From 66fa9f0267f60a47b9c88064ab65de8ec8343687 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Mon, 26 Oct 2020 16:00:34 +0100 Subject: [PATCH] Update Content - 2020-10-26 --- content/zettels/complementary_filters.md | 16 +++--- content/zettels/electronic_active_filters.md | 50 ++++++++++++++++++ content/zettels/electronic_passive_filters.md | 44 +++++++++++++++ content/zettels/mass_spring_damper_systems.md | 48 +++++++++++++++++ content/zettels/operational_amplifiers.md | 10 ++++ ...ec_active_second_order_low_pass_filter.png | Bin 0 -> 19245 bytes ...c_passive_first_order_high_pass_filter.png | Bin 0 -> 9195 bytes ...ec_passive_first_order_low_pass_filter.png | Bin 0 -> 9907 bytes ..._passive_second_order_high_pass_filter.png | Bin 0 -> 13025 bytes ...c_passive_second_order_low_pass_filter.png | Bin 0 -> 13233 bytes static/ox-hugo/mass_spring_damper_system.png | Bin 0 -> 4469 bytes static/ox-hugo/mech_sys_alone.png | Bin 0 -> 3771 bytes 12 files changed, 161 insertions(+), 7 deletions(-) create mode 100644 content/zettels/electronic_active_filters.md create mode 100644 content/zettels/electronic_passive_filters.md create mode 100644 content/zettels/operational_amplifiers.md create mode 100644 static/ox-hugo/elec_active_second_order_low_pass_filter.png create mode 100644 static/ox-hugo/elec_passive_first_order_high_pass_filter.png create mode 100644 static/ox-hugo/elec_passive_first_order_low_pass_filter.png create mode 100644 static/ox-hugo/elec_passive_second_order_high_pass_filter.png create mode 100644 static/ox-hugo/elec_passive_second_order_low_pass_filter.png create mode 100644 static/ox-hugo/mass_spring_damper_system.png create mode 100644 static/ox-hugo/mech_sys_alone.png diff --git a/content/zettels/complementary_filters.md b/content/zettels/complementary_filters.md index f0bf725..84b7c9d 100644 --- a/content/zettels/complementary_filters.md +++ b/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} + +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. . diff --git a/content/zettels/electronic_active_filters.md b/content/zettels/electronic_active_filters.md new file mode 100644 index 0000000..3b93608 --- /dev/null +++ b/content/zettels/electronic_active_filters.md @@ -0,0 +1,50 @@ ++++ +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}\\) + + + +{{< 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> diff --git a/content/zettels/electronic_passive_filters.md b/content/zettels/electronic_passive_filters.md new file mode 100644 index 0000000..4be03f8 --- /dev/null +++ b/content/zettels/electronic_passive_filters.md @@ -0,0 +1,44 @@ ++++ +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} + + + +{{< 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} + + + +{{< 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} + + + +{{< 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} + + + +{{< 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> diff --git a/content/zettels/mass_spring_damper_systems.md b/content/zettels/mass_spring_damper_systems.md index 4fd835e..d189389 100644 --- a/content/zettels/mass_spring_damper_systems.md +++ b/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 + + + +{{< 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> diff --git a/content/zettels/operational_amplifiers.md b/content/zettels/operational_amplifiers.md new file mode 100644 index 0000000..c82fcfa --- /dev/null +++ b/content/zettels/operational_amplifiers.md @@ -0,0 +1,10 @@ ++++ +title = "Operational Amplifiers" +author = ["Thomas Dehaeze"] +draft = false ++++ + +Tags +: + +<./biblio/references.bib> diff --git a/static/ox-hugo/elec_active_second_order_low_pass_filter.png b/static/ox-hugo/elec_active_second_order_low_pass_filter.png new file mode 100644 index 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