Add inkscape directory

.gitignore

@@ -1,5 +1,3 @@
-mat/
-figures/
 ltximg/
 *.autosave
 slprj/

figs/inkscape/convert_svg.sh

@@ -0,0 +1,18 @@
+#!/bin/bash
+
+# Directory containing SVG files
+INPUT_DIR="."
+
+# Loop through all SVG files in the directory
+for svg_file in "$INPUT_DIR"/*.svg; do
+    # Check if there are SVG files in the directory
+    if [ -f "$svg_file" ]; then
+        # Output PDF file name
+        pdf_file="../${svg_file%.svg}.pdf"
+        png_file="../${svg_file%.svg}"
+        
+        # Convert SVG to PDF using Inkscape
+        inkscape "$svg_file" --export-filename="$pdf_file" && \
+            pdftocairo -png -singlefile -cropbox "$pdf_file" "$png_file"
+    fi
+done

figs/inkscape/test_apa_2dof_model.svg

@@ -6,7 +6,7 @@
    version="1.1"
    id="svg3816"
    sodipodi:docname="test_apa_2dof_model.svg"
-   inkscape:version="1.3.2 (091e20ef0f, 2023-11-25, custom)"
+   inkscape:version="1.4 (e7c3feb100, 2024-10-09)"
    xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
    xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
    xmlns="http://www.w3.org/2000/svg"
@@ -23,16 +23,16 @@
      inkscape:pageshadow="2"
      inkscape:zoom="5.6"
      inkscape:cx="125.71429"
-     inkscape:cy="98.125"
+     inkscape:cy="98.214286"
      inkscape:document-units="mm"
-     inkscape:current-layer="layer5"
+     inkscape:current-layer="layer6"
      inkscape:document-rotation="0"
      showgrid="false"
      inkscape:snap-midpoints="true"
-     inkscape:window-width="2534"
+     inkscape:window-width="2560"
-     inkscape:window-height="1367"
+     inkscape:window-height="1440"
-     inkscape:window-x="11"
+     inkscape:window-x="0"
-     inkscape:window-y="60"
+     inkscape:window-y="0"
      inkscape:window-maximized="1"
      inkscape:showpageshadow="2"
      inkscape:pagecheckerboard="0"
@@ -412,6 +412,15 @@
          style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:0.625;stroke-linejoin:round;stroke-opacity:1"
          id="path6140-7" />
     </marker>
+    <g
+       id="g8810">
+      <g
+         id="g1074">
+        <path
+           d="m 3.65625,-3.984375 h 0.859375 c 0.203125,0 0.296875,0 0.296875,-0.203125 0,-0.109375 -0.09375,-0.109375 -0.265625,-0.109375 H 3.71875 L 3.921875,-5.4375 c 0.046875,-0.203125 0.1875,-0.90625 0.25,-1.03125 0.078125,-0.1875 0.25,-0.34375 0.46875,-0.34375 0.03125,0 0.296875,0 0.484375,0.1875 -0.4375,0.03125 -0.546875,0.390625 -0.546875,0.53125 0,0.234375 0.1875,0.359375 0.375,0.359375 C 5.21875,-5.734375 5.5,-5.96875 5.5,-6.34375 c 0,-0.453125 -0.453125,-0.6875 -0.859375,-0.6875 -0.34375,0 -0.96875,0.1875 -1.265625,1.171875 -0.0625,0.203125 -0.09375,0.3125 -0.328125,1.5625 h -0.6875 c -0.203125,0 -0.3125,0 -0.3125,0.1875 0,0.125 0.09375,0.125 0.28125,0.125 h 0.65625 L 2.25,-0.046875 c -0.1875,0.96875 -0.359375,1.875 -0.875,1.875 -0.046875,0 -0.28125,0 -0.484375,-0.1875 C 1.359375,1.609375 1.453125,1.25 1.453125,1.109375 1.453125,0.875 1.265625,0.75 1.078125,0.75 0.8125,0.75 0.53125,0.984375 0.53125,1.359375 c 0,0.4375 0.4375,0.6875 0.84375,0.6875 0.546875,0 0.953125,-0.59375 1.125,-0.96875 0.328125,-0.625 0.546875,-1.828125 0.5625,-1.90625 z m 0,0"
+           id="path8091" />
+      </g>
+    </g>
   </defs>
   <metadata
      id="metadata3813">
@@ -723,7 +732,7 @@
        width="38.718697"
        height="16.183527"
        x="15.21064"
-       y="19.260626"
+       y="19.35512"
        rx="0.076119758"
        ry="0.076119766" />
     <text
@@ -951,24 +960,6 @@
         </g>
       </g>
     </g>
-    <g
-       inkscape:label=""
-       transform="translate(36.551226,24.635454)"
-       id="g35">
-      <g
-         fill="#000000"
-         fill-opacity="1"
-         id="g34"
-         transform="matrix(0.352778,0,0,0.352778,-78.4308,-3.97995)">
-        <g
-           id="use1"
-           transform="translate(222.011,16.438)">
-          <path
-             d="m 3.4375,-4.5 h 1.984375 c 0.140625,0 0.546875,0 0.546875,-0.390625 0,-0.265625 -0.234375,-0.265625 -0.453125,-0.265625 h -3.28125 c -0.28125,0 -0.6875,0 -1.234375,0.59375 -0.3125,0.34375 -0.6875,0.984375 -0.6875,1.046875 0,0.078125 0.0625,0.09375 0.125,0.09375 0.09375,0 0.09375,-0.03125 0.15625,-0.109375 C 1.21875,-4.5 1.84375,-4.5 2.140625,-4.5 H 3.125 l -1.234375,4.09375 c -0.0625,0.171875 -0.0625,0.203125 -0.0625,0.234375 0,0.140625 0.078125,0.296875 0.328125,0.296875 0.359375,0 0.421875,-0.3125 0.46875,-0.5 z m 0,0"
-             id="path2" />
-        </g>
-      </g>
-    </g>
     <g
        inkscape:label=""
        transform="translate(55.142421,23.297371)"
@@ -1062,5 +1053,23 @@
         </g>
       </g>
     </g>
+    <g
+       inkscape:label=""
+       transform="translate(36.348066,23.363614)"
+       id="g5">
+      <g
+         fill="#000000"
+         fill-opacity="1"
+         id="g2-1"
+         transform="matrix(0.352778,0,0,0.352778,-65.4658,-2.43972)">
+        <g
+           id="use1-1"
+           transform="translate(185.041,13.947)">
+          <path
+             d="m 3.65625,-3.984375 h 0.859375 c 0.203125,0 0.296875,0 0.296875,-0.203125 0,-0.109375 -0.09375,-0.109375 -0.265625,-0.109375 H 3.71875 L 3.921875,-5.4375 c 0.046875,-0.203125 0.1875,-0.90625 0.25,-1.03125 0.078125,-0.1875 0.25,-0.34375 0.46875,-0.34375 0.03125,0 0.296875,0 0.484375,0.1875 -0.4375,0.03125 -0.546875,0.390625 -0.546875,0.53125 0,0.234375 0.1875,0.359375 0.375,0.359375 C 5.21875,-5.734375 5.5,-5.96875 5.5,-6.34375 c 0,-0.453125 -0.453125,-0.6875 -0.859375,-0.6875 -0.34375,0 -0.96875,0.1875 -1.265625,1.171875 -0.0625,0.203125 -0.09375,0.3125 -0.328125,1.5625 h -0.6875 c -0.203125,0 -0.3125,0 -0.3125,0.1875 0,0.125 0.09375,0.125 0.28125,0.125 h 0.65625 L 2.25,-0.046875 c -0.1875,0.96875 -0.359375,1.875 -0.875,1.875 -0.046875,0 -0.28125,0 -0.484375,-0.1875 C 1.359375,1.609375 1.453125,1.25 1.453125,1.109375 1.453125,0.875 1.265625,0.75 1.078125,0.75 0.8125,0.75 0.53125,0.984375 0.53125,1.359375 c 0,0.4375 0.4375,0.6875 0.84375,0.6875 0.546875,0 0.953125,-0.59375 1.125,-0.96875 0.328125,-0.625 0.546875,-1.828125 0.5625,-1.90625 z m 0,0"
+             id="path2-1" />
+        </g>
+      </g>
+    </g>
   </g>
 </svg>

figs/inkscape/test_apa_2dof_model_simscape.svg

@@ -6,7 +6,7 @@
    version="1.1"
    id="svg3816"
    sodipodi:docname="test_apa_2dof_model_simscape.svg"
-   inkscape:version="1.3.2 (091e20ef0f, 2023-11-25, custom)"
+   inkscape:version="1.4 (e7c3feb100, 2024-10-09)"
    xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
    xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
    xmlns="http://www.w3.org/2000/svg"
@@ -21,18 +21,18 @@
      borderopacity="1.0"
      inkscape:pageopacity="0.0"
      inkscape:pageshadow="2"
-     inkscape:zoom="2.8"
+     inkscape:zoom="3.959798"
-     inkscape:cx="188.92857"
+     inkscape:cx="164.65486"
-     inkscape:cy="134.82143"
+     inkscape:cy="132.07745"
      inkscape:document-units="mm"
-     inkscape:current-layer="layer1"
+     inkscape:current-layer="layer5"
      inkscape:document-rotation="0"
      showgrid="false"
      inkscape:snap-midpoints="true"
-     inkscape:window-width="2534"
+     inkscape:window-width="2560"
-     inkscape:window-height="1367"
+     inkscape:window-height="1440"
-     inkscape:window-x="11"
+     inkscape:window-x="0"
-     inkscape:window-y="60"
+     inkscape:window-y="0"
      inkscape:window-maximized="1"
      inkscape:showpageshadow="2"
      inkscape:pagecheckerboard="0"
@@ -454,6 +454,15 @@
          style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:0.625;stroke-linejoin:round;stroke-opacity:1"
          id="path6140-2" />
     </marker>
+    <g
+       id="g1793">
+      <g
+         id="g362">
+        <path
+           d="m 3.65625,-3.984375 h 0.859375 c 0.203125,0 0.296875,0 0.296875,-0.203125 0,-0.109375 -0.09375,-0.109375 -0.265625,-0.109375 H 3.71875 L 3.921875,-5.4375 c 0.046875,-0.203125 0.1875,-0.90625 0.25,-1.03125 0.078125,-0.1875 0.25,-0.34375 0.46875,-0.34375 0.03125,0 0.296875,0 0.484375,0.1875 -0.4375,0.03125 -0.546875,0.390625 -0.546875,0.53125 0,0.234375 0.1875,0.359375 0.375,0.359375 C 5.21875,-5.734375 5.5,-5.96875 5.5,-6.34375 c 0,-0.453125 -0.453125,-0.6875 -0.859375,-0.6875 -0.34375,0 -0.96875,0.1875 -1.265625,1.171875 -0.0625,0.203125 -0.09375,0.3125 -0.328125,1.5625 h -0.6875 c -0.203125,0 -0.3125,0 -0.3125,0.1875 0,0.125 0.09375,0.125 0.28125,0.125 h 0.65625 L 2.25,-0.046875 c -0.1875,0.96875 -0.359375,1.875 -0.875,1.875 -0.046875,0 -0.28125,0 -0.484375,-0.1875 C 1.359375,1.609375 1.453125,1.25 1.453125,1.109375 1.453125,0.875 1.265625,0.75 1.078125,0.75 0.8125,0.75 0.53125,0.984375 0.53125,1.359375 c 0,0.4375 0.4375,0.6875 0.84375,0.6875 0.546875,0 0.953125,-0.59375 1.125,-0.96875 0.328125,-0.625 0.546875,-1.828125 0.5625,-1.90625 z m 0,0"
+           id="path8413" />
+      </g>
+    </g>
   </defs>
   <metadata
      id="metadata3813">
@@ -848,7 +857,7 @@
      inkscape:groupmode="layer"
      id="layer5"
      inkscape:label="text"
-     transform="translate(15.517906,12.168219)">
+     transform="translate(15.5179, 12.1682)">
     <g
        inkscape:label=""
        transform="translate(-2.1167635,17.133502)"
@@ -1035,24 +1044,6 @@
         </g>
       </g>
     </g>
-    <g
-       inkscape:label=""
-       transform="translate(36.551226,24.635454)"
-       id="g35">
-      <g
-         fill="#000000"
-         fill-opacity="1"
-         id="g34"
-         transform="matrix(0.352778,0,0,0.352778,-78.4308,-3.97995)">
-        <g
-           id="g85"
-           transform="translate(222.011,16.438)">
-          <path
-             d="m 3.4375,-4.5 h 1.984375 c 0.140625,0 0.546875,0 0.546875,-0.390625 0,-0.265625 -0.234375,-0.265625 -0.453125,-0.265625 h -3.28125 c -0.28125,0 -0.6875,0 -1.234375,0.59375 -0.3125,0.34375 -0.6875,0.984375 -0.6875,1.046875 0,0.078125 0.0625,0.09375 0.125,0.09375 0.09375,0 0.09375,-0.03125 0.15625,-0.109375 C 1.21875,-4.5 1.84375,-4.5 2.140625,-4.5 H 3.125 l -1.234375,4.09375 c -0.0625,0.171875 -0.0625,0.203125 -0.0625,0.234375 0,0.140625 0.078125,0.296875 0.328125,0.296875 0.359375,0 0.421875,-0.3125 0.46875,-0.5 z m 0,0"
-             id="path84" />
-        </g>
-      </g>
-    </g>
     <g
        inkscape:label=""
        transform="translate(55.142421,23.297371)"
@@ -1115,5 +1106,23 @@
         </g>
       </g>
     </g>
+    <g
+       inkscape:label=""
+       transform="translate(36.449303,23.245)"
+       id="g5">
+      <g
+         fill="#000000"
+         fill-opacity="1"
+         id="g2-1"
+         transform="matrix(0.352778,0,0,0.352778,-65.4658,-2.43972)">
+        <g
+           id="use1-1"
+           transform="translate(185.041,13.947)">
+          <path
+             d="m 3.65625,-3.984375 h 0.859375 c 0.203125,0 0.296875,0 0.296875,-0.203125 0,-0.109375 -0.09375,-0.109375 -0.265625,-0.109375 H 3.71875 L 3.921875,-5.4375 c 0.046875,-0.203125 0.1875,-0.90625 0.25,-1.03125 0.078125,-0.1875 0.25,-0.34375 0.46875,-0.34375 0.03125,0 0.296875,0 0.484375,0.1875 -0.4375,0.03125 -0.546875,0.390625 -0.546875,0.53125 0,0.234375 0.1875,0.359375 0.375,0.359375 C 5.21875,-5.734375 5.5,-5.96875 5.5,-6.34375 c 0,-0.453125 -0.453125,-0.6875 -0.859375,-0.6875 -0.34375,0 -0.96875,0.1875 -1.265625,1.171875 -0.0625,0.203125 -0.09375,0.3125 -0.328125,1.5625 h -0.6875 c -0.203125,0 -0.3125,0 -0.3125,0.1875 0,0.125 0.09375,0.125 0.28125,0.125 h 0.65625 L 2.25,-0.046875 c -0.1875,0.96875 -0.359375,1.875 -0.875,1.875 -0.046875,0 -0.28125,0 -0.484375,-0.1875 C 1.359375,1.609375 1.453125,1.25 1.453125,1.109375 1.453125,0.875 1.265625,0.75 1.078125,0.75 0.8125,0.75 0.53125,0.984375 0.53125,1.359375 c 0,0.4375 0.4375,0.6875 0.84375,0.6875 0.546875,0 0.953125,-0.59375 1.125,-0.96875 0.328125,-0.625 0.546875,-1.828125 0.5625,-1.90625 z m 0,0"
+             id="path2-1" />
+        </g>
+      </g>
+    </g>
   </g>
 </svg>

figs/inkscape/test_apa_iff_schematic.svg

@@ -19,17 +19,17 @@
    xmlns:cc="http://creativecommons.org/ns#"
    xmlns:dc="http://purl.org/dc/elements/1.1/">
   <sodipodi:namedview
-     inkscape:current-layer="layer9"
+     inkscape:current-layer="g841"
      inkscape:window-maximized="1"
-     inkscape:window-y="60"
+     inkscape:window-y="0"
-     inkscape:window-x="11"
+     inkscape:window-x="0"
-     inkscape:cy="140.18392"
+     inkscape:cy="140.3607"
      inkscape:cx="197.9899"
      inkscape:zoom="2.8284271"
      showgrid="false"
      id="namedview835"
-     inkscape:window-height="1367"
+     inkscape:window-height="1200"
-     inkscape:window-width="2534"
+     inkscape:window-width="1920"
      inkscape:pageshadow="2"
      inkscape:pageopacity="0"
      guidetolerance="10"
@@ -3736,7 +3736,7 @@
     </g>
     <g
        id="g1470"
-       transform="translate(-213.6103,94.361419)"
+       transform="translate(-199.21908,94.072346)"
        inkscape:label="">
       <g
          id="g7335">
@@ -3751,50 +3751,6 @@
              width="100%"
              height="100%" />
         </g>
-        <g
-           style="fill:#000000;fill-opacity:1"
-           id="g6756">
-          <use
-             xlink:href="#symbol1905"
-             x="298.70401"
-             y="93.917999"
-             id="use5395"
-             width="100%"
-             height="100%" />
-        </g>
-        <g
-           style="fill:#000000;fill-opacity:1"
-           id="g4172">
-          <use
-             xlink:href="#symbol8146"
-             x="309.2225"
-             y="93.917999"
-             id="use6006"
-             width="100%"
-             height="100%" />
-        </g>
-        <g
-           style="fill:#000000;fill-opacity:1"
-           id="g7594">
-          <use
-             xlink:href="#symbol9931"
-             x="314.20099"
-             y="93.917999"
-             id="use5176"
-             width="100%"
-             height="100%" />
-        </g>
-        <g
-           style="fill:#000000;fill-opacity:1"
-           id="g6669">
-          <use
-             xlink:href="#symbol7717"
-             x="319.70633"
-             y="93.917999"
-             id="use5032"
-             width="100%"
-             height="100%" />
-        </g>
       </g>
     </g>
     <path

