Analysis of the resonance frequencies of the APA
BIN
figs/apa300ml_meas_freq_bending_x.pdf
Normal file
BIN
figs/apa300ml_meas_freq_bending_x.png
Normal file
After Width: | Height: | Size: 69 KiB |
BIN
figs/apa300ml_meas_freq_bending_y.pdf
Normal file
BIN
figs/apa300ml_meas_freq_bending_y.png
Normal file
After Width: | Height: | Size: 70 KiB |
BIN
figs/apa300ml_meas_freq_compare.pdf
Normal file
BIN
figs/apa300ml_meas_freq_compare.png
Normal file
After Width: | Height: | Size: 151 KiB |
BIN
figs/apa300ml_meas_freq_torsion_z.pdf
Normal file
BIN
figs/apa300ml_meas_freq_torsion_z.png
Normal file
After Width: | Height: | Size: 61 KiB |
BIN
figs/measurement_setup_X_bending.png
Normal file
After Width: | Height: | Size: 714 KiB |
BIN
figs/measurement_setup_Y_bending.png
Normal file
After Width: | Height: | Size: 753 KiB |
BIN
figs/measurement_setup_torsion.png
Normal file
After Width: | Height: | Size: 885 KiB |
BIN
figs/measurement_setup_torsion_bis.png
Normal file
After Width: | Height: | Size: 754 KiB |
BIN
figs/mode_bending_x.gif
Normal file
After Width: | Height: | Size: 722 KiB |
BIN
figs/mode_bending_x.png
Normal file
After Width: | Height: | Size: 21 KiB |
BIN
figs/mode_bending_y.gif
Normal file
After Width: | Height: | Size: 750 KiB |
BIN
figs/mode_bending_y.png
Normal file
After Width: | Height: | Size: 24 KiB |
BIN
figs/mode_torsion_z.gif
Normal file
After Width: | Height: | Size: 636 KiB |
BIN
figs/mode_torsion_z.png
Normal file
After Width: | Height: | Size: 24 KiB |
BIN
matlab/mat/apa300ml_bending_X_top.mat
Normal file
BIN
matlab/mat/apa300ml_bending_Y_top.mat
Normal file
BIN
matlab/mat/apa300ml_torsion_left.mat
Normal file
BIN
matlab/mat/apa300ml_torsion_right.mat
Normal file
BIN
matlab/mat/apa300ml_torsion_top.mat
Normal file
@ -1612,5 +1612,872 @@ It is the expected behavior as shown in the Figure [[fig:souleille18_results]] (
|
||||
#+caption: Results obtained in cite:souleille18_concep_activ_mount_space_applic
|
||||
[[file:figs/souleille18_results.png]]
|
||||
|
||||
* Bibliography :ignore:
|
||||
* Test Bench APA300ML - Simscape Model
|
||||
** Introduction
|
||||
** 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
|
||||
|
||||
#+begin_src matlab :tangle no
|
||||
addpath('matlab/test_bench_apa300ml/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :eval no
|
||||
addpath('test_bench_apa300ml/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
open('test_bench_apa300ml.slx')
|
||||
#+end_src
|
||||
|
||||
** Nano Hexapod object
|
||||
#+begin_src matlab
|
||||
n_hexapod = struct();
|
||||
#+end_src
|
||||
|
||||
*** APA - 2 DoF
|
||||
#+begin_src matlab
|
||||
n_hexapod.actuator = struct();
|
||||
|
||||
n_hexapod.actuator.type = 1;
|
||||
|
||||
n_hexapod.actuator.k = ones(6,1)*0.35e6; % [N/m]
|
||||
n_hexapod.actuator.ke = ones(6,1)*1.5e6; % [N/m]
|
||||
n_hexapod.actuator.ka = ones(6,1)*43e6; % [N/m]
|
||||
|
||||
n_hexapod.actuator.c = ones(6,1)*3e1; % [N/(m/s)]
|
||||
n_hexapod.actuator.ce = ones(6,1)*1e1; % [N/(m/s)]
|
||||
n_hexapod.actuator.ca = ones(6,1)*1e1; % [N/(m/s)]
|
||||
|
||||
n_hexapod.actuator.Leq = ones(6,1)*0.056; % [m]
|
||||
|
||||
n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
|
||||
n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
|
||||
#+end_src
|
||||
|
||||
*** APA - Flexible Frame
|
||||
#+begin_src matlab
|
||||
n_hexapod.actuator.type = 2;
|
||||
|
||||
n_hexapod.actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix
|
||||
n_hexapod.actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix
|
||||
n_hexapod.actuator.xi = 0.01; % Damping ratio
|
||||
n_hexapod.actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m]
|
||||
|
||||
n_hexapod.actuator.ks = 235e6; % Stiffness of one stack [N/m]
|
||||
n_hexapod.actuator.cs = 1e1; % Stiffness of one stack [N/m]
|
||||
|
||||
n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
|
||||
n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
|
||||
#+end_src
|
||||
|
||||
*** APA - Fully Flexible
|
||||
#+begin_src matlab
|
||||
