From 3a1ab301d915b6bd2b39e5b34794bf49052fd731 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Fri, 31 Jul 2020 13:57:13 +0200 Subject: [PATCH] Add flexor FEM model --- data/flexor_ID16/22921061.STEP | 2177 ++++++++++++++++++++ data/flexor_ID16/cp91_2MDoF_6modes.sub | Bin 0 -> 1048576 bytes data/flexor_ID16/flexor_ID16.STEP | 2147 +++++++++++++++++++ data/flexor_ID16/flexor_ID16.slx | Bin 0 -> 37501 bytes data/flexor_ID16/mat_K_6modes_2MDoF.matrix | 20 + data/flexor_ID16/mat_M_6modes_2MDoF.matrix | 20 + data/flexor_ID16/out_nodes_3D.txt | 40 + index.org | 439 +++- 8 files changed, 4835 insertions(+), 8 deletions(-) create mode 100755 data/flexor_ID16/22921061.STEP create mode 100755 data/flexor_ID16/cp91_2MDoF_6modes.sub create mode 100644 data/flexor_ID16/flexor_ID16.STEP create mode 100644 data/flexor_ID16/flexor_ID16.slx create mode 100755 data/flexor_ID16/mat_K_6modes_2MDoF.matrix create mode 100755 data/flexor_ID16/mat_M_6modes_2MDoF.matrix create mode 100755 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[10, 7]: 1.200e+02 [10, 8]:-7.200e+01 [10, 9]: 1.320e+00 [10,10]: 3.469e+01 [10,11]:-7.750e+00 [10,12]:-5.000e-01 [10,13]: 0.000e+00 [10,14]: 0.000e+00 [10,15]: 0.000e+00 [10,16]: 0.000e+00 [10,17]: 0.000e+00 [10,18]: 0.000e+00 +[11, 1]: 2.656e+02 [11, 2]: 1.357e-01 [11, 3]:-1.329e+00 [11, 4]: 2.641e-04 [11, 5]:-3.294e+01 [11, 6]:-2.516e-03 [11, 7]:-4.800e+03 [11, 8]:-6.400e+01 [11, 9]: 1.188e+01 [11,10]:-7.750e+00 [11,11]: 1.300e+02 [11,12]:-5.000e-01 [11,13]: 0.000e+00 [11,14]: 0.000e+00 [11,15]: 0.000e+00 [11,16]: 0.000e+00 [11,17]: 0.000e+00 [11,18]: 0.000e+00 +[12, 1]:-1.333e+00 [12, 2]:-2.542e+00 [12, 3]:-1.784e+00 [12, 4]: 3.780e-04 [12, 5]:-2.446e-03 [12, 6]:-2.358e+02 [12, 7]:-4.800e+01 [12, 8]:-8.000e+00 [12, 9]: 2.216e+00 [12,10]:-5.000e-01 [12,11]:-5.000e-01 [12,12]: 2.385e+02 [12,13]: 0.000e+00 [12,14]: 0.000e+00 [12,15]: 0.000e+00 [12,16]: 0.000e+00 [12,17]: 0.000e+00 [12,18]: 0.000e+00 +[13, 1]: 0.000e+00 [13, 2]: 0.000e+00 [13, 3]: 0.000e+00 [13, 4]: 0.000e+00 [13, 5]: 0.000e+00 [13, 6]: 0.000e+00 [13, 7]: 0.000e+00 [13, 8]: 0.000e+00 [13, 9]: 0.000e+00 [13,10]: 0.000e+00 [13,11]: 0.000e+00 [13,12]: 0.000e+00 [13,13]: 4.356e+09 [13,14]: 0.000e+00 [13,15]: 0.000e+00 [13,16]: 0.000e+00 [13,17]: 0.000e+00 [13,18]: 0.000e+00 +[14, 1]: 0.000e+00 [14, 2]: 0.000e+00 [14, 3]: 0.000e+00 [14, 4]: 0.000e+00 [14, 5]: 0.000e+00 [14, 6]: 0.000e+00 [14, 7]: 0.000e+00 [14, 8]: 0.000e+00 [14, 9]: 0.000e+00 [14,10]: 0.000e+00 [14,11]: 0.000e+00 [14,12]: 0.000e+00 [14,13]: 0.000e+00 [14,14]: 4.593e+09 [14,15]: 0.000e+00 [14,16]: 0.000e+00 [14,17]: 0.000e+00 [14,18]: 0.000e+00 +[15, 1]: 0.000e+00 [15, 2]: 0.000e+00 [15, 3]: 0.000e+00 [15, 4]: 0.000e+00 [15, 5]: 0.000e+00 [15, 6]: 0.000e+00 [15, 7]: 0.000e+00 [15, 8]: 0.000e+00 [15, 9]: 0.000e+00 [15,10]: 0.000e+00 [15,11]: 0.000e+00 [15,12]: 0.000e+00 [15,13]: 0.000e+00 [15,14]: 0.000e+00 [15,15]: 4.948e+09 [15,16]: 0.000e+00 [15,17]: 0.000e+00 [15,18]: 0.000e+00 +[16, 1]: 0.000e+00 [16, 2]: 0.000e+00 [16, 3]: 0.000e+00 [16, 4]: 0.000e+00 [16, 5]: 0.000e+00 [16, 6]: 0.000e+00 [16, 7]: 0.000e+00 [16, 8]: 0.000e+00 [16, 9]: 0.000e+00 [16,10]: 0.000e+00 [16,11]: 