', 'height', 'full');
+  exportFig('figs/sensors_nominal_dynamics.pdf', 'width', 'half', 'height', 'tall');
 #+end_src
 
 #+name: fig:sensors_nominal_dynamics
@@ -201,11 +208,11 @@ The bode plot of the sensors nominal dynamics as well as their defined dynamical
   xlabel('Frequency [Hz]'); ylabel('Magnitude');
   ylim([0, 5]);
   xlim([freqs(1), freqs(end)]);
-  legend('location', 'northwest');
+  legend('location', 'northwest', 'FontSize', 8);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/sensors_uncertainty_weights.pdf', 'width', 'wide', 'height', 'normal');
+  exportFig('figs/sensors_uncertainty_weights.pdf', 'width', 'half', 'height', 'short');
 #+end_src
 
 #+name: fig:sensors_uncertainty_weights
@@ -228,8 +235,9 @@ The bode plot of the sensors nominal dynamics as well as their defined dynamical
   set(gca, 'XTickLabel',[]);
   ylabel('Magnitude $[\frac{V}{m/s}]$');
   ylim([1e-2, 2e3]);
-  legend('location', 'northeast');
+  legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 2);
   hold off;
+  ylim([1e-2, 1e4])
 
   % Phase
   ax2 = subplot(2,1,2);
@@ -250,7 +258,7 @@ The bode plot of the sensors nominal dynamics as well as their defined dynamical
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/sensors_nominal_dynamics_and_uncertainty.pdf', 'width', 'full', 'height', 'full');
+  exportFig('figs/sensors_nominal_dynamics_and_uncertainty.pdf', 'width', 'half', 'height', 'tall');
 #+end_src
 
 #+name: fig:sensors_nominal_dynamics_and_uncertainty
@@ -285,14 +293,14 @@ The weights $N_1$ and $N_2$ representing the amplitude spectral density of the s
   plot(freqs, abs(squeeze(freqresp(N1, freqs, 'Hz'))), '-', 'DisplayName', '$|N_1(j\omega)|$');
   plot(freqs, abs(squeeze(freqresp(N2, freqs, 'Hz'))), '-', 'DisplayName', '$|N_2(j\omega)|$');
   set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[ \frac{m/s}{\sqrt{Hz}} \right]$');
+  xlabel('Frequency [Hz]'); ylabel('ASD $\left[ \frac{m/s}{\sqrt{Hz}} \right]$');
   hold off;
   xlim([freqs(1), freqs(end)]);
-  legend('location', 'northeast');
+  legend('location', 'northeast', 'FontSize', 8);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/sensors_noise.pdf', 'width', 'normal', 'height', 'normal');
+  exportFig('figs/sensors_noise.pdf', 'width', 'half', 'height', 'short');
 #+end_src
 
 #+name: fig:sensors_noise
@@ -387,10 +395,6 @@ The uncertainty set of the transfer function from $\hat{x}$ to $x$ at frequency
 ** Introduction                                                      :ignore:
 In this section, the complementary filters $H_1(s)$ and $H_2(s)$ are designed in order to minimize the RMS value of super sensor noise $\sigma_n$.
 
-#+name: fig:sensor_fusion_noise_arch
-#+caption: Optimal Sensor Fusion Architecture
-[[file:figs-tikz/sensor_fusion_noise_arch.png]]
-
 The RMS value of the super sensor noise is (neglecting the model uncertainty):
 \begin{equation}
 \begin{aligned}
@@ -479,7 +483,7 @@ The obtained complementary filters are shown in Figure [[fig:htwo_comp_filters]]
   set(gca, 'XTickLabel',[]);
   ylabel('Magnitude');
   hold off;
-  legend('location', 'northeast');
+  legend('location', 'northeast', 'FontSize', 8);
 
   % Phase
   ax2 = subplot(2,1,2);
@@ -496,7 +500,7 @@ The obtained complementary filters are shown in Figure [[fig:htwo_comp_filters]]
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/htwo_comp_filters.pdf', 'width', 'full', 'height', 'tall');
+  exportFig('figs/htwo_comp_filters.pdf', 'width', 'half', 'height', 'tall');
 #+end_src
 
 #+name: fig:htwo_comp_filters
@@ -507,7 +511,7 @@ The obtained complementary filters are shown in Figure [[fig:htwo_comp_filters]]
 ** Super Sensor Noise
 <<sec:H2_super_sensor_noise>>
 