n_hexapod.actuator.type = 3;
|
||||
|
||||
n_hexapod.actuator.K = readmatrix('APA300ML_full_mat_K.CSV'); % Stiffness Matrix
|
||||
n_hexapod.actuator.M = readmatrix('APA300ML_full_mat_M.CSV'); % Mass Matrix
|
||||
n_hexapod.actuator.xi = 0.01; % Damping ratio
|
||||
n_hexapod.actuator.P = extractNodes('APA300ML_full_out_nodes_3D.txt'); % Node coordiantes [m]
|
||||
|
||||
n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
|
||||
n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
|
||||
#+end_src
|
||||
|
||||
** Identification
|
||||
#+begin_src matlab
|
||||
%% Options for Linearized
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'test_bench_apa300ml';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Va'], 1, 'openinput'); io_i = io_i + 1; % Actuator Voltage
|
||||
io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage
|
||||
io(io_i) = linio([mdl, '/dL'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Outputs
|
||||
io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1; % Vertical Motion
|
||||
|
||||
%% Run the linearization
|
||||
Ga = linearize(mdl, io, 0.0, options);
|
||||
Ga.InputName = {'Va'};
|
||||
Ga.OutputName = {'Vs', 'dL', 'z'};
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 3, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(Ga('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', '')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Ga('Vs', 'Va'), freqs, 'Hz'))))
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-180, 180])
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 3, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(Ga('dL', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Encoder')
|
||||
plot(freqs, abs(squeeze(freqresp(Ga('z', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Interferometer')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Ga('dL', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Ga('z', 'Va'), freqs, 'Hz'))))
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-180, 180])
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
** Compare 2-DoF with flexible
|
||||
*** APA - 2 DoF
|
||||
#+begin_src matlab
|
||||
n_hexapod = struct();
|
||||
|
||||
n_hexapod.actuator = struct();
|
||||
|
||||
n_hexapod.actuator.type = 1;
|
||||
|
||||
n_hexapod.actuator.k = ones(6,1)*0.35e6; % [N/m]
|
||||
n_hexapod.actuator.ke = ones(6,1)*1.5e6; % [N/m]
|
||||
n_hexapod.actuator.ka = ones(6,1)*43e6; % [N/m]
|
||||
|
||||
n_hexapod.actuator.c = ones(6,1)*3e1; % [N/(m/s)]
|
||||
n_hexapod.actuator.ce = ones(6,1)*1e1; % [N/(m/s)]
|
||||
n_hexapod.actuator.ca = ones(6,1)*1e1; % [N/(m/s)]
|
||||
|
||||
n_hexapod.actuator.Leq = ones(6,1)*0.056; % [m]
|
||||
|
||||
n_hexapod.actuator.Ga = ones(6,1)*-2.15; % Actuator gain [N/V]
|
||||
n_hexapod.actuator.Gs = ones(6,1)*2.305e-08; % Sensor gain [V/m]
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
G_2dof = linearize(mdl, io, 0.0, options);
|
||||
G_2dof.InputName = {'Va'};
|
||||
G_2dof.OutputName = {'Vs', 'dL', 'z'};
|
||||
#+end_src
|
||||
|
||||
*** APA - Fully Flexible
|
||||
#+begin_src matlab
|
||||
n_hexapod = struct();
|
||||
|
||||
n_hexapod.actuator.type = 3;
|
||||
|
||||
n_hexapod.actuator.K = readmatrix('APA300ML_full_mat_K.CSV'); % Stiffness Matrix
|
||||
n_hexapod.actuator.M = readmatrix('APA300ML_full_mat_M.CSV'); % Mass Matrix
|
||||
n_hexapod.actuator.xi = 0.01; % Damping ratio
|
||||
n_hexapod.actuator.P = extractNodes('APA300ML_full_out_nodes_3D.txt'); % Node coordiantes [m]
|
||||
|
||||
n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
|
||||
n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
G_flex = linearize(mdl, io, 0.0, options);
|
||||
G_flex.InputName = {'Va'};
|
||||
G_flex.OutputName = {'Vs', 'dL', 'z'};
|
||||
#+end_src
|
||||
|
||||
*** Comparison
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 4, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_2dof('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', '$G_a$')
|
||||