0.000e+00 [16,12]: 0.000e+00 [16,13]: 0.000e+00 [16,14]: 0.000e+00 [16,15]: 0.000e+00 [16,16]: 1.919e+10 [16,17]: 0.000e+00 [16,18]: 0.000e+00 +[17, 1]: 0.000e+00 [17, 2]: 0.000e+00 [17, 3]: 0.000e+00 [17, 4]: 0.000e+00 [17, 5]: 0.000e+00 [17, 6]: 0.000e+00 [17, 7]: 0.000e+00 [17, 8]: 0.000e+00 [17, 9]: 0.000e+00 [17,10]: 0.000e+00 [17,11]: 0.000e+00 [17,12]: 0.000e+00 [17,13]: 0.000e+00 [17,14]: 0.000e+00 [17,15]: 0.000e+00 [17,16]: 0.000e+00 [17,17]: 2.147e+10 [17,18]: 0.000e+00 +[18, 1]: 0.000e+00 [18, 2]: 0.000e+00 [18, 3]: 0.000e+00 [18, 4]: 0.000e+00 [18, 5]: 0.000e+00 [18, 6]: 0.000e+00 [18, 7]: 0.000e+00 [18, 8]: 0.000e+00 [18, 9]: 0.000e+00 [18,10]: 0.000e+00 [18,11]: 0.000e+00 [18,12]: 0.000e+00 [18,13]: 0.000e+00 [18,14]: 0.000e+00 [18,15]: 0.000e+00 [18,16]: 0.000e+00 [18,17]: 0.000e+00 [18,18]: 3.336e+10 diff --git a/data/flexor_ID16/mat_M_6modes_2MDoF.matrix b/data/flexor_ID16/mat_M_6modes_2MDoF.matrix new file mode 100755 index 0000000..98688d9 --- /dev/null +++ b/data/flexor_ID16/mat_M_6modes_2MDoF.matrix @@ -0,0 +1,20 @@ + +MAT_M: +[ 1, 1]: 1.624e-02 [ 1, 2]: 9.999e-10 [ 1, 3]:-3.692e-08 [ 1, 4]:-1.155e-10 [ 1, 5]: 2.049e-04 [ 1, 6]:-2.881e-11 [ 1, 7]: 4.064e-03 [ 1, 8]: 4.955e-08 [ 1, 9]: 7.368e-08 [ 1,10]: 1.379e-10 [ 1,11]:-7.160e-06 [ 1,12]: 6.897e-11 [ 1,13]:-2.028e-05 [ 1,14]: 5.554e-02 [ 1,15]: 3.599e-06 [ 1,16]: 2.900e-06 [ 1,17]: 8.272e-02 [ 1,18]:-2.468e-06 +[ 2, 1]: 9.999e-10 [ 2, 2]: 1.848e-02 [ 2, 3]:-3.219e-07 [ 2, 4]:-2.074e-04 [ 2, 5]:-1.119e-10 [ 2, 6]:-2.255e-09 [ 2, 7]: 2.195e-08 [ 2, 8]: 4.013e-03 [ 2, 9]: 2.886e-07 [ 2,10]: 9.997e-06 [ 2,11]:-3.644e-10 [ 2,12]:-3.744e-12 [ 2,13]:-1.437e-05 [ 2,14]:-5.095e-06 [ 2,15]: 8.806e-02 [ 2,16]:-1.237e-02 [ 2,17]: 1.500e-07 [ 2,18]: 3.313e-02 +[ 3, 1]:-3.692e-08 [ 3, 2]:-3.219e-07 [ 3, 3]: 1.804e-02 [ 3, 4]: 7.130e-10 [ 3, 5]:-1.637e-09 [ 3, 6]: 1.340e-09 [ 3, 7]: 3.136e-07 [ 3, 8]: 7.272e-08 [ 3, 9]: 2.993e-03 [ 3,10]: 1.259e-09 [ 3,11]:-5.922e-10 [ 3,12]: 1.317e-09 [ 3,13]: 5.819e-06 [ 3,14]: 3.227e-06 [ 3,15]:-3.103e-06 [ 3,16]: 4.241e-06 [ 3,17]:-9.604e-07 [ 3,18]:-2.639e-06 +[ 4, 1]:-1.155e-10 [ 4, 2]:-2.074e-04 [ 4, 3]: 7.130e-10 [ 4, 4]: 3.510e-06 [ 4, 5]:-1.359e-12 [ 4, 6]:-5.567e-13 [ 4, 7]: 1.778e-10 [ 4, 8]:-6.847e-06 [ 4, 9]:-7.847e-10 [ 4,10]:-1.254e-09 [ 4,11]: 9.463e-13 [ 4,12]: 1.958e-12 [ 4,13]: 4.641e-08 [ 4,14]: 1.613e-08 [ 4,15]:-2.170e-04 [ 4,16]: 6.874e-05 [ 4,17]:-1.637e-08 [ 4,18]:-5.990e-04 +[ 5, 1]: 2.049e-04 [ 5, 2]:-1.119e-10 [ 5, 3]:-1.637e-09 [ 5, 4]:-1.359e-12 [ 5, 5]: 3.311e-06 [ 5, 6]: 1.683e-13 [ 5, 7]: 9.441e-06 [ 5, 8]: 3.860e-11 [ 5, 9]: 1.766e-09 [ 5,10]:-2.762e-13 [ 5,11]:-1.297e-09 [ 5,12]: 1.810e-12 [ 5,13]:-6.036e-08 [ 5,14]: 1.813e-04 [ 5,15]: 9.642e-09 [ 5,16]: 2.704e-08 [ 5,17]: 8.113e-04 [ 5,18]:-2.302e-08 +[ 6, 1]:-2.881e-11 [ 6, 2]:-2.255e-09 [ 6, 3]: 1.340e-09 [ 6, 4]:-5.567e-13 [ 6, 5]: 1.683e-13 [ 6, 6]: 3.708e-07 [ 6, 7]: 8.410e-11 [ 6, 8]: 9.292e-10 [ 6, 9]:-1.086e-09 [ 6,10]: 2.396e-12 [ 6,11]:-5.002e-13 [ 6,12]: 6.502e-08 [ 6,13]: 2.552e-04 [ 6,14]: 9.650e-08 [ 6,15]: 6.459e-09 [ 6,16]:-9.240e-10 [ 6,17]:-5.548e-09 [ 6,18]: 3.141e-08 +[ 7, 1]: 4.064e-03 [ 7, 2]: 2.195e-08 [ 7, 3]: 3.136e-07 [ 7, 4]: 1.778e-10 [ 7, 5]: 9.441e-06 [ 7, 6]: 8.410e-11 [ 7, 7]: 1.674e-02 [ 7, 8]:-7.211e-08 [ 7, 9]:-3.482e-07 [ 7,10]:-2.155e-10 [ 7,11]:-1.699e-04 [ 7,12]:-6.684e-11 [ 7,13]:-3.188e-05 [ 7,14]: 8.552e-02 [ 7,15]: 4.929e-06 [ 7,16]:-4.308e-06 [ 7,17]:-9.224e-03 [ 7,18]: 1.941e-06 +[ 8, 1]: 4.955e-08 [ 8, 2]: 4.013e-03 [ 8, 3]: 7.272e-08 [ 8, 4]:-6.847e-06 [ 8, 5]: 3.860e-11 [ 8, 6]: 9.292e-10 [ 8, 7]:-7.211e-08 [ 8, 8]: 1.459e-02 [ 8, 9]:-3.946e-08 [ 8,10]: 1.670e-04 [ 8,11]: 4.772e-10 [ 8,12]: 1.298e-09 [ 8,13]: 2.789e-06 [ 8,14]:-2.877e-06 [ 8,15]: 5.546e-02 [ 8,16]: 7.601e-02 [ 8,17]:-2.596e-06 [ 8,18]:-6.673e-03 +[ 9, 1]: 7.368e-08 [ 9, 2]: 2.886e-07 [ 9, 3]: 2.993e-03 [ 9, 4]:-7.847e-10 [ 9, 5]: 1.766e-09 [ 9, 6]:-1.086e-09 [ 9, 7]:-3.482e-07 [ 9, 8]:-3.946e-08 [ 9, 9]: 1.708e-02 [ 9,10]:-1.230e-09 [ 9,11]: 4.937e-10 [ 9,12]:-1.568e-09 [ 9,13]:-5.366e-06 [ 9,14]:-4.779e-06 [ 9,15]: 2.951e-06 [ 9,16]:-1.252e-06 [ 9,17]: 5.979e-06 [ 9,18]:-2.257e-06 +[10, 1]: 1.379e-10 [10, 2]: 9.997e-06 [10, 3]: 1.259e-09 [10, 4]:-1.254e-09 [10, 5]:-2.762e-13 [10, 6]: 2.396e-12 [10, 7]:-2.155e-10 [10, 8]: 1.670e-04 [10, 9]:-1.230e-09 [10,10]: 2.413e-06 [10,11]:-1.085e-13 [10,12]:-1.860e-12 [10,13]: 9.566e-09 [10,14]:-1.039e-08 [10,15]: 1.953e-04 [10,16]: 6.785e-04 [10,17]:-2.458e-08 [10,18]:-7.855e-05 +[11, 1]:-7.160e-06 [11, 2]:-3.644e-10 [11, 3]:-5.922e-10 [11, 4]: 9.463e-13 [11, 5]:-1.297e-09 [11, 6]:-5.002e-13 [11, 7]:-1.699e-04 [11, 8]: 4.772e-10 [11, 9]: 4.937e-10 [11,10]:-1.085e-13 [11,11]: 2.569e-06 [11,12]:-1.144e-12 [11,13]: 7.355e-08 [11,14]:-2.049e-04 [11,15]:-1.424e-08 [11,16]: 5.036e-08 [11,17]: 4.737e-05 [11,18]:-1.820e-08 +[12, 1]: 6.897e-11 [12, 2]:-3.744e-12 [12, 3]: 1.317e-09 [12, 4]: 1.958e-12 [12, 5]: 1.810e-12 [12, 6]: 6.502e-08 [12, 7]:-6.684e-11 [12, 8]: 1.298e-09 [12, 9]:-1.568e-09 [12,10]:-1.860e-12 [12,11]:-1.144e-12 [12,12]: 4.129e-07 [12,13]: 2.609e-04 [12,14]: 9.485e-08 [12,15]: 4.034e-08 [12,16]:-2.487e-08 [12,17]: 4.305e-09 [12,18]: 7.568e-09 +[13, 1]:-2.028e-05 [13, 2]:-1.437e-05 [13, 3]: 5.819e-06 [13, 4]: 4.641e-08 [13, 5]:-6.036e-08 [13, 6]: 2.552e-04 [13, 7]:-3.188e-05 [13, 8]: 2.789e-06 [13, 9]:-5.366e-06 [13,10]: 9.566e-09 [13,11]: 7.355e-08 [13,12]: 2.609e-04 [13,13]: 1.000e+00 [13,14]: 0.000e+00 [13,15]: 0.000e+00 [13,16]: 0.000e+00 [13,17]: 0.000e+00 [13,18]: 0.000e+00 +[14, 1]: 5.554e-02 [14, 2]:-5.095e-06 [14, 3]: 3.227e-06 [14, 4]: 1.613e-08 [14, 5]: 1.813e-04 [14, 6]: 9.650e-08 [14, 7]: 8.552e-02 [14, 8]:-2.877e-06 [14, 9]:-4.779e-06 [14,10]:-1.039e-08 [14,11]:-2.049e-04 [14,12]: 9.485e-08 [14,13]: 0.000e+00 [14,14]: 1.000e+00 [14,15]: 0.000e+00 [14,16]: 0.000e+00 [14,17]: 0.000e+00 [14,18]: 0.000e+00 +[15, 1]: 3.599e-06 [15, 2]: 8.806e-02 [15, 3]:-3.103e-06 [15, 4]:-2.170e-04 [15, 5]: 9.642e-09 [15, 6]: 6.459e-09 [15, 7]: 4.929e-06 [15, 8]: 5.546e-02 [15, 9]: 2.951e-06 [15,10]: 1.953e-04 [15,11]:-1.424e-08 [15,12]: 4.034e-08 [15,13]: 0.000e+00 [15,14]: 0.000e+00 [15,15]: 1.000e+00 [15,16]: 0.000e+00 [15,17]: 0.000e+00 [15,18]: 0.000e+00 +[16, 1]: 2.900e-06 [16, 2]:-1.237e-02 [16, 3]: 4.241e-06 [16, 4]: 6.874e-05 [16, 5]: 2.704e-08 [16, 6]:-9.240e-10 [16, 7]:-4.308e-06 [16, 8]: 