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< title > Complementary Filters Shaping Using \(\mathcal{H}_\infty\) Synthesis - Tikz Figures< / title >
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< h1 class = "title" > Complementary Filters Shaping Using \(\mathcal{H}_\infty\) Synthesis - Tikz Figures< / h1 >
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< h2 > Table of Contents< / h2 >
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< li > < a href = "#org9059d4e" > 1. Fig 1: Sensor Fusion Architecture< / a > < / li >
< li > < a href = "#orgf8987c9" > 2. Fig 2: Sensor fusion architecture with sensor dynamics uncertainty< / a > < / li >
< li > < a href = "#org1801a90" > 3. Fig 3: Uncertainty set of the super sensor dynamics< / a > < / li >
< li > < a href = "#org355bde0" > 4. Fig 4: Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters< / a > < / li >
< li > < a href = "#org879ecb3" > 5. Fig 5: Magnitude of a weighting function generated using the proposed formula< / a > < / li >
< li > < a href = "#org2b1f7ae" > 6. Fig 6: Frequency response of the weighting functions and complementary filters obtained using \(\mathcal{H}_\infty\) synthesis< / a > < / li >
< li > < a href = "#org84a7e33" > 7. Fig 7: Architecture for \(\mathcal{H}_\infty\) synthesis of three complementary filters< / a > < / li >
< li > < a href = "#org20bfce3" > 8. Fig 8: Frequency response of the weighting functions and three complementary filters obtained using \(\mathcal{H}_\infty\) synthesis< / a > < / li >
< li > < a href = "#orgb08c277" > 9. Fig 9: Specifications and weighting functions magnitude used for \(\mathcal{H}_\infty\) synthesis< / a > < / li >
< li > < a href = "#org74b4762" > 10. Fig 10: Comparison of the FIR filters (solid) with the filters obtained with \(\mathcal{H}_\infty\) synthesis (dashed)< / a > < / li >
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Configuration file is accessible < a href = "config.html" > here< / a > .
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< h2 id = "org9059d4e" > < span class = "section-number-2" > 1< / span > Fig 1: Sensor Fusion Architecture< / h2 >
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< div id = "org9c10944" class = "figure" >
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< p > < img src = "figs/fusion_super_sensor.png" alt = "fusion_super_sensor.png" / >
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< p > < span class = "figure-number" > Figure 1: < / span > Sensor Fusion Architecture (< a href = "./figs/fusion_super_sensor.png" > png< / a > , < a href = "./figs/fusion_super_sensor.pdf" > pdf< / a > , < a href = "./figs/fusion_super_sensor.tex" > tex< / a > ).< / p >
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< h2 id = "orgf8987c9" > < span class = "section-number-2" > 2< / span > Fig 2: Sensor fusion architecture with sensor dynamics uncertainty< / h2 >
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< p > < img src = "figs/sensor_fusion_dynamic_uncertainty.png" alt = "sensor_fusion_dynamic_uncertainty.png" / >
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< p > < span class = "figure-number" > Figure 2: < / span > Sensor fusion architecture with sensor dynamics uncertainty (< a href = "./figs/sensor_fusion_dynamic_uncertainty.png" > png< / a > , < a href = "./figs/sensor_fusion_dynamic_uncertainty.pdf" > pdf< / a > , < a href = "./figs/sensor_fusion_dynamic_uncertainty.tex" > tex< / a > ).< / p >
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< h2 id = "org1801a90" > < span class = "section-number-2" > 3< / span > Fig 3: Uncertainty set of the super sensor dynamics< / h2 >
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< p > < span class = "figure-number" > Figure 3: < / span > 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) (< a href = "./figs/uncertainty_set_super_sensor.png" > png< / a > , < a href = "./figs/uncertainty_set_super_sensor.pdf" > pdf< / a > , < a href = "./figs/uncertainty_set_super_sensor.tex" > tex< / a > ).< / p >
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< h2 id = "org355bde0" > < span class = "section-number-2" > 4< / span > Fig 4: Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters< / h2 >
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< p > < span class = "figure-number" > Figure 4: < / span > Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters (< a href = "./figs/h_infinity_robust_fusion.png" > png< / a > , < a href = "./figs/h_infinity_robust_fusion.pdf" > pdf< / a > , < a href = "./figs/h_infinity_robust_fusion.tex" > tex< / a > ).< / p >