plot(freqs, abs(squeeze(freqresp(G_flex('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', '$G_s$')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_2dof('Vs', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_flex('Vs', 'Va'), freqs, 'Hz'))))
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-180, 180])
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 4, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_2dof('dL', 'Va'), freqs, 'Hz'))), 'DisplayName', '$G_a$')
|
||||
plot(freqs, abs(squeeze(freqresp(G_flex('dL', 'Va'), freqs, 'Hz'))), 'DisplayName', '$G_s$')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $d_L/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_2dof('dL', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_flex('dL', 'Va'), freqs, 'Hz'))))
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-180, 180])
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 4, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_2dof('z', 'Va'), freqs, 'Hz'))), 'DisplayName', '$G_a$')
|
||||
plot(freqs, abs(squeeze(freqresp(G_flex('z', 'Va'), freqs, 'Hz'))), 'DisplayName', '$G_s$')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $z/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_2dof('z', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_flex('z', 'Va'), freqs, 'Hz'))))
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-180, 180])
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
* Test Bench Struts - Simscape Model
|
||||
** Introduction
|
||||
** 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
|
||||
|
||||
#+begin_src matlab :tangle no
|
||||
addpath('matlab/');
|
||||
addpath('matlab/test_bench_struts/');
|
||||
addpath('matlab/png/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :eval no
|
||||
addpath('test_bench_struts/');
|
||||
addpath('png/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
open('test_bench_struts.slx')
|
||||
#+end_src
|
||||
|
||||
** Nano Hexapod object
|
||||
#+begin_src matlab
|
||||
n_hexapod = struct();
|
||||
#+end_src
|
||||
|
||||
*** Flexible Joint - Bot
|
||||
#+begin_src matlab
|
||||
n_hexapod.flex_bot = struct();
|
||||
|
||||
n_hexapod.flex_bot.type = 1; % 1: 2dof / 2: 3dof / 3: 4dof
|
||||
|
||||
n_hexapod.flex_bot.kRx = ones(6,1)*5; % X bending stiffness [Nm/rad]
|
||||
n_hexapod.flex_bot.kRy = ones(6,1)*5; % Y bending stiffness [Nm/rad]
|
||||
n_hexapod.flex_bot.kRz = ones(6,1)*260; % Torsionnal stiffness [Nm/rad]
|
||||
n_hexapod.flex_bot.kz = ones(6,1)*1e8; % Axial stiffness [N/m]
|
||||
|
||||
n_hexapod.flex_bot.cRx = ones(6,1)*0.1; % [Nm/(rad/s)]
|
||||
n_hexapod.flex_bot.cRy = ones(6,1)*0.1; % [Nm/(rad/s)]
|
||||
n_hexapod.flex_bot.cRz = ones(6,1)*0.1; % [Nm/(rad/s)]
|
||||
n_hexapod.flex_bot.cz = ones(6,1)*1e2; %[N/(m/s)]
|
||||
#+end_src
|
||||
|
||||
*** Flexible Joint - Top
|
||||
#+begin_src matlab
|
||||
n_hexapod.flex_top = struct();
|
||||
|
||||
n_hexapod.flex_top.type = 2; % 1: 2dof / 2: 3dof / 3: 4dof
|
||||
|
||||
n_hexapod.flex_top.kRx = ones(6,1)*5; % X bending stiffness [Nm/rad]
|
||||
n_hexapod.flex_top.kRy = ones(6,1)*5; % Y bending stiffness [Nm/rad]
|
||||
n_hexapod.flex_top.kRz = ones(6,1)*260; % Torsionnal stiffness [Nm/rad]
|
||||
n_hexapod.flex_top.kz = ones(6,1)*1e8; % Axial stiffness [N/m]
|
||||
|
||||
n_hexapod.flex_top.cRx = ones(6,1)*0.1; % [Nm/(rad/s)]
|
||||
n_hexapod.flex_top.cRy = ones(6,1)*0.1; % [Nm/(rad/s)]
|
||||
n_hexapod.flex_top.cRz = ones(6,1)*0.1; % [Nm/(rad/s)]
|
||||
n_hexapod.flex_top.cz = ones(6,1)*1e2; %[N/(m/s)]
|
||||
#+end_src
|
||||
|
||||
*** APA - 2 DoF
|
||||
#+begin_src matlab
|
||||
n_hexapod.actuator = struct();
|
||||
|
||||
n_hexapod.actuator.type = 1;
|
||||
|
||||
n_hexapod.actuator.k = ones(6,1)*0.35e6; % [N/m]
|
||||
n_hexapod.actuator.ke = ones(6,1)*1.5e6; % [N/m]
|
||||
n_hexapod.actuator.ka = ones(6,1)*43e6; % [N/m]
|
||||
|
||||
n_hexapod.actuator.c = ones(6,1)*3e1; % [N/(m/s)]
|
||||
n_hexapod.actuator.ce = ones(6,1)*1e1; % [N/(m/s)]
|
||||
n_hexapod.actuator.ca = ones(6,1)*1e1; % [N/(m/s)]
|
||||
|
||||