figs/inkscape/test_apa_schematic.svg

@@ -19,17 +19,17 @@
    xmlns:cc="http://creativecommons.org/ns#"
    xmlns:dc="http://purl.org/dc/elements/1.1/">
   <sodipodi:namedview
-     inkscape:current-layer="layer9"
+     inkscape:current-layer="g841"
      inkscape:window-maximized="1"
-     inkscape:window-y="60"
+     inkscape:window-y="38"
-     inkscape:window-x="11"
+     inkscape:window-x="965"
-     inkscape:cy="139.83037"
+     inkscape:cy="140.18392"
      inkscape:cx="197.9899"
      inkscape:zoom="2.8284271"
      showgrid="false"
      id="namedview835"
-     inkscape:window-height="1367"
+     inkscape:window-height="1147"
-     inkscape:window-width="2534"
+     inkscape:window-width="940"
      inkscape:pageshadow="2"
      inkscape:pageopacity="0"
      guidetolerance="10"
@@ -3736,7 +3736,7 @@
     </g>
     <g
        id="g1470"
-       transform="translate(-213.6103,94.361419)"
+       transform="translate(-199.21908,94.072346)"
        inkscape:label="">
       <g
          id="g7335">
@@ -3753,48 +3753,7 @@
         </g>
         <g
            style="fill:#000000;fill-opacity:1"
-           id="g6756">
+           id="g6756" />
-          <use
-             xlink:href="#symbol1905"
-             x="298.70401"
-             y="93.917999"
-             id="use5395"
-             width="100%"
-             height="100%" />
-        </g>
-        <g
-           style="fill:#000000;fill-opacity:1"
-           id="g4172">
-          <use
-             xlink:href="#symbol8146"
-             x="309.2225"
-             y="93.917999"
-             id="use6006"
-             width="100%"
-             height="100%" />
-        </g>
-        <g
-           style="fill:#000000;fill-opacity:1"
-           id="g7594">
-          <use
-             xlink:href="#symbol9931"
-             x="314.20099"
-             y="93.917999"
-             id="use5176"
-             width="100%"
-             height="100%" />
-        </g>
-        <g
-           style="fill:#000000;fill-opacity:1"
-           id="g6669">
-          <use
-             xlink:href="#symbol7717"
-             x="319.70633"
-             y="93.917999"
-             id="use5032"
-             width="100%"
-             height="100%" />
-        </g>
       </g>
     </g>
     <path

matlab/STEPS/new_APA300ML_K.CSV

@@ -0,0 +1,36 @@
+1.744402696391601562e+08,1.173046853524446487e+04,-1.969436961065530777e+05,2.501017098440788686e+02,-2.560579583892583847e+06,-1.899893907159566879e+02,1.752544851888548955e+07,-2.823264051224628929e+03,2.536675589742744341e+04,5.932569664288348577e+01,2.585690718283675960e+05,1.535942065353383441e+02,-9.579453944435191154e+07,-5.166229400217183866e+03,-1.450978033041961119e+07,8.502649080017397409e+01,-6.072457395437035011e+05,1.069146866389201023e+01,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-9.617117871302969754e+07,-3.740975046028171619e+03,1.468135727062481828e+07,1.305061695147310274e+01,-6.086246289691759739e+05,-1.705391376733786757e+01,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+1.173046853524446487e+04,3.380881940276336670e+07,-2.904061509445309639e+02,6.429955422680377960e+05,-1.805951826442033052e+02,-1.721230121768265963e+04,8.767926680533855688e+02,2.139992294824984856e+06,-1.334165130902401870e+02,-3.680227672435727436e+04,1.153694332698808012e+01,-1.200429118606130942e+03,-5.748325323460194340e+03,-1.828295581201418862e+07,-6.034463249195978278e+02,1.421803861242151761e+05,-3.139749116546579444e+01,-1.095427582235363661e+05,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-6.858935878766094902e+03,-1.766585588561022282e+07,1.027269122215824154e+03,1.383535108383237093e+05,-5.452573088538952106e+01,1.094424907674457354e+05,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+-1.969436961065530777e+05,-2.904061509445309639e+02,7.180228948753356934e+06,-4.191198939457535744e+00,3.348216503895819187e+03,-5.723647825978696346e+01,-2.564568953003105707e+04,-2.251276071782485815e+02,-7.065558524079563795e+05,6.076555855249353044e+00,-3.930580146726879320e+02,4.587947019869559995e+00,-1.991787934829686582e+07,-5.235887496248033131e+02,-3.229564589008683339e+06,5.262529540712023390e+00,-1.208744926620664046e+05,1.424312293847378896e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,2.014046873393118009e+07,1.039122652330098390e+03,-3.244108507233656943e+06,-8.975687908473821253e+00,1.222793608300175110e+05,4.342871241200932708e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+2.501017098440788686e+02,6.429955422680377960e+05,-4.191198939457535744e+00,1.257837617977801710e+04,-3.860365137683402281e+00,-3.153544715064927004e+02,1.335800304787062487e+01,3.680604728527541738e+04,-2.599195946453221495e+00,-6.267107432629717323e+02,1.744027112364179288e-01,-2.084929454160896967e+01,-1.230212997972084850e+02,-3.455396809652444790e+05,-1.447027866731582435e+01,2.545374036461411833e+03,-7.290869690213988008e-01,-1.434654668054021613e+03,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-1.404384124149315767e+02,-3.342619085884379456e+05,2.126067515522382223e+01,2.476266453216099308e+03,-1.141845778900164809e+00,1.432525262796827292e+03,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+-2.560579583892583847e+06,-1.805951826442033052e+02,3.348216503895819187e+03,-3.860365137683402281e+00,3.790471155559550971e+04,3.697536068793851882e+00,-2.585831415196759335e+05,4.159282586899098533e+01,-3.891622113227713271e+02,-8.741525898193742705e-01,-3.815129732011501801e+03,-2.254397219928608642e+00,1.406250232242587022e+06,9.437971849929999735e+01,2.063777277245984878e+05,-1.389856252396208802e+00,8.934224411231405611e+03,-1.940140841564073071e-01,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,1.412912493169219932e+06,4.462263810720907031e+01,-2.093367820160742558e+05,-9.689028389860054880e-02,8.960659112550843929e+03,2.435876178151705207e-01,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+-1.899893907159566879e+02,-1.721230121768265963e+04,-5.723647825978696346e+01,-3.153544715064927004e+02,3.697536068793851882e+00,2.059473986569233239e+04,-3.453490463707362323e+01,-1.265841550565414764e+03,2.583577134001870945e-01,2.181001658191178194e+01,-5.047887470928991149e-01,1.853817766482919751e+02,2.465670512631395468e+02,3.345554343318864703e+05,2.476297489781632066e+01,-2.241609259264927459e+03,1.681638225351537841e+00,-5.883385698611023145e+02,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-2.204275533754648109e+01,-3.160772915639634593e+05,3.221514036837085371e+01,2.088652841762301705e+03,-2.980949524682580121e-01,-6.728012955789077978e+02,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+1.752544851888548955e+07,8.767926680533855688e+02,-2.564568953003105707e+04,1.335800304787062487e+01,-2.585831415196759335e+05,-3.453490463707362323e+01,1.741333286506042480e+08,-2.827626410622242838e+04,2.097095107223987579e+05,6.085684825120260939e+02,2.555920665538191795e+06,1.436628528188914061e+03,-9.560541327547924221e+07,3.414384224411527975e+04,1.447832450459527783e+07,2.620078190217518568e+02,6.057699273815253982e+05,-1.734505509271484698e+02,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-9.605336389409454167e+07,-6.744370821682321548e+03,-1.466238832584385946e+07,-6.764871118026709951e+01,6.076918246019518701e+05,-1.996680892124047091e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+-2.823264051224628929e+03,2.139992294824984856e+06,-2.251276071782485815e+02,3.680604728527541738e+04,4.159282586899098533e+01,-1.265841550565414764e+03,-2.827626410622242838e+04,3.382764337400054932e+07,3.454605852067470551e+03,-6.434279082531034946e+05,-4.463350027288543060e+02,-1.681527257143333554e+04,2.545570466924470384e+04,-1.828134027596507594e+07,-3.347235020817402983e+03,-1.421411263422719494e+05,-1.669346087804744911e+02,-1.092597634176448482e+05,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,5.643823467662790790e+03,-1.768629539284346625e+07,1.177566606439067982e+02,-1.384912463906705088e+05,-3.705746951032824654e+01,1.094895310465261718e+05,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+2.536675589742744341e+04,-1.334165130902401870e+02,-7.065558524079563795e+05,-2.599195946453221495e+00,-3.891622113227713271e+02,2.583577134001870945e-01,2.097095107223987579e+05,3.454605852067470551e+03,7.180346490249633789e+06,-7.385389286838471889e+01,3.531009459540247917e+03,-6.341057244432158768e+01,1.991169969156065956e+07,-2.099897554177860002e+03,-3.228328971143316943e+06,-1.788570826001569003e+01,-1.208227002702799218e+05,2.507738365892498678e+01,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-2.014677595821649581e+07,-1.221291899086289504e+03,-3.245461666698290035e+06,-6.125832596248569573e+00,1.223284693116245908e+05,1.171666539050030842e+01,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+5.932569664288348577e+01,-3.680227672435727436e+04,6.076555855249353044e+00,-6.267107432629717323e+02,-8.741525898193742705e-01,2.181001658191178194e+01,6.085684825120260939e+02,-6.434279082531034946e+05,-7.385389286838471889e+01,1.258805480963783339e+04,9.579858319146296708e+00,3.075899537462100852e+02,-5.483342708688905986e+02,3.455493795960730058e+05,7.177579635330130259e+01,2.545187530338771921e+03,3.555045113840542115e+00,1.429904939957392116e+03,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-1.195599074089100213e+02,3.346808053823320661e+05,-3.998459191473443752e+00,2.478986152822093572e+03,8.448195578476358492e-01,-1.433247683861512314e+03,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+2.585690718283675960e+05,1.153694332698808012e+01,-3.930580146726879320e+02,1.744027112364179288e-01,-3.815129732011501801e+03,-5.047887470928991149e-01,2.555920665538191795e+06,-4.463350027288543060e+02,3.531009459540247917e+03,9.579858319146296708e+00,3.783404339120723307e+04,2.209793612576322630e+01,-1.403404072635334684e+06,5.327763254027486255e+02,2.059056985502665630e+05,4.073050497035751505e+00,8.912120484085759017e+03,-2.587147655221556874e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-1.411085664731516037e+06,-9.797826752269980943e+01,-2.090436499957474880e+05,-1.006897005356855557e+00,8.946330276896916985e+03,-8.336194119191131513e-02,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+1.535942065353383441e+02,-1.200429118606130942e+03,4.587947019869559995e+00,-2.084929454160896967e+01,-2.254397219928608642e+00,1.853817766482919751e+02,1.436628528188914061e+03,-1.681527257143333554e+04,-6.341057244432158768e+01,3.075899537462100852e+02,2.209793612576322630e+01,2.052738350544311106e+04,-9.826208642368133042e+02,3.332244938553936663e+05,1.282877013019194692e+02,2.232822273964662600e+03,6.291592578123225366e+00,-5.890633051628398107e+02,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-6.076018703957838625e+02,-3.152087921652187943e+05,-6.946507203107393025e+01,-2.082347314756840206e+03,3.857246463516023738e+00,-6.707033963158243068e+02,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+-9.579453944435191154e+07,-5.748325323460194340e+03,-1.991787934829686582e+07,-1.230212997972084850e+02,1.406250232242587022e+06,2.465670512631395468e+02,-9.560541327547924221e+07,2.545570466924470384e+04,1.991169969156065956e+07,-5.483342708688905986e+02,-1.403404072635334684e+06,-9.826208642368133042e+02,3.318434552094860077e+08,-1.915875347960824365e+04,1.929944502499242662e+04,-2.343921825459110551e+02,8.810312069528708889e+02,1.493617980736307800e+02,-1.259285941881640702e+08,-2.296693025931494958e+01,-4.973869092907989398e+01,-8.523117686490877531e-02,-9.672426468659978127e-01,1.531747000561665573e+00,-1.451490830136055127e+07,-5.256591036211029859e+02,-1.307004955561656971e+04,3.212014037927704635e+01,5.977269552894540539e+02,2.639711023698038161e+01,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+-5.166229400217183866e+03,-1.828295581201418862e+07,-5.235887496248033131e+02,-3.455396809652444790e+05,9.437971849929999735e+01,3.345554343318864703e+05,3.414384224411527975e+04,-1.828134027596507594e+07,-2.099897554177860002e+03,3.455493795960730058e+05,5.327763254027486255e+02,3.332244938553936663e+05,-1.915875347960824365e+04,4.004816925317478180e+07,3.974420270413160324e+03,-2.098224071812960574e+02,2.055384607449149996e+02,3.627257703706470784e+05,-2.296693026366983759e+01,-6.715601323315028101e+06,-1.442663612688193098e+01,4.786333283097121694e-02,-3.841205565074119477e-01,1.343559704962231335e+05,-9.795892588531307410e+03,3.231728158194186632e+06,-1.336507186684277258e+03,1.548409030579605314e+02,1.088995400351595890e+02,6.787577024925049045e+03,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+-1.450978033041961119e+07,-6.034463249195978278e+02,-3.229564589008683339e+06,-1.447027866731582435e+01,2.063777277245984878e+05,2.476297489781632066e+01,1.447832450459527783e+07,-3.347235020817402983e+03,-3.228328971143316943e+06,7.177579635330130259e+01,2.059056985502665630e+05,1.282877013019194692e+02,1.929944502499242662e+04,3.974420270413160324e+03,1.295414612709236145e+07,2.081154361320659518e+01,9.672403445114847273e+04,-2.841886639493168332e+01,-4.973869074427057058e+01,-1.442663422199257184e+01,-6.718615125007174909e+06,1.837393573841836769e-01,-1.344307193039822450e+05,4.038975173798462492e-01,1.220611952837056015e+04,-9.312150998954166425e+00,2.223625580527911079e+05,-1.474716818839482357e+00,-1.204946117271472031e+04,-5.379471302812643074e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+8.502649080017397409e+01,1.421803861242151761e+05,5.262529540712023390e+00,2.545374036461411833e+03,-1.389856252396208802e+00,-2.241609259264927459e+03,2.620078190217518568e+02,-1.421411263422719494e+05,-1.788570826001569003e+01,2.545187530338771921e+03,4.073050497035751505e+00,2.232822273964662600e+03,-2.343921825459110551e+02,-2.098224071812960574e+02,2.081154361320659518e+01,3.381814565817359835e+03,9.823988482544336875e-01,-2.842683595091330062e+00,-8.523117754180020711e-02,4.786333032647860364e-02,1.837393532623536885e-01,-6.704960212853733310e+02,3.633307055224577198e-03,-8.352815187562256938e-04,-1.125568968279865203e+02,1.705147617358943535e+02,-8.372104263790760115e+00,1.591222690050299775e+02,4.125787712216713032e-01,2.199104840673911099e-01,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+-6.072457395437035011e+05,-3.139749116546579444e+01,-1.208744926620664046e+05,-7.290869690213988008e-01,8.934224411231405611e+03,1.681638225351537841e+00,6.057699273815253982e+05,-1.669346087804744911e+02,-1.208227002702799218e+05,3.555045113840542115e+00,8.912120484085759017e+03,6.291592578123225366e+00,8.810312069528708889e+02,2.055384607449149996e+02,9.672403445114847273e+04,9.823988482544336875e-01,1.381730899367682287e+04,-1.306263250609540627e+00,1.022304989247004414e+00,1.929450832886629996e-01,1.343138856962799036e+05,-3.716267020195118675e-03,1.641871488571831833e+03,-5.428851641340770584e-03,5.937586501856167160e+02,-7.399306012645411101e+00,1.065927278588290574e+04,-9.601414140480102333e-03,-5.798905631820359758e+02,-2.753351424750548615e-01,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+1.069146866389201023e+01,-1.095427582235363661e+05,1.424312293847378896e+00,-1.434654668054021613e+03,-1.940140841564073071e-01,-5.883385698611023145e+02,-1.734505509271484698e+02,-1.092597634176448482e+05,2.507738365892498678e+01,1.429904939957392116e+03,-2.587147655221556874e+00,-5.890633051628398107e+02,1.493617980736307800e+02,3.627257703706470784e+05,-2.841886639493168332e+01,-2.842683595091330062e+00,-1.306263250609540627e+00,1.205923870277627429e+04,6.130700091207046398e-01,-1.342680824364233995e+05,-1.731681374066056378e-01,1.079251872367681386e-03,-4.637772997335254388e-03,1.640742048754984125e+03,1.278421439422345429e+01,-9.655166294015903986e+03,2.090339405928489214e+00,-3.325221534590916406e-01,-1.503692905719020700e-01,-8.469952154732245830e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-1.259285941881640702e+08,-2.296693026366983759e+01,-4.973869074427057058e+01,-8.523117754180020711e-02,1.022304989247004414e+00,6.130700091207046398e-01,3.822965004465780258e+08,-1.336739949432667345e+03,6.378588031604886055e+01,3.082174140613460622e-01,4.234272648245678283e-01,-1.571383308310032589e+01,-2.563679062584076226e+08,1.359706857164242138e+03,-1.404718861915171146e+01,-2.229862451404187595e-01,2.628715968057804275e-01,-1.301205084079992957e+01,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-2.296693025931494958e+01,-6.715601323315028101e+06,-1.442663422199257184e+01,4.786333032647860364e-02,1.929450832886629996e-01,-1.342680824364233995e+05,-1.336739949432667345e+03,4.350122705347800255e+07,1.957856860056053847e+02,2.515907289466667862e-01,-1.085888424234440208e+00,2.337212338764142478e+05,1.359706857430019227e+03,-3.678562573015485704e+07,-1.813590182308544172e+02,-2.994540605795350530e-01,-2.157171074360348939e+00,3.676353102304631611e+05,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-4.973869092907989398e+01,-1.442663612688193098e+01,-6.718615125007174909e+06,1.837393532623536885e-01,1.343138856962799036e+05,-1.731681374066056378e-01,6.378588031604886055e+01,1.957856860056053847e+02,4.353685975719666481e+07,-1.861295283670187928e-01,-2.340673813938918756e+05,7.870346611261993530e-01,-1.404718921438325197e+01,-1.813590182334592100e+02,-3.681824463219259679e+07,2.390194742474704981e-03,-3.678667919459957629e+05,2.436247889698279323e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-8.523117686490877531e-02,4.786333283097121694e-02,1.837393573841836769e-01,-6.704960212853733310e+02,-3.716267020195118675e-03,1.079251872367681386e-03,3.082174140613460622e-01,2.515907289466667862e-01,-1.861295283670187928e-01,2.024423914250182861e+03,5.360606194457773199e-04,4.276630340245723971e-03,-2.229862417234471650e-01,-2.994540613010485686e-01,2.390195302723441273e-03,-1.353927892964923103e+03,-4.121563467805344771e-03,2.547732451613882176e-03,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-9.672426468659978127e-01,-3.841205565074119477e-01,-1.344307193039822450e+05,3.633307055224577198e-03,1.641871488571831833e+03,-4.637772997335254388e-03,4.234272648245678283e-01,-1.085888424234440208e+00,-2.340673813938918756e+05,5.360606194457773199e-04,9.543837582828324230e+03,-2.567880640081732224e-02,5.438153770273856935e-01,1.470009281300860948e+00,3.684981006978523219e+05,-4.169367396855250263e-03,1.561481714715517001e+03,-1.444843311415766607e-02,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,1.531747000561665573e+00,1.343559704962231335e+05,4.038975173798462492e-01,-8.352815187562256938e-04,-5.428851641340770584e-03,1.640742048754984125e+03,-1.571383308310032589e+01,2.337212338764142478e+05,7.870346611261993530e-01,4.276630340245723971e-03,-2.567880640081732224e-02,9.536749916310538538e+03,1.418208630493782607e+01,-3.680772043726553093e+05,-1.190932464348406938e+00,-3.441348781025865833e-03,-8.866896793763956452e-03,1.558290942237508489e+03,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+-9.617117871302969754e+07,-6.858935878766094902e+03,2.014046873393118009e+07,-1.404384124149315767e+02,1.412912493169219932e+06,-2.204275533754648109e+01,-9.605336389409454167e+07,5.643823467662790790e+03,-2.014677595821649581e+07,-1.195599074089100213e+02,-1.411085664731516037e+06,-6.076018703957838625e+02,-1.451490830136055127e+07,-9.795892588531307410e+03,1.220611952837056015e+04,-1.125568968279865203e+02,5.937586501856167160e+02,1.278421439422345429e+01,-2.563679062584076226e+08,1.359706857430019227e+03,-1.404718921438325197e+01,-2.229862417234471650e-01,5.438153770273856935e-01,1.418208630493782607e+01,4.631073571672515869e+08,9.651298126757144928e+03,-5.884848077749134973e+03,2.270093894418096170e+01,3.348145406302064657e+02,5.665534762665629387e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+-3.740975046028171619e+03,-1.766585588561022282e+07,1.039122652330098390e+03,-3.342619085884379456e+05,4.462263810720907031e+01,-3.160772915639634593e+05,-6.744370821682321548e+03,-1.768629539284346625e+07,-1.221291899086289504e+03,3.346808053823320661e+05,-9.797826752269980943e+01,-3.152087921652187943e+05,-5.256591036211029859e+02,3.231728158194186632e+06,-9.312150998954166425e+00,1.705147617358943535e+02,-7.399306012645411101e+00,-9.655166294015903986e+03,1.359706857164242138e+03,-3.678562573015485704e+07,-1.813590182334592100e+02,-2.994540613010485686e-01,1.470009281300860948e+00,-3.680772043726553093e+05,9.651298126757144928e+03,6.890604885045289993e+07,3.728403375111520290e+02,-1.680589605796023989e+01,-1.515916765250676690e+01,-5.933549090688759461e+05,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+1.468135727062481828e+07,1.027269122215824154e+03,-3.244108507233656943e+06,2.126067515522382223e+01,-2.093367820160742558e+05,3.221514036837085371e+01,-1.466238832584385946e+07,1.177566606439067982e+02,-3.245461666698290035e+06,-3.998459191473443752e+00,-2.090436499957474880e+05,-6.946507203107393025e+01,-1.307004955561656971e+04,-1.336507186684277258e+03,2.223625580527911079e+05,-8.372104263790760115e+00,1.065927278588290574e+04,2.090339405928489214e+00,-1.404718861915171146e+01,-1.813590182308544172e+02,-3.681824463219259679e+07,2.390195302723441273e-03,3.684981006978523219e+05,-1.190932464348406938e+00,-5.884848077749134973e+03,3.728403375111520290e+02,4.308545224823570251e+07,1.657384812602685997e+01,1.353084229763732292e+05,-1.311631346036301693e+01,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+1.305061695147310274e+01,1.383535108383237093e+05,-8.975687908473821253e+00,2.476266453216099308e+03,-9.689028389860054880e-02,2.088652841762301705e+03,-6.764871118026709951e+01,-1.384912463906705088e+05,-6.125832596248569573e+00,2.478986152822093572e+03,-1.006897005356855557e+00,-2.082347314756840206e+03,3.212014037927704635e+01,1.548409030579605314e+02,-1.474716818839482357e+00,1.591222690050299775e+02,-9.601414140480102333e-03,-3.325221534590916406e-01,-2.229862451404187595e-01,-2.994540605795350530e-01,2.390194742474704981e-03,-1.353927892964923103e+03,-4.169367396855250263e-03,-3.441348781025865833e-03,2.270093894418096170e+01,-1.680589605796023989e+01,1.657384812602685997e+01,3.991206250780451228e+03,-6.005423099344966431e-01,-8.171649694413645193e-01,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+-6.086246289691759739e+05,-5.452573088538952106e+01,1.222793608300175110e+05,-1.141845778900164809e+00,8.960659112550843929e+03,-2.980949524682580121e-01,6.076918246019518701e+05,-3.705746951032824654e+01,1.223284693116245908e+05,8.448195578476358492e-01,8.946330276896916985e+03,3.857246463516023738e+00,5.977269552894540539e+02,1.088995400351595890e+02,-1.204946117271472031e+04,4.125787712216713032e-01,-5.798905631820359758e+02,-1.503692905719020700e-01,2.628715968057804275e-01,-2.157171074360348939e+00,-3.678667919459957629e+05,-4.121563467805344771e-03,1.561481714715517001e+03,-8.866896793763956452e-03,3.348145406302064657e+02,-1.515916765250676690e+01,1.353084229763732292e+05,-6.005423099344966431e-01,1.591034889785207633e+04,3.434176472019743187e-01,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+-1.705391376733786757e+01,1.094424907674457354e+05,4.342871241200932708e+00,1.432525262796827292e+03,2.435876178151705207e-01,-6.728012955789077978e+02,-1.996680892124047091e+00,1.094895310465261718e+05,1.171666539050030842e+01,-1.433247683861512314e+03,-8.336194119191131513e-02,-6.707033963158243068e+02,2.639711023698038161e+01,6.787577024925049045e+03,-5.379471302812643074e+00,2.199104840673911099e-01,-2.753351424750548615e-01,-8.469952154732245830e+00,-1.301205084079992957e+01,3.676353102304631611e+05,2.436247889698279323e+00,2.547732451613882176e-03,-1.444843311415766607e-02,1.558290942237508489e+03,5.665534762665629387e+00,-5.933549090688759461e+05,-1.311631346036301693e+01,-8.171649694413645193e-01,3.434176472019743187e-01,1.412160518234821211e+04,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,1.469688321340944767e+09,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,1.472551825290932655e+09,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,1.638369111490185499e+09,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,1.644348420887326717e+09,0.000000000000000000e+00,0.000000000000000000e+00
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,3.335297040023203850e+09,0.000000000000000000e+00
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,3.378175081680267811e+09