-The Power Spectral Density of the individual sensors' noise $\Phi_{n_1}, \Phi_{n_2}$ and of the super sensor noise $\Phi_{n_{\mathcal{H}_2}}$ are computed below and shown in Figure [[fig:psd_sensors_htwo_synthesis]].
+The Power Spectral Density of the individual sensors' noise $\Phi_{n_1}, \Phi_{n_2}$ and of the super sensor noise $\Phi_{n_{\mathcal{H}_2}}$ are computed below.
 #+begin_src matlab
   PSD_S1 = abs(squeeze(freqresp(N1,    freqs, 'Hz'))).^2;
   PSD_S2 = abs(squeeze(freqresp(N2,    freqs, 'Hz'))).^2;
@@ -515,6 +519,8 @@ The Power Spectral Density of the individual sensors' noise $\Phi_{n_1}, \Phi_{n
            abs(squeeze(freqresp(N2*H2, freqs, 'Hz'))).^2;
 #+end_src
 
+The obtained ASD are shown in Figure [[fig:psd_sensors_htwo_synthesis]].
+
 The RMS value of the individual sensors and of the super sensor are listed in Table [[tab:rms_noise_H2]].
 #+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
   data2orgtable([sqrt(trapz(freqs, PSD_S1)); sqrt(trapz(freqs, PSD_S2)); sqrt(trapz(freqs, PSD_H2))], ...
@@ -536,18 +542,18 @@ The RMS value of the individual sensors and of the super sensor are listed in Ta
 #+begin_src matlab :exports none
   figure;
   hold on;
-  plot(freqs, PSD_S1, '-',  'DisplayName', '$\Phi_{n_1}$');
+  plot(freqs, sqrt(PSD_S1), '-',  'DisplayName', '$\phi_{n_1}$');
-  plot(freqs, PSD_S2, '-',  'DisplayName', '$\Phi_{n_2}$');
+  plot(freqs, sqrt(PSD_S2), '-',  'DisplayName', '$\phi_{n_2}$');
-  plot(freqs, PSD_H2, 'k-', 'DisplayName', '$\Phi_{n_{\mathcal{H}_2}}$');
+  plot(freqs, sqrt(PSD_H2), 'k-', 'DisplayName', '$\phi_{n_{\mathcal{H}_2}}$');
   set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('Power Spectral Density $\left[ \frac{(m/s)^2}{Hz} \right]$');
+  xlabel('Frequency [Hz]'); ylabel('ASD $\left[ \frac{m/s}{\sqrt{Hz}} \right]$');
   hold off;
   xlim([freqs(1), freqs(end)]);
-  legend('location', 'northeast');
+  legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/psd_sensors_htwo_synthesis.pdf', 'width', 'wide', 'height', 'normal');
+  exportFig('figs/psd_sensors_htwo_synthesis.pdf', 'width', 'half', 'height', 'short');
 #+end_src
 
 #+name: fig:psd_sensors_htwo_synthesis
@@ -585,12 +591,12 @@ The resulting noises are displayed in Figure [[fig:sensor_noise_H2_time_domain]]
   plot(t, v, 'k--', 'DisplayName', '$x$');
   hold off;
   xlabel('Time [s]'); ylabel('Velocity [m/s]');
-  legend('location', 'southwest');
+  legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
   ylim([-0.3, 0.3]);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/super_sensor_time_domain_h2.pdf', 'width', 'wide', 'height', 'normal');
+  exportFig('figs/super_sensor_time_domain_h2.pdf', 'width', 'half', 'height', 'normal');
 #+end_src
 
 #+name: fig:super_sensor_time_domain_h2
@@ -609,12 +615,12 @@ The resulting noises are displayed in Figure [[fig:sensor_noise_H2_time_domain]]
   plot(t, (lsim(H1, n1, t)+lsim(H2, n2, t)), '-', 'DisplayName', '$n$');
   hold off;
   xlabel('Time [s]'); ylabel('Sensor Noise [m/s]');
-  legend();
+  legend('FontSize', 8);
   ylim([-0.2, 0.2]);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/sensor_noise_H2_time_domain.pdf', 'width', 'wide', 'height', 'normal');
+  exportFig('figs/sensor_noise_H2_time_domain.pdf', 'width', 'half', 'height', 'normal');
 #+end_src
 