7.601e-02 [16, 9]:-1.252e-06 [16,10]: 6.785e-04 [16,11]: 5.036e-08 [16,12]:-2.487e-08 [16,13]: 0.000e+00 [16,14]: 0.000e+00 [16,15]: 0.000e+00 [16,16]: 1.000e+00 [16,17]: 0.000e+00 [16,18]: 0.000e+00 +[17, 1]: 8.272e-02 [17, 2]: 1.500e-07 [17, 3]:-9.604e-07 [17, 4]:-1.637e-08 [17, 5]: 8.113e-04 [17, 6]:-5.548e-09 [17, 7]:-9.224e-03 [17, 8]:-2.596e-06 [17, 9]: 5.979e-06 [17,10]:-2.458e-08 [17,11]: 4.737e-05 [17,12]: 4.305e-09 [17,13]: 0.000e+00 [17,14]: 0.000e+00 [17,15]: 0.000e+00 [17,16]: 0.000e+00 [17,17]: 1.000e+00 [17,18]: 0.000e+00 +[18, 1]:-2.468e-06 [18, 2]: 3.313e-02 [18, 3]:-2.639e-06 [18, 4]:-5.990e-04 [18, 5]:-2.302e-08 [18, 6]: 3.141e-08 [18, 7]: 1.941e-06 [18, 8]:-6.673e-03 [18, 9]:-2.257e-06 [18,10]:-7.855e-05 [18,11]:-1.820e-08 [18,12]: 7.568e-09 [18,13]: 0.000e+00 [18,14]: 0.000e+00 [18,15]: 0.000e+00 [18,16]: 0.000e+00 [18,17]: 0.000e+00 [18,18]: 1.000e+00 diff --git a/data/flexor_ID16/out_nodes_3D.txt b/data/flexor_ID16/out_nodes_3D.txt new file mode 100755 index 0000000..f6adc91 --- /dev/null +++ b/data/flexor_ID16/out_nodes_3D.txt @@ -0,0 +1,40 @@ + + LIST ALL SELECTED NODES. DSYS= 0 + + *** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 *** + DISTRIBUTED ANSYS Academic Research + + 00208316 VERSION=WINDOWS x64 16:37:53 JUL 30, 2020 CP= 3.062 + + Flex-FV--Modal (B5) + + + + NODE X Y Z THXY THYZ THZX + 181278 0.0000 0.0000 0.10000E-008 0.00 0.00 0.00 + 181279 0.0000 0.0000 -0.10000E-008 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 Academic Research + + 00208316 VERSION=WINDOWS x64 16:37:53 JUL 30, 2020 CP= 3.062 + + Flex-FV--Modal (B5) + + + NODE LABEL SUPPORT + 181278 UX + 181278 UY + 181278 UZ + 181278 ROTX + 181278 ROTY + 181278 ROTZ + 181279 UX + 181279 UY + 181279 UZ + 181279 ROTX + 181279 ROTY + 181279 ROTZ diff --git a/index.org b/index.org index 288a709..348a277 100644 --- a/index.org +++ b/index.org @@ -166,15 +166,15 @@ Parameters for the APA95ML: #+begin_src matlab d33 = 3e-10; % Strain constant [m/V] n = 80; % Number of layers per stack - eT = 1.6e-8; % Permittivity under constant stress [F/m] + eT = 1.6e-7; % Permittivity under constant stress [F/m] sD = 2e-11; % Elastic compliance under constant electric displacement [m2/N] ka = 235e6; % Stack stiffness [N/m] C = 5e-6; % Stack capactiance [F] #+end_src #+begin_src matlab - na = 3; % Number of stacks used as actuator - ns = 0; % Number of stacks used as force sensor + na = 2; % Number of stacks used as actuator + ns = 1; % Number of stacks used as force sensor #+end_src The ratio of the developed force to applied voltage is $d_{33} n k_a$ in [N/V]. @@ -185,7 +185,7 @@ We denote this constant by $g_a$ and: #+end_src #+RESULTS: -: 1.88 +: 3.76 From cite:fleming14_desig_model_contr_nanop_system (page 123), the relation between relative displacement and generated voltage is: \[ V_s = \frac{d_{33}}{\epsilon^T s^D n} \Delta h \] @@ -201,7 +201,7 @@ where: #+end_src #+RESULTS: -: 5.8594 +: 1.1719 ** Identification of the Dynamics The flexible element is imported using the =Reduced Order Flexible Solid= simscape block. @@ -622,6 +622,47 @@ The two identified dynamics are compared in Figure [[fig:dynamics_act_disp_comp_ save('../test-bench-apa/mat/fem_model_5kg.mat', 'G') #+end_src +** Dynamics from input voltage to output voltage +#+begin_src matlab + m = 5; +#+end_src + +#+begin_src matlab + %% Name of the Simulink File + mdl = 'piezo_amplified_3d'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/Va'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; + + G = -linearize(mdl, io); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(1, 4, 5000); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(freqresp(G, freqs, 'Hz')))); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G, freqs, 'Hz'))))); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([10, 5e3]); +#+end_src + * APA300ML ** Matlab Init :noexport:ignore: #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) @@ -643,6 +684,11 @@ The two identified dynamics are compared in Figure [[fig:dynamics_act_disp_comp_ ** Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates We first extract the stiffness and mass matrices. +#+begin_src matlab + K = extractMatrix('mat_K-48modes-7MDoF.matrix'); + M = extractMatrix('mat_M-48modes-7MDoF.matrix'); +#+end_src + #+begin_src matlab K = extractMatrix('mat_K-80modes-7MDoF.matrix'); M = extractMatrix('mat_M-80modes-7MDoF.matrix'); @@ -768,9 +814,6 @@ where: #+RESULTS: : 5.8594 - - - ** Identification of the Dynamics The flexible element is imported using the =Reduced Order Flexible Solid= simscape block. @@ -976,6 +1019,386 @@ The two identified dynamics are compared in Figure [[fig:dynamics_act_disp_comp_ xlabel('Real Part'); ylabel('Imaginary Part'); #+end_src +** Sensor Fusion +- [ ] What is the goal of that? Special control properties, lower the sensor noise? + +Use the relative motion sensor at low frequency and the force sensor at high frequency. +#+begin_src matlab + m = 10; +#+end_src + +#+begin_src matlab + %% Name of the Simulink File + mdl = 'APA300ML_test_bench'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/Va'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/y'], 1, 'openoutput'); io_i = io_i + 1; + + G = linearize(mdl, io); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(1, 5, 1000); + + Gresp = squeeze(freqresp(G, freqs, 'Hz')); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(Gresp(1, :)), '-'); + plot(freqs, abs(Gresp(2, :)), '-'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*unwrap(angle(Gresp(1, :))), '-', ... + 'DisplayName', 'Force'); + plot(freqs, 180/pi*unwrap(angle(Gresp(2, :))), '-', ... + 'DisplayName', 'Displacement'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + ylim([-390 30]); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); + legend('location', 'southwest'); +#+end_src + +Merge around 1kHz +#+begin_src matlab :exports none + freqs = logspace(1, 5, 1000); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(Gresp(1, :).*squeeze(freqresp(0.0065/s^2, freqs, 'Hz'))'), '-'); + plot(freqs, abs(Gresp(2, :)), '-'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*unwrap(angle(Gresp(1, :).