Rework all the Matlab computation

paper/paper.org

@@ -320,7 +320,7 @@ Let's validate the proposed design method of complementary filters with a simple
 - the gain of both filters is equal to $10^{-3}$ away from the merging frequency
 
 The weighting functions $W_1(s)$ and $W_2(s)$ are designed using eqref:eq:weight_formula.
-The parameters used are summarized in table ref:tab:weights_params and the magnitude of the weighting functions is shown in Fig. ref:fig:hinf_synthesis_results.
+The parameters used are summarized in table ref:tab:weights_params and the magnitude of the weighting functions is shown in Fig. ref:fig:hinf_filters_results.
 
 #+name: tab:weights_params
 #+caption: Parameters used for $W_1(s)$ and $W_2(s)$
@@ -334,16 +334,16 @@ The parameters used are summarized in table ref:tab:weights_params and the magni
 | $G_c$                  | $0.5$    | $0.5$    |
 | $n$                    | $2$      | $3$      |
 
-The bode plots of the obtained complementary filters are shown in Fig. ref:fig:hinf_synthesis_results and their transfer functions in the Laplace domain are given below.
+The bode plots of the obtained complementary filters are shown in Fig. ref:fig:hinf_filters_results and their transfer functions in the Laplace domain are given below.
 \begin{align*}
   H_1(s) &= \frac{10^{-8} (s+6.6e^9) (s+3450)^2 (s^2 + 49s + 895)}{(s+6.6e^4) (s^2 + 106 s + 3e^3) (s^2 + 72s + 3580)}\\
   H_2(s) &= \frac{(s+6.6e^4) (s+160) (s+4)^3}{(s+6.6e^4) (s^2 + 106 s + 3e^3) (s^2 + 72s + 3580)}
 \end{align*}
 
-#+name: fig:hinf_synthesis_results
+#+name: fig:hinf_filters_results
 #+caption: Frequency response of the weighting functions and complementary filters obtained using $\mathcal{H}_\infty$ synthesis
 #+attr_latex: :scale 1
-[[file:figs/hinf_synthesis_results.pdf]]
+[[file:figs/hinf_filters_results.pdf]]
 
 ** Synthesis of Three Complementary Filters
 <<sec:hinf_three_comp_filters>>
@@ -380,13 +380,13 @@ By choosing $H_1(s) \triangleq 1 - H_2(s) - H_3(s)$, the proposed $\mathcal{H}_\
 
 *** Example of generated complementary filters                     :ignore:
 An example is given to validate the method where three sensors are used in different frequency bands (up to $\SI{1}{Hz}$, from $1$ to $\SI{10}{Hz}$ and above $\SI{10}{Hz}$ respectively).
-Three weighting functions are designed using eqref:eq:weight_formula and shown by dashed curves in Fig. ref:fig:hinf_three_synthesis_results.
-The bode plots of the obtained complementary filters are shown in Fig. ref:fig:hinf_three_synthesis_results.
+Three weighting functions are designed using eqref:eq:weight_formula and shown by dashed curves in Fig. ref:fig:three_complementary_filters_results.
+The bode plots of the obtained complementary filters are shown in Fig. ref:fig:three_complementary_filters_results.
 
-#+name: fig:hinf_three_synthesis_results
+#+name: fig:three_complementary_filters_results
 #+caption: Frequency response of the weighting functions and three complementary filters obtained using $\mathcal{H}_\infty$ synthesis
 #+attr_latex: :scale 1
-[[file:figs/hinf_three_synthesis_results.pdf]]
+[[file:figs/three_complementary_filters_results.pdf]]
 
 * Application: Design of Complementary Filters used in the Active Vibration Isolation System at the LIGO
 <<sec:application_ligo>>