 #+name: fig:sensor_noise_H2_time_domain
@@ -647,7 +653,7 @@ As a result the super sensor signal can not be used for feedback applications ab
   set(gca, 'XTickLabel',[]);
   ylabel('Magnitude');
   ylim([1e-2, 1e1]);
-  legend('location', 'southeast');
+  legend('location', 'southeast', 'FontSize', 8);
   hold off;
 
   % Phase
@@ -667,7 +673,7 @@ As a result the super sensor signal can not be used for feedback applications ab
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/super_sensor_dynamical_uncertainty_H2.pdf', 'width', 'full', 'height', 'full');
+  exportFig('figs/super_sensor_dynamical_uncertainty_H2.pdf', 'width', 'half', 'height', 'tall');
 #+end_src
 
 #+name: fig:super_sensor_dynamical_uncertainty_H2
@@ -777,7 +783,7 @@ The uncertainty bounds of the two individual sensor as well as the wanted maximu
   set(gca, 'XTickLabel',[]);
   ylabel('Magnitude');
   ylim([1e-2, 1e1]);
-  legend('location', 'southeast');
+  legend('location', 'southeast', 'FontSize', 8);
   hold off;
 
   % Phase
@@ -797,7 +803,7 @@ The uncertainty bounds of the two individual sensor as well as the wanted maximu
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/weight_uncertainty_bounds_Wu.pdf', 'width', 'full', 'height', 'full');
+  exportFig('figs/weight_uncertainty_bounds_Wu.pdf', 'width', 'half', 'height', 'tall');
 #+end_src
 
 #+name: fig:weight_uncertainty_bounds_Wu
@@ -878,16 +884,15 @@ The obtained complementary filters as well as the wanted upper bounds are shown
   hold on;
   plot(freqs, 1./abs(squeeze(freqresp(Wu*W1, freqs, 'Hz'))), '--', 'DisplayName', '$1/|W_uW_1|$');
   plot(freqs, 1./abs(squeeze(freqresp(Wu*W2, freqs, 'Hz'))), '--', 'DisplayName', '$1/|W_uW_2|$');
-
   set(gca,'ColorOrderIndex',1)
-  plot(freqs, abs(squeeze(freqresp(H1, freqs, 'Hz'))), '-', 'DisplayName', '$H_1$');
+  plot(freqs, abs(squeeze(freqresp(H1, freqs, 'Hz'))), '-', 'DisplayName', '$|H_1|$');
-  plot(freqs, abs(squeeze(freqresp(H2, freqs, 'Hz'))), '-', 'DisplayName', '$H_2$');
+  plot(freqs, abs(squeeze(freqresp(H2, freqs, 'Hz'))), '-', 'DisplayName', '$|H_2|$');
 
   hold off;
   set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
   ylabel('Magnitude');
   set(gca, 'XTickLabel',[]);
-  legend('location', 'northeast');
+  legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
 
   ax2 = subplot(2,1,2);
   hold on;
@@ -903,7 +908,7 @@ The obtained complementary filters as well as the wanted upper bounds are shown
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/hinf_comp_filters.pdf', 'width', 'full', 'height', 'full');
+  exportFig('figs/hinf_comp_filters.pdf', 'width', 'half', 'height', 'tall');
 #+end_src
 
 #+name: fig:hinf_comp_filters
@@ -942,7 +947,7 @@ The $\mathcal{H}_\infty$ synthesis thus allows to design filters such that the s
   set(gca, 'XTickLabel',[]);
   ylabel('Magnitude');
   ylim([1e-2, 1e1]);
-  legend('location', 'southeast');
+  legend('location', 'southeast', 'FontSize', 8);
   hold off;
 
   % Phase
@@ -964,7 +969,7 @@ The $\mathcal{H}_\infty$ synthesis thus allows to design filters such that the s
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/super_sensor_dynamical_uncertainty_Hinf.pdf', 'width', 'full', 'height', 'full');
+  exportFig('figs/super_sensor_dynamical_uncertainty_Hinf.pdf', 'width', 'half', 'height', 'tall');
 #+end_src
 
 #+name: fig:super_sensor_dynamical_uncertainty_Hinf
@@ -973,10 +978,8 @@ The $\mathcal{H}_\infty$ synthesis thus allows to design filters such that the s
 [[file:figs/super_sensor_dynamical_uncertainty_Hinf.png]]
 
 ** Super sensor noise
-We now compute the obtain Power Spectral Density of the super sensor's noise (Figure [[fig:psd_sensors_hinf_synthesis]]).
+We now compute the obtain Power Spectral Density of the super sensor's noise.
-
+The Amplitude Spectral Densities are shown in Figure [[fig:psd_sensors_hinf_synthesis]].
-The obtained RMS of the super sensor noise in the $\mathcal{H}_2$ and $\mathcal{H}_\infty$ case are shown in Table [[tab:rms_noise_comp_H2_Hinf]].
-As expected, the super sensor obtained from the $\mathcal{H}_\infty$ synthesis is much noisier than the super sensor obtained from the $\mathcal{H}_2$ synthesis.
 
