#+caption: Uncertainty region of the super sensor dynamics in the complex plane (solid circle), of the sensor 1 (dotted circle) and of the sensor 2 (dashed circle) ([[./figs/uncertainty_set_super_sensor.png][png]], [[./figs/uncertainty_set_super_sensor.pdf][pdf]], [[./figs/uncertainty_set_super_sensor.tex][tex]]).
#+caption: Architecture used for $\mathcal{H}_\infty$ synthesis of complementary filters ([[./figs/h_infinity_robust_fusion.png][png]], [[./figs/h_infinity_robust_fusion.pdf][pdf]], [[./figs/h_infinity_robust_fusion.tex][tex]]).
\addlegendimage{color=mycolor1, dashed, line width=1.5pt}
\addlegendentry{$W_1^{-1}$};
\addlegendimage{color=mycolor2, dashed, line width=1.5pt}
\addlegendentry{$W_2^{-1}$};
\addplot [color=mycolor1, line width=1.5pt]
table [x=freqs, y=H1p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
\addlegendentry{$H_1$};
\addplot [color=mycolor2, line width=1.5pt]
table [x=freqs, y=H2p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
\addlegendentry{$H_2$};
\end{axis}
\end{tikzpicture}
#+end_src
#+name: fig:hinf_synthesis_results
#+caption: Frequency response of the weighting functions and complementary filters obtained using $\mathcal{H}_\infty$ synthesis ([[./figs/hinf_synthesis_results.png][png]], [[./figs/hinf_synthesis_results.pdf][pdf]], [[./figs/hinf_synthesis_results.tex][tex]]).
#+caption: Architecture for $\mathcal{H}_\infty$ synthesis of three complementary filters ([[./figs/comp_filter_three_hinf.png][png]], [[./figs/comp_filter_three_hinf.pdf][pdf]], [[./figs/comp_filter_three_hinf.tex][tex]]).
\addplot [color=mycolor1, dashed, line width=1.5pt]
table [x=freqs, y=W1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_weights.csv};
\addlegendentry{${W_1}^{-1}$};
\addplot [color=mycolor1, line width=1.5pt]
table [x=freqs, y=H1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
\addlegendentry{$H_1$};
\addplot [color=mycolor2, dashed, line width=1.5pt]
table [x=freqs, y=W2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_weights.csv};
\addlegendentry{${W_2}^{-1}$};
\addplot [color=mycolor2, line width=1.5pt]
table [x=freqs, y=H2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
\addlegendentry{$H_2$};
\addplot [color=mycolor3, dashed, line width=1.5pt]
table [x=freqs, y=W3, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_weights.csv};
\addlegendentry{${W_3}^{-1}$};
\addplot [color=mycolor3, line width=1.5pt]
table [x=freqs, y=H3, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
\addlegendentry{$H_3$};
\end{axis}
\begin{axis}[%
width=1.0\fwidth,
height=0.4\fheight,
at={(0.0\fwidth, 0.0\fheight)},
scale only axis,
xmode=log,
xmin=0.1,
xmax=100,
xminorticks=true,
xlabel={Frequency [Hz]},
ymin=-240,
ymax=240,
ytick={-180, -90, 0, 90, 180},
ylabel={Phase [deg]},
xminorgrids,
]
\addplot [color=mycolor1, line width=1.5pt]
table [x=freqs, y=H1p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
\addplot [color=mycolor2, line width=1.5pt]
table [x=freqs, y=H2p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
\addplot [color=mycolor3, line width=1.5pt]
table [x=freqs, y=H3p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
\end{axis}
\end{tikzpicture}
#+end_src
#+name: fig:hinf_three_synthesis_results
#+caption: Frequency response of the weighting functions and three complementary filters obtained using $\mathcal{H}_\infty$ synthesis ([[./figs/hinf_three_synthesis_results.png][png]], [[./figs/hinf_three_synthesis_results.pdf][pdf]], [[./figs/hinf_three_synthesis_results.tex][tex]]).
table [x=freqs, y=wHm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matligo_weights.csv};
\addlegendentry{$|w_H|^{-1}$}
\addplot [color=mycolor2, line width=1.5pt]
table [x=freqs, y=wLm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matligo_weights.csv};
\addlegendentry{$|w_L|^{-1}$}
\addplot [color=black, dotted, line width=1.5pt]
table[row sep=crcr]{%
0.0005 0.008\\
0.008 0.008\\
};
\addlegendentry{Specifications}
\addplot [color=black, dotted, line width=1.5pt, forget plot]
table[row sep=crcr]{%
0.008 0.008\\
0.04 1\\
};
\addplot [color=black, dotted, line width=1.5pt, forget plot]
table[row sep=crcr]{%
0.04 3\\
0.1 3\\
};
\addplot [color=black, dotted, line width=1.5pt]
table[row sep=crcr]{%
0.1 0.045\\
2 0.045\\
};
\end{axis}
\end{tikzpicture}
#+end_src
#+name: fig:ligo_weights
#+caption: Specifications and weighting functions magnitude used for $\mathcal{H}_\infty$ synthesis ([[./figs/ligo_weights.png][png]], [[./figs/ligo_weights.pdf][pdf]], [[./figs/ligo_weights.tex][tex]]).
table [x=freqs, y=Hhm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
\addlegendentry{$H_H(s)$ - $\mathcal{H}_\infty$}
\addplot [color=mycolor1, dashed, line width=1.5pt]
table [x=freqs, y=Hhm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
\addlegendentry{$H_H(s)$ - FIR}
\addplot [color=mycolor2, line width=1.5pt]
table [x=freqs, y=Hlm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
\addlegendentry{$H_L(s)$ - $\mathcal{H}_\infty$}
\addplot [color=mycolor2, dashed, line width=1.5pt]
table [x=freqs, y=Hlm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
\addlegendentry{$H_L(s)$ - FIR}
\end{axis}
\begin{axis}[%
width=1.0\fwidth,
height=0.3\fheight,
at={(0.0\fwidth, 0.0\fheight)},
scale only axis,
xmode=log,
xmin=0.001,
xmax=1,
xtick={0.001, 0.01, 0.1, 1},
xminorticks=true,
xlabel={Frequency [Hz]},
ymin=-180,
ymax=180,
ytick={-180, -90, 0, 90, 180},
ylabel={Phase [deg]},
xminorgrids,
]
\addplot [color=mycolor1, line width=1.5pt, forget plot]
table [x=freqs, y=Hhp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
\addplot [color=mycolor1, dashed, line width=1.5pt, forget plot]
table [x=freqs, y=Hhp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
\addplot [color=mycolor2, line width=1.5pt, forget plot]
table [x=freqs, y=Hlp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
\addplot [color=mycolor2, dashed, line width=1.5pt, forget plot]
table [x=freqs, y=Hlp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
\end{axis}
\end{tikzpicture}
#+end_src
#+name: fig:comp_fir_ligo_hinf
#+caption: Comparison of the FIR filters (solid) with the filters obtained with $\mathcal{H}_\infty$ synthesis (dashed) ([[./figs/comp_fir_ligo_hinf.png][png]], [[./figs/comp_fir_ligo_hinf.pdf][pdf]], [[./figs/comp_fir_ligo_hinf.tex][tex]]).