n_hexapod.actuator.Leq = ones(6,1)*0.056; % [m]
|
||||
|
||||
n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
|
||||
n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
|
||||
#+end_src
|
||||
|
||||
*** APA - Flexible Frame
|
||||
#+begin_src matlab
|
||||
n_hexapod.actuator.type = 2;
|
||||
|
||||
n_hexapod.actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix
|
||||
n_hexapod.actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix
|
||||
n_hexapod.actuator.xi = 0.01; % Damping ratio
|
||||
n_hexapod.actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m]
|
||||
|
||||
n_hexapod.actuator.ks = 235e6; % Stiffness of one stack [N/m]
|
||||
n_hexapod.actuator.cs = 1e1; % Stiffness of one stack [N/m]
|
||||
|
||||
n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
|
||||
n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
|
||||
#+end_src
|
||||
|
||||
*** APA - Fully Flexible
|
||||
#+begin_src matlab
|
||||
n_hexapod.actuator.type = 3;
|
||||
|
||||
n_hexapod.actuator.K = readmatrix('APA300ML_full_mat_K.CSV'); % Stiffness Matrix
|
||||
n_hexapod.actuator.M = readmatrix('APA300ML_full_mat_M.CSV'); % Mass Matrix
|
||||
n_hexapod.actuator.xi = 0.01; % Damping ratio
|
||||
n_hexapod.actuator.P = extractNodes('APA300ML_full_out_nodes_3D.txt'); % Node coordiantes [m]
|
||||
|
||||
n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
|
||||
n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
|
||||
#+end_src
|
||||
|
||||
|
||||
** Identification
|
||||
#+begin_src matlab
|
||||
%% Options for Linearized
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'test_bench_struts';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Va'], 1, 'openinput'); io_i = io_i + 1; % Actuator Voltage
|
||||
io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage
|
||||
io(io_i) = linio([mdl, '/dL'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Outputs
|
||||
io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1; % Vertical Motion
|
||||
|
||||
%% Run the linearization
|
||||
Gs = linearize(mdl, io, 0.0, options);
|
||||
Gs.InputName = {'Va'};
|
||||
Gs.OutputName = {'Vs', 'dL', 'z'};
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 3, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', '')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))))
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-180, 180])
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 4, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(Gs('dL', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Encoder')
|
||||
plot(freqs, abs(squeeze(freqresp(Gs('z', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Interferometer')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('dL', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('z', 'Va'), freqs, 'Hz'))))
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-180, 180])
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
** Compare flexible joints
|
||||
*** Perfect
|
||||
#+begin_src matlab
|
||||
n_hexapod.flex_bot.type = 1; % 1: 2dof / 2: 3dof / 3: 4dof
|
||||
n_hexapod.flex_top.type = 2; % 1: 2dof / 2: 3dof / 3: 4dof
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Gp = linearize(mdl, io, 0.0, options);
|
||||
Gp.InputName = {'Va'};
|
||||
Gp.OutputName = {'Vs', 'dL', 'z'};
|
||||
#+end_src
|
||||
|
||||
*** Top Flexible
|
||||
#+begin_src matlab
|
||||
n_hexapod.flex_bot.type = 1; % 1: 2dof / 2: 3dof / 3: 4dof
|
||||
n_hexapod.flex_top.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Gt = linearize(mdl, io, 0.0, options);
|
||||
Gt.InputName = {'Va'};
|
||||
Gt.OutputName = {'Vs', 'dL', 'z'};
|
||||
#+end_src
|
||||
|
||||
*** Bottom Flexible
|
||||
#+begin_src matlab
|
||||
n_hexapod.flex_bot.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof
|
||||
n_hexapod.flex_top.type = 2; % 1: 2dof / 2: 3dof / 3: 4dof
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Gb = linearize(mdl, io, 0.0, options);
|
||||
Gb.InputName = {'Va'};
|
||||
Gb.OutputName = {'Vs', 'dL', 'z'};
|
||||