matlab/STEPS/new_APA300ML_M.CSV

@@ -0,0 +1,36 @@
+1.941213933847590195e-02,2.310691197165990401e-06,-6.853119574810857080e-04,6.612731190357267145e-08,-2.124350418392126989e-04,-3.186520103250434904e-08,-7.864953839513322189e-04,-1.680552130615625499e-08,6.487386747731482134e-05,4.448283877924326928e-09,-1.282375226629819308e-05,-1.130559433117855173e-08,1.526362035234832271e-03,-4.668798262241766000e-07,-1.745064246003368231e-04,-1.109205516216676591e-08,1.544662515470008208e-05,8.972501296723185406e-11,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,1.825396452580777939e-03,-9.948861092355896187e-07,-1.034228641590971315e-04,1.522106844068990743e-08,1.690480000801803878e-05,1.441457762661818876e-09,1.881964318465226618e-02,1.891852489691360148e-02,-1.238269560363562845e-02,1.271698470055658038e-02,6.397636245733210475e-05,4.153205762773307878e-05
+2.310691197165990401e-06,1.943609346183238634e-02,5.687014815324954440e-07,2.120317930720709359e-04,-4.683521070265611152e-08,-2.349598559263136761e-05,1.224360209015569793e-08,-2.047251337326190838e-04,1.797836318080478077e-07,3.082596304036931558e-06,-2.521079345886402218e-09,9.517828092227884476e-08,-6.012824888898950053e-07,1.092008746110128756e-03,-4.075956429499612055e-07,-9.763978711736015292e-06,-1.987758171848280986e-09,6.670361559754391166e-08,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-7.158027451354804802e-07,1.159216052945812037e-03,2.660180134760386451e-07,-1.035270525781877414e-05,-1.795051316941698216e-09,-1.976296487166061230e-07,1.224693738571713620e-05,8.425724786988658956e-06,-2.792987281876710131e-06,9.478632026860526287e-07,1.613066166058059253e-03,3.030574880783558789e-03
+-6.853119574810857080e-04,5.687014815324954440e-07,1.872739354901406528e-02,1.444333359744646647e-08,3.195270572159647189e-05,-8.108348132069285121e-08,-6.429170013528339258e-05,-1.064767952096105371e-08,6.783242618058941899e-05,4.442693852819327324e-10,-9.632798561576065082e-07,-2.095933397095325157e-09,1.541469013830646436e-03,-1.520641514743615230e-06,1.107535705745923927e-03,9.538186728237329641e-09,1.070990473706994234e-05,3.544724999441598161e-09,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-8.297489567196014888e-04,1.146143076979051826e-06,1.008587175066319973e-03,-7.360197755104747025e-09,-6.014060089449772913e-06,-3.171276286116626543e-10,1.133680337432957375e-02,1.142618693889066450e-02,2.857030399578119537e-02,-2.680324778367691729e-02,-1.615816014206646941e-06,-2.410470030098440860e-06
+6.612731190357267145e-08,2.120317930720709359e-04,1.444333359744646647e-08,3.692363755531924753e-06,-1.266256049903284503e-09,-1.365872736439924150e-07,2.665178880535470890e-09,-3.084581282055957268e-06,2.834990996170338077e-09,4.481696527529056075e-08,-6.236341747891780627e-12,1.779342700461133972e-09,-2.592797813725633417e-08,1.916887368246320887e-05,-1.088587234809755458e-08,-1.307659106231961651e-07,-1.371872544347609066e-10,-3.153899031763136528e-08,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-2.020229090800761086e-08,1.937900423841364833e-05,5.911734192184404569e-09,-1.337146920477737147e-07,-8.590801361534870548e-11,2.743826692408501919e-08,1.436582493590590977e-07,7.922083192776589500e-08,-1.071932885513176235e-07,7.450178844215838462e-08,1.345104998114586439e-04,1.596360248084656398e-04
+-2.124350418392126989e-04,-4.683521070265611152e-08,3.195270572159647189e-05,-1.266256049903284503e-09,3.590921845948433530e-06,2.009777238506123157e-09,1.279902904051491226e-05,-6.386610813300896725e-10,-9.733303561213900540e-07,-5.056528560849447805e-11,2.069326399202210192e-07,1.886815484087454092e-10,-2.544385541755165984e-05,3.707082594656183519e-08,1.468530030759727023e-05,-4.243149899898385559e-11,-2.448298541627253018e-07,-5.590924880090475142e-11,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-2.858074900228838454e-05,-2.543915903920236373e-09,-1.068803865801896532e-05,-1.011591300875160494e-10,-2.598378281351281043e-07,-4.046046526084699107e-11,-6.570127307142901866e-04,-6.827902319201428804e-04,3.400612310843032860e-04,-3.367586741383695207e-04,-1.150469137000843430e-06,-7.980334714743009670e-07
+-3.186520103250434904e-08,-2.349598559263136761e-05,-8.108348132069285121e-08,-1.365872736439924150e-07,2.009777238506123157e-09,7.776028688273636800e-07,7.592799419934575786e-09,1.004935963923786855e-07,-8.469403359801861923e-10,-1.856728942679448409e-09,1.397568791723178051e-10,-1.126064051088119230e-08,-3.698909740289534638e-08,-1.527197530382847228e-05,2.490881922315957171e-08,1.135895377817342258e-07,-2.599344357150243908e-10,5.402095541390601796e-08,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-3.171752631634308571e-09,1.439966444769548844e-05,-5.418257032113064294e-08,-9.500069516313784108e-08,-2.714730510660179609e-11,5.889423296747125739e-08,-1.454886499857698024e-06,-1.467810156137431251e-06,1.119155214117794464e-07,-7.368557067191898770e-08,7.529278844748940917e-05,1.054460659418814784e-04
+-7.864953839513322189e-04,1.224360209015569793e-08,-6.429170013528339258e-05,2.665178880535470890e-09,1.279902904051491226e-05,7.592799419934575786e-09,1.936839424331349840e-02,-6.358219232105812892e-06,6.871934750650472018e-04,1.683098447874357815e-07,2.115449842446825339e-04,1.190186098013398869e-07,1.538299014562874477e-03,1.186034141511475154e-06,1.649047740387377873e-04,-2.919426313306010560e-09,-1.549089912388516689e-05,-4.084385389688405339e-09,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,1.834751766225578996e-03,2.072563560783651399e-06,1.106693884727988310e-04,2.050764899570531600e-08,-1.693913639835141984e-05,1.194113690682714162e-09,-1.969432159947379773e-02,1.761267283589188284e-02,1.183571470812026967e-02,1.305851599488310963e-02,7.627161198701218922e-05,-6.736815642436647068e-05
+-1.680552130615625499e-08,-2.047251337326190838e-04,-1.064767952096105371e-08,-3.084581282055957268e-06,-6.386610813300896725e-10,1.004935963923786855e-07,-6.358219232105812892e-06,1.944387627925764361e-02,4.481095192191438439e-06,-2.122179093273560125e-04,-1.582380322151094441e-07,-2.343772817635101703e-05,2.180664968086653286e-06,1.090021847386008196e-03,-1.325207022276374876e-06,9.780504204745329067e-06,-1.292151508003754848e-08,7.511041181527693849e-08,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-3.059618648662299498e-07,1.157683486489578068e-03,1.782376302113344743e-06,1.032889897373744964e-05,1.600251588192170695e-09,-1.874599877388423470e-07,4.398710235357963626e-05,-4.021663156733676115e-05,-8.064526618404580449e-06,-7.870485172931396018e-06,-1.476869621335119001e-03,3.139462475834862813e-03
+6.487386747731482134e-05,1.797836318080478077e-07,6.783242618058941899e-05,2.834990996170338077e-09,-9.733303561213900540e-07,-8.469403359801861923e-10,6.871934750650472018e-04,4.481095192191438439e-06,1.872959885100724045e-02,-9.392836229850749527e-08,3.196630046360530894e-05,-8.679998208815885555e-08,-1.540562157272232224e-03,-3.211631223362770827e-06,1.107677407028960070e-03,-2.125535756356327197e-08,1.070176872494440215e-05,3.277061426382349801e-09,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,8.249260854195300877e-04,-3.020900418177957161e-07,1.008187505784626002e-03,-5.431135818807517315e-09,-5.987095299618908152e-06,6.824619934408483737e-09,1.198063854549607024e-02,-1.071648125635806491e-02,2.762137869609124566e-02,2.779524621483461105e-02,6.396349705883477659e-06,-7.178265281339794152e-06
+4.448283877924326928e-09,3.082596304036931558e-06,4.442693852819327324e-10,4.481696527529056075e-08,-5.056528560849447805e-11,-1.856728942679448409e-09,1.683098447874357815e-07,-2.122179093273560125e-04,-9.392836229850749527e-08,3.696746652010075394e-06,3.809476660346366963e-09,1.351500300912581044e-07,-7.582898023929323033e-08,-1.912489292310461906e-05,3.059894527932759745e-08,-1.309475477200604720e-07,4.567583816274247120e-10,3.136273933020337405e-08,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-6.971991155784749461e-09,-1.932642698623366717e-05,-3.794309408768694963e-08,-1.331075184990356830e-07,5.303552142693448525e-11,-2.764453687589907377e-08,-7.883218209394655155e-07,7.231128982414243997e-07,1.390555016856702733e-07,1.383036516171899185e-07,1.260494752831484622e-04,-1.669819827237249796e-04
+-1.282375226629819308e-05,-2.521079345886402218e-09,-9.632798561576065082e-07,-6.236341747891780627e-12,2.069326399202210192e-07,1.397568791723178051e-10,2.115449842446825339e-04,-1.582380322151094441e-07,3.196630046360530894e-05,3.809476660346366963e-09,3.574098435821176575e-06,3.613692814474959499e-09,2.571703324963967274e-05,7.669385345986570922e-08,1.452879165408184470e-05,3.682406089942980847e-10,-2.461022313525857294e-07,-1.059262998319987124e-10,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,2.887998487463856165e-05,3.288516376513685405e-08,-1.055770094538843161e-05,3.121916283144174185e-10,-2.613327439889342815e-07,-5.458446541142112155e-11,-6.932359453207107610e-04,6.403525414646151805e-04,3.264668782645281349e-04,3.470192054947058929e-04,1.302217507469648515e-06,-1.167864297673097961e-06
+-1.130559433117855173e-08,9.517828092227884476e-08,-2.095933397095325157e-09,1.779342700461133972e-09,1.886815484087454092e-10,-1.126064051088119230e-08,1.190186098013398869e-07,-2.343772817635101703e-05,-8.679998208815885555e-08,1.351500300912581044e-07,3.613692814474959499e-09,7.757695963174168962e-07,4.368770391376741256e-08,-1.522078089210777707e-05,2.930159568836635825e-08,-1.131598818971280712e-07,-3.552475283087915462e-10,5.386136083780798815e-08,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,1.008940598184176653e-08,1.435242704912165699e-05,-4.979022525411427824e-08,9.441702961115332008e-08,-1.189957346717065192e-10,5.888186072025247609e-08,-1.776327396779503142e-06,1.626132217819994026e-06,3.830190144507871440e-07,3.979793982428114251e-07,-7.014790702965414796e-05,1.100035191216949956e-04
+1.526362035234832271e-03,-6.012824888898950053e-07,1.541469013830646436e-03,-2.592797813725633417e-08,-2.544385541755165984e-05,-3.698909740289534638e-08,1.538299014562874477e-03,2.180664968086653286e-06,-1.540562157272232224e-03,-7.582898023929323033e-08,2.571703324963967274e-05,4.368770391376741256e-08,2.986150961437222112e-02,1.837457899577931049e-06,5.766586351359107368e-06,4.841119164733790273e-08,2.948232702095594310e-08,1.974223905610059264e-08,5.091123938364686650e-03,-4.383963382862310267e-08,-8.081374946674897003e-09,-1.972958873469937791e-11,-1.969257510833621199e-11,2.988684731656464994e-10,-2.055700329282352239e-04,2.053840914860103202e-07,-1.467289711993278230e-06,-2.964915560938937971e-08,-4.030814840418233802e-08,1.445823713673591054e-09,-4.108810992287108992e-04,1.111183163165435986e-02,7.325450917873890236e-04,-3.910526894050984914e-02,-9.420151958147768409e-05,3.453461855854075797e-05
+-4.668798262241766000e-07,1.092008746110128756e-03,-1.520641514743615230e-06,1.916887368246320887e-05,3.707082594656183519e-08,-1.527197530382847228e-05,1.186034141511475154e-06,1.090021847386008196e-03,-3.211631223362770827e-06,-1.912489292310461906e-05,7.669385345986570922e-08,-1.522078089210777707e-05,1.837457899577931049e-06,3.218547693514104552e-02,9.913067422507177697e-07,3.812867152105378774e-09,-3.591523398174396785e-08,-2.108516202299742771e-05,4.159172597265905179e-08,4.054472130860127359e-03,-4.753341995849418890e-09,-7.251586823941397826e-13,5.024282928859449837e-11,-4.135490626555723883e-05,8.626457598531354822e-07,-3.542644875461494706e-04,-2.697335560719813495e-06,-1.362451752186638181e-08,-1.089494183560040162e-08,-3.019849457068207243e-07,-9.540480261086760230e-05,2.446184193988854341e-05,1.620157683078033846e-05,9.378239470252840688e-06,1.979859123547628337e-04,6.585405890344845498e-03
+-1.745064246003368231e-04,-4.075956429499612055e-07,1.107535705745923927e-03,-1.088587234809755458e-08,1.468530030759727023e-05,2.490881922315957171e-08,1.649047740387377873e-04,-1.325207022276374876e-06,1.107677407028960070e-03,3.059894527932759745e-08,1.452879165408184470e-05,2.930159568836635825e-08,5.766586351359107368e-06,9.913067422507177697e-07,3.241392210858601991e-02,2.826896782085633299e-09,2.494926375463015075e-05,-4.586027165322266898e-09,-9.379374892211356229e-09,-8.212250259567689323e-10,4.053331753043787344e-03,6.863989912003353074e-11,4.136592647600709953e-05,-9.726390444143104754e-11,2.729356834007309451e-06,-1.694904395080998821e-07,1.937803252000565041e-04,2.354358050462486528e-09,-3.515825087423761183e-06,-3.215485076494392053e-09,-1.946356060912559499e-02,-5.780217604255443245e-04,5.430085880767075018e-02,9.389446152417336858e-04,6.146339638147958791e-06,-3.255823302210306017e-05
+-1.109205516216676591e-08,-9.763978711736015292e-06,9.538186728237329641e-09,-1.307659106231961651e-07,-4.243149899898385559e-11,1.135895377817342258e-07,-2.919426313306010560e-09,9.780504204745329067e-06,-2.125535756356327197e-08,-1.309475477200604720e-07,3.682406089942980847e-10,-1.131598818971280712e-07,4.841119164733790273e-08,3.812867152105378774e-09,2.826896782085633299e-09,1.197354116511651694e-06,-8.710836376291208011e-11,-7.738116909447681827e-10,9.911005190491681491e-12,7.602083596587937240e-12,-1.187213132887638470e-10,8.591904977869292189e-08,-4.949215588068326058e-13,-2.884750699188225426e-14,1.512958221847471467e-08,-2.276716342384895093e-08,-4.303388819892330946e-09,-3.119944507179045601e-08,-4.454992569061680859e-11,-5.585493543004513094e-11,-2.069260688929290748e-07,7.197964515646434027e-07,5.448228904204791382e-08,1.688887893556412354e-07,-1.364675539721801737e-04,3.781353956144509504e-06
+1.544662515470008208e-05,-1.987758171848280986e-09,1.070990473706994234e-05,-1.371872544347609066e-10,-2.448298541627253018e-07,-2.599344357150243908e-10,-1.549089912388516689e-05,-1.292151508003754848e-08,1.070176872494440215e-05,4.567583816274247120e-10,-2.461022313525857294e-07,-3.552475283087915462e-10,2.948232702095594310e-08,-3.591523398174396785e-08,2.494926375463015075e-05,-8.710836376291208011e-11,1.165583691757589372e-06,-3.622147920792200526e-11,3.538954534897608382e-11,3.160579113571414151e-11,-4.126356894708871576e-05,-5.313289727044697289e-13,-3.915368815505351380e-07,7.285872772944631792e-13,-4.110737946960289818e-08,7.079765227559003553e-09,6.336777987880577912e-06,3.189841438041415004e-11,1.180044505841544294e-09,-5.291890048070587499e-11,5.992902476904993128e-05,1.255897582375219958e-06,2.784942101815185726e-04,4.533099716390055372e-06,1.851660229479581726e-07,-6.445332080019974148e-07
+8.972501296723185406e-11,6.670361559754391166e-08,3.544724999441598161e-09,-3.153899031763136528e-08,-5.590924880090475142e-11,5.402095541390601796e-08,-4.084385389688405339e-09,7.511041181527693849e-08,3.277061426382349801e-09,3.136273933020337405e-08,-1.059262998319987124e-10,5.386136083780798815e-08,1.974223905610059264e-08,-2.108516202299742771e-05,-4.586027165322266898e-09,-7.738116909447681827e-10,-3.622147920792200526e-11,1.385343650278670499e-06,2.983657779277850696e-10,4.128354504694781260e-05,-6.431660186683227755e-11,-4.220126134146356053e-14,3.155252229994924052e-13,-3.914826726919548336e-07,-3.070547711393259436e-09,7.805257063886365597e-07,3.418720664979126018e-09,4.816189388064040918e-11,9.521828372182657872e-12,3.742716077475449824e-10,9.801773076303316427e-08,4.094727481606651026e-09,1.654722106776775455e-08,-3.752332913638815351e-08,7.462457530283788874e-07,2.546721043522765592e-05