 #+begin_src matlab
   PSD_S2   = abs(squeeze(freqresp(N2,    freqs, 'Hz'))).^2;
@@ -985,6 +988,9 @@ As expected, the super sensor obtained from the $\mathcal{H}_\infty$ synthesis i
              abs(squeeze(freqresp(N2*H2, freqs, 'Hz'))).^2;
 #+end_src
 
+The obtained RMS of the super sensor noise in the $\mathcal{H}_2$ and $\mathcal{H}_\infty$ case are shown in Table [[tab:rms_noise_comp_H2_Hinf]].
+As expected, the super sensor obtained from the $\mathcal{H}_\infty$ synthesis is much noisier than the super sensor obtained from the $\mathcal{H}_2$ synthesis.
+
 #+begin_src matlab :exports none
   H2_filters = load('./mat/H2_filters.mat', 'H2', 'H1');
 
@@ -995,19 +1001,19 @@ As expected, the super sensor obtained from the $\mathcal{H}_\infty$ synthesis i
 #+begin_src matlab :exports none
   figure;
   hold on;
-  plot(freqs, PSD_S1,   '-',   'DisplayName', '$\Phi_{n_1}$');
+  plot(freqs, sqrt(PSD_S1),   '-',   'DisplayName', '$\phi_{n_1}$');
-  plot(freqs, PSD_S2,   '-',   'DisplayName', '$\Phi_{n_2}$');
+  plot(freqs, sqrt(PSD_S2),   '-',   'DisplayName', '$\phi_{n_2}$');
-  plot(freqs, PSD_H2,   'k-',  'DisplayName', '$\Phi_{n_{\mathcal{H}_2}}$');
+  plot(freqs, sqrt(PSD_H2),   'k-',  'DisplayName', '$\phi_{n_{\mathcal{H}_2}}$');
-  plot(freqs, PSD_Hinf, 'k--', 'DisplayName', '$\Phi_{n_{\mathcal{H}_\infty}}$');
+  plot(freqs, sqrt(PSD_Hinf), 'k--', 'DisplayName', '$\phi_{n_{\mathcal{H}_\infty}}$');
   set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('Power Spectral Density $\left[ \frac{(m/s)^2}{Hz} \right]$');
+  xlabel('Frequency [Hz]'); ylabel('ASD $\left[ \frac{m/s}{\sqrt{Hz}} \right]$');
   hold off;
   xlim([freqs(1), freqs(end)]);
-  legend('location', 'northeast');
+  legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/psd_sensors_hinf_synthesis.pdf', 'width', 'wide', 'height', 'normal');
+  exportFig('figs/psd_sensors_hinf_synthesis.pdf', 'width', 'half', 'height', 'normal');
 #+end_src
 
 #+name: fig:psd_sensors_hinf_synthesis
@@ -1135,7 +1141,7 @@ The obtained complementary filters are shown in Figure [[fig:htwo_hinf_comp_filt
   ylabel('Magnitude');
   set(gca, 'XTickLabel',[]);
   ylim([1e-3, 2]);
-  legend('location', 'southwest');
+  legend('location', 'southeast', 'FontSize', 8);
 
   ax2 = subplot(2,1,2);
   hold on;
@@ -1151,7 +1157,7 @@ The obtained complementary filters are shown in Figure [[fig:htwo_hinf_comp_filt
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/htwo_hinf_comp_filters.pdf', 'width', 'full', 'height', 'full');
+  exportFig('figs/htwo_hinf_comp_filters.pdf', 'width', 'half', 'height', 'tall');
 #+end_src
 
 #+name: fig:htwo_hinf_comp_filters
@@ -1160,7 +1166,7 @@ The obtained complementary filters are shown in Figure [[fig:htwo_hinf_comp_filt
 [[file:figs/htwo_hinf_comp_filters.png]]
 
 ** Obtained Super Sensor's noise
-The Power Spectral Density of the super sensor's noise is shown in Figure [[fig:psd_sensors_htwo_hinf_synthesis]].
+The Amplitude Spectral Density of the super sensor's noise is shown in Figure [[fig:psd_sensors_htwo_hinf_synthesis]].
 
