From 62a745a697cb715af660279ab5b4a04600dc2dea Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Thu, 26 Mar 2020 17:19:47 +0100 Subject: [PATCH] Add file about force control --- docs/figs/control_cascade_force_F.pdf | Bin 0 -> 74609 bytes docs/figs/control_cascade_force_F.png | Bin 0 -> 18543 bytes docs/figs/control_cascade_force_tau.pdf | Bin 0 -> 74417 bytes docs/figs/control_cascade_force_tau.png | Bin 0 -> 16144 bytes org/control_force.org | 126 ++++++++++++++++++++++++ 5 files changed, 126 insertions(+) create mode 100644 docs/figs/control_cascade_force_F.pdf create mode 100644 docs/figs/control_cascade_force_F.png create mode 100644 docs/figs/control_cascade_force_tau.pdf create mode 100644 docs/figs/control_cascade_force_tau.png create mode 100644 org/control_force.org diff --git a/docs/figs/control_cascade_force_F.pdf b/docs/figs/control_cascade_force_F.pdf new file mode 100644 index 0000000000000000000000000000000000000000..aa1d56a5def1073b366dc9d8f96d627ebefeb313 GIT binary 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header-args:matlab+ :output-dir figs +#+PROPERTY: header-args:matlab+ :tangle no +#+PROPERTY: header-args:matlab+ :mkdirp yes + +#+PROPERTY: header-args:shell :eval no-export + +#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}") +#+PROPERTY: header-args:latex+ :imagemagick t :fit yes +#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150 +#+PROPERTY: header-args:latex+ :imoutoptions -quality 100 +#+PROPERTY: header-args:latex+ :results file raw replace +#+PROPERTY: header-args:latex+ :buffer no +#+PROPERTY: header-args:latex+ :eval no-export +#+PROPERTY: header-args:latex+ :exports results +#+PROPERTY: header-args:latex+ :mkdirp yes +#+PROPERTY: header-args:latex+ :output-dir figs +#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png") +:END: + +Cascade Control where the inner loop goal is to control the total wrench (forces and torques) applied to the upper part of the nano-hexapod. + +The force will induce an acceleration of the upper part, thus we can consider the new input $\bm{r}_\mathcal{F}$ as an acceleration input. + +Ideas: +- This can be used as *feedforward*: we now the wanted 6dof reference path for the sample, thus we can compute the required acceleration and thus the required force. To do so, we need information on the inertia of the sample. + +#+begin_src latex :file control_cascade_force_F.pdf + \begin{tikzpicture} + % Blocs + \node[block={3.0cm}{3.0cm}] (P) {Plant}; + \coordinate[] (inputF) at ($(P.south west)!0.5!(P.north west)$); + \coordinate[] (outputF) at ($(P.south east)!0.8!(P.north east)$); + \coordinate[] (outputX) at ($(P.south east)!0.5!(P.north east)$); + \coordinate[] (outputL) at ($(P.south east)!0.2!(P.north east)$); + + \node[block, left= of inputF] (Jt) {$\bm{J}^{-T}$}; + \node[block, left= of Jt] (K) {$\bm{K}_\mathcal{F}$}; + \node[addb={+}{}{-}{}{}, left= of K] (subF) {}; + \node[block, left= of subF] (Kx) {$\bm{K}_\mathcal{X}$}; + \node[block, align=center, left= of Kx] (Ex) {Compute\\Pos. Error}; + + \node[block, above=0.4 of P] (J) {$\bm{J}^{T}$}; + + % Connections and labels + \draw[->] (outputL) -- ++(1, 0) node[above left]{$d\bm{\mathcal{L}}$}; + + \draw[->] (outputF) -- ++(1, 0); + \draw[->] ($(outputF) + (0.6, 0)$)node[branch]{} node[below]{$\bm{\tau}_m$} |- (J.east); + \draw[->] (J.west) -| (subF.north)node[above left]{$\bm{\mathcal{F}}_m$}; + \draw[->] (subF.east) -- (K.west) node[above left]{$\bm{\epsilon}_{\mathcal{F}}$}; + \draw[->] (K.east) -- (Jt.west) node[above left]{$\bm{\mathcal{F}}$}; + \draw[->] (Jt.east) -- (inputF) node[above left]{$\bm{\tau}$}; + + \draw[->] (outputX) -- ++(1.6, 0) node[above left]{$\bm{\mathcal{X}}$}; + \draw[->] ($(outputX) + (1.2, 0)$)node[branch]{} -- ++(0, -2) -| (Ex.south); + + \draw[->] (Ex.east) -- (Kx.west) node[above left]{$\bm{\epsilon}_{\mathcal{X}_n}$}; + \draw[->] (Kx.east) -- (subF.west) node[above left]{$\bm{r}_{\mathcal{F}}$}; + \draw[<-] (Ex.west) -- ++(-1, 0) node[above right]{$\bm{r}_{\mathcal{X}}$}; + \end{tikzpicture} +#+end_src + +#+RESULTS: +[[file:figs/control_cascade_force_F.png]] + +#+begin_src latex :file control_cascade_force_tau.pdf + \begin{tikzpicture} + % Blocs + \node[block={3.0cm}{3.0cm}] (P) {Plant}; + \coordinate[] (inputF) at ($(P.south west)!0.5!(P.north west)$); + \coordinate[] (outputF) at ($(P.south east)!0.8!(P.north east)$); + \coordinate[] (outputX) at ($(P.south east)!0.5!(P.north east)$); + \coordinate[] (outputL) at ($(P.south east)!0.2!(P.north east)$); + + \node[block, left= of inputF] (K) {$\bm{K}_\tau$}; + \node[addb={+}{}{-}{}{}, left= of K] (subF) {}; + \node[block, left= of subF] (J) {$\bm{J}^{-T}$}; + \node[block, left= of J] (Kx) {$\bm{K}_\mathcal{X}$}; + \node[block, align=center, left= of Kx] (Ex) {Compute\\Pos. Error}; + + % Connections and labels + \draw[->] (outputL) -- ++(1, 0) node[above left]{$d\bm{\mathcal{L}}$}; + + \draw[->] (outputF) -- ++(1, 0); + \draw[->] ($(outputF) + (0.6, 0)$)node[branch]{} node[below]{$\bm{\tau}_m$} -- ++(0, 1) -| (subF.north); + \draw[->] (subF.east) -- (K.west) node[above left]{$\bm{\epsilon}_\tau$}; + \draw[->] (K.east) -- (inputF) node[above left]{$\bm{\tau}$}; + + \draw[->] (outputX) -- ++(1.6, 0) node[above left]{$\bm{\mathcal{X}}$}; + \draw[->] ($(outputX) + (1.2, 0)$)node[branch]{} -- ++(0, -2) -| (Ex.south); + + \draw[->] (Ex.east) -- (Kx.west) node[above left]{$\bm{\epsilon}_{\mathcal{X}_n}$}; + \draw[->] (Kx.east) -- (J.west) node[above left]{$\bm{r}_{\mathcal{F}}$}; + \draw[->] (J.east) -- (subF.west) node[above left]{$\bm{r}_\tau$}; + \draw[<-] (Ex.west) -- ++(-1, 0) node[above right]{$\bm{r}_{\mathcal{X}}$}; + \end{tikzpicture} +#+end_src + +#+RESULTS: +[[file:figs/control_cascade_force_tau.png]]