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,5.091123938364686650e-03,4.159172597265905179e-08,-9.379374892211356229e-09,9.911005190491681491e-12,3.538954534897608382e-11,2.983657779277850696e-10,1.583804751296818969e-02,2.764552624015981664e-08,1.014379559126019070e-08,1.153439328600758867e-10,3.539753090424785178e-11,-8.306211574661732851e-10,2.477556402518308297e-03,1.880851193525713907e-08,8.982190997557711488e-10,4.116010459447206072e-11,1.817857605242105993e-12,1.891389500963166072e-11,2.073421799822446093e-15,-1.138809436590432493e-15,-1.702611758654926040e-15,-5.835123821385638269e-15,4.132798200330907072e-12,8.821234789810766910e-12
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-4.383963382862310267e-08,4.054472130860127359e-03,-8.212250259567689323e-10,7.602083596587937240e-12,3.160579113571414151e-11,4.128354504694781260e-05,2.764552624015981664e-08,1.721772780991420032e-02,1.509444005163282295e-08,3.702328369107352955e-11,1.190056124912058633e-10,-4.937630312587707680e-05,3.009224882287702546e-08,2.141532485208008565e-03,-4.058763386641857807e-09,-2.028567037525057206e-11,3.383267869024265468e-11,-1.193704763819182377e-05,-2.516039987071683396e-15,-1.562401258202842405e-15,2.666509142730746717e-15,-1.158774714470924039e-15,-8.131918756291314033e-12,1.188328975713573192e-12
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-8.081374946674897003e-09,-4.753341995849418890e-09,4.053331753043787344e-03,-1.187213132887638470e-10,-4.126356894708871576e-05,-6.431660186683227755e-11,1.014379559126019070e-08,1.509444005163282295e-08,1.722581901142078084e-02,2.755193502055623391e-10,4.941038299932088687e-05,-3.286059169241361173e-10,-6.231070845657670637e-10,1.707909043242850349e-09,2.140022201587438687e-03,-7.900119137371452147e-11,1.192925297945728013e-05,-4.678056785305476066e-11,5.660280438197084154e-17,8.551483531987762465e-16,-5.969503920414246988e-16,-2.654149709078034299e-16,-6.106324138504044733e-12,-1.326305358464349752e-12
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-1.972958873469937791e-11,-7.251586823941397826e-13,6.863989912003353074e-11,8.591904977869292189e-08,-5.313289727044697289e-13,-4.220126134146356053e-14,1.153439328600758867e-10,3.702328369107352955e-11,2.755193502055623391e-10,2.616882487805848604e-07,2.280385139959450865e-12,4.234388089142069637e-13,-4.669968500564964040e-11,-3.161101620480069108e-12,5.241902428093128381e-11,4.266412736924540662e-08,-4.016682469026852481e-14,3.118629056580021306e-14,1.776430379302809414e-17,7.030967543637565320e-18,-1.911984201216578828e-17,-1.205291239363705762e-17,3.515002771263806779e-14,1.766743374898922161e-14
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,-1.969257510833621199e-11,5.024282928859449837e-11,4.136592647600709953e-05,-4.949215588068326058e-13,-3.915368815505351380e-07,3.155252229994924052e-13,3.539753090424785178e-11,1.190056124912058633e-10,4.941038299932088687e-05,2.280385139959450865e-12,5.827927961875376182e-07,-3.594129558547875935e-12,7.240992462209523527e-14,-6.502906668644756475e-11,-1.197685726933055244e-05,1.667763431235762149e-13,-5.368267313587042094e-08,4.490520252150802351e-13,1.445329597349431595e-18,-1.658565793799726192e-18,-1.796559012265829621e-19,4.409543043730753992e-18,2.063137467005570282e-14,5.134207147499640655e-15
+0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,2.988684731656464994e-10,-4.135490626555723883e-05,-9.726390444143104754e-11,-2.884750699188225426e-14,7.285872772944631792e-13,-3.914826726919548336e-07,-8.306211574661732851e-10,-4.937630312587707680e-05,-3.286059169241361173e-10,4.234388089142069637e-13,-3.594129558547875935e-12,5.818935528024568841e-07,9.926589276620312321e-12,1.197311366666095167e-05,9.536280436285995002e-12,4.021442367385905087e-14,2.167697357644009390e-13,-5.365327390046775115e-08,4.506551971194674612e-18,-2.877960456941318961e-19,-5.729980766802166529e-18,-1.756968475032437969e-17,-9.361618284169833124e-15,1.760854135105245653e-14
+1.825396452580777939e-03,-7.158027451354804802e-07,-8.297489567196014888e-04,-2.020229090800761086e-08,-2.858074900228838454e-05,-3.171752631634308571e-09,1.834751766225578996e-03,-3.059618648662299498e-07,8.249260854195300877e-04,-6.971991155784749461e-09,2.887998487463856165e-05,1.008940598184176653e-08,-2.055700329282352239e-04,8.626457598531354822e-07,2.729356834007309451e-06,1.512958221847471467e-08,-4.110737946960289818e-08,-3.070547711393259436e-09,2.477556402518308297e-03,3.009224882287702546e-08,-6.231070845657670637e-10,-4.669968500564964040e-11,7.240992462209523527e-14,9.926589276620312321e-12,2.391356883711306253e-02,-1.282145787409289225e-06,-3.214155515042224764e-06,-1.415542412953668694e-08,-4.512693350843216138e-08,-1.074240338808274180e-08,3.191121693611184218e-04,-1.599890007583958454e-02,-3.737501023978322969e-04,2.400533582340593983e-02,-5.538566902308577033e-05,-2.121173219752555380e-06
+-9.948861092355896187e-07,1.159216052945812037e-03,1.146143076979051826e-06,1.937900423841364833e-05,-2.543915903920236373e-09,1.439966444769548844e-05,2.072563560783651399e-06,1.157683486489578068e-03,-3.020900418177957161e-07,-1.932642698623366717e-05,3.288516376513685405e-08,1.435242704912165699e-05,2.053840914860103202e-07,-3.542644875461494706e-04,-1.694904395080998821e-07,-2.276716342384895093e-08,7.079765227559003553e-09,7.805257063886365597e-07,1.880851193525713907e-08,2.141532485208008565e-03,1.707909043242850349e-09,-3.161101620480069108e-12,-6.502906668644756475e-11,1.197311366666095167e-05,-1.282145787409289225e-06,2.644144318977177666e-02,2.220456255461496306e-07,1.176098605668647304e-08,2.359203311164662301e-08,7.009095324435605080e-05,2.213511168617307708e-05,2.048393085872325645e-05,-1.667719041491555529e-06,-1.046137039038549768e-06,-2.516898199548532372e-04,-1.100484971190517081e-02
+-1.034228641590971315e-04,2.660180134760386451e-07,1.008587175066319973e-03,5.911734192184404569e-09,-1.068803865801896532e-05,-5.418257032113064294e-08,1.106693884727988310e-04,1.782376302113344743e-06,1.008187505784626002e-03,-3.794309408768694963e-08,-1.055770094538843161e-05,-4.979022525411427824e-08,-1.467289711993278230e-06,-2.697335560719813495e-06,1.937803252000565041e-04,-4.303388819892330946e-09,6.336777987880577912e-06,3.418720664979126018e-09,8.982190997557711488e-10,-4.058763386641857807e-09,2.140022201587438687e-03,5.241902428093128381e-11,-1.197685726933055244e-05,9.536280436285995002e-12,-3.214155515042224764e-06,2.220456255461496306e-07,2.652586541210986623e-02,-8.797591818841949475e-09,-7.191235935496872707e-05,-8.173614603832773301e-09,5.076392695497881219e-02,1.535313106913188761e-03,2.490093298161156002e-02,4.561714289173275519e-04,2.608381728323489595e-06,4.122464722970570645e-05
+1.522106844068990743e-08,-1.035270525781877414e-05,-7.360197755104747025e-09,-1.337146920477737147e-07,-1.011591300875160494e-10,-9.500069516313784108e-08,2.050764899570531600e-08,1.032889897373744964e-05,-5.431135818807517315e-09,-1.331075184990356830e-07,3.121916283144174185e-10,9.441702961115332008e-08,-2.964915560938937971e-08,-1.362451752186638181e-08,2.354358050462486528e-09,-3.119944507179045601e-08,3.189841438041415004e-11,4.816189388064040918e-11,4.116010459447206072e-11,-2.028567037525057206e-11,-7.900119137371452147e-11,4.266412736924540662e-08,1.667763431235762149e-13,4.021442367385905087e-14,-1.415542412953668694e-08,1.176098605668647304e-08,-8.797591818841949475e-09,1.127609153437166272e-06,1.375647397098802915e-11,-7.418269852293293593e-11,-1.228865852920092457e-07,-3.346235774910663652e-07,-2.823085799794089686e-08,-4.112486883734950474e-08,4.088961039747382258e-04,-1.149228524899360260e-05
+1.690480000801803878e-05,-1.795051316941698216e-09,-6.014060089449772913e-06,-8.590801361534870548e-11,-2.598378281351281043e-07,-2.714730510660179609e-11,-1.693913639835141984e-05,1.600251588192170695e-09,-5.987095299618908152e-06,5.303552142693448525e-11,-2.613327439889342815e-07,-1.189957346717065192e-10,-4.030814840418233802e-08,-1.089494183560040162e-08,-3.515825087423761183e-06,-4.454992569061680859e-11,1.180044505841544294e-09,9.521828372182657872e-12,1.817857605242105993e-12,3.383267869024265468e-11,1.192925297945728013e-05,-4.016682469026852481e-14,-5.368267313587042094e-08,2.167697357644009390e-13,-4.512693350843216138e-08,2.359203311164662301e-08,-7.191235935496872707e-05,1.375647397098802915e-11,7.085690757528244913e-07,1.674732427043832613e-10,-1.266942667803092190e-04,-4.741112135793510514e-06,-1.628848455992283281e-04,-3.170015743576760585e-06,-3.811215191746712750e-08,-3.899691803600627811e-07
+1.441457762661818876e-09,-1.976296487166061230e-07,-3.171276286116626543e-10,2.743826692408501919e-08,-4.046046526084699107e-11,5.889423296747125739e-08,1.194113690682714162e-09,-1.874599877388423470e-07,6.824619934408483737e-09,-2.764453687589907377e-08,-5.458446541142112155e-11,5.888186072025247609e-08,1.445823713673591054e-09,-3.019849457068207243e-07,-3.215485076494392053e-09,-5.585493543004513094e-11,-5.291890048070587499e-11,3.742716077475449824e-10,1.891389500963166072e-11,-1.193704763819182377e-05,-4.678056785305476066e-11,3.118629056580021306e-14,4.490520252150802351e-13,-5.365327390046775115e-08,-1.074240338808274180e-08,7.009095324435605080e-05,-8.173614603832773301e-09,-7.418269852293293593e-11,1.674732427043832613e-10,9.590931888019099317e-07,-1.040354184986034090e-08,-4.083893214533423480e-08,-3.150528908047722833e-08,4.889792300394978986e-09,4.306966049310867438e-06,1.576809419363080537e-04
+1.881964318465226618e-02,1.224693738571713620e-05,1.133680337432957375e-02,1.436582493590590977e-07,-6.570127307142901866e-04,-1.454886499857698024e-06,-1.969432159947379773e-02,4.398710235357963626e-05,1.198063854549607024e-02,-7.883218209394655155e-07,-6.932359453207107610e-04,-1.776327396779503142e-06,-4.108810992287108992e-04,-9.540480261086760230e-05,-1.946356060912559499e-02,-2.069260688929290748e-07,5.992902476904993128e-05,9.801773076303316427e-08,2.073421799822446093e-15,-2.516039987071683396e-15,5.660280438197084154e-17,1.776430379302809414e-17,1.445329597349431595e-18,4.506551971194674612e-18,3.191121693611184218e-04,2.213511168617307708e-05,5.076392695497881219e-02,-1.228865852920092457e-07,-1.266942667803092190e-04,-1.040354184986034090e-08,1.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+1.891852489691360148e-02,8.425724786988658956e-06,1.142618693889066450e-02,7.922083192776589500e-08,-6.827902319201428804e-04,-1.467810156137431251e-06,1.761267283589188284e-02,-4.021663156733676115e-05,-1.071648125635806491e-02,7.231128982414243997e-07,6.403525414646151805e-04,1.626132217819994026e-06,1.111183163165435986e-02,2.446184193988854341e-05,-5.780217604255443245e-04,7.197964515646434027e-07,1.255897582375219958e-06,4.094727481606651026e-09,-1.138809436590432493e-15,-1.562401258202842405e-15,8.551483531987762465e-16,7.030967543637565320e-18,-1.658565793799726192e-18,-2.877960456941318961e-19,-1.599890007583958454e-02,2.048393085872325645e-05,1.535313106913188761e-03,-3.346235774910663652e-07,-4.741112135793510514e-06,-4.083893214533423480e-08,0.000000000000000000e+00,1.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+-1.238269560363562845e-02,-2.792987281876710131e-06,2.857030399578119537e-02,-1.071932885513176235e-07,3.400612310843032860e-04,1.119155214117794464e-07,1.183571470812026967e-02,-8.064526618404580449e-06,2.762137869609124566e-02,1.390555016856702733e-07,3.264668782645281349e-04,3.830190144507871440e-07,7.325450917873890236e-04,1.620157683078033846e-05,5.430085880767075018e-02,5.448228904204791382e-08,2.784942101815185726e-04,1.654722106776775455e-08,-1.702611758654926040e-15,2.666509142730746717e-15,-5.969503920414246988e-16,-1.911984201216578828e-17,-1.796559012265829621e-19,-5.729980766802166529e-18,-3.737501023978322969e-04,-1.667719041491555529e-06,2.490093298161156002e-02,-2.823085799794089686e-08,-1.628848455992283281e-04,-3.150528908047722833e-08,0.000000000000000000e+00,0.000000000000000000e+00,1.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+1.271698470055658038e-02,9.478632026860526287e-07,-2.680324778367691729e-02,7.450178844215838462e-08,-3.367586741383695207e-04,-7.368557067191898770e-08,1.305851599488310963e-02,-7.870485172931396018e-06,2.779524621483461105e-02,1.383036516171899185e-07,3.470192054947058929e-04,3.979793982428114251e-07,-3.910526894050984914e-02,9.378239470252840688e-06,9.389446152417336858e-04,1.688887893556412354e-07,4.533099716390055372e-06,-3.752332913638815351e-08,-5.835123821385638269e-15,-1.158774714470924039e-15,-2.654149709078034299e-16,-1.205291239363705762e-17,4.409543043730753992e-18,-1.756968475032437969e-17,2.400533582340593983e-02,-1.046137039038549768e-06,4.561714289173275519e-04,-4.112486883734950474e-08,-3.170015743576760585e-06,4.889792300394978986e-09,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,1.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00
+6.397636245733210475e-05,1.613066166058059253e-03,-1.615816014206646941e-06,1.345104998114586439e-04,-1.150469137000843430e-06,7.529278844748940917e-05,7.627161198701218922e-05,-1.476869621335119001e-03,6.396349705883477659e-06,1.260494752831484622e-04,1.302217507469648515e-06,-7.014790702965414796e-05,-9.420151958147768409e-05,1.979859123547628337e-04,6.146339638147958791e-06,-1.364675539721801737e-04,1.851660229479581726e-07,7.462457530283788874e-07,4.132798200330907072e-12,-8.131918756291314033e-12,-6.106324138504044733e-12,3.515002771263806779e-14,2.063137467005570282e-14,-9.361618284169833124e-15,-5.538566902308577033e-05,-2.516898199548532372e-04,2.608381728323489595e-06,4.088961039747382258e-04,-3.811215191746712750e-08,4.306966049310867438e-06,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,1.000000000000000000e+00,0.000000000000000000e+00
+4.153205762773307878e-05,3.030574880783558789e-03,-2.410470030098440860e-06,1.596360248084656398e-04,-7.980334714743009670e-07,1.054460659418814784e-04,-6.736815642436647068e-05,3.139462475834862813e-03,-7.178265281339794152e-06,-1.669819827237249796e-04,-1.167864297673097961e-06,1.100035191216949956e-04,3.453461855854075797e-05,6.585405890344845498e-03,-3.255823302210306017e-05,3.781353956144509504e-06,-6.445332080019974148e-07,2.546721043522765592e-05,8.821234789810766910e-12,1.188328975713573192e-12,-1.326305358464349752e-12,1.766743374898922161e-14,5.134207147499640655e-15,1.760854135105245653e-14,-2.121173219752555380e-06,-1.100484971190517081e-02,4.122464722970570645e-05,-1.149228524899360260e-05,-3.899691803600627811e-07,1.576809419363080537e-04,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,0.000000000000000000e+00,1.000000000000000000e+00