 A time domain simulation is shown in Figure [[fig:super_sensor_time_domain_h2_hinf]].
 
@@ -1190,20 +1196,20 @@ The RMS values of the super sensor noise for the presented three synthesis are l
 #+begin_src matlab :exports none
   figure;
   hold on;
-  plot(freqs, PSD_S1,     '-',   'DisplayName', '$\Phi_{n_1}$');
+  plot(freqs, sqrt(PSD_S1),     '-',   'DisplayName', '$\Phi_{n_1}$');
-  plot(freqs, PSD_S2,     '-',   'DisplayName', '$\Phi_{n_2}$');
+  plot(freqs, sqrt(PSD_S2),     '-',   'DisplayName', '$\Phi_{n_2}$');
-  plot(freqs, PSD_H2,     'k-',  'DisplayName', '$\Phi_{n_{\mathcal{H}_2}}$');
+  plot(freqs, sqrt(PSD_H2),     'k-',  'DisplayName', '$\Phi_{n_{\mathcal{H}_2}}$');
-  plot(freqs, PSD_Hinf,   'k--', 'DisplayName', '$\Phi_{n_{\mathcal{H}_\infty}}$');
+  plot(freqs, sqrt(PSD_Hinf),   'k--', 'DisplayName', '$\Phi_{n_{\mathcal{H}_\infty}}$');
-  plot(freqs, PSD_H2Hinf, 'k-.', 'DisplayName', '$\Phi_{n_{\mathcal{H}_2/\mathcal{H}_\infty}}$');
+  plot(freqs, sqrt(PSD_H2Hinf), 'k-.', 'DisplayName', '$\Phi_{n_{\mathcal{H}_2/\mathcal{H}_\infty}}$');
   set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('Power Spectral Density [$(m/s)^2/Hz$]');
+  xlabel('Frequency [Hz]'); ylabel('ASD $\left[ \frac{m/s}{\sqrt{Hz}} \right]$');
   hold off;
   xlim([freqs(1), freqs(end)]);
-  legend('location', 'northeast');
+  legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 3);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/psd_sensors_htwo_hinf_synthesis.pdf', 'width', 'wide', 'height', 'normal');
+  exportFig('figs/psd_sensors_htwo_hinf_synthesis.pdf', 'width', 'half', 'height', 'normal');
 #+end_src
 
 #+name: fig:psd_sensors_htwo_hinf_synthesis
@@ -1236,12 +1242,12 @@ The RMS values of the super sensor noise for the presented three synthesis are l
   plot(t, v, 'k--', 'DisplayName', '$x$');
   hold off;
   xlabel('Time [s]'); ylabel('Velocity [m/s]');
-  legend('location', 'southwest');
+  legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 3);
   ylim([-0.3, 0.3]);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/super_sensor_time_domain_h2_hinf.pdf', 'width', 'wide', 'height', 'normal');
+  exportFig('figs/super_sensor_time_domain_h2_hinf.pdf', 'width', 'half', 'height', 'normal');
 #+end_src
 
 #+name: fig:super_sensor_time_domain_h2_hinf
@@ -1294,7 +1300,7 @@ The uncertainty on the super sensor's dynamics is shown in Figure [[fig:super_se
   set(gca, 'XTickLabel',[]);
   ylabel('Magnitude');
   ylim([1e-2, 1e1]);
-  legend('location', 'southeast');
+  legend('location', 'southeast', 'FontSize', 8);
   hold off;
 
   % Phase
@@ -1316,7 +1322,7 @@ The uncertainty on the super sensor's dynamics is shown in Figure [[fig:super_se
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-  exportFig('figs/super_sensor_dynamical_uncertainty_Htwo_Hinf.pdf', 'width', 'full', 'height', 'full');
+  exportFig('figs/super_sensor_dynamical_uncertainty_Htwo_Hinf.pdf', 'width', 'half', 'height', 'tall');
 #+end_src
 
 #+name: fig:super_sensor_dynamical_uncertainty_Htwo_Hinf