From 5c609777f1221a7e25033d88605654c3ad0e9d18 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Thu, 9 Dec 2021 10:17:54 +0100 Subject: [PATCH] Add 311 and 111 kinematics. Correct crystal positions --- dcm-simscape.org | 329 ++++++++-- figs/actuator_jacobian_111_points.pdf | Bin 70479 -> 60371 bytes figs/actuator_jacobian_111_points.png | Bin 120685 -> 53329 bytes figs/actuator_jacobian_111_points.svg | 568 ------------------ figs/actuator_jacobian_311_points.pdf | Bin 37933 -> 71979 bytes figs/actuator_jacobian_311_points.png | Bin 32283 -> 73863 bytes ...tuator_jacobian_forward_kinematics_111.pdf | Bin 0 -> 46528 bytes ...tuator_jacobian_forward_kinematics_111.png | Bin 0 -> 3750 bytes ...tuator_jacobian_forward_kinematics_111.svg | 185 ++++++ ...tuator_jacobian_forward_kinematics_311.pdf | Bin 0 -> 46774 bytes ...tuator_jacobian_forward_kinematics_311.png | Bin 0 -> 4006 bytes ...tuator_jacobian_forward_kinematics_311.svg | 188 ++++++ ...tuator_jacobian_inverse_kinematics_111.pdf | Bin 0 -> 43706 bytes ...tuator_jacobian_inverse_kinematics_111.png | Bin 0 -> 3629 bytes ...tuator_jacobian_inverse_kinematics_111.svg | 173 ++++++ ...tuator_jacobian_inverse_kinematics_311.pdf | Bin 0 -> 43953 bytes ...tuator_jacobian_inverse_kinematics_311.png | Bin 0 -> 3911 bytes ...tuator_jacobian_inverse_kinematics_311.svg | 176 ++++++ ...sensor_jacobian_forward_kinematics_111.pdf | Bin 0 -> 43527 bytes ...sensor_jacobian_forward_kinematics_111.png | Bin 0 -> 3622 bytes ...sensor_jacobian_forward_kinematics_111.svg | 173 ++++++ ...sensor_jacobian_forward_kinematics_311.pdf | Bin 0 -> 43527 bytes ...sensor_jacobian_forward_kinematics_311.png | Bin 0 -> 3884 bytes ...sensor_jacobian_forward_kinematics_311.svg | 173 ++++++ ...tic_sensor_jacobian_inverse_kinematics.pdf | Bin 40708 -> 40708 bytes ...tic_sensor_jacobian_inverse_kinematics.png | Bin 3514 -> 3760 bytes ...tic_sensor_jacobian_inverse_kinematics.svg | 16 +- ...sensor_jacobian_inverse_kinematics_111.pdf | Bin 0 -> 40708 bytes ...sensor_jacobian_inverse_kinematics_111.png | Bin 0 -> 3514 bytes ...sensor_jacobian_inverse_kinematics_111.svg | 161 +++++ ...sensor_jacobian_inverse_kinematics_311.pdf | Bin 0 -> 40708 bytes ...sensor_jacobian_inverse_kinematics_311.png | Bin 0 -> 3760 bytes ...sensor_jacobian_inverse_kinematics_311.svg | 161 +++++ figs/sensor_111_crystal_points.pdf | Bin 51420 -> 51409 bytes figs/sensor_111_crystal_points.png | Bin 6642 -> 6694 bytes figs/sensor_111_crystal_points.svg | 97 ++- figs/sensor_311_crystal_points.pdf | Bin 0 -> 51420 bytes figs/sensor_311_crystal_points.png | Bin 0 -> 6767 bytes figs/sensor_311_crystal_points.svg | 206 +++++++ matlab/mat/Khac_iff.mat | Bin 1041 -> 1041 bytes matlab/mat/dcm_kinematics.mat | Bin 299 -> 470 bytes matlab/simscape_dcm.slx | Bin 57776 -> 57776 bytes 42 files changed, 1940 insertions(+), 666 deletions(-) delete mode 100644 figs/actuator_jacobian_111_points.svg create mode 100644 figs/schematic_actuator_jacobian_forward_kinematics_111.pdf create mode 100644 figs/schematic_actuator_jacobian_forward_kinematics_111.png