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Reworked IFF section

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tdehaeze committed 2020-11-12 18:40:48 +01:00
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index.org
+223 -263
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@@ -45,7 +45,6 @@ In this document, Finite Element Models (FEM) of parts of the Nano-Hexapod are d
A first geometry of a Flexible joint is modelled and its characteristics are identified from the Stiffness matrix as well as from the Simscape model.
- Section [[sec:flexor_025]]:
An optimized flexible joint is developed for the Nano-Hexapod and is then imported in a Simscape model.
- Section [[sec:integral_force_feedback]]:
- Section [[sec:strut_fem]]:
A super element of a complete strut is exported.
@@ -91,8 +90,8 @@ The remote point used are also shown in this figure.
** Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates
We first extract the stiffness and mass matrices.
#+begin_src matlab
K = readmatrix('mat_K.CSV');
M = readmatrix('mat_M.CSV');
K = readmatrix('APA300ML_mat_K.CSV');
M = readmatrix('APA300ML_mat_M.CSV');
#+end_src
#+begin_src matlab :exports results :results value table replace :tangle no
@@ -133,7 +132,7 @@ We first extract the stiffness and mass matrices.
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');
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('APA300ML_out_nodes_3D.txt');
#+end_src
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
@@ -804,6 +803,203 @@ The dynamics of the Simscape simplified model is identified and compared with th
#+RESULTS:
[[file:figs/apa300ml_comp_simpler_simscape.png]]
** Integral Force Feedback
In this section, Integral Force Feedback control architecture is applied on the APA300ML.
First, the plant (dynamics from voltage actuator to voltage sensor is identified).
#+begin_src matlab :exports none
Kiff = tf(0);
#+end_src
The payload mass is set to 10kg.
#+begin_src matlab
m = 10;
#+end_src
#+begin_src matlab :exports none
%% Name of the Simulink File
mdl = 'APA300ML_IFF';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/w'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/Fd'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/APA300ML'], 1, 'openoutput'); io_i = io_i + 1;
G_ol = linearize(mdl, io);
G_ol.InputName = {'w', 'f', 'F'};
G_ol.OutputName = {'x1', 'Fs'};
G = G_ol({'Fs'}, {'f'});
#+end_src
The obtained dynamics is shown in Figure [[fig:piezo_amplified_iff_plant]].
#+begin_src matlab :exports none
freqs = logspace(1, 5, 1000);
figure;
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
ax1 = nexttile([2,1]);
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 = nexttile;
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);
ylim([-390 30]);
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/piezo_amplified_iff_plant.pdf', 'width', 'wide', 'height', 'tall');
#+end_src
#+name: fig:piezo_amplified_iff_plant
#+caption: IFF Plant
#+RESULTS:
[[file:figs/piezo_amplified_iff_plant.png]]
The controller is defined below and the loop gain is shown in Figure [[fig:piezo_amplified_iff_loop_gain]].
#+begin_src matlab
Kiff = -1e3/s;
#+end_src
#+begin_src matlab :exports none
freqs = logspace(1, 5, 1000);
figure;
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(G*Kiff, freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude'); set(gca, 'XTickLabel',[]);
hold off;
ax2 = nexttile;
hold on;
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G*Kiff, freqs, 'Hz')))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
yticks(-360:90:360);
ylim([-180 180]);
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/piezo_amplified_iff_loop_gain.pdf', 'width', 'wide', 'height', 'tall');
#+end_src
#+name: fig:piezo_amplified_iff_loop_gain
#+caption: IFF Loop Gain
#+RESULTS:
[[file:figs/piezo_amplified_iff_loop_gain.png]]
Now the closed-loop system is identified again and compare with the open loop system in Figure [[fig:piezo_amplified_iff_comp]].
It is the expected behavior as shown in the Figure [[fig:souleille18_results]] (from cite:souleille18_concep_activ_mount_space_applic).