#+end_src
|
||||
|
||||
*** Both Flexible
|
||||
#+begin_src matlab
|
||||
n_hexapod.flex_bot.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof
|
||||
n_hexapod.flex_top.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Gf = linearize(mdl, io, 0.0, options);
|
||||
Gf.InputName = {'Va'};
|
||||
Gf.OutputName = {'Vs', 'dL', 'z'};
|
||||
#+end_src
|
||||
|
||||
*** Comparison
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 4, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(Gp('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Perfect')
|
||||
plot(freqs, abs(squeeze(freqresp(Gt('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Top')
|
||||
plot(freqs, abs(squeeze(freqresp(Gb('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Bot')
|
||||
plot(freqs, abs(squeeze(freqresp(Gf('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Flex')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gp('Vs', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gt('Vs', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gb('Vs', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf('Vs', 'Va'), freqs, 'Hz'))))
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-180, 180])
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 4, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(Gp('dL', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Perfect')
|
||||
plot(freqs, abs(squeeze(freqresp(Gt('dL', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Top')
|
||||
plot(freqs, abs(squeeze(freqresp(Gb('dL', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Bot')
|
||||
plot(freqs, abs(squeeze(freqresp(Gf('dL', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Flex')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $d_L/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gp('dL', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gt('dL', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gb('dL', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf('dL', 'Va'), freqs, 'Hz'))))
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-180, 180])
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 4, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(Gp('z', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Perfect')
|
||||
plot(freqs, abs(squeeze(freqresp(Gt('z', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Top')
|
||||
plot(freqs, abs(squeeze(freqresp(Gb('z', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Bot')
|
||||
plot(freqs, abs(squeeze(freqresp(Gf('z', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Flex')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $z/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gp('z', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gt('z', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gb('z', 'Va'), freqs, 'Hz'))))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf('z', 'Va'), freqs, 'Hz'))))
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-180, 180])
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
* Resonance frequencies - APA300ML
|
||||
** Introduction
|
||||
|
||||
Three main resonances are foreseen to be problematic for the control of the APA300ML:
|
||||
- Mode in X-bending at 189Hz (Figure [[fig:mode_bending_x]])
|
||||
- Mode in Y-bending at 285Hz (Figure [[fig:mode_bending_y]])
|
||||
- Mode in Z-torsion at 400Hz (Figure [[fig:mode_torsion_z]])
|
||||
|
||||
#+name: fig:mode_bending_x
|
||||
#+caption: X-bending mode (189Hz)
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
[[file:figs/mode_bending_x.gif]]
|
||||
|
||||
#+name: fig:mode_bending_y
|
||||
#+caption: Y-bending mode (285Hz)
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
[[file:figs/mode_bending_y.gif]]
|
||||
|
||||
#+name: fig:mode_torsion_z
|
||||
#+caption: Z-torsion mode (400Hz)
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
[[file:figs/mode_torsion_z.gif]]
|
||||
|
||||
These modes are present when flexible joints are fixed to the ends of the APA300ML.