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< h2 id = "org879ecb3" > < span class = "section-number-2" > 5< / span > Fig 5: Magnitude of a weighting function generated using the proposed formula< / h2 >
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< p > < span class = "figure-number" > Figure 5: < / span > Magnitude of a weighting function generated using the proposed formula (< a href = "./figs/weight_formula.png" > png< / a > , < a href = "./figs/weight_formula.pdf" > pdf< / a > , < a href = "./figs/weight_formula.tex" > tex< / a > ).< / p >
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< h2 id = "org2b1f7ae" > < span class = "section-number-2" > 6< / span > Fig 6: Frequency response of the weighting functions and complementary filters obtained using \(\mathcal{H}_\infty\) synthesis< / h2 >
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< p > < span class = "figure-number" > Figure 6: < / span > Frequency response of the weighting functions and complementary filters obtained using \(\mathcal{H}_\infty\) synthesis (< a href = "./figs/hinf_synthesis_results.png" > png< / a > , < a href = "./figs/hinf_synthesis_results.pdf" > pdf< / a > , < a href = "./figs/hinf_synthesis_results.tex" > tex< / a > ).< / p >
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< p > < img src = "figs/comp_filter_three_hinf.png" alt = "comp_filter_three_hinf.png" / >
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< p > < span class = "figure-number" > Figure 7: < / span > Architecture for \(\mathcal{H}_\infty\) synthesis of three complementary filters (< a href = "./figs/comp_filter_three_hinf.png" > png< / a > , < a href = "./figs/comp_filter_three_hinf.pdf" > pdf< / a > , < a href = "./figs/comp_filter_three_hinf.tex" > tex< / a > ).< / p >
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< h2 id = "org20bfce3" > < span class = "section-number-2" > 8< / span > Fig 8: Frequency response of the weighting functions and three complementary filters obtained using \(\mathcal{H}_\infty\) synthesis< / h2 >
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< p > < span class = "figure-number" > Figure 8: < / span > Frequency response of the weighting functions and three complementary filters obtained using \(\mathcal{H}_\infty\) synthesis (< a href = "./figs/hinf_three_synthesis_results.png" > png< / a > , < a href = "./figs/hinf_three_synthesis_results.pdf" > pdf< / a > , < a href = "./figs/hinf_three_synthesis_results.tex" > tex< / a > ).< / p >
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< h2 id = "orgb08c277" > < span class = "section-number-2" > 9< / span > Fig 9: Specifications and weighting functions magnitude used for \(\mathcal{H}_\infty\) synthesis< / h2 >
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< p > < span class = "figure-number" > Figure 9: < / span > Specifications and weighting functions magnitude used for \(\mathcal{H}_\infty\) synthesis (< a href = "./figs/ligo_weights.png" > png< / a > , < a href = "./figs/ligo_weights.pdf" > pdf< / a > , < a href = "./figs/ligo_weights.tex" > tex< / a > ).< / p >
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< h2 id = "org74b4762" > < span class = "section-number-2" > 10< / span > Fig 10: Comparison of the FIR filters (solid) with the filters obtained with \(\mathcal{H}_\infty\) synthesis (dashed)< / h2 >
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< div id = "org6bce6a7" class = "figure" >
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< p > < img src = "figs/comp_fir_ligo_hinf.png" alt = "comp_fir_ligo_hinf.png" / >
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< p > < span class = "figure-number" > Figure 10: < / span > Comparison of the FIR filters (solid) with the filters obtained with \(\mathcal{H}_\infty\) synthesis (dashed) (< a href = "./figs/comp_fir_ligo_hinf.png" > png< / a > , < a href = "./figs/comp_fir_ligo_hinf.pdf" > pdf< / a > , < a href = "./figs/comp_fir_ligo_hinf.tex" > tex< / a > ).< / p >
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< div id = "postamble" class = "status" >
< p class = "author" > Author: Thomas Dehaeze< / p >
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< p class = "date" > Created: 2020-11-12 jeu. 10:44< / p >
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