#+begin_src matlab :exports none
clear io; io_i = 1;
io(io_i) = linio([mdl, '/w'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/Fd'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/APA300ML'], 1, 'output'); io_i = io_i + 1;
Giff = linearize(mdl, io);
Giff.InputName = {'w', 'f', 'F'};
Giff.OutputName = {'x1', 'Fs'};
#+end_src
#+begin_src matlab :exports none
freqs = logspace(0, 3, 1000);
figure;
tiledlayout(2, 3, 'TileSpacing', 'None', 'Padding', 'None');
ax1 = nexttile;
hold on;
plot(freqs, abs(squeeze(freqresp(G_ol('x1', 'w'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Giff('x1', 'w'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); ylabel('$x_1/w$ [m/m]')
ax2 = nexttile;
hold on;
plot(freqs, abs(squeeze(freqresp(G_ol('x1', 'f'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Giff('x1', 'f'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); ylabel('$x_1/f$ [m/N]');
ax3 = nexttile;
hold on;
plot(freqs, abs(squeeze(freqresp(G_ol('x1', 'F'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Giff('x1', 'F'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); ylabel('$x_1/F$ [m/N]');
ax4 = nexttile;
hold on;
plot(freqs, abs(squeeze(freqresp(G_ol('Fs', 'w'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Giff('Fs', 'w'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('$F_s/w$ [N/m]');
ax5 = nexttile;
hold on;
plot(freqs, abs(squeeze(freqresp(G_ol('Fs', 'f'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Giff('Fs', 'f'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('$F_s/f$ [N/N]');
ax6 = nexttile;
hold on;
plot(freqs, abs(squeeze(freqresp(G_ol('Fs', 'F'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Giff('Fs', 'F'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('$F_s/F$ [N/N]');
linkaxes([ax1,ax2,ax3,ax4,ax5,ax6],'x');
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/piezo_amplified_iff_comp.pdf', 'width', 'full', 'height', 'full');
#+end_src
#+name: fig:piezo_amplified_iff_comp
#+caption: OL and CL transfer functions
#+RESULTS:
[[file:figs/piezo_amplified_iff_comp.png]]
#+name: fig:souleille18_results
#+caption: Results obtained in cite:souleille18_concep_activ_mount_space_applic
[[file:figs/souleille18_results.png]]
* First Flexible Joint Geometry
:PROPERTIES:
:header-args:matlab+: :tangle matlab/flexor_ID16.m
@@ -1074,8 +1270,8 @@ The obtained geometry is shown in Figure [[fig:optimal_flexor]].
** Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates
We first extract the stiffness and mass matrices.
#+begin_src matlab
K = readmatrix('mat_K.CSV');
M = readmatrix('mat_M.CSV');
K = readmatrix('flex025_mat_K.CSV');
M = readmatrix('flex025_mat_M.CSV');
#+end_src
#+begin_src matlab :exports results :results value table replace :tangle no
@@ -1116,7 +1312,7 @@ We first extract the stiffness and mass matrices.
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');
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('flex025_out_nodes_3D.txt');
#+end_src
#+begin_src matlab :exports results :results value table replace :tangle no
@@ -1264,276 +1460,40 @@ The two obtained dynamics are compared in Figure
#+RESULTS:
[[file:figs/flexor_ID16_compare_bushing_joint.png]]
* Force Sensor and Integral Force Feedback with an Amplified Piezoelectric Actuator
<<sec:integral_force_feedback>>
** Introduction :ignore:
In this section, we try to replicate the results obtained in cite:souleille18_concep_activ_mount_space_applic.
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
** Comparison with a stiffer Flexible Joint
The stiffness matrix with the flexible joint with a "hinge" size of 0.50mm is loaded.
#+begin_src matlab
addpath('./data/piezo_amplified_IFF/');
K_050 = readmatrix('flex050_mat_K.CSV');
#+end_src
#+begin_src matlab :exports none
open('piezo_amplified_IFF');
Its parameters are compared with the Flexible Joint with a size of 0.25mm in the table below.