|
||||
|
||||
In this section, we try to find the resonance frequency of these modes when one end of the APA is fixed and the other is free.
|
||||
|
||||
** 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
|
||||
|
||||
#+begin_src matlab :tangle no
|
||||
addpath('matlab/');
|
||||
addpath('matlab/mat/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :eval no
|
||||
addpath('mat/');
|
||||
#+end_src
|
||||
|
||||
** Setup
|
||||
|
||||
The measurement setup is shown in Figure [[fig:measurement_setup_torsion]].
|
||||
A Laser vibrometer is measuring the difference of motion of two points.
|
||||
The APA is excited with an instrumented hammer and the transfer function from the hammer to the measured rotation is computed.
|
||||
|
||||
#+begin_note
|
||||
- Laser Doppler Vibrometer Polytec OFV512
|
||||
- Instrumented hammer
|
||||
#+end_note
|
||||
|
||||
#+name: fig:measurement_setup_torsion
|
||||
#+caption: Measurement setup with a Laser Doppler Vibrometer and one instrumental hammer
|
||||
#+attr_latex: :width 0.7\linewidth
|
||||
[[file:figs/measurement_setup_torsion.png]]
|
||||
|
||||
** Bending - X
|
||||
|
||||
The setup to measure the X-bending motion is shown in Figure [[fig:measurement_setup_X_bending]].
|
||||
The APA is excited with an instrumented hammer having a solid metallic tip.
|
||||
The impact point is on the back-side of the APA aligned with the top measurement point.
|
||||
|
||||
#+name: fig:measurement_setup_X_bending
|
||||
#+caption: X-Bending measurement setup
|
||||
#+attr_latex: :width 0.7\linewidth
|
||||
[[file:figs/measurement_setup_X_bending.png]]
|
||||
|
||||
The data is loaded.
|
||||
#+begin_src matlab
|
||||
bending_X = load('apa300ml_bending_X_top.mat')
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Ts = bending_X.Track1_X_Resolution; % Sampling frequency [Hz]
|
||||
#+end_src
|
||||
|
||||
The transfer function from the input force to the output "rotation" (difference between the two measured distances).
|
||||
#+begin_src matlab
|
||||
win = hann(ceil(1/Ts));
|
||||
[G_bending_X, f] = tfestimate(bending_X.Track1, bending_X.Track2, win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
|
||||
The result is shown in Figure [[fig:apa300ml_meas_freq_bending_x]].
|
||||
|
||||
The can clearly observe a nice peak at 280Hz, and then peaks at the odd "harmonics" (third "harmonic" at 840Hz, and fifth "harmonic" at 1400Hz).
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, abs(G_bending_X), 'k-');
|
||||
hold off;
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude');
|
||||
xlim([50, 2e3]); ylim([1e-5, 2e-1]);
|
||||
text(280, 5.5e-2,{'280Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(840, 2.0e-3,{'840Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(1400, 7.0e-3,{'1400Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/apa300ml_meas_freq_bending_x.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:apa300ml_meas_freq_bending_x
|
||||
#+caption: Obtained FRF for the X-bending
|
||||
#+RESULTS:
|
||||
[[file:figs/apa300ml_meas_freq_bending_x.png]]
|
||||
|
||||
** Bending - Y
|
||||
|
||||
The setup to measure the Y-bending is shown in Figure [[fig:measurement_setup_Y_bending]].
|
||||
|
||||
The impact point of the instrumented hammer is located on the back surface of the top interface (on the back of the 2 measurements points).
|
||||
|
||||
#+name: fig:measurement_setup_Y_bending
|
||||
#+caption: Y-Bending measurement setup
|
||||
#+attr_latex: :width 0.7\linewidth
|
||||
[[file:figs/measurement_setup_Y_bending.png]]
|
||||
|
||||
The data is loaded, and the transfer function from the force to the measured rotation is computed.
|
||||
#+begin_src matlab
|
||||
bending_Y = load('apa300ml_bending_Y_top.mat')
|
||||
[G_bending_Y, ~] = tfestimate(bending_Y.Track1, bending_Y.Track2, win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
|
||||
The results are shown in Figure [[fig:apa300ml_meas_freq_bending_y]].
|
||||
The main resonance is at 412Hz, and we also see the third "harmonic" at 1220Hz.