matlab/STEPS/new_APA300ML_out_nodes_3D.txt

@@ -0,0 +1,61 @@
+
+ LIST ALL SELECTED NODES.   DSYS=      0
+
+ *** ANSYS - ENGINEERING ANALYSIS SYSTEM  RELEASE 2020 R2          20.2     ***
+ DISTRIBUTED ANSYS Mechanical Enterprise                       
+
+ 00208316  VERSION=WINDOWS x64   10:10:05  MAR 26, 2021 CP=      2.188
+
+ Unknown                                                                       
+
+
+
+    NODE        X             Y             Z           THXY     THYZ     THZX
+        1   0.0000        0.0000       0.28000E-001     0.00     0.00     0.00
+  1228810   0.0000        0.0000      -0.28000E-001     0.00     0.00     0.00
+  1228811 -0.30000E-001   0.0000        0.0000          0.00     0.00     0.00
+  1228812  0.10000E-001   0.0000        0.0000          0.00     0.00     0.00
+  1228813  0.30000E-001   0.0000        0.0000          0.00     0.00     0.00
+
+ LIST MASTERS ON ALL SELECTED NODES.
+ CURRENT DOF SET= UX   UY   UZ   ROTX ROTY ROTZ
+
+ *** ANSYS - ENGINEERING ANALYSIS SYSTEM  RELEASE 2020 R2          20.2     ***
+ DISTRIBUTED ANSYS Mechanical Enterprise                       
+
+ 00208316  VERSION=WINDOWS x64   10:10:05  MAR 26, 2021 CP=      2.188
+
+ Unknown                                                                       
+
+
+     NODE  LABEL     SUPPORT
+         1  UX  
+         1  UY  
+         1  UZ  
+         1  ROTX
+         1  ROTY
+         1  ROTZ
+   1228810  UX  
+   1228810  UY  
+   1228810  UZ  
+   1228810  ROTX
+   1228810  ROTY
+   1228810  ROTZ
+   1228811  UX  
+   1228811  UY  
+   1228811  UZ  
+   1228811  ROTX
+   1228811  ROTY
+   1228811  ROTZ
+   1228812  UX  
+   1228812  UY  
+   1228812  UZ  
+   1228812  ROTX
+   1228812  ROTY
+   1228812  ROTZ
+   1228813  UX  
+   1228813  UY  
+   1228813  UZ  
+   1228813  ROTX
+   1228813  ROTY
+   1228813  ROTZ

matlab/src/extractNodes.m

@@ -0,0 +1,91 @@
+function [int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes(filename)
+% extractNodes -
+%
+% Syntax: [n_xyz, nodes] = extractNodes(filename)
+%
+% Inputs:
+%    - filename - relative or absolute path of the file that contains the Matrix
+%
+% Outputs:
+%    - n_xyz -
+%    - nodes - table containing the node numbers and corresponding dof of the interfaced DoFs
+
+arguments
+    filename
+end
+
+fid = fopen(filename,'rt');
+
+if fid == -1
+    error('Error opening the file');
+end
+
+n_xyz = []; % Contains nodes coordinates
+n_i = []; % Contains nodes indices
+
+n_num = []; % Contains node numbers
+n_dof = {}; % Contains node directions
+
+while 1
+    % Read a line
+    nextline = fgetl(fid);
+
+    % End of the file
+    if ~isstr(nextline), break, end
+
+    % Line just before the list of nodes coordinates
+    if contains(nextline, 'NODE') && ...
+            contains(nextline, 'X') && ...
+            contains(nextline, 'Y') && ...
+            contains(nextline, 'Z')
+
+        while 1
+            nextline = fgetl(fid);
+
+            if nextline < 0, break, end
+
+            c = sscanf(nextline, ' %f');
+
+            if isempty(c), break, end
+
+            n_xyz = [n_xyz; c(2:4)'];
+            n_i = [n_i; c(1)];
+        end
+    end
+
+    if nextline < 0, break, end
+
+    % Line just before the list of node DOF
+  if contains(nextline, 'NODE') && ...
+         contains(nextline, 'LABEL')
+
+        while 1
+            nextline = fgetl(fid);
+
+            if nextline < 0, break, end
+
+            c = sscanf(nextline, ' %d %s');
+
+            if isempty(c), break, end
+
+            n_num = [n_num; c(1)];
+
+            n_dof{length(n_dof)+1} = char(c(2:end)');
+        end
+
+        nodes = table(n_num, string(n_dof'), 'VariableNames', {'node_i', 'node_dof'});
+    end
+
+    if nextline < 0, break, end
+end
+
+fclose(fid);
+
+int_i = unique(nodes.('node_i')); % indices of interface nodes
+
+% Extract XYZ coordinates of only the interface nodes
+if length(n_xyz) > 0 && length(n_i) > 0
+    int_xyz = n_xyz(logical(sum(n_i.*ones(1, length(int_i)) == int_i', 2)), :);
+else
+    int_xyz = n_xyz;
+end

matlab/src/initializeAPA.m

@@ -53,26 +53,22 @@ if args.Ga == 0
     switch args.type
       case '2dof'
         actuator.Ga = -2.5796;
-      case 'flexible frame'
-        actuator.Ga = 1; % TODO
       case 'flexible'
         actuator.Ga = 23.2;
     end
 else
-    actuator.Ga = args.Ga; % Actuator gain [N/V]
+    actuator.Ga = args.Ga; % Actuator sensitivity [N/V]
 end
 
 if args.Gs == 0
     switch args.type
       case '2dof'
         actuator.Gs = 466664;
-      case 'flexible frame'
-        actuator.Gs = 1; % TODO
       case 'flexible'
         actuator.Gs = -4898341;
     end
 else
-    actuator.Gs = args.Gs; % Sensor gain [V/m]
+    actuator.Gs = args.Gs; % Sensor sensitivity [V/m]
 end
 
 actuator.k  = args.k;  % [N/m]

matlab/test_apa_1_basic_meas.m

@@ -11,21 +11,6 @@ addpath('./mat/'); % Path for data
 %% Colors for the figures
 colors = colororder;
 
-% Geometrical Measurements
-% <<sec:test_apa_geometrical_measurements>>
-
-% To measure the flatness of the two mechanical interfaces of the APA300ML, a small measurement bench is installed on top of a metrology granite with very good flatness.
-
-% As shown in Figure ref:fig:test_apa_flatness_setup, the APA is fixed to a clamp while a measuring probe[fn:3] is used to measure the height of 4 points on each of the APA300ML interfaces.
-
-% From the X-Y-Z coordinates of the measured 8 points, the flatness is estimated by best fitting[fn:4] a plane through all the points.
-
-% #+name: fig:test_apa_flatness_setup
-% #+attr_latex: :width 0.4\linewidth
-% #+caption: Measurement setup for flatness estimation of the two mechanical interfaces
-% [[file:figs/test_apa_flatness_setup.png]]
-
-
 %% Measured height for all the APA at the 8 locations
 apa1 = 1e-6*[0, -0.5 , 3.5  , 3.5  , 42   , 45.5, 52.5 , 46];
 apa2 = 1e-6*[0, -2.5 , -3   , 0    , -1.5 , 1   , -2   , -4];
@@ -61,47 +46,17 @@ for i = 1:7
     apa_d(i) = min_d;
 end
 
-% Stroke and Hysteresis Measurement
-% <<sec:test_apa_stroke_measurements>>
-
-% The goal is here to verify that the stroke of the APA300ML is as specified in the datasheet.
-% To do so, one side of the APA is fixed to the granite, and a displacement probe[fn:2] is located on the other side as shown in Figure ref:fig:test_apa_stroke_bench.
-
-% Then, the voltage across the two actuator stacks is varied from $-20\,V$ to $150\,V$ using a DAC and a voltage amplifier.
-% Note that the voltage is here slowly varied as the displacement probe has a very low measurement bandwidth (see Figure ref:fig:test_apa_stroke_bench, left).
-
-% #+name: fig:test_apa_stroke_bench
-% #+caption: Bench to measured the APA stroke
-% #+attr_latex: :width 0.9\linewidth
-% [[file:figs/test_apa_stroke_bench.jpg]]
-
-% The measured APA displacement is shown as a function of the applied voltage in Figure ref:fig:test_apa_stroke_result, right.
-
-% Typical hysteresis curves for piezoelectric stack actuators can be observed.
-% The measured stroke is approximately $250\,\mu m$ when using only two of the three stacks, which is enough for the current application.
-% This is even above what is specified as the nominal stroke in the data-sheet ($304\,\mu m$, therefore $\approx 200\,\mu m$ if only two stacks are used).
-
-% It is clear from Figure ref:fig:test_apa_stroke_result that "APA 3" has an issue compared to the other units.
-% This confirms the abnormal electrical measurements made in Section ref:sec:test_apa_electrical_measurements.
-% This unit was send sent back to Cedrat and a new one was shipped back.
-% From now on, only the six APA that behave as expected will be used.
-
-
 %% Load the measured strokes
 load('meas_apa_stroke.mat', 'apa300ml_2s')
 
-%% Results of the measured APA stroke
+%% Generated voltage across the two piezoelectric stack actuators to estimate the stroke of the APA300ML
 figure;
-tiledlayout(1, 2, 'TileSpacing', 'Compact', 'Padding', 'None');
-
-% Generated voltage across the two piezoelectric stack actuators to estimate the stroke of the APA300ML
-ax1 = nexttile();
 plot(apa300ml_2s{1}.t - apa300ml_2s{1}.t(1), 20*apa300ml_2s{1}.V, 'k-')
 xlabel('Time [s]'); ylabel('Voltage [V]')
 ylim([-20, 160])
 
-% Measured displacement as a function of the applied voltage
+%% Measured displacement as a function of the applied voltage
-ax2 = nexttile();
+figure;
 hold on;
 for i = 1:7
     plot(20*apa300ml_2s{i}.V, 1e6*apa300ml_2s{i}.d, 'DisplayName', sprintf('APA %i', i))
@@ -111,48 +66,6 @@ xlabel('Voltage [V]'); ylabel('Displacement [$\mu m$]')
 legend('location', 'southwest', 'FontSize', 8)
 xlim([-20, 150]); ylim([-250, 0]);
 
-% Flexible Mode Measurement
-% SCHEDULED: <2024-03-27 Wed>
-% <<sec:test_apa_spurious_resonances>>
-
-% In this section, the flexible modes of the APA300ML are investigated both experimentally and using a Finite Element Model.
-
-% To experimentally estimate these modes, the APA is fixed on one end (see Figure ref:fig:test_apa_meas_setup_torsion).
-% A Laser Doppler Vibrometer[fn:6] is used to measure the difference of motion between two "red" points (i.e. the torsion of the APA along the vertical direction) and an instrumented hammer[fn:7] is used to excite the flexible modes.
-% Using this setup, the transfer function from the injected force to the measured rotation can be computed in different conditions and the frequency and mode shapes of the flexible modes can be estimated.
-
-% The flexible modes for the same condition (i.e. one mechanical interface of the APA300ML fixed) are estimated using a finite element software and the results are shown in Figure ref:fig:test_apa_mode_shapes.
-
-% #+name: fig:test_apa_mode_shapes
-% #+caption: Spurious resonances - Change this with the updated FEM analysis of the APA300ML
-% #+attr_latex: :width 0.9\linewidth
-% [[file:figs/test_apa_mode_shapes.png]]
-
-% #+name: fig:test_apa_meas_setup_torsion
-% #+caption: Measurement setup with a Laser Doppler Vibrometer and one instrumental hammer. Here the $Z$ torsion is measured.
-% #+attr_latex: :width 0.6\linewidth
-% [[file:figs/test_apa_meas_setup_torsion.jpg]]
-
-% Two other similar measurements are performed to measured the bending of the APA around the $X$ direction and around the $Y$ direction (see Figure ref:fig:test_apa_meas_setup_modes).
-
-% #+name: fig:test_apa_meas_setup_modes
-% #+caption: Experimental setup to measured flexible modes of the APA300ML. For the bending in the $X$ direction, the impact point is located at the back of the top measurement point. For the bending in the $Y$ direction, the impact point is located on the back surface of the top interface (on the back of the 2 measurements points).
-% #+begin_figure
-% #+attr_latex: :caption \subcaption{\label{fig:test_apa_meas_setup_X_bending}$X$ bending}
-% #+attr_latex: :options {0.49\textwidth}
-% #+begin_subfigure
-% #+attr_latex: :width 0.95\linewidth
-% [[file:figs/test_apa_meas_setup_X_bending.jpg]]
-% #+end_subfigure
-% #+attr_latex: :caption \subcaption{\label{fig:test_apa_meas_setup_Y_bending}$Y$ Bending}
-% #+attr_latex: :options {0.49\textwidth}
-% #+begin_subfigure
-% #+attr_latex: :width 0.95\linewidth
-% [[file:figs/test_apa_meas_setup_Y_bending.jpg]]
-% #+end_subfigure
-% #+end_figure
-
-
 %% X-Bending Identification
 % Load Data
 bending_X = load('apa300ml_bending_X_top.mat');
@@ -173,37 +86,14 @@ bending_Y = load('apa300ml_bending_Y_top.mat');
 % Compute the transfer function
 [G_bending_Y, ~]  = tfestimate(bending_Y.Track1, bending_Y.Track2, win, Noverlap, Nfft, 1/Ts);
 
-%% Z-Torsion identification
-% Load data
-torsion = load('apa300ml_torsion_top.mat');
-
-% Compute transfer function
-[G_torsion_top, ~]  = tfestimate(torsion.Track1, torsion.Track2, win, Noverlap, Nfft, 1/Ts);
-
-% Load Data
-torsion = load('apa300ml_torsion_left.mat');
-
-% Compute transfer function
-[G_torsion, ~]  = tfestimate(torsion.Track1, torsion.Track2, win, Noverlap, Nfft, 1/Ts);
-
-
-
-% The three measured frequency response functions are shown in Figure ref:fig:test_apa_meas_freq_compare.
-% - a clear $x$ bending mode at $280\,\text{Hz}$
-% - a clear $y$ bending mode at $412\,\text{Hz}$
-% - for the $z$ torsion test, the $y$ bending mode is also excited and observed, and we may see a mode at $800\,\text{Hz}$
-
-
 figure;
 hold on;
 plot(f, abs(G_bending_X), 'DisplayName', '$X$ bending');
 plot(f, abs(G_bending_Y), 'DisplayName', '$Y$ bending');
-plot(f, abs(G_torsion),   'DisplayName', '$Z$ torsion');
 text(280, 5.5e-2,{'280Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
 text(412, 1.5e-2,{'412Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
-text(800, 6e-4,{'800Hz'}, 'VerticalAlignment', 'bottom','HorizontalAlignment','center')
 hold off;
 set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
 xlabel('Frequency [Hz]'); ylabel('Amplitude');
-xlim([50, 2e3]); ylim([5e-5, 2e-1]);
+xlim([100, 1e3]); ylim([5e-5, 2e-1]);
 legend('location', 'northeast', 'FontSize', 8)

matlab/test_apa_2_dynamics.m

@@ -11,16 +11,6 @@ addpath('./mat/'); % Path for data
 %% Colors for the figures
 colors = colororder;
 