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
data2orgtable([1e-6*K(3,3), 1e-6*K(2,2), K(4,4), K(5,5), K(6,6) ; 1e-6*K_050(3,3), 1e-6*K_050(2,2), K_050(4,4), K_050(5,5), K_050(6,6)]', {'Axial Stiffness Dz [N/um]', 'Shear Stiffness [N/um]', 'Bending Stiffness Rx [Nm/rad]', 'Bending Stiffness Ry [Nm/rad]', 'Torsion Stiffness Rz [Nm/rad]'}, {'*Caracteristic*', '*0.25 mm*', '*0.50 mm*'}, ' %.1f ');
#+end_src
** Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates
We first extract the stiffness and mass matrices.
#+begin_src matlab
K = extractMatrix('piezo_amplified_IFF_K.txt');
M = extractMatrix('piezo_amplified_IFF_M.txt');
#+end_src
Then, we extract the coordinates of the interface nodes.
#+begin_src matlab
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('piezo_amplified_IFF.txt');
#+end_src
** IFF Plant
The transfer function from the force actuator to the force sensor is identified and shown in Figure [[fig:piezo_amplified_iff_plant]].
#+begin_src matlab
Kiff = tf(0);
#+end_src
#+begin_src matlab
m = 0;
#+end_src
#+begin_src matlab
%% Name of the Simulink File
mdl = 'piezo_amplified_IFF';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Kiff'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/G'], 1, 'openoutput'); io_i = io_i + 1;
Gf = linearize(mdl, io);
#+end_src
#+begin_src matlab
m = 10;
#+end_src
#+begin_src matlab
Gfm = linearize(mdl, io);
#+end_src
#+begin_src matlab :exports none
freqs = logspace(1, 5, 1000);
figure;
ax1 = subplot(2,1,1);
hold on;
plot(freqs, abs(squeeze(freqresp(Gf, freqs, 'Hz'))), '-');
plot(freqs, abs(squeeze(freqresp(Gfm, 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(Gf, freqs, 'Hz')))), '-', ...
'DisplayName', '$m = 0kg$');
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gfm, freqs, 'Hz')))), '-', ...
'DisplayName', '$m = 10kg$');
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
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/piezo_amplified_iff_plant.pdf', 'width', 'full', 'height', 'full');
#+end_src
#+name: fig:piezo_amplified_iff_plant
#+caption: IFF Plant
#+RESULTS:
[[file:figs/piezo_amplified_iff_plant.png]]
** IFF controller
The controller is defined and the loop gain is shown in Figure [[fig:piezo_amplified_iff_loop_gain]].
#+begin_src matlab
Kiff = -1e12/s;
#+end_src
#+begin_src matlab :exports none
freqs = logspace(1, 5, 1000);
figure;
ax1 = subplot(2,1,1);
hold on;
plot(freqs, abs(squeeze(freqresp(Gf*Kiff, freqs, 'Hz'))), '-');
plot(freqs, abs(squeeze(freqresp(Gfm*Kiff, 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(Gf*Kiff, freqs, 'Hz')))), '-', ...
'DisplayName', '$m = 0kg$');
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gfm*Kiff, freqs, 'Hz')))), '-', ...