create mode 100644 figs/schematic_actuator_jacobian_forward_kinematics_111.svg create mode 100644 figs/schematic_actuator_jacobian_forward_kinematics_311.pdf create mode 100644 figs/schematic_actuator_jacobian_forward_kinematics_311.png create mode 100644 figs/schematic_actuator_jacobian_forward_kinematics_311.svg create mode 100644 figs/schematic_actuator_jacobian_inverse_kinematics_111.pdf create mode 100644 figs/schematic_actuator_jacobian_inverse_kinematics_111.png create mode 100644 figs/schematic_actuator_jacobian_inverse_kinematics_111.svg create mode 100644 figs/schematic_actuator_jacobian_inverse_kinematics_311.pdf create mode 100644 figs/schematic_actuator_jacobian_inverse_kinematics_311.png create mode 100644 figs/schematic_actuator_jacobian_inverse_kinematics_311.svg create mode 100644 figs/schematic_sensor_jacobian_forward_kinematics_111.pdf create mode 100644 figs/schematic_sensor_jacobian_forward_kinematics_111.png create mode 100644 figs/schematic_sensor_jacobian_forward_kinematics_111.svg create mode 100644 figs/schematic_sensor_jacobian_forward_kinematics_311.pdf create mode 100644 figs/schematic_sensor_jacobian_forward_kinematics_311.png create mode 100644 figs/schematic_sensor_jacobian_forward_kinematics_311.svg create mode 100644 figs/schematic_sensor_jacobian_inverse_kinematics_111.pdf create mode 100644 figs/schematic_sensor_jacobian_inverse_kinematics_111.png create mode 100644 figs/schematic_sensor_jacobian_inverse_kinematics_111.svg create mode 100644 figs/schematic_sensor_jacobian_inverse_kinematics_311.pdf create mode 100644 figs/schematic_sensor_jacobian_inverse_kinematics_311.png create mode 100644 figs/schematic_sensor_jacobian_inverse_kinematics_311.svg create mode 100644 figs/sensor_311_crystal_points.pdf create mode 100644 figs/sensor_311_crystal_points.png create mode 100644 figs/sensor_311_crystal_points.svg diff --git a/dcm-simscape.org b/dcm-simscape.org index c92dc12..85f14db 100644 --- a/dcm-simscape.org +++ b/dcm-simscape.org @@ -144,17 +144,17 @@ ans = 1e3*(dz(end) - dz(1)) #+RESULTS: : 24.963 -** Kinematics (111 Crystal) +** Kinematics (311 Crystal) *** Introduction :ignore: -The reference frame is taken at the center of the 111 second crystal. +The reference frame is taken at the center of the 311 second crystal. -*** Interferometers - 111 Crystal +*** Interferometers - 311 Crystal -Three interferometers are pointed to the bottom surface of the 111 crystal. +Three interferometers are pointed to the bottom surface of the 311 crystal. -The position of the measurement points are shown in Figure [[fig:sensor_111_crystal_points]] as well as the origin where the motion of the crystal is computed. +The position of the measurement points are shown in Figure [[fig:sensor_311_crystal_points]] as well as the origin where the motion of the crystal is computed. -#+begin_src latex :file sensor_111_crystal_points.pdf +#+begin_src latex :file sensor_311_crystal_points.pdf \begin{tikzpicture} % Crystal \draw (-15/2, -3.5/2) rectangle (15/2, 3.5/2); @@ -174,6 +174,255 @@ The position of the measurement points are shown in Figure [[fig:sensor_111_crys \draw[->] (0, 0) -- ++(0, -1) node[below]{$y$}; \draw[fill, color=black] (0, 0) circle (0.05); + \node[left] at (0,0) {$\mathcal{O}_{311}$}; +\end{tikzpicture} +#+end_src + +#+name: fig:sensor_311_crystal_points +#+caption: Bottom view of the second crystal 311. Position of the measurement points. +#+RESULTS: +[[file:figs/sensor_311_crystal_points.png]] + +The inverse kinematics consisting of deriving the interferometer measurements from the motion of the crystal (see Figure [[fig:schematic_sensor_jacobian_inverse_kinematics_311]]): +\begin{equation} +\begin{bmatrix} +x_1 \\ x_2 \\ x_3 +\end{bmatrix} += +\bm{J}_{s,311} +\begin{bmatrix} +d_z \\ r_y \\ r_x +\end{bmatrix} +\end{equation} + +#+begin_src latex :file schematic_sensor_jacobian_inverse_kinematics_311.pdf +\begin{tikzpicture} + % Blocs + \node[block] (Js) {$\bm{J}_{s,311}$}; + + % Connections and labels + \draw[->] ($(Js.west)+(-1.5,0)$) node[above right]{$\begin{bmatrix} d_z \\ r_y \\ r_x \end{bmatrix}$} -- (Js.west); + \draw[->] (Js.east) -- ++(1.5, 0) node[above left]{$\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}$}; +\end{tikzpicture} +#+end_src + +#+name: fig:schematic_sensor_jacobian_inverse_kinematics_311 +#+caption: Inverse Kinematics - Interferometers +#+RESULTS: +[[file:figs/schematic_sensor_jacobian_inverse_kinematics_311.png]] + + +From the Figure [[fig:sensor_311_crystal_points]], the inverse kinematics can be solved as follow (for small motion): +\begin{equation} +\bm{J}_{s,311} += +\begin{bmatrix} +1 & 0.07 & -0.015 \\ +1 & 0 & 0.015 \\ +1 & -0.07 & -0.015 +\end{bmatrix} +\end{equation} + +#+begin_src matlab +%% Sensor Jacobian matrix for 311 crystal +J_s_311 = [1, 0.07, -0.015 + 1, 0, 0.015 + 1, -0.07, -0.015]; +#+end_src + +#+begin_src matlab :exports results :results value table replace :tangle no +data2orgtable(J_s_311, {}, {}, ' %.3f '); +#+end_src + +#+name: tab:jacobian_sensor_311 +#+caption: Sensor Jacobian $\bm{J}_{s,311}$ +#+attr_latex: :environment tabularx :width 0.3\linewidth :align ccc +#+attr_latex: :center t :booktabs t +#+RESULTS: +| 1.0 | 0.07 | -0.015 | +| 1.0 | 0.0 | 0.015 | +| 1.0 | -0.07 | -0.015 | + +The forward kinematics is solved by inverting the Jacobian matrix (see Figure [[fig:schematic_sensor_jacobian_forward_kinematics_311]]). +\begin{equation} +\begin{bmatrix} +d_z \\ r_y \\ r_x +\end{bmatrix} += +\bm{J}_{s,311}^{-1} +\begin{bmatrix} +x_1 \\ x_2 \\ x_3 +\end{bmatrix} +\end{equation} + +#+begin_src latex :file schematic_sensor_jacobian_forward_kinematics_311.pdf +\begin{tikzpicture} + % Blocs + \node[block] (Js_inv) {$\bm{J}_{s,311}^{-1}$}; + + % Connections and labels + \draw[->] ($(Js_inv.west)+(-1.5,0)$) node[above right]{$\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}$} -- (Js_inv.west); + \draw[->] (Js_inv.east) -- ++(1.5, 0) node[above left]{$\begin{bmatrix} d_z \\ r_y \\ r_x \end{bmatrix}$}; +\end{tikzpicture} +#+end_src + +#+name: fig:schematic_sensor_jacobian_forward_kinematics_311 +#+caption: Forward Kinematics - Interferometers +#+RESULTS: +[[file:figs/schematic_sensor_jacobian_forward_kinematics_311.png]] + +#+begin_src matlab :exports results :results value table replace :tangle no +data2orgtable(inv(J_s_311), {}, {}, ' %.2f '); +#+end_src + +#+name: tab:inverse_jacobian_sensor_311 +#+caption: Inverse of the sensor Jacobian $\bm{J}_{s,311}^{-1}$ +#+attr_latex: :environment tabularx :width 0.3\linewidth :align ccc +#+attr_latex: :center t :booktabs t +#+RESULTS: +| 0.25 | 0.5 | 0.25 | +| 7.14 | 0.0 | -7.14 | +| -16.67 | 33.33 | -16.67 | + +*** Piezo - 311 Crystal + +The location of the actuators with respect with the center of the 311 second crystal are shown in Figure [[fig:actuator_jacobian_311_points]]. + +#+name: fig:actuator_jacobian_311_points +#+caption: Location of actuators with respect to the center of the 311 second crystal (bottom view) +#+attr_latex: :width \linewidth +[[file:figs/actuator_jacobian_311_points.png]] + +Inverse Kinematics consist of deriving the axial (z) motion of the 3 actuators from the motion of the crystal's center. +\begin{equation} +\begin{bmatrix} +d_{u_r} \\ d_{u_h} \\ d_{d} +\end{bmatrix} += +\bm{J}_{a,311} +\begin{bmatrix} +d_z \\ r_y \\ r_x +\end{bmatrix} +\end{equation} + +#+begin_src latex :file schematic_actuator_jacobian_inverse_kinematics_311.pdf +\begin{tikzpicture} + % Blocs + \node[block] (Ja) {$\bm{J}_{a,311}$}; + + % Connections and labels + \draw[->] ($(Ja.west)+(-1.5,0)$) node[above right]{$\begin{bmatrix} d_z \\ r_y \\ r_x \end{bmatrix}$} -- (Ja.west); + \draw[->] (Ja.east) -- ++(1.5, 0) node[above left]{$\begin{bmatrix} d_{u_r} \\ d_{u_h} \\ d_d \end{bmatrix}$}; +\end{tikzpicture} +#+end_src + +#+name: fig:schematic_sensor_jacobian_inverse_kinematics_311 +#+caption: Inverse Kinematics - Actuators +#+RESULTS: +[[file:figs/schematic_actuator_jacobian_inverse_kinematics_311.png]] + +Based on the geometry in Figure [[fig:actuator_jacobian_311_points]], we obtain: +\begin{equation} +\bm{J}_{a,311} += +\begin{bmatrix} +1 & 0.14 & -0.1525 \\ +1 & 0.14 & 0.0675 \\ +1 & -0.14 & -0.0425 +\end{bmatrix} +\end{equation} + +#+begin_src matlab +%% Actuator Jacobian - 311 crystal +J_a_311 = [1, 0.14, -0.1525 + 1, 0.14, 0.0675 + 1, -0.14, -0.0425]; +#+end_src + +#+begin_src matlab :exports results :results value table replace :tangle no +data2orgtable(J_a_311, {}, {}, ' %.4f '); +#+end_src + +#+name: tab:jacobian_actuator_311 +#+caption: Actuator Jacobian $\bm{J}_{a,311}$ +#+attr_latex: :environment tabularx :width 0.3\linewidth :align ccc +#+attr_latex: :center t :booktabs t +#+RESULTS: +| 1.0 | 0.14 | -0.1525 | +| 1.0 | 0.14 | 0.0675 | +| 1.0 | -0.14 | -0.0425 | + +The forward Kinematics is solved by inverting the Jacobian matrix: +\begin{equation} +\begin{bmatrix} +d_z \\ r_y \\ r_x +\end{bmatrix} += +\bm{J}_{a,311}^{-1} +\begin{bmatrix} +d_{u_r} \\ d_{u_h} \\ d_{d} +\end{bmatrix} +\end{equation} + +#+begin_src latex :file schematic_actuator_jacobian_forward_kinematics_311.pdf +\begin{tikzpicture} + % Blocs + \node[block] (Ja_inv) {$\bm{J}_{a,311}^{-1}$}; + + % Connections