-% Hysteresis
-% <<ssec:test_apa_hysteresis>>
-
-% As the payload is vertically guided without friction, the hysteresis of the APA can be estimated from the motion of the payload.
-
-% A quasi static sinusoidal excitation $V_a$ with an offset of $65\,V$ (halfway between $-20\,V$ and $150\,V$), and an amplitude varying from $4\,V$ up to $80\,V$.
-
-% For each excitation amplitude, the vertical displacement $d_e$ of the mass is measured and displayed as a function of the applied voltage..
-
-
 %% Load measured data - hysteresis
 apa_hyst = load('frf_data_1_hysteresis.mat', 't', 'u', 'de');
 
@@ -29,12 +19,6 @@ apa_hyst.t = apa_hyst.t - apa_hyst.t(1);
 
 ampls = [0.1, 0.2, 0.4, 1, 2, 4]; % Excitation voltage amplitudes
 
-
-
-% The measured displacements as a function of the output voltages are shown in Figure ref:fig:test_apa_meas_hysteresis.
-% It is interesting to see that the hysteresis is increasing with the excitation amplitude.
-
-
 %% Measured displacement as a function of the output voltage
 figure;
 
@@ -50,18 +34,6 @@ legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
 xlim([-20, 150]);
 ylim([-120, 120]);
 
-% Axial stiffness
-% <<ssec:test_apa_stiffness>>
-
-% In order to estimate the stiffness of the APA, a weight with known mass $m_a = 6.4\,\text{kg}$ is added on top of the suspended granite and the deflection $d_e$ is measured using the encoder.
-
-% The APA stiffness can then be estimated from equation eqref:eq:test_apa_stiffness.
-
-% \begin{equation} \label{eq:test_apa_stiffness}
-%   k_{\text{apa}} = \frac{m_a g}{\Delta d_e}
-% \end{equation}
-
-
 %% Load data for stiffness measurement
 apa_nums = [1 2 4 5 6 8];
 apa_mass = {};
@@ -73,13 +45,6 @@ end
 
 added_mass = 6.4; % Added mass [kg]
 
-
-
-% The measured displacement $d_e$ as a function of time is shown in Figure ref:fig:test_apa_meas_stiffness_time.
-% It can be seen that there are some drifts in the measured displacement (probably due to piezoelectric creep) and the that displacement does not come back to the initial position after the mass is removed (probably due to piezoelectric hysteresis).
-% These two effects induce some uncertainties in the measured stiffness.
-
-
 %% Plot the deflection at a function of time
 figure;
 hold on;
@@ -103,40 +68,6 @@ text(18.5, -20, sprintf('$d_2$'), 'horizontalalignment', 'left');
 hold off;
 xlabel('Time [s]'); ylabel('Displacement $d_e$ [$\mu$m]');
 
-
-
-% #+name: tab:test_apa_measured_stiffnesses
-% #+caption: Measured stiffnesses (in $N/\mu m$)
-% #+attr_latex: :environment tabularx :width 0.2\linewidth :align ccc
-% #+attr_latex: :center t :booktabs t :float t
-% #+RESULTS:
-% | APA | $k_1$ | $k_2$ |
-% |-----+-------+-------|
-% |   1 |  1.68 |   1.9 |
-% |   2 |  1.69 |   1.9 |
-% |   4 |   1.7 |  1.91 |
-% |   5 |   1.7 |  1.93 |
-% |   6 |   1.7 |  1.92 |
-% |   8 |  1.73 |  1.98 |
-
-% The stiffness can also be computed using equation eqref:eq:test_apa_res_freq by knowing the main vertical resonance frequency $\omega_z \approx 95\,\text{Hz}$ (estimated by the dynamical measurements shown in section ref:ssec:test_apa_meas_dynamics) and the suspended mass $m_{\text{sus}} = 5.7\,\text{kg}$.
-
-% \begin{equation} \label{eq:test_apa_res_freq}
-% \omega_z = \sqrt{\frac{k}{m_{\text{sus}}}}
-% \end{equation}
-
-% The obtain stiffness is $k \approx 2\,N/\mu m$ which is close to the values found in the documentation and by the "static deflection" method.
-
-
-% However, changes in the electrical impedance connected to the piezoelectric stacks impacts the mechanical compliance (or stiffness) of the piezoelectric stack [[cite:&reza06_piezoel_trans_vibrat_contr_dampin chap. 2]].
-
-% To estimate this effect, the stiffness of the APA if measured using the "static deflection" method in two cases:
-% - $k_{\text{os}}$: piezoelectric stacks left unconnected (or connect to the high impedance ADC)
-% - $k_{\text{sc}}$: piezoelectric stacks short circuited (or connected to the voltage amplifier with small output impedance)
-
-% The open-circuit stiffness is estimated at $k_{\text{oc}} \approx 2.3\,N/\mu m$ and the closed-circuit stiffness $k_{\text{sc}} \approx 1.7\,N/\mu m$.
-
-
 %% Load Data
 add_mass_oc = load('frf_data_1_add_mass_open_circuit.mat',   't', 'de');
 add_mass_cc = load('frf_data_1_add_mass_closed_circuit.mat', 't', 'de');
@@ -149,12 +80,6 @@ add_mass_cc.de = add_mass_cc.de - mean(add_mass_cc.de(add_mass_cc.t<11));
 apa_k_oc = 9.8 * added_mass / (mean(add_mass_oc.de(add_mass_oc.t > 12 & add_mass_oc.t < 12.5)) - mean(add_mass_oc.de(add_mass_oc.t > 20 & add_mass_oc.t < 20.5)));
 apa_k_sc = 9.8 * added_mass / (mean(add_mass_cc.de(add_mass_cc.t > 12 & add_mass_cc.t < 12.5)) - mean(add_mass_cc.de(add_mass_cc.t > 20 & add_mass_cc.t < 20.5)));
 
-% Dynamics
-% <<ssec:test_apa_meas_dynamics>>
-
-% In this section, the dynamics of the system from the excitation voltage $u$ to encoder measured displacement $d_e$  and to the force sensor voltage $V_s$ is identified.
-
-
 %% Identification using sweep sine (low frequency)
 load('frf_data_sweep.mat');
 load('frf_data_noise_hf.mat');
@@ -193,17 +118,6 @@ end
 %% Save the identified dynamics for further analysis
 save('mat/meas_apa_frf.mat', 'f', 'Ts', 'enc_frf', 'iff_frf', 'apa_nums');
 
-
-
-% The obtained transfer functions for the 6 APA between the excitation voltage $u$ and the encoder displacement $d_e$ are shown in Figure ref:fig:test_apa_frf_encoder.
-% The obtained transfer functions are close to a mass-spring-damper system.
-% The following can be observed:
-% - A "stiffness line" indicating a static gain equal to $\approx -17\,\mu m/V$.
-%   The minus sign comes from the fact that an increase in voltage stretches the piezoelectric stack that then reduces the height of the APA
-% - A lightly damped resonance at $95\,\text{Hz}$
-% - A "mass line" up to $\approx 800\,\text{Hz}$, above which some resonances appear. These additional resonances might be coming from the limited stiffness of the encoder support or from the limited compliance of the APA support.
-
-
 %% Plot the FRF from u to de
 figure;
 tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
@@ -218,7 +132,7 @@ hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
 ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]);
 hold off;
-legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
+legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
 ylim([1e-8, 1e-3]);
 
 ax2 = nexttile;
@@ -235,28 +149,6 @@ yticks(-360:90:360);
 linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 
-
-
-% #+name: fig:test_apa_frf_encoder
-% #+caption: Estimated Frequency Response Function from generated voltage $u$ to the encoder displacement $d_e$ for the 6 APA300ML
-% #+RESULTS:
-% [[file:figs/test_apa_frf_encoder.png]]
-
-% The dynamics from $u$ to the measured voltage across the sensor stack $V_s$ is also identified and shown in Figure ref:fig:test_apa_frf_force.
-
-% A lightly damped resonance is observed at $95\,\text{Hz}$ and a lightly damped anti-resonance at $41\,\text{Hz}$.
-% No additional resonances is present up to at least $2\,\text{kHz}$ indicating at Integral Force Feedback can be applied without stability issues from high frequency flexible modes.
-
-% As illustrated by the Root Locus, the poles of the closed-loop system converges to the zeros of the open-loop plant.
-% Suppose that a controller with a very high gain is implemented such that the voltage $V_s$ across the sensor stack is zero.
-% In that case, because of the very high controller gain, no stress and strain is present on the sensor stack (and on the actuator stacks are well, as they are both in series).
-% Such closed-loop system would therefore virtually corresponds to a system for which the piezoelectric stacks have been removed and just the mechanical shell is kept.
-% From this analysis, the axial stiffness of the shell can be estimated to be $k_{\text{shell}} = 5.7 \cdot (2\pi \cdot 41)^2 = 0.38\,N/\mu m$.
-% # TODO - Compare with FEM result
-
-% Such reasoning can lead to very interesting insight into the system just from an open-loop identification.
-
-
 %% Plot the FRF from u to Vs
 figure;
 tiledlayout(2, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
@@ -288,18 +180,56 @@ yticks(-360:90:360); ylim([-180, 180]);
 linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 
-% Effect of the resistor on the IFF Plant
+%% Long measurement
-% <<ssec:test_apa_resistance_sensor_stack>>
+long_noise = load('frf_struts_align_3_noise_long.mat', 't', 'u', 'Vs');
 
-% A resistor $R \approx 80.6\,k\Omega$ is added in parallel with the sensor stack which has the effect to form a high pass filter with the capacitance of the stack.
+% Long window for fine frequency axis
+Ts = 1e-4; % Sampling Time [s]
+Nfft = floor(10/Ts);
+win = hanning(Nfft);
+Noverlap = floor(Nfft/2);
 
-% As explain before, this is done for two reasons:
+% Transfer function estimation
-% 1. Limit the voltage offset due to the input bias current of the ADC
+[frf_noise, f] = tfestimate(long_noise.u, long_noise.Vs, win, Noverlap, Nfft, 1/Ts);
-% 2. Limit the low frequency gain
+[coh_noise, ~] = mscohere(long_noise.u, long_noise.Vs, win, Noverlap, Nfft, 1/Ts);
 
-% The (low frequency) transfer function from $u$ to $V_s$ with and without this resistor have been measured and are compared in Figure ref:fig:test_apa_effect_resistance.
+%% Bode plot of the FRF from u to de
-% It is confirmed that the added resistor as the effect of adding an high pass filter with a cut-off frequency of $\approx 0.35\,\text{Hz}$.
+figure;
+tiledlayout(1, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
 
+nexttile();
+hold on;
+plot(f, coh_noise, '.-');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+xlabel('Frequency [Hz]'); ylabel('Coherence [-]');
+hold off;
+xlim([38, 45]);
+ylim([0, 1]);
+
+%% Bode plot of the FRF from u to de
+figure;
+tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
+
+ax1 = nexttile([2,1]);
+hold on;
+plot(f, abs(frf_noise), '.-');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude'); set(gca, 'XTickLabel',[]);
+hold off;
+
+ax2 = nexttile;
+hold on;
+plot(f, 180/pi*angle(frf_noise), '.-');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+hold off;
+yticks(-360:90:360); ylim([-180, 0]);
+
+linkaxes([ax1,ax2],'x');
+xlim([38, 45]);
 
 %% Load the data
 wi_k = load('frf_data_1_sweep_lf_with_R.mat', 't', 'Vs', 'u'); % With the resistor
@@ -320,41 +250,40 @@ R = 80.6e3; % Parallel Resistor [Ohm]
 
 f0 = 1/(2*pi*R*C); % Crossover frequency of RC HPF [Hz]
 
-G_hpf = 0.6*(s/2*pi*f0)/(1 + s/2*pi*f0);
+G_hpf = 0.6*(s/(2*pi*f0))/(1 + s/(2*pi*f0));
 
 %% Compare the HPF model and the measured FRF
 figure;
-tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
+tiledlayout(2, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
 
-ax1 = nexttile([2,1]);
+ax1 = nexttile();
 hold on;
 plot(f, abs(frf_wo_k), 'DisplayName', 'Without $R$');
 plot(f, abs(frf_wi_k), 'DisplayName', 'With $R$');
+plot(f, abs(squeeze(freqresp(G_hpf, f, 'Hz'))), 'k--', 'DisplayName', 'RC model');
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-ylabel('Amplitude $V_s/u$ [V/V]'); set(gca, 'XTickLabel',[]);
+ylabel('Amplitude [V/V]'); set(gca, 'XTickLabel',[]);
 hold off;
-ylim([1e-1, 1e0]);
+ylim([2e-1, 1e0]);
-legend('location', 'southeast')
+yticks([0.2, 0.5, 1]);
+legend('location', 'southeast', 'FontSize', 8);
 
 ax2 = nexttile;
 hold on;
 plot(f, 180/pi*angle(frf_wo_k));
 plot(f, 180/pi*angle(frf_wi_k));
+plot(f, 180/pi*angle(squeeze(freqresp(G_hpf, f, 'Hz'))), 'k--', 'DisplayName', 'RC');
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
 xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
 hold off;
-yticks(-360:45:360); ylim([-45, 90]);
+yticks(-360:45:360); ylim([-5, 60]);
+yticks([0, 15, 30, 45, 60]);
 
 linkaxes([ax1,ax2],'x');
 xlim([0.2, 8]);
-
+xticks([0.2, 0.5, 1, 2, 5]);
-% Integral Force Feedback
-% <<ssec:test_apa_iff_locus>>
-
-% This test bench can also be used to estimate the damping added by the implementation of an Integral Force Feedback strategy.
-
 
 %% Load identification Data
 data = load("2023-03-17_11-28_iff_plant.mat");
@@ -368,19 +297,6 @@ Noverlap = floor(Nfft/2);
 %% Compute the transfer function from applied force to measured rotation
 [G_iff, f]  = tfestimate(data.id_plant, data.Vs, win, Noverlap, Nfft, 1/Ts);
 
-
-
-% First, the transfer function eqref:eq:test_apa_iff_manual_fit is manually tuned to match the identified dynamics from generated voltage $u$ to the measured sensor stack voltage $V_s$ in Section ref:ssec:test_apa_meas_dynamics.
-
-% The obtained parameter values are $\omega_{\textsc{hpf}} = 0.4\, \text{Hz}$, $\omega_{z} = 42.7\, \text{Hz}$, $\xi_{z} = 0.4\,\%$, $\omega_{p} = 95.2\, \text{Hz}$, $\xi_{p} = 2\,\%$ and $g_0 = 0.64$.
-
-% \begin{equation} \label{eq:test_apa_iff_manual_fit}
-% G_{\textsc{iff},m}(s) = g_0 \cdot \frac{1 + 2 \xi_z \frac{s}{\omega_z} + \frac{s^2}{\omega_z^2}}{1 + 2 \xi_p \frac{s}{\omega_p} + \frac{s^2}{\omega_p^2}} \cdot \frac{s}{\omega_{\textsc{hpf}} + s}
-% \end{equation}
-
-% The comparison between the identified plant and the manually tuned transfer function is done in Figure ref:fig:test_apa_iff_plant_comp_manual_fit.
-
-
 %% Basic manually tuned model
 w0z = 2*pi*42.7; % Zero frequency
 xiz = 0.004; % Zero damping
@@ -417,36 +333,11 @@ ylim([-90, 180])
 linkaxes([ax1,ax2],'x');
 xlim([0.2, 1e3]);
 
-
-
-% #+name: fig:test_apa_iff_plant_comp_manual_fit
-% #+caption: Identified IFF plant and manually tuned model of the plant (a time delay of $200\,\mu s$ is added to the model of the plant to better match the identified phase)
-% #+RESULTS:
-% [[file:figs/test_apa_iff_plant_comp_manual_fit.png]]
-
-% The implemented Integral Force Feedback Controller transfer function is shown in equation eqref:eq:test_apa_Kiff_formula.
-% It contains an high pass filter (cut-off frequency of $2\,\text{Hz}$) to limit the low frequency gain, a low pass filter to add integral action above $20\,\text{Hz}$, a second low pass filter to add robustness to high frequency resonances and a tunable gain $g$.
-
-% \begin{equation} \label{eq:test_apa_Kiff_formula}
-% K_{\textsc{iff}}(s) = -10 \cdot g \cdot \frac{s}{s + 2\pi \cdot 2} \cdot \frac{1}{1 + 2\pi \cdot 20} \cdot \frac{1}{s + 2\pi\cdot 2000}
-% \end{equation}
-
-
 %% Integral Force Feedback Controller
 K_iff = -10*(1/(s + 2*pi*20)) * ... % LPF: provides integral action above 20Hz
             (s/(s + 2*pi*2))  * ... % HPF: limit low frequency gain
             (1/(1 + s/2/pi/2e3));   % LPF: more robust to high frequency resonances
 
-
-
-% To estimate how the dynamics of the APA changes when the Integral Force Feedback controller is implemented, the test bench shown in Figure ref:fig:test_apa_iff_schematic is used.
-% The transfer function from the "damped" plant input $u\prime$ to the encoder displacement $d_e$ is identified for several IFF controller gains $g$.
-
-% #+name: fig:test_apa_iff_schematic
-% #+caption: Figure caption
-% [[file:figs/test_apa_iff_schematic.png]]
-
-
 %% Load Data
 data = load("2023-03-17_14-10_damped_plants_new.mat");
 
@@ -460,7 +351,7 @@ Noverlap = floor(Nfft/2);
 [~, f]  = tfestimate(data.data(1).id_plant(1:end), data.data(1).dL(1:end), win, Noverlap, Nfft, 1/Ts);
 
 %% Gains used for analysis are between 1 and 50
-i_kept = [5:10]
+i_kept = [5:10];
 
 %% Identify the damped plant from u' to de for different IFF gains
 G_dL_frf = {zeros(1,length(i_kept))};
@@ -470,13 +361,6 @@ for i = 1:length(i_kept)
     G_dL_frf(i) = {G_dL};
 end
 