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, abs(G_bending_Y), 'k-');
|
||||
hold off;
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude');
|
||||
xlim([50, 2e3]); ylim([1e-5, 3e-2])
|
||||
text(412, 1.5e-2,{'412Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(1218, 1.5e-2,{'1220Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/apa300ml_meas_freq_bending_y.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:apa300ml_meas_freq_bending_y
|
||||
#+caption: Obtained FRF for the Y-bending
|
||||
#+RESULTS:
|
||||
[[file:figs/apa300ml_meas_freq_bending_y.png]]
|
||||
|
||||
** Torsion - Z
|
||||
|
||||
Finally, we measure the Z-torsion resonance as shown in Figure [[fig:measurement_setup_torsion_bis]].
|
||||
|
||||
The excitation is shown on the other side of the APA, on the side to excite the torsion motion.
|
||||
|
||||
#+name: fig:measurement_setup_torsion_bis
|
||||
#+caption: Z-Torsion measurement setup
|
||||
#+attr_latex: :width 0.7\linewidth
|
||||
[[file:figs/measurement_setup_torsion_bis.png]]
|
||||
|
||||
The data is loaded, and the transfer function computed.
|
||||
#+begin_src matlab
|
||||
torsion = load('apa300ml_torsion_left.mat')
|
||||
[G_torsion, ~] = tfestimate(torsion_left.Track1, torsion_left.Track2, win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
|
||||
The results are shown in Figure [[fig:apa300ml_meas_freq_torsion_z]].
|
||||
We observe a first peak at 267Hz, which corresponds to the X-bending mode that was measured at 280Hz.
|
||||
And then a second peak at 415Hz, which corresponds to the X-bending mode that was measured at 412Hz.
|
||||
The mode in pure torsion is probably at higher frequency (peak around 1kHz?).
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, abs(G_torsion), 'k-');
|
||||
hold off;
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude');
|
||||
xlim([50, 2e3]); ylim([1e-5, 2e-2])
|
||||
text(415, 4.3e-3,{'415Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(267, 8e-4,{'267Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/apa300ml_meas_freq_torsion_z.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:apa300ml_meas_freq_torsion_z
|
||||
#+caption: Obtained FRF for the Z-torsion
|
||||
#+RESULTS:
|
||||
[[file:figs/apa300ml_meas_freq_torsion_z.png]]
|
||||
|
||||
** Compare
|
||||
The three measurements are shown in Figure [[fig:apa300ml_meas_freq_compare]].
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, abs(G_torsion), 'DisplayName', 'Torsion');
|
||||
plot(f, abs(G_bending_X), 'DisplayName', 'Bending - X');
|
||||
plot(f, abs(G_bending_Y), 'DisplayName', 'Bending - Y');
|
||||
hold off;
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude');
|
||||
xlim([50, 2e3]); ylim([1e-5, 1e-1]);
|
||||
legend('location', 'southeast');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/apa300ml_meas_freq_compare.pdf', 'width', 'full', 'height', 'tall');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:apa300ml_meas_freq_compare
|
||||
#+caption: Obtained FRF - Comparison
|
||||
#+RESULTS:
|
||||
[[file:figs/apa300ml_meas_freq_compare.png]]
|
||||
|
||||
** Conclusion
|
||||
|
||||
#+name: tab:apa300ml_measured_modes_freq
|
||||
#+caption: Measured frequency of the modes
|
||||
#+attr_latex: :environment tabularx :width 0.3\linewidth :align lX
|
||||
#+attr_latex: :center t :booktabs t :float t
|
||||
| Mode | Measured Frequency |
|
||||
|-----------+--------------------|
|
||||
| X-Bending | 280Hz |
|
||||
| Y-Bending | 410Hz |
|
||||
| Z-Torsion | ? |
|
||||
|
||||
* Bibliography :ignore:
|
||||
#+latex: \printbibliography
|
||||
|