and labels + \draw[->] ($(Ja_inv.west)+(-1.5,0)$) node[above right]{$\begin{bmatrix} d_{u_r} \\ d_{u_h} \\ d_d \end{bmatrix}$} -- (Ja_inv.west); + \draw[->] (Ja_inv.east) -- ++(1.5, 0) node[above left]{$\begin{bmatrix} d_z \\ r_y \\ r_x \end{bmatrix}$}; +\end{tikzpicture} +#+end_src + +#+name: fig:schematic_actuator_jacobian_forward_kinematics_311 +#+caption: Forward Kinematics - Actuators for 311 crystal +#+RESULTS: +[[file:figs/schematic_actuator_jacobian_forward_kinematics_311.png]] + +#+begin_src matlab :exports results :results value table replace :tangle no +data2orgtable(inv(J_a_311), {}, {}, ' %.4f '); +#+end_src + +#+name: tab:inverse_jacobian_actuator_311 +#+caption: Inverse of the actuator Jacobian $\bm{J}_{a,311}^{-1}$ +#+attr_latex: :environment tabularx :width 0.3\linewidth :align ccc +#+attr_latex: :center t :booktabs t +#+RESULTS: +| 0.0568 | 0.4432 | 0.5 | +| 1.7857 | 1.7857 | -3.5714 | +| -4.5455 | 4.5455 | 0.0 | + +** Kinematics (111 Crystal) +*** Introduction :ignore: +The reference frame is taken at the center of the 111 second crystal. + +*** Interferometers - 111 Crystal + +Three interferometers are pointed to the bottom surface of the 111 crystal. + +The position of the measurement points are shown in Figure [[fig:sensor_111_crystal_points]] as well as the origin where the motion of the crystal is computed. + +#+begin_src latex :file sensor_111_crystal_points.pdf +\begin{tikzpicture} + % Crystal + \draw (-15/2, -3.5/2) rectangle (15/2, 3.5/2); + + % Measurement Points + \node[branch] (a1) at (-7, -1.5){}; + \node[branch] (a2) at ( 0, 1.5){}; + \node[branch] (a3) at ( 7, -1.5){}; + + % Labels + \node[right] at (a1) {$\mathcal{O}_1 = (-0.07, 0.015)$}; + \node[right] at (a2) {$\mathcal{O}_2 = (0, -0.015)$}; + \node[left] at (a3) {$\mathcal{O}_3 = ( 0.07, 0.015)$}; + + % Origin + \draw[->] (0, 0) node[] -- ++(1, 0) node[right]{$x$}; + \draw[->] (0, 0) -- ++(0, -1) node[below]{$y$}; + \draw[fill, color=black] (0, 0) circle (0.05); + \node[left] at (0,0) {$\mathcal{O}_{111}$}; \end{tikzpicture} #+end_src @@ -183,7 +432,7 @@ The position of the measurement points are shown in Figure [[fig:sensor_111_crys #+RESULTS: [[file:figs/sensor_111_crystal_points.png]] -The inverse kinematics consisting of deriving the interferometer measurements from the motion of the crystal (see Figure [[fig:schematic_sensor_jacobian_inverse_kinematics]]): +The inverse kinematics consisting of deriving the interferometer measurements from the motion of the crystal (see Figure [[fig:schematic_sensor_jacobian_inverse_kinematics_111]]): \begin{equation} \begin{bmatrix} x_1 \\ x_2 \\ x_3 @@ -195,7 +444,7 @@ d_z \\ r_y \\ r_x \end{bmatrix} \end{equation} -#+begin_src latex :file schematic_sensor_jacobian_inverse_kinematics.pdf +#+begin_src latex :file schematic_sensor_jacobian_inverse_kinematics_111.pdf \begin{tikzpicture} % Blocs \node[block] (Js) {$\bm{J}_{s,111}$}; @@ -206,10 +455,10 @@ d_z \\ r_y \\ r_x \end{tikzpicture} #+end_src -#+name: fig:schematic_sensor_jacobian_inverse_kinematics +#+name: fig:schematic_sensor_jacobian_inverse_kinematics_111 #+caption: Inverse Kinematics - Interferometers #+RESULTS: -[[file:figs/schematic_sensor_jacobian_inverse_kinematics.png]] +[[file:figs/schematic_sensor_jacobian_inverse_kinematics_111.png]] From the Figure [[fig:sensor_111_crystal_points]], the inverse kinematics can be solved as follow (for small motion): @@ -217,17 +466,17 @@ From the Figure [[fig:sensor_111_crystal_points]], the inverse kinematics can be \bm{J}_{s,111} = \begin{bmatrix} -1 & 0.07 & -0.015 \\ -1 & 0 & 0.015 \\ -1 & -0.07 & -0.015 +1 & 0.07 & 0.015 \\ +1 & 0 & -0.015 \\ +1 & -0.07 & 0.015 \end{bmatrix} \end{equation} #+begin_src matlab %% Sensor Jacobian matrix for 111 crystal -J_s_111 = [1, 0.07, -0.015 - 1, 0, 0.015 - 1, -0.07, -0.015]; +J_s_111 = [1, 0.07, 0.015 + 1, 0, -0.015 + 1, -0.07, 0.015]; #+end_src #+begin_src matlab :exports results :results value table replace :tangle no @@ -239,11 +488,11 @@ data2orgtable(J_s_111, {}, {}, ' %.3f '); #+attr_latex: :environment tabularx :width 0.3\linewidth :align ccc #+attr_latex: :center t :booktabs t #+RESULTS: -| 1.0 | 0.07 | -0.015 | -| 1.0 | 0.0 | 0.015 | -| 1.0 | -0.07 | -0.015 | +| 1.0 | 0.07 | 0.015 | +| 1.0 | 0.0 | -0.015 | +| 1.0 | -0.07 | 0.015 | -The forward kinematics is solved by inverting the Jacobian matrix (see Figure [[fig:schematic_sensor_jacobian_forward_kinematics]]). +The forward kinematics is solved by inverting the Jacobian matrix (see Figure [[fig:schematic_sensor_jacobian_forward_kinematics_111]]). \begin{equation} \begin{bmatrix} d_z \\ r_y \\ r_x @@ -255,7 +504,7 @@ x_1 \\ x_2 \\ x_3 \end{bmatrix} \end{equation} -#+begin_src latex :file schematic_sensor_jacobian_forward_kinematics.pdf +#+begin_src latex :file schematic_sensor_jacobian_forward_kinematics_111.pdf \begin{tikzpicture} % Blocs \node[block] (Js_inv) {$\bm{J}_{s,111}^{-1}$}; @@ -266,10 +515,10 @@ x_1 \\ x_2 \\ x_3 \end{tikzpicture} #+end_src -#+name: fig:schematic_sensor_jacobian_forward_kinematics +#+name: fig:schematic_sensor_jacobian_forward_kinematics_111 #+caption: Forward Kinematics - Interferometers #+RESULTS: -[[file:figs/schematic_sensor_jacobian_forward_kinematics.png]] +[[file:figs/schematic_sensor_jacobian_forward_kinematics_111.png]] #+begin_src matlab :exports results :results value table replace :tangle no data2orgtable(inv(J_s_111), {}, {}, ' %.2f '); @@ -280,9 +529,9 @@ data2orgtable(inv(J_s_111), {}, {}, ' %.2f '); #+attr_latex: :environment tabularx :width 0.3\linewidth :align ccc #+attr_latex: :center t :booktabs t #+RESULTS: -| 0.25 | 0.5 | 0.25 | -| 7.14 | 0.0 | -7.14 | -| -16.67 | 33.33 | -16.67 | +| 0.25 | 0.5 | 0.25 | +| 7.14 | 0.0 | -7.14 | +| 16.67 | -33.33 | 16.67 | *** Piezo - 111 Crystal @@ -305,7 +554,7 @@ d_z \\ r_y \\ r_x \end{bmatrix} \end{equation} -#+begin_src latex :file schematic_actuator_jacobian_inverse_kinematics.pdf +#+begin_src latex :file schematic_actuator_jacobian_inverse_kinematics_111.pdf \begin{tikzpicture} % Blocs \node[block] (Ja) {$\bm{J}_{a,111}$}; @@ -316,10 +565,10 @@ d_z \\ r_y \\ r_x \end{tikzpicture} #+end_src -#+name: fig:schematic_sensor_jacobian_inverse_kinematics +#+name: fig:schematic_sensor_jacobian_inverse_kinematics_111 #+caption: Inverse Kinematics - Actuators #+RESULTS: -[[file:figs/schematic_actuator_jacobian_inverse_kinematics.png]] +[[file:figs/schematic_actuator_jacobian_inverse_kinematics_111.png]] Based on the geometry in Figure [[fig:actuator_jacobian_111_points]], we obtain: \begin{equation} @@ -328,7 +577,7 @@ Based on the geometry in Figure [[fig:actuator_jacobian_111_points]], we obtain: \begin{bmatrix} 1 & 0.14 & -0.1525 \\ 1 & 0.14 & 0.0675 \\ -1 & -0.14 & -0.0425 +1 & -0.14 & 0.0425 \end{bmatrix} \end{equation} @@ -336,7 +585,7 @@ Based on the geometry in Figure [[fig:actuator_jacobian_111_points]], we obtain: %% Actuator Jacobian - 111 crystal J_a_111 = [1, 0.14, -0.1525 1, 0.14, 0.0675 - 1, -0.14, -0.0425]; + 1, -0.14, 0.0425]; #+end_src #+begin_src matlab :exports results :results value table replace :tangle no @@ -350,7 +599,7 @@ data2orgtable(J_a_111, {}, {}, ' %.4f '); #+RESULTS: | 1.0 | 0.14 | -0.1525 | | 1.0 | 0.14 | 0.0675 | -| 1.0 | -0.14 | -0.0425 | +| 1.0 | -0.14 | 0.0425 | The forward Kinematics is solved by inverting the Jacobian matrix: \begin{equation} @@ -364,7 +613,7 @@ d_{u_r} \\ d_{u_h} \\ d_{d} \end{bmatrix} \end{equation} -#+begin_src latex :file schematic_actuator_jacobian_forward_kinematics.pdf +#+begin_src latex :file schematic_actuator_jacobian_forward_kinematics_111.pdf \begin{tikzpicture} % Blocs \node[block] (Ja_inv) {$\bm{J}_{a,111}^{-1}$}; @@ -375,10 +624,10 @@ d_{u_r} \\ d_{u_h} \\ d_{d} \end{tikzpicture} #+end_src -#+name: fig:schematic_actuator_jacobian_forward_kinematics +#+name: fig:schematic_actuator_jacobian_forward_kinematics_111 #+caption: Forward Kinematics - Actuators for 111 crystal #+RESULTS: -[[file:figs/schematic_actuator_jacobian_forward_kinematics.png]] +[[file:figs/schematic_actuator_jacobian_forward_kinematics_111.png]] #+begin_src matlab :exports results :results value table replace :tangle no data2orgtable(inv(J_a_111), {}, {}, ' %.4f '); @@ -389,8 +638,8 @@ data2orgtable(inv(J_a_111), {}, {}, ' %.4f '); #+attr_latex: :environment tabularx :width 0.3\linewidth :align ccc #+attr_latex: :center t :booktabs t #+RESULTS: -| 0.0568 | 0.4432 | 0.5 | -| 1.7857 | 1.7857 | -3.5714 | +| 0.25 | 0.25 | 0.5 | +| 0.4058 | 3.1656 | -3.5714 | | -4.5455 | 4.5455 | 0.0 | ** TODO Inputs and Outputs :noexport: @@ -402,11 +651,11 @@ Disturbances: ** Save Kinematics #+begin_src matlab :exports none :tangle no -save('matlab/mat/dcm_kinematics.mat', 'J_a_111', 'J_s_111') +save('matlab/mat/dcm_kinematics.mat', 'J_a_311', 'J_s_311', 'J_a_111', 'J_s_111') #+end_src #+begin_src matlab :eval no -save('mat/dcm_kinematics.mat', 'J_a_111', 'J_s_111') +save('mat/dcm_kinematics.mat', 'J_a_311', 'J_s_311', 'J_a_111', 'J_s_111') #+end_src * Open Loop System Identification @@ -1560,7 +1809,7 @@ load('Kiff.mat'); #+begin_src matlab :exports none %% Identification of the damped plant with IFF controller.type = 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