*squeeze(freqresp(1/s^2, freqs, 'Hz'))')), '-', ... + 'DisplayName', 'Force'); + plot(freqs, 180/pi*unwrap(angle(Gresp(2, :))), '-', ... + 'DisplayName', 'Displacement'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); + legend('location', 'southwest'); +#+end_src + +LPF and HPF +#+begin_src matlab + n = 3; w0 = 2*pi*1e3; G0 = 1/10; G1 = 1e5; Gc = 1/2; + W1 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n; + + n = 3; w0 = 2*pi*1e3; G0 = 1e5; G1 = 0.1; Gc = 1/2; + W2 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n; +#+end_src + +#+begin_src matlab + P = [W1 -W1; + 0 W2; + 1 0]; + + [H2, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on'); + H1 = 1 - H2; +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(1, 5, 1000); + + Gresp = squeeze(freqresp(G, freqs, 'Hz')); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(Gresp(1, :).*squeeze(freqresp(0.0065/s^2*H2, freqs, 'Hz'))'), '-'); + plot(freqs, abs(Gresp(2, :).*squeeze(freqresp(H1, freqs, 'Hz'))'), '-'); + plot(freqs, abs(Gresp(2, :).*squeeze(freqresp(H1, freqs, 'Hz'))' + Gresp(1, :).*squeeze(freqresp(0.0065/s^2*H2, freqs, 'Hz'))'), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*unwrap(angle(Gresp(1, :).*squeeze(freqresp(0.0065/s^2*H2, freqs, 'Hz'))')), '-', ... + 'DisplayName', 'Force'); + plot(freqs, 180/pi*unwrap(angle(Gresp(2, :).*squeeze(freqresp(H1, freqs, 'Hz'))')), '-', ... + 'DisplayName', 'Displacement'); + plot(freqs, 180/pi*unwrap(angle(Gresp(2, :).*squeeze(freqresp(H1, freqs, 'Hz'))' + Gresp(1, :).*squeeze(freqresp(0.0065/s^2*H2, freqs, 'Hz'))')), 'k--', ... + 'DisplayName', 'Super Sensor'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); + legend('location', 'southwest'); +#+end_src + +#+begin_src matlab :exports none + Gss = -zpk(G(1)*0.0065/s^2*H2 + G(2)*H1); + + freqs = logspace(1, 5, 1000); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(freqresp(Gss, freqs, 'Hz'))'), '-'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*(angle(squeeze(freqresp(Gss, freqs, 'Hz'))')), '-', ... + 'DisplayName', 'Force'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); + legend('location', 'southwest'); +#+end_src + +Root locus +#+begin_src matlab + figure; + + gains = logspace(4, 7, 100); + + hold on; + plot(real(pole(Gss)), imag(pole(Gss)), 'kx'); + plot(real(tzero(Gss)), imag(tzero(Gss)), 'ko'); + for k = 1:length(gains) + cl_poles = pole(feedback(Gss, gains(k)*s)); + plot(real(cl_poles), imag(cl_poles), 'k.'); + end + hold off; + axis square; + xlim([-500, 10]); ylim([0, 510]); + + xlabel('Real Part'); ylabel('Imaginary Part'); +#+end_src + +* Flexible Joint +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) + <> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes + <> +#+end_src + +#+begin_src matlab + addpath('./src/'); + addpath('./data/flexor_ID16/'); +#+end_src + +#+begin_src matlab :exports none + open('flexor_ID16.slx'); +#+end_src + +** Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates +We first extract the stiffness and mass matrices. +#+begin_src matlab + K = extractMatrix('mat_K_6modes_2MDoF.matrix'); + M = extractMatrix('mat_M_6modes_2MDoF.matrix'); +#+end_src + +Then, we extract the coordinates of the interface nodes. +#+begin_src matlab + [int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('out_nodes_3D.txt'); +#+end_src + +#+begin_src matlab + save('./mat/flexor_ID16.