-
-
-% The identified dynamics are then fitted by second order transfer functions.
-% The comparison between the identified damped dynamics and the fitted second order transfer functions is done in Figure ref:fig:test_apa_identified_damped_plants for different gains $g$.
-% It is clear that large amount of damping is added when the gain is increased and that the frequency of the pole is shifted to lower frequencies.
-
-
 %% Fit the data with 2nd order transfer function using vectfit3
 opts = struct();
 
@@ -519,24 +403,10 @@ for i = 1:length(i_kept)
 end
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-xlabel('Frequency [Hz]'); ylabel('Amplitude $d_L/V_a$ [m/V]');
+xlabel('Frequency [Hz]'); ylabel('Amplitude $d_e/u^\prime$ [m/V]');
 xlim([10, 1e3]);
 legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
 
-
-
-% #+name: fig:test_apa_identified_damped_plants
-% #+caption: Identified dynamics (solid lines) and fitted transfer functions (dashed lines) from $u\prime$ to $d_e$ for different IFF gains
-% #+RESULTS:
-% [[file:figs/test_apa_identified_damped_plants.png]]
-
-% The evolution of the pole in the complex plane as a function of the controller gain $g$ (i.e. the "root locus") is computed:
-% - using the IFF plant model eqref:eq:test_apa_iff_manual_fit and the implemented controller eqref:eq:test_apa_Kiff_formula
-% - from the fitted transfer functions of the damped plants experimentally identified for several controller gains
-
-% The two obtained root loci are compared in Figure ref:fig:test_apa_iff_root_locus and are in good agreement considering that the damped plants were only fitted using a second order transfer function.
-
-
 %% Root Locus of the APA300ML with Integral Force Feedback
 % Comparison between the computed root locus from the plant model and the root locus estimated from the damped plant pole identification
 gains = logspace(-1, 3, 1000);
@@ -562,9 +432,9 @@ end
 for i = 1:length(i_kept)
     plot(real(pole(G_dL_id{i})), imag(pole(G_dL_id{i})), 'x', 'color', [colors(i,:), 1], 'DisplayName', sprintf('g = %1.f', data.gains(i_kept(i))));
 end
-ylim([0, 700]);
-xlim([-600,100]);
 xlabel('Real Part')
 ylabel('Imaginary Part')
-axis square
+axis equal
-legend('location', 'northwest');
+ylim([0, 610]);
+xlim([-300,0]);
+legend('location', 'southwest', 'FontSize', 8);

matlab/test_apa_3_model_2dof.m

@@ -27,15 +27,8 @@ io(io_i) = linio([mdl, '/u'],  1, 'openinput');  io_i = io_i + 1; % DAC Voltage
 io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage
 io(io_i) = linio([mdl, '/de'], 1, 'openoutput'); io_i = io_i + 1; % Encoder
 
-% Tuning of the APA model
+%% Frequency vector for analysis
-% <<ssec:test_apa_2dof_model_tuning>>
+freqs = 5*logspace(0, 3, 1000);
-
-% 9 parameters ($m$, $k_1$, $c_1$, $k_e$, $c_e$, $k_a$, $c_a$, $g_s$ and $g_a$) have to be tuned such that the dynamics of the model (Figure ref:fig:test_apa_2dof_model_simscape) well represents the identified dynamics in Section ref:sec:test_apa_dynamics.
-
-% #+name: fig:test_apa_2dof_model_simscape
-% #+caption: Schematic of the two degrees of freedom model of the APA300ML with input $V_a$ and outputs $d_e$ and $V_s$
-% [[file:figs/test_apa_2dof_model_simscape.png]]
-
 
 %% Stiffness values for the 2DoF APA model
 k1 = 0.38e6; % Estimated Shell Stiffness [N/m]
@@ -48,12 +41,12 @@ ka = 1.5*(ktot-k1); % Stiffness of the (two) actuator stacks [N/m]
 ke = 2*ka; % Stiffness of the Sensor stack [N/m]
 
 %% Damping values for the 2DoF APA model
-c1 = 20;   % Damping for the Shell [N/(m/s)]
+c1 = 5;   % Damping for the Shell [N/(m/s)]
-ca = 100;  % Damping of the actuators stacks [N/(m/s)]
+ca = 50;  % Damping of the actuators stacks [N/(m/s)]
 ce = 2*ca; % Damping of the sensor stack [N/(m/s)]
 
-%% Estimation ot the sensor and actuator gains
+%% Estimation ot the sensor and actuator sensitivities
-% Initialize the structure with unitary sensor and actuator "gains"
+% Initialize the structure with unitary sensor and actuator "sensitivities"
 n_hexapod = struct();
 n_hexapod.actuator = initializeAPA(...
     'type', '2dof', ...
@@ -67,36 +60,26 @@ n_hexapod.actuator = initializeAPA(...
     'Gs', 1    ... % Sensor constant [V/m]
 );
 
-c_granite = 0; % Do not take into account damping added by the air bearing
+c_granite = 50; % Do not take into account damping added by the air bearing
 
 % Run the linearization
 G_norm = linearize(mdl, io, 0.0, opts);
 G_norm.InputName  = {'u'};
 G_norm.OutputName = {'Vs', 'de'};
 
-% Load Identification Data to estimate the two gains
+% Load Identification Data to estimate the two sensitivities
 load('meas_apa_frf.mat', 'f', 'Ts', 'enc_frf', 'iff_frf', 'apa_nums');
 
-% Estimation ot the Actuator Gain
+% Estimation ot the Actuator sensitivity
 fa = 10; % Frequency where the two FRF should match [Hz]
 [~, i_f] = min(abs(f - fa));
 ga = -abs(enc_frf(i_f,1))./abs(evalfr(G_norm('de', 'u'), 1i*2*pi*fa));
 
-% Estimation ot the Sensor Gain
+% Estimation ot the Sensor sensitivity
 fs = 600; % Frequency where the two FRF should match [Hz]
 [~, i_f] = min(abs(f - fs));
 gs = -abs(iff_frf(i_f,1))./abs(evalfr(G_norm('Vs', 'u'), 1i*2*pi*fs))/ga;
 
-% Obtained Dynamics
-% <<ssec:test_apa_2dof_model_result>>
-
-% The dynamics of the 2DoF APA300ML model is now extracted using optimized parameters (listed in Table ref:tab:test_apa_2dof_parameters) from the Simscape model.
-% It is compared with the experimental data in Figure ref:fig:test_apa_2dof_comp_frf.
-
-% A good match can be observed between the model and the experimental data, both for the encoder and for the force sensor.
-% This indicates that this model represents well the axial dynamics of the APA300ML.
-
-
 %% 2DoF APA300ML with optimized parameters
 n_hexapod = struct();
 n_hexapod.actuator = initializeAPA( ...
@@ -117,9 +100,8 @@ G_2dof.InputName  = {'u'};
 G_2dof.OutputName = {'Vs', 'de'};
 
 %% Comparison of the measured FRF and the optimized 2DoF model of the APA300ML
-freqs = 5*logspace(0, 3, 1000);
 figure;
-tiledlayout(3, 2, 'TileSpacing', 'Compact', 'Padding', 'None');
+tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
 
 ax1 = nexttile([2,1]);
 hold on;
@@ -135,7 +117,26 @@ hold off;
 ylim([1e-8, 1e-3]);
 legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
 
-ax1b = nexttile([2,1]);
+ax2 = nexttile;
+hold on;
+for i = 1:length(apa_nums)
+    plot(f, 180/pi*angle(enc_frf(:, i)), 'color', [0,0,0,0.2]);
+end
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_2dof('de', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:))
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+hold off;
+yticks(-360:90:360); ylim([-180, 180]);
+
+linkaxes([ax1,ax2],'x');
+xlim([10, 2e3]);
+
+%% Comparison of the measured FRF and the optimized 2DoF model of the APA300ML
+figure;
+tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
+
+ax1 = nexttile([2,1]);
 hold on;
 plot(f, abs(iff_frf(:, 1)), 'color', [0,0,0,0.2], 'DisplayName', 'Identified');
 for i = 2:length(apa_nums)
@@ -151,18 +152,6 @@ legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
 
 ax2 = nexttile;
 hold on;
-for i = 1:length(apa_nums)
-    plot(f, 180/pi*angle(enc_frf(:, i)), 'color', [0,0,0,0.2]);
-end
-plot(freqs, 180/pi*angle(squeeze(freqresp(G_2dof('de', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:))
-hold off;
-set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
-xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
-hold off;
-yticks(-360:90:360); ylim([-180, 180]);
-
-ax2b = nexttile;
-hold on;
 for i = 1:length(apa_nums)
     plot(f, 180/pi*angle(iff_frf(:, i)), 'color', [0,0,0,0.2]);
 end
@@ -173,5 +162,5 @@ xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
 hold off;
 yticks(-360:90:360); ylim([-180, 180]);
 
-linkaxes([ax1,ax2,ax1b,ax2b],'x');
+linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);

matlab/test_apa_4_model_flexible.m

@@ -27,14 +27,8 @@ io(io_i) = linio([mdl, '/u'],  1, 'openinput');  io_i = io_i + 1; % DAC Voltage
 io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage
 io(io_i) = linio([mdl, '/de'], 1, 'openoutput'); io_i = io_i + 1; % Encoder
 
-% Identification of the Actuator and Sensor constants
+%% Frequency vector for analysis
-% <<ssec:test_apa_flexible_ga_gs>>
+freqs = 5*logspace(0, 3, 1000);
-
-% Once the APA300ML /super element/ is included in the Simscape model, the transfer function from $F_a$ to $d_L$ and $d_e$ can be identified.
-% The gains $g_a$ and $g_s$ can then be tuned such that the gain of the transfer functions are matching the identified ones.
-
-% By doing so, $g_s = 4.9\,V/\mu m$ and $g_a = 23.2\,N/V$ are obtained.
-
 
 %% Identification of the actuator and sensor "constants"
 % Initialize the APA as a flexible body with unity "constants"
@@ -43,7 +37,7 @@ n_hexapod.actuator = initializeAPA(...
     'ga', 1, ...
     'gs', 1);
 
-c_granite = 100; % Rought estimation of the damping added by the air bearing
+c_granite = 50; % Rought estimation of the damping added by the air bearing
 
 % Identify the dynamics
 G_norm = linearize(mdl, io, 0.0, opts);
@@ -59,83 +53,12 @@ ga = -mean(abs(enc_frf(f>10 & f<20)))./dcgain(G_norm('de', 'u'));
 % Sensor Constant in [V/m]
 gs = -mean(abs(iff_frf(f>400 & f<500)))./(ga*abs(squeeze(freqresp(G_norm('Vs', 'u'), 1e3, 'Hz'))));
 
-
-
-
-% To make sure these "gains" are physically valid, it is possible to estimate them from physical properties of the piezoelectric stack material.
-
-% From [[cite:&fleming14_desig_model_contr_nanop_system p. 123]], the relation between relative displacement $d_L$ of the sensor stack and generated voltage $V_s$ is given by eqref:eq:test_apa_piezo_strain_to_voltage and from [[cite:&fleming10_integ_strain_force_feedb_high]] the relation between the force $F_a$ and the applied voltage $V_a$ is given by eqref:eq:test_apa_piezo_voltage_to_force.
-
-% \begin{subequations}
-% \begin{align}
-%   V_s &= \underbrace{\frac{d_{33}}{\epsilon^T s^D n}}_{g_s} d_L \label{eq:test_apa_piezo_strain_to_voltage} \\
-%   F_a &= \underbrace{d_{33} n k_a}_{g_a} \cdot V_a, \quad k_a = \frac{c^{E} A}{L} \label{eq:test_apa_piezo_voltage_to_force}
-% \end{align}
-% \end{subequations}
-
-% Parameters used in equations eqref:eq:test_apa_piezo_strain_to_voltage and eqref:eq:test_apa_piezo_voltage_to_force are described in Table ref:tab:test_apa_piezo_properties.
-
-% Unfortunately, the manufacturer of the stack was not willing to share the piezoelectric material properties of the stack used in the APA300ML.
-% However, based on available properties of the APA300ML stacks in the data-sheet, the soft Lead Zirconate Titanate "THP5H" from Thorlabs seemed to match quite well the observed properties.
-% The properties of this "THP5H" material used to compute $g_a$ and $g_s$ are listed in Table ref:tab:test_apa_piezo_properties.
-
-% From these parameters, $g_s = 5.1\,V/\mu m$ and $g_a = 26\,N/V$ were obtained which are very close to the identified constants using the experimentally identified transfer functions.
-
-% #+name: tab:test_apa_piezo_properties
-% #+caption: Piezoelectric properties used for the estimation of the sensor and actuators "gains"
-% #+attr_latex: :environment tabularx :width 1\linewidth :align ccX
-% #+attr_latex: :center t :booktabs t
-% | *Parameter*    | *Value*                    | *Description*                                                |
-% |----------------+----------------------------+--------------------------------------------------------------|
-% | $d_{33}$       | $680 \cdot 10^{-12}\,m/V$  | Piezoelectric constant                                       |
-% | $\epsilon^{T}$ | $4.0 \cdot 10^{-8}\,F/m$   | Permittivity under constant stress                           |
-% | $s^{D}$        | $21 \cdot 10^{-12}\,m^2/N$ | Elastic compliance understand constant electric displacement |
-% | $c^{E}$        | $48 \cdot 10^{9}\,N/m^2$   | Young's modulus of elasticity                                |
-% | $L$            | $20\,mm$ per stack         | Length of the stack                                          |
-% | $A$            | $10^{-4}\,m^2$             | Area of the piezoelectric stack                              |
-% | $n$            | $160$ per stack            | Number of layers in the piezoelectric stack                  |
-
-
-%% Estimate "Sensor Constant" - (THP5H)
-d33 = 680e-12;        % Strain constant [m/V]
-n   = 160;            % Number of layers per stack
-eT  = 4500*8.854e-12; % Permittivity under constant stress [F/m]
-sD  = 21e-12;         % Compliance under constant electric displacement [m2/N]
-
-gs = d33/(eT*sD*n);   % Sensor Constant [V/m]
-
-%% Estimate "Actuator Constant" - (THP5H)
-d33 = 680e-12;   % Strain constant [m/V]
-n   = 320;       % Number of layers
-
-cE  = 1/sD;      % Youngs modulus [N/m^2]
-A   = (10e-3)^2; % Area of the stacks [m^2]
-L   = 40e-3;     % Length of the two stacks [m]
-ka  = cE*A/L;    % Stiffness of the two stacks [N/m]
-
-ga = d33*n*ka;   % Actuator Constant [N/V]
-
-% Comparison of the obtained dynamics
-% <<ssec:test_apa_flexible_comp_frf>>
-
-% The obtained dynamics using the /super element/ with the tuned "sensor gain" and "actuator gain" are compared with the experimentally identified frequency response functions in Figure ref:fig:test_apa_super_element_comp_frf.
-
-% A good match between the model and the experimental results is observed.
-% - the /super element/
-
-% This model represents fairly
-
-% The flexible model is a bit "soft" as compared with the experimental results.
-
-% This method can be used to model piezoelectric stack actuators as well as amplified piezoelectric stack actuators.
-
-
 %% Idenfify the dynamics of the Simscape model with correct actuator and sensor "constants"
 % Initialize the APA
 n_hexapod.actuator = initializeAPA(...
     'type', 'flexible', ...
-    'ga',   23.2, ... % Actuator gain [N/V]
+    'ga',   23.2, ... % Actuator sensitivity [N/V]
-    'gs',   -4.9e6);    % Sensor gain [V/m]
+    'gs',   -4.9e6);    % Sensor sensitivity [V/m]
 
 % Identify with updated constants
 G_flex = exp(-Ts*s)*linearize(mdl, io, 0.0, opts);
@@ -143,9 +66,8 @@ G_flex.InputName  = {'u'};
 G_flex.OutputName = {'Vs', 'de'};
 
 %% Comparison of the measured FRF and the "Flexible" model of the APA300ML
-freqs = 5*logspace(0, 3, 1000);
 figure;
-tiledlayout(3, 2, 'TileSpacing', 'Compact', 'Padding', 'None');
+tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
 
 ax1 = nexttile([2,1]);
 hold on;
@@ -161,7 +83,26 @@ hold off;
 ylim([1e-8, 1e-3]);
 legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
 
-ax1b = nexttile([2,1]);
+ax2 = nexttile;
+hold on;
+for i = 1:length(apa_nums)
+    plot(f, 180/pi*angle(enc_frf(:, i)), 'color', [0,0,0,0.2]);
+end
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_flex('de', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:))
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+hold off;
+yticks(-360:90:360); ylim([-180, 180]);
+
+linkaxes([ax1,ax2],'x');
+xlim([10, 2e3]);
+
+%% Comparison of the measured FRF and the "Flexible" model of the APA300ML
+figure;
+tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
+
+ax1 = nexttile([2,1]);
 hold on;
 plot(f, abs(iff_frf(:, 1)), 'color', [0,0,0,0.2], 'DisplayName', 'Identified');
 for i = 2:length(apa_nums)
@@ -177,18 +118,6 @@ legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
 
 ax2 = nexttile;
 hold on;
-for i = 1:length(apa_nums)
-    plot(f, 180/pi*angle(enc_frf(:, i)), 'color', [0,0,0,0.2]);
-end
-plot(freqs, 180/pi*angle(squeeze(freqresp(G_flex('de', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:))
-hold off;
-set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
-xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
-hold off;
-yticks(-360:90:360); ylim([-180, 180]);
-
-ax2b = nexttile;
-hold on;
 for i = 1:length(apa_nums)
     plot(f, 180/pi*angle(iff_frf(:, i)), 'color', [0,0,0,0.2]);
 end
@@ -199,5 +128,5 @@ xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
 hold off;
 yticks(-360:90:360); ylim([-180, 180]);
 
-linkaxes([ax1,ax2,ax1b,ax2b],'x');
+linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);

preamble.tex

@@ -1,135 +1,16 @@
-\usepackage{float}
+\usepackage[      %
+    acronym,      % Separate acronyms and glossary
+    toc,          % appear in ToC
+    automake,     % auto-use the makeglossaries command (requires shell-escape)
+    nonumberlist, % don't back reference pages
+    nogroupskip,  % don't group by letter
+    nopostdot     % don't add a dot at the end of each element
+]{glossaries}
 
-\usepackage{caption,tabularx,booktabs}
+\usepackage[stylemods=longextra]{glossaries-extra}
-\usepackage{bm}
 