'DisplayName', '$m = 10kg$');
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
yticks(-360:90:360);
ylim([-180 180]);
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 :tangle no :exports results :results file replace
exportFig('figs/piezo_amplified_iff_loop_gain.pdf', 'width', 'full', 'height', 'full');
#+end_src
#+name: fig:piezo_amplified_iff_loop_gain
#+caption: IFF Loop Gain
#+RESULTS:
[[file:figs/piezo_amplified_iff_loop_gain.png]]
** Closed Loop System
#+begin_src matlab
m = 10;
#+end_src
#+begin_src matlab
Kiff = -1e12/s;
#+end_src
#+begin_src matlab
%% Name of the Simulink File
mdl = 'piezo_amplified_IFF';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Dw'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/Fd'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/d'], 1, 'openoutput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/G'], 1, 'output'); io_i = io_i + 1;
Giff = linearize(mdl, io);
Giff.InputName = {'w', 'f', 'F'};
Giff.OutputName = {'x1', 'Fs'};
#+end_src
#+begin_src matlab
Kiff = tf(0);
#+end_src
#+begin_src matlab
G = linearize(mdl, io);
G.InputName = {'w', 'f', 'F'};
G.OutputName = {'x1', 'Fs'};
#+end_src
#+begin_src matlab :exports none
freqs = logspace(1, 3, 1000);
figure;
ax1 = subplot(2, 3, 1);
title('$\displaystyle \frac{x_1}{w}$')
hold on;
plot(freqs, abs(squeeze(freqresp(G('x1', 'w'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Giff('x1', 'w'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/m]');xlabel('Frequency [Hz]');
ax2 = subplot(2, 3, 2);
title('$\displaystyle \frac{x_1}{f}$')
hold on;
plot(freqs, abs(squeeze(freqresp(G('x1', 'f'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Giff('x1', 'f'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]');xlabel('Frequency [Hz]');
ax3 = subplot(2, 3, 3);
title('$\displaystyle \frac{x_1}{F}$')
hold on;
plot(freqs, abs(squeeze(freqresp(G('x1', 'F'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Giff('x1', 'F'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]');xlabel('Frequency [Hz]');
ax4 = subplot(2, 3, 4);
title('$\displaystyle \frac{F_s}{w}$')
hold on;
plot(freqs, abs(squeeze(freqresp(G('Fs', 'w'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Giff('Fs', 'w'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/m]');xlabel('Frequency [Hz]');
ax5 = subplot(2, 3, 5);
title('$\displaystyle \frac{F_s}{f}$')
hold on;
plot(freqs, abs(squeeze(freqresp(G('Fs', 'f'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Giff('Fs', 'f'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]');xlabel('Frequency [Hz]');
ax6 = subplot(2, 3, 6);
title('$\displaystyle \frac{F_s}{F}$')
hold on;
plot(freqs, abs(squeeze(freqresp(G('Fs', 'F'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Giff('Fs', 'F'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
linkaxes([ax1,ax2,ax3,ax4,ax5,ax6],'x');
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/piezo_amplified_iff_comp.pdf', 'width', 1500, 'height', 'full');
#+end_src
#+name: fig:piezo_amplified_iff_comp
#+caption: OL and CL transfer functions
#+RESULTS:
[[file:figs/piezo_amplified_iff_comp.png]]
#+name: fig:souleille18_results
#+caption: Results obtained in cite:souleille18_concep_activ_mount_space_applic
[[file:figs/souleille18_results.png]]
| *Caracteristic* | *0.25 mm* | *0.50 mm* |
|-------------------------------+-----------+-----------|
| Axial Stiffness Dz [N/um] | 94.0 | 124.7 |
| Shear Stiffness [N/um] | 12.7 | 25.8 |
| Bending Stiffness Rx [Nm/rad] | 4.8 | 26.0 |
| Bending Stiffness Ry [Nm/rad] | 4.8 | 26.0 |
| Torsion Stiffness Rz [Nm/rad] | 260.2 | 538.0 |
* Complete Strut with Encoder
<<sec:strut_fem>>
** Introduction
Now, the full nano-hexapod strut is modelled using Ansys.
The 3D as well as the interface nodes are shown in Figure [[fig:strut_encoder_points3]].
#+name: fig:strut_encoder_points3
#+caption: Interface points
[[file:data/strut_encoder/points3.jpg]]
[[file:figs/strut_fem_nodes.jpg]]
Flexible joints have 0.25mm width.
The flexible joints used have a 0.25mm width size.
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
matlab/APA300ML.slx
BIN
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