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K'); +#+end_src + +** Output parameters +#+begin_src matlab + load('./mat/flexor_ID16.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K'); +#+end_src + +#+begin_src matlab :exports results :results value table replace :tangle no + data2orgtable([length(n_i); length(int_i); size(M,1) - 6*length(int_i); size(M,1)], {'Total number of Nodes', 'Number of interface Nodes', 'Number of Modes', 'Size of M and K matrices'}, {}, ' %.0f '); +#+end_src + +#+RESULTS: +| Total number of Nodes | 2 | +| Number of interface Nodes | 2 | +| Number of Modes | 6 | +| Size of M and K matrices | 18 | + +#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*) + data2orgtable([[1:length(int_i)]', int_i, int_xyz], {}, {'Node i', 'Node Number', 'x [m]', 'y [m]', 'z [m]'}, ' %f '); +#+end_src + +#+caption: Coordinates of the interface nodes +#+RESULTS: +| Node i | Node Number | x [m] | y [m] | z [m] | +|--------+-------------+-------+-------+-------| +| 1.0 | 181278.0 | 0.0 | 0.0 | 0.0 | +| 2.0 | 181279.0 | 0.0 | 0.0 | -0.0 | + +#+begin_src matlab :exports results :results value table replace :tangle no + data2orgtable(K(1:10, 1:10), {}, {}, ' %.2e '); +#+end_src + +#+caption: First 10x10 elements of the Stiffness matrix +#+RESULTS: +| 11200000.0 | 195.0 | 2220.0 | -0.719 | -265.0 | 1.59 | -11200000.0 | -213.0 | -2220.0 | 0.147 | +| 195.0 | 11400000.0 | 1290.0 | -148.0 | -0.188 | 2.41 | -212.0 | -11400000.0 | -1290.0 | 148.0 | +| 2220.0 | 1290.0 | 119000000.0 | 1.31 | 1.49 | 1.79 | -2220.0 | -1290.0 | -119000000.0 | -1.31 | +| -0.719 | -148.0 | 1.31 | 33.0 | 0.000488 | -0.000977 | 0.141 | 148.0 | -1.31 | -33.0 | +| -265.0 | -0.188 | 1.49 | 0.000488 | 33.0 | 0.00293 | 266.0 | 0.154 | -1.49 | 0.00026 | +| 1.59 | 2.41 | 1.79 | -0.000977 | 0.00293 | 236.0 | -1.32 | -2.55 | -1.79 | 0.000379 | +| -11200000.0 | -212.0 | -2220.0 | 0.141 | 266.0 | -1.32 | 11400000.0 | 24600.0 | 1640.0 | 120.0 | +| -213.0 | -11400000.0 | -1290.0 | 148.0 | 0.154 | -2.55 | 24600.0 | 11400000.0 | 1290.0 | -72.0 | +| -2220.0 | -1290.0 | -119000000.0 | -1.31 | -1.49 | -1.79 | 1640.0 | 1290.0 | 119000000.0 | 1.32 | +| 0.147 | 148.0 | -1.31 | -33.0 | 0.00026 | 0.000379 | 120.0 | -72.0 | 1.32 | 34.7 | + + +#+begin_src matlab :exports results :results value table replace :tangle no + data2orgtable(M(1:10, 1:10), {}, {}, ' %.1g '); +#+end_src + +#+caption: First 10x10 elements of the Mass matrix +#+RESULTS: +| 0.02 | 1e-09 | -4e-08 | -1e-10 | 0.0002 | -3e-11 | 0.004 | 5e-08 | 7e-08 | 1e-10 | +| 1e-09 | 0.02 | -3e-07 | -0.0002 | -1e-10 | -2e-09 | 2e-08 | 0.004 | 3e-07 | 1e-05 | +| -4e-08 | -3e-07 | 0.02 | 7e-10 | -2e-09 | 1e-09 | 3e-07 | 7e-08 | 0.003 | 1e-09 | +| -1e-10 | -0.0002 | 7e-10 | 4e-06 | -1e-12 | -6e-13 | 2e-10 | -7e-06 | -8e-10 | -1e-09 | +| 0.0002 | -1e-10 | -2e-09 | -1e-12 | 3e-06 | 2e-13 | 9e-06 | 4e-11 | 2e-09 | -3e-13 | +| -3e-11 | -2e-09 | 1e-09 | -6e-13 | 2e-13 | 4e-07 | 8e-11 | 9e-10 | -1e-09 | 2e-12 | +| 0.004 | 2e-08 | 3e-07 | 2e-10 | 9e-06 | 8e-11 | 0.02 | -7e-08 | -3e-07 | -2e-10 | +| 5e-08 | 0.004 | 7e-08 | -7e-06 | 4e-11 | 9e-10 | -7e-08 | 0.01 | -4e-08 | 0.0002 | +| 7e-08 | 3e-07 | 0.003 | -8e-10 | 2e-09 | -1e-09 | -3e-07 | -4e-08 | 0.02 | -1e-09 | +| 1e-10 | 1e-05 | 1e-09 | -1e-09 | -3e-13 | 2e-12 | -2e-10 | 0.0002 | -1e-09 | 2e-06 | + +Using =K=, =M= and =int_xyz=, we can use the =Reduced Order Flexible Solid= simscape block. + +** Flexible Joint Characteristics +#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*) + data2orgtable([1e-6*K(3,3), K(4,4), K(5,5), K(6,6)]', {'Axial Stiffness [N/um]', 'Bending Stiffness [Nm/rad]', 'Bending Stiffness [Nm/rad]', 'Torsion Stiffness [Nm/rad]'}, {'*Caracteristic*', '*Value*'}, ' %0.f '); +#+end_src + +#+RESULTS: +| *Caracteristic* | *Value* | +|----------------------------+---------| +| Axial Stiffness [N/um] | 119 | +| Bending Stiffness [Nm/rad] | 33 | +| Bending Stiffness [Nm/rad] | 33 | +| Torsion Stiffness [Nm/rad] | 236 | + +** Identification +#+begin_src matlab + m = 10; +#+end_src + +The dynamics is identified from the applied force to the measured relative displacement. +#+begin_src matlab + %% Name of the Simulink File + mdl = 'flexor_ID16'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/T'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1; + + G = linearize(mdl, io); +#+end_src + +#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*) + data2orgtable([1e-6*K(3,3), K(4,4), K(5,5), K(6,6) ; 1e-6./dcgain(G(3,3)), 1./dcgain(G(4,4)), 1./dcgain(G(5,5)), 1./dcgain(G(6,6))]', {'Axial Stiffness Dz [N/um]', 'Bending Stiffness Rx [Nm/rad]', 'Bending Stiffness Ry [Nm/rad]', 'Torsion Stiffness Rz [Nm/rad]'}, {'*Caracteristic*', '*Value*', '*Identification*'}, ' %0.f '); +#+end_src + +#+RESULTS: +| *Caracteristic* | *Value* | *Identification* | +|-------------------------------+---------+------------------| +| Axial Stiffness Dz [N/um] | 119 | 119 | +| Bending Stiffness Rx [Nm/rad] | 33 | 34 | +| Bending Stiffness Ry [Nm/rad] | 33 | 126 | +| Torsion Stiffness Rz [Nm/rad] | 236 | 238 | + +#+begin_src matlab :exports none + freqs = logspace(0, 5, 1000); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(freqresp(G(1,1), freqs, 'Hz'))), '-'); + plot(freqs, abs(squeeze(freqresp(G(2,2), freqs, 'Hz'))), '-'); + plot(freqs, abs(squeeze(freqresp(G(3,3), freqs, 'Hz'))), '-'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on + plot(freqs, 180/pi*(angle(squeeze(freqresp(G(1,1), freqs, 'Hz')))), '-'); + plot(freqs, 180/pi*(angle(squeeze(freqresp(G(2,2), freqs, 'Hz')))), '-'); + plot(freqs, 180/pi*(angle(squeeze(freqresp(G(3,3), freqs, 'Hz')))), '-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(0, 5, 1000); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(freqresp(G(4,4), freqs, 'Hz'))), '-'); + plot(freqs, abs(squeeze(freqresp(G(5,5), freqs, 'Hz'))), '-'); + plot(freqs, abs(squeeze(freqresp(G(6,6), freqs, 'Hz'))), '-'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on + plot(freqs, 180/pi*(angle(squeeze(freqresp(G(4,4), freqs, 'Hz')))), '-'); + plot(freqs, 180/pi*(angle(squeeze(freqresp(G(5,5), freqs, 'Hz')))), '-'); + plot(freqs, 180/pi*(angle(squeeze(freqresp(G(6,6), freqs, 'Hz')))), '-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + * Integral Force Feedback with Amplified Piezo ** Matlab Init :noexport:ignore: #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)