-\usepackage{xpatch} % Recommanded for biblatex
+\setabbreviationstyle[acronym]{long-short}
-\usepackage[        % use biblatex for bibliography
+\setglossarystyle{long-name-desc}
-    backend=biber,  % use biber backend (bibtex replacement) or bibtex
-    style=ieee,     % bib style
-    hyperref=true,  % activate hyperref support
-    backref=true,   % activate backrefs
-    isbn=false,     % don't show isbn tags
-    url=false,      % don't show url tags
-    doi=false,      % don't show doi tags
-    urldate=long,   % display type for dates
-    maxnames=3,     %
-    minnames=1,     %
-    maxbibnames=5,  %
-    minbibnames=3,  %
-    maxcitenames=2, %
-    mincitenames=1  %
-    ]{biblatex}
 
-\setlength\bibitemsep{1.1\itemsep}
+\makeindex
-
+\makeglossaries
-% \renewcommand*{\bibfont}{\footnotesize}
-
-\usepackage{caption}
-\usepackage{subcaption}
-
-\captionsetup[figure]{labelfont=bf}
-\captionsetup[subfigure]{labelfont=bf}
-\captionsetup[listing]{labelfont=bf}
-\captionsetup[table]{labelfont=bf}
-
-\usepackage{xcolor}
-
-\definecolor{my-blue}{HTML}{6b7adb}
-\definecolor{my-pale-blue}{HTML}{e6e9f9}
-\definecolor{my-red}{HTML}{db6b6b}
-\definecolor{my-pale-red}{HTML}{f9e6e6}
-\definecolor{my-green}{HTML}{6bdbb6}
-\definecolor{my-pale-green}{HTML}{e6f9f3}
-\definecolor{my-yellow}{HTML}{dbd26b}
-\definecolor{my-pale-yellow}{HTML}{f9f7e6}
-\definecolor{my-orange}{HTML}{dba76b}
-\definecolor{my-pale-orange}{HTML}{f9f0e6}
-\definecolor{my-grey}{HTML}{a3a3a3}
-\definecolor{my-pale-grey}{HTML}{f0f0f0}
-\definecolor{my-turq}{HTML}{6bc7db}
-\definecolor{my-pale-turq}{HTML}{e6f6f9}
-
-\usepackage{inconsolata}
-
-\usepackage[newfloat=true, chapter]{minted}
-\usemintedstyle{autumn}
-
-\setminted{frame=lines,breaklines=true,tabsize=4,fontsize=\scriptsize,autogobble=true,labelposition=topline,bgcolor=my-pale-grey}
-\setminted[matlab]{label=Matlab}
-\setminted[latex]{label=LaTeX}
-\setminted[bash]{label=Bash}
-\setminted[python]{label=Python}
-\setminted[text]{label=Results}
-\setminted[md]{label=Org Mode}
-
-\setmintedinline{fontsize=\normalsize,bgcolor=my-pale-grey}
-
-\usepackage[most]{tcolorbox}
-
-\tcbuselibrary{minted}
-
-\newtcolorbox{seealso}{   enhanced,breakable,colback=my-pale-grey,colframe=my-grey,fonttitle=\bfseries,title=See Also}
-\newtcolorbox{hint}{      enhanced,breakable,colback=my-pale-grey,colframe=my-grey,fonttitle=\bfseries,title=Hint}
-\newtcolorbox{definition}{enhanced,breakable,colback=my-pale-red, colframe=my-red, fonttitle=\bfseries,title=Definition}
-\newtcolorbox{important}{ enhanced,breakable,colback=my-pale-red, colframe=my-red, fonttitle=\bfseries,title=Important}
-\newtcolorbox{exampl}[1][]{    enhanced,breakable,colback=my-pale-green,colframe=my-green,fonttitle=\bfseries,title=Example,#1}
-\newtcolorbox{exercice}{  enhanced,breakable,colback=my-pale-yellow,colframe=my-yellow,fonttitle=\bfseries,title=Exercice}
-\newtcolorbox{question}{  enhanced,breakable,colback=my-pale-yellow,colframe=my-yellow,fonttitle=\bfseries,title=Question}
-\newtcolorbox{answer}{    enhanced,breakable,colback=my-pale-turq,colframe=my-turq,fonttitle=\bfseries,title=Answer}
-\newtcolorbox{summary}{   enhanced,breakable,colback=my-pale-blue,colframe=my-blue,fonttitle=\bfseries,title=Summary}
-\newtcolorbox{note}{      enhanced,breakable,colback=my-pale-blue,colframe=my-blue,fonttitle=\bfseries,title=Note}
-\newtcolorbox{caution}{   enhanced,breakable,colback=my-pale-orange,colframe=my-orange,fonttitle=\bfseries,title=Caution}
-\newtcolorbox{warning}{   enhanced,breakable,colback=my-pale-orange,colframe=my-orange,fonttitle=\bfseries,title=Warning}
-
-\newtcolorbox{my-quote}[1]{%
-  colback=my-pale-grey,
-  grow to right by=-10mm,
-  grow to left by=-10mm,
-  boxrule=0pt,
-  boxsep=0pt,
-  breakable,
-  enhanced jigsaw,
-  borderline west={4pt}{0pt}{my-grey}}
-
-\renewenvironment{quote}{\begin{my-quote}}{\end{my-quote}}
-
-\newtcolorbox{my-verse}[1]{%
-  colback=my-pale-grey,
-  grow to right by=-10mm,
-  grow to left by=-10mm,
-  boxrule=0pt,
-  boxsep=0pt,
-  breakable,
-  enhanced jigsaw,
-  borderline west={4pt}{0pt}{my-grey}}
-
-\renewenvironment{verse}{\begin{my-verse}}{\end{my-verse}}
-
-\usepackage{environ}% http://ctan.org/pkg/environ
-\NewEnviron{aside}{%
-  \marginpar{\BODY}
-}
-
-\renewenvironment{verbatim}{\VerbatimEnvironment\begin{minted}[]{text}}{\end{minted}}
-
-\usepackage{soul}
-\sethlcolor{my-pale-grey}
-
-\let\OldTexttt\texttt
-\renewcommand{\texttt}[1]{{\ttfamily\hl{\mbox{\,#1\,}}}}
-
-\makeatletter
-\preto\Gin@extensions{png,}
-\DeclareGraphicsRule{.png}{pdf}{.pdf}{\noexpand\Gin@base.pdf}
-\preto\Gin@extensions{gif,}
-\DeclareGraphicsRule{.gif}{png}{.png}{\noexpand\Gin@base.png}
-\makeatother
-
-\usepackage{hyperref}
-\hypersetup{
-  colorlinks = true,
-  allcolors = my-blue
-}
-
-\usepackage{hypcap}

preamble_extra.tex

@@ -0,0 +1,134 @@
+\usepackage{float}
+\usepackage{enumitem}
+
+\usepackage{caption,tabularx,booktabs}
+\usepackage{bm}
+
+\usepackage{xpatch} % Recommanded for biblatex
+\usepackage[        % use biblatex for bibliography
+    backend=biber,  % use biber backend (bibtex replacement) or bibtex
+    style=ieee,     % bib style
+    hyperref=true,  % activate hyperref support
+    backref=true,   % activate backrefs
+    isbn=false,     % don't show isbn tags
+    url=false,      % don't show url tags
+    doi=false,      % don't show doi tags
+    urldate=long,   % display type for dates
+    maxnames=3,     %
+    minnames=1,     %
+    maxbibnames=5,  %
+    minbibnames=3,  %
+    maxcitenames=2, %
+    mincitenames=1  %
+    ]{biblatex}
+
+\setlength\bibitemsep{1.1\itemsep}
+
+\usepackage{caption}
+\usepackage{subcaption}
+
+\captionsetup[figure]{labelfont=bf}
+\captionsetup[subfigure]{labelfont=bf}
+\captionsetup[listing]{labelfont=bf}
+\captionsetup[table]{labelfont=bf}
+
+\usepackage{xcolor}
+
+\definecolor{my-blue}{HTML}{6b7adb}
+\definecolor{my-pale-blue}{HTML}{e6e9f9}
+\definecolor{my-red}{HTML}{db6b6b}
+\definecolor{my-pale-red}{HTML}{f9e6e6}
+\definecolor{my-green}{HTML}{6bdbb6}
+\definecolor{my-pale-green}{HTML}{e6f9f3}
+\definecolor{my-yellow}{HTML}{dbd26b}
+\definecolor{my-pale-yellow}{HTML}{f9f7e6}
+\definecolor{my-orange}{HTML}{dba76b}
+\definecolor{my-pale-orange}{HTML}{f9f0e6}
+\definecolor{my-grey}{HTML}{a3a3a3}
+\definecolor{my-pale-grey}{HTML}{f0f0f0}
+\definecolor{my-turq}{HTML}{6bc7db}
+\definecolor{my-pale-turq}{HTML}{e6f6f9}
+
+\usepackage{inconsolata}
+
+\usepackage[newfloat=true, chapter]{minted}
+\usemintedstyle{autumn}
+
+\setminted{frame=lines,breaklines=true,tabsize=4,fontsize=\scriptsize,autogobble=true,labelposition=topline,bgcolor=my-pale-grey}
+\setminted[matlab]{label=Matlab}
+\setminted[latex]{label=LaTeX}
+\setminted[bash]{label=Bash}
+\setminted[python]{label=Python}
+\setminted[text]{label=Results}
+\setminted[md]{label=Org Mode}
+
+\setmintedinline{fontsize=\normalsize,bgcolor=my-pale-grey}
+
+\usepackage[most]{tcolorbox}
+
+\tcbuselibrary{minted}
+
+\newtcolorbox{seealso}{   enhanced,breakable,colback=my-pale-grey,colframe=my-grey,fonttitle=\bfseries,title=See Also}
+\newtcolorbox{hint}{      enhanced,breakable,colback=my-pale-grey,colframe=my-grey,fonttitle=\bfseries,title=Hint}
+\newtcolorbox{definition}{enhanced,breakable,colback=my-pale-red, colframe=my-red, fonttitle=\bfseries,title=Definition}
+\newtcolorbox{important}{ enhanced,breakable,colback=my-pale-red, colframe=my-red, fonttitle=\bfseries,title=Important}
+\newtcolorbox{exampl}[1][]{    enhanced,breakable,colback=my-pale-green,colframe=my-green,fonttitle=\bfseries,title=Example,#1}
+\newtcolorbox{exercice}{  enhanced,breakable,colback=my-pale-yellow,colframe=my-yellow,fonttitle=\bfseries,title=Exercice}
+\newtcolorbox{question}{  enhanced,breakable,colback=my-pale-yellow,colframe=my-yellow,fonttitle=\bfseries,title=Question}
+\newtcolorbox{answer}{    enhanced,breakable,colback=my-pale-turq,colframe=my-turq,fonttitle=\bfseries,title=Answer}
+\newtcolorbox{summary}{   enhanced,breakable,colback=my-pale-blue,colframe=my-blue,fonttitle=\bfseries,title=Summary}
+\newtcolorbox{note}{      enhanced,breakable,colback=my-pale-blue,colframe=my-blue,fonttitle=\bfseries,title=Note}
+\newtcolorbox{caution}{   enhanced,breakable,colback=my-pale-orange,colframe=my-orange,fonttitle=\bfseries,title=Caution}
+\newtcolorbox{warning}{   enhanced,breakable,colback=my-pale-orange,colframe=my-orange,fonttitle=\bfseries,title=Warning}
+
+\newtcolorbox{my-quote}[1]{%
+  colback=my-pale-grey,
+  grow to right by=-10mm,
+  grow to left by=-10mm,
+  boxrule=0pt,
+  boxsep=0pt,
+  breakable,
+  enhanced jigsaw,
+  borderline west={4pt}{0pt}{my-grey}}
+
+\renewenvironment{quote}{\begin{my-quote}}{\end{my-quote}}
+
+\newtcolorbox{my-verse}[1]{%
+  colback=my-pale-grey,
+  grow to right by=-10mm,
+  grow to left by=-10mm,
+  boxrule=0pt,
+  boxsep=0pt,
+  breakable,
+  enhanced jigsaw,
+  borderline west={4pt}{0pt}{my-grey}}
+
+\renewenvironment{verse}{\begin{my-verse}}{\end{my-verse}}
+
+\usepackage{environ}% http://ctan.org/pkg/environ
+\NewEnviron{aside}{%
+  \marginpar{\BODY}
+}
+
+\renewenvironment{verbatim}{\VerbatimEnvironment\begin{minted}[]{text}}{\end{minted}}
+
+\usepackage{soul}
+\sethlcolor{my-pale-grey}
+
+\let\OldTexttt\texttt
+\renewcommand{\texttt}[1]{{\ttfamily\hl{\mbox{\,#1\,}}}}
+
+\makeatletter
+\preto\Gin@extensions{png,}
+\DeclareGraphicsRule{.png}{pdf}{.pdf}{\noexpand\Gin@base.pdf}
+\preto\Gin@extensions{gif,}
+\DeclareGraphicsRule{.gif}{png}{.png}{\noexpand\Gin@base.png}
+\makeatother
+
+\usepackage{hyperref}
+\hypersetup{
+  colorlinks = true,
+  allcolors = my-blue
+}
+
+\usepackage{hypcap}

test-bench-apa.bib

@@ -1,3 +1,30 @@
+@article{wehrsdorfer95_large_signal_measur_piezoel_stack,
+  author          = {Wehrsdorfer, E and Borchhardt, G and Karthe, W and Helke,
+                  G},
+  title           = {Large Signal Measurements on Piezoelectric Stacks},
+  journal         = {Ferroelectrics},
+  volume          = 174,
+  number          = 1,
+  pages           = {259--275},
+  year            = 1995,
+  publisher       = {Taylor \& Francis},
+}
+
+
+
+
+@book{fleming14_desig_model_contr_nanop_system,
+  author          = {Andrew J. Fleming and Kam K. Leang},
+  title           = {Design, Modeling and Control of Nanopositioning Systems},
+  year            = 2014,
+  publisher       = {Springer International Publishing},
+  url             = {https://doi.org/10.1007/978-3-319-06617-2},
+  doi             = {10.1007/978-3-319-06617-2},
+  series          = {Advances in Industrial Control},
+}
+
+
+
 @book{reza06_piezoel_trans_vibrat_contr_dampin,
   author          = {Reza, Moheimani and Andrew, Fleming},
   title           = {Piezoelectric Transducers for Vibration Control and
@@ -10,6 +37,64 @@
 
 
 
+@book{preumont18_vibrat_contr_activ_struc_fourt_edition,
+  author          = {Andre Preumont},
+  title           = {Vibration Control of Active Structures - Fourth Edition},
+  year            = 2018,
+  publisher       = {Springer International Publishing},
+  url             = {https://doi.org/10.1007/978-3-319-72296-2},
+  doi             = {10.1007/978-3-319-72296-2},
+  keywords        = {favorite, parallel robot},
+  series          = {Solid Mechanics and Its Applications},
+}
+
+
+
+@inproceedings{spanos95_soft_activ_vibrat_isolat,
+  author          = {J. Spanos and Z. Rahman and G. Blackwood},
+  title           = {A Soft 6-axis Active Vibration Isolator},
+  booktitle       = {Proceedings of 1995 American Control Conference - ACC'95},
+  year            = 1995,
+  doi             = {10.1109/acc.1995.529280},
+  url             = {https://doi.org/10.1109/acc.1995.529280},
+  keywords        = {parallel robot},
+}
+
+
+
+@article{thayer02_six_axis_vibrat_isolat_system,
+  author          = {Doug Thayer and Mark Campbell and Juris Vagners and Andrew
+                  von Flotow},
+  title           = {Six-Axis Vibration Isolation System Using Soft Actuators
+                  and Multiple Sensors},
+  journal         = {Journal of Spacecraft and Rockets},
+  volume          = 39,
+  number          = 2,
+  pages           = {206-212},
+  year            = 2002,
+  doi             = {10.2514/2.3821},
+  url             = {https://doi.org/10.2514/2.3821},
+  keywords        = {parallel robot},
+}
+
+
+
+@article{hauge04_sensor_contr_space_based_six,
+  author          = {G.S. Hauge and M.E. Campbell},
+  title           = {Sensors and Control of a Space-Based Six-Axis Vibration
+                  Isolation System},
+  journal         = {Journal of Sound and Vibration},
+  volume          = 269,
+  number          = {3-5},
+  pages           = {913-931},
+  year            = 2004,
+  doi             = {10.1016/s0022-460x(03)00206-2},
+  url             = {https://doi.org/10.1016/s0022-460x(03)00206-2},
+  keywords        = {parallel robot, favorite},
+}
+
+
+
 @article{souleille18_concep_activ_mount_space_applic,
   author          = {Souleille, Adrien and Lampert, Thibault and Lafarga, V and
                   Hellegouarch, Sylvain and Rondineau, Alan and Rodrigues,
@@ -26,18 +111,6 @@
 
 
 
-@book{fleming14_desig_model_contr_nanop_system,
-  author          = {Andrew J. Fleming and Kam K. Leang},
-  title           = {Design, Modeling and Control of Nanopositioning Systems},
-  year            = 2014,
-  publisher       = {Springer International Publishing},
-  url             = {https://doi.org/10.1007/978-3-319-06617-2},
-  doi             = {10.1007/978-3-319-06617-2},
-  series          = {Advances in Industrial Control},
-}
-
-
-
 @article{fleming10_integ_strain_force_feedb_high,
   author          = {Fleming, Andrew J and Leang, Kam K},
   title           = {Integrated Strain and Force Feedback for High-Performance
@@ -53,16 +126,21 @@
 
 
 
-@article{fleming10_integ_strain_force_feedb_high,
+@article{gustavsen99_ration_approx_frequen_domain_respon,
-  author          = {Fleming, Andrew J and Leang, Kam K},
+  author          = {Gustavsen, B.; Semlyen, A.},
-  title           = {Integrated Strain and Force Feedback for High-Performance
+  title           = {Rational Approximation of Frequency Domain Responses By
-                  Control of Piezoelectric Actuators},
+                  Vector Fitting},
-  journal         = {Sensors and Actuators A: Physical},
+  journal         = {IEEE Transactions on Power Delivery},
-  volume          = 161,
+  volume          = 14,
-  number          = {1-2},
+  year            = 1999,
-  pages           = {256--265},
+  doi             = {10.1109/61.772353},
-  year            = 2010,
+  url             = {https://doi.org/10.1109/61.772353},
-  publisher       = {Elsevier},
+  issne           = {1937-4208},
-  keywords        = {flexure,nanostage},
+  issnp           = {0885-8977},
+  issue           = 3,
+  month           = 7,
+  page            = {1052--1061},
+  publisher       = {IEEE},
+  keywords        = {Motors},
 }