Update Content - 2020-10-26

content/zettels/complementary_filters.md

@@ -4,13 +4,15 @@ author = ["Thomas Dehaeze"]
 draft = false
 +++
 
-Backlinks:
-
--   [Advances in internal model control technique: a review and future prospects]({{< relref "saxena12_advan_inter_model_contr_techn" >}})
--   [Actuator Fusion]({{< relref "actuator_fusion" >}})
--   [Sensor Fusion]({{< relref "sensor_fusion" >}})
-
 Tags
 :
 
-<./biblio/references.bib>
+
+## Complementary Filters Synthesis {#complementary-filters-synthesis}
+
+The shaping of complementary filters can be done using the \\(\mathcal{H}\_\infty\\) synthesis ([Dehaeze, Vermat, and Christophe 2019](#orgc79060a)).
+
+
+## Bibliography {#bibliography}
+
+<a id="orgc79060a"></a>Dehaeze, Thomas, Mohit Vermat, and Collette Christophe. 2019. “Complementary Filters Shaping Using \\(mathcalH\_Infty\\) Synthesis.” In _7th International Conference on Control, Mechatronics and Automation (ICCMA)_, 459–64. <https://doi.org/10.1109/ICCMA46720.2019.8988642>.

content/zettels/electronic_active_filters.md

@@ -0,0 +1,50 @@
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+title = "Electronic Active Filters"
+author = ["Thomas Dehaeze"]
+draft = false
++++
+
+Tags
+: [Operational Amplifiers]({{< relref "operational_amplifiers" >}})
+
+TODOS:
+
+-   [X] Electronics circuits containing input voltage, output voltage, Op-amp, RLC components
+-   [ ] Bode plots of the filters
+-   [ ] Inputs and output impedance
+
+
+## Low Pass Filter {#low-pass-filter}
+
+\begin{equation}
+  \frac{V\_o}{V\_i}(s) = \frac{1}{R^2 C\_1 C\_2 s^2 + 2 R C\_2 s + 1}
+\end{equation}
+
+\begin{equation}
+  \frac{V\_o}{V\_i}(s) = \frac{1}{\frac{s^2}{\omega\_0^2} + 2 \xi \frac{s}{\omega\_0} + 1}
+\end{equation}
+
+With:
+
+-   \\(\omega\_0 = \frac{1}{R\sqrt{C\_1 C\_2}}\\)
+-   \\(\xi = \frac{C\_2}{C\_1}\\)
+
+<a id="org21a1d35"></a>
+
+{{< figure src="/ox-hugo/elec_active_second_order_low_pass_filter.png" caption="Figure 1: Second Order Low Pass Filter" >}}
+
+
+## High Pass Filter {#high-pass-filter}
+
+Same as [1](#org21a1d35) but by exchanging R1 with C1 and R2 with C2
+
+\begin{equation}
+  \frac{V\_o}{V\_i}(s) = \frac{R^2 C\_1 C\_2 s^2}{R^2 C\_1 C\_2 s^2 + 2 R C\_2 s + 1}
+\end{equation}
+
+With:
+
+-   \\(\omega\_0 = \frac{1}{R\sqrt{C\_1 C\_2}}\\)
+-   \\(\xi = \frac{C\_2}{C\_1}\\)
+
+<./biblio/references.bib>

content/zettels/electronic_passive_filters.md

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+title = "Electronic Passive Filters"
+author = ["Thomas Dehaeze"]
+draft = false
++++
+
+Tags
+:
+
+TODOS:
+
+-   [X] Electronics circuits containing input voltage, output voltage, R L and C components
+-   [ ] Bode plot of the filter from input voltage to output voltage
+-   [ ] Equation of the transfer functions with nice parameters (\\(\omega\_c\\), \\(\xi\\))
+
+
+## First Order Low Pass Filter {#first-order-low-pass-filter}
+
+<a id="orgf718550"></a>
+
+{{< figure src="/ox-hugo/elec_passive_first_order_low_pass_filter.png" caption="Figure 1: First Order Low Pass Filter using an RC circuit" >}}
+
+
+## First Order High Pass Filter {#first-order-high-pass-filter}
+
+<a id="orgc9b929d"></a>
+
+{{< figure src="/ox-hugo/elec_passive_first_order_high_pass_filter.png" caption="Figure 2: First Order High Pass Filter using an RC circuit" >}}
+
+
+## Second Order Low Pass Filter {#second-order-low-pass-filter}
+
+<a id="orgb56edb0"></a>
+
+{{< figure src="/ox-hugo/elec_passive_second_order_low_pass_filter.png" caption="Figure 3: Second Order Low Pass Filter using an RLC circuit" >}}
+
+
+## Second Order High Pass Filter {#second-order-high-pass-filter}
+
+<a id="org1bcacc5"></a>
+
+{{< figure src="/ox-hugo/elec_passive_second_order_high_pass_filter.png" caption="Figure 4: Second Order High Pass Filter using an RLC circuit" >}}
+
+<./biblio/references.bib>

content/zettels/mass_spring_damper_systems.md

@@ -7,4 +7,52 @@ draft = false
 Tags
 :
 
+
+## Actuated Mass Spring Damper System {#actuated-mass-spring-damper-system}
+
+Let's consider Figure [1](#orgeec8f0f) where:
+
+-   \\(m\\) is the mass in [kg]
+-   \\(ḱ\\) is the spring stiffness in [N/m]
+-   \\(c\\) is the damping coefficient in [N/(m/s)]
+-   \\(F\\) is the actuator force in [N]
+-   \\(F\_d\\) is external force applied to the mass in [N]
+-   \\(w\\) is ground motion
+-   \\(x\\) is the absolute mass motion
+
+<a id="orgeec8f0f"></a>
+
+{{< figure src="/ox-hugo/mass_spring_damper_system.png" caption="Figure 1: Mass Spring Damper System" >}}
+
+Let's write the transfer function from \\(F\\) to \\(x\\):
+
+\begin{equation}
+  \frac{x}{F}(s) = \frac{1}{m s^2 + c s + k}
+\end{equation}
+
+This can be re-written as:
+
+\begin{equation}
+  \frac{x}{F}(s) = \frac{1/k}{\frac{s^2}{\omega\_0^2} + 2 \xi \frac{s}{\omega\_0} + 1}
+\end{equation}
+
+with:
+
+-   \\(\omega\_0\\) the natural frequency in [rad/s]
+-   \\(\xi\\) the damping ratio
+
+
+## Transmissibility {#transmissibility}
+
+\begin{equation}
+  \frac{x}{w}(s) = \frac{1}{\frac{s^2}{\omega\_0^2} + 2 \xi \frac{s}{\omega\_0} + 1}
+\end{equation}
+
+
+## Compliance {#compliance}
+
+\begin{equation}
+  \frac{x}{F\_d}(s) = \frac{1/k}{\frac{s^2}{\omega\_0^2} + 2 \xi \frac{s}{\omega\_0} + 1}
+\end{equation}
+
 <./biblio/references.bib>

content/zettels/operational_amplifiers.md

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++++
+title = "Operational Amplifiers"
+author = ["Thomas Dehaeze"]
+draft = false
++++
+
+Tags
+:
+
+<./biblio/references.bib>