From 433dc17d1c47e44b1c38946c38a14fdb45a61825 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Tue, 8 Jun 2021 22:14:48 +0200 Subject: [PATCH] Analysis of FRF data (DVF + IFF) --- figs/IMG_20210608_152917.jpg | Bin 0 -> 659420 bytes figs/IMG_20210608_154722.jpg | Bin 0 -> 547275 bytes figs/enc_struts_dvf_coh.pdf | Bin 0 -> 803330 bytes figs/enc_struts_dvf_coh.png | Bin 0 -> 128985 bytes figs/enc_struts_dvf_frf.pdf | Bin 0 -> 1017467 bytes figs/enc_struts_dvf_frf.png | Bin 0 -> 238216 bytes figs/enc_struts_iff_coh.pdf | Bin 0 -> 753720 bytes figs/enc_struts_iff_coh.png | Bin 0 -> 80941 bytes figs/enc_struts_iff_frf.pdf | Bin 0 -> 1003508 bytes figs/enc_struts_iff_frf.png | Bin 0 -> 200946 bytes matlab/mat/jacobian.mat | Bin 0 -> 355 bytes ref.bib | 24 ++ test-bench-nano-hexapod.html | 212 +++++++++++++++++- test-bench-nano-hexapod.org | 423 +++++++++++++++++++++++++++++++++++ test-bench-nano-hexapod.pdf | Bin 0 -> 4890499 bytes 15 files changed, 653 insertions(+), 6 deletions(-) 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    +

    IMG_20210608_152917.jpg +

    +

    Figure 1: Nano-Hexapod

    +
    + + +
    +

    IMG_20210608_154722.jpg +

    +

    Figure 2: Nano-Hexapod and the control electronics

    +
    + + + +
    +

    2 Encoders fixed to the Struts

    +
    +
    +
    +

    2.1 Introduction

    +
    + +
    +

    2.2 Load Data

    +
    +
    +
    meas_data_lf = {};
    +
    +for i = 1:6
    +    meas_data_lf(i) = {load(sprintf('mat/frf_data_exc_strut_%i_noise_lf.mat', i), 't', 'Va', 'Vs', 'de')};
    +    meas_data_hf(i) = {load(sprintf('mat/frf_data_exc_strut_%i_noise_hf.mat', i), 't', 'Va', 'Vs', 'de')};
    +end
    +
    +
    +
    +
    + +
    +

    2.3 Spectral Analysis - Setup

    +
    +
    +
    % Sampling Time [s]
    +Ts = (meas_data_lf{1}.t(end) - (meas_data_lf{1}.t(1)))/(length(meas_data_lf{1}.t)-1);
    +
    +% Sampling Frequency [Hz]
    +Fs = 1/Ts;
    +
    +% Hannning Windows
    +win = hanning(ceil(1*Fs));
    +
    +
    + +

    +And we get the frequency vector. +

    +
    +
    [~, f] = tfestimate(meas_data_lf{1}.Va, meas_data_lf{1}.de, win, [], [], 1/Ts);
    +
    +
    + +
    +
    i_lf = f < 250; % Points for low frequency excitation
    +i_hf = f > 250; % Points for high frequency excitation
    +
    +
    +
    +
    + +
    +

    2.4 DVF Plant

    +
    +

    +First, let’s compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure 3). +

    + +
    +
    %% Coherence
    +coh_dvf_lf = zeros(length(f), 6, 6);
    +coh_dvf_hf = zeros(length(f), 6, 6);
    +
    +for i = 1:6
    +    coh_dvf_lf(:, :, i) = mscohere(meas_data_lf{i}.Va, meas_data_lf{i}.de, win, [], [], 1/Ts);
    +    coh_dvf_hf(:, :, i) = mscohere(meas_data_hf{i}.Va, meas_data_hf{i}.de, win, [], [], 1/Ts);
    +end
    +
    +
    +
    + + +
    +

    enc_struts_dvf_coh.png +

    +

    Figure 3: Obtained coherence for the DVF plant

    +
    + +

    +Then the 6x6 transfer function matrix is estimated (Figure 4). +

    +
    +
    %% DVF Plant
    +G_dvf_lf = zeros(length(f), 6, 6);
    +G_dvf_hf = zeros(length(f), 6, 6);
    +
    +for i = 1:6
    +    G_dvf_lf(:, :, i) = tfestimate(meas_data_lf{i}.Va, meas_data_lf{i}.de, win, [], [], 1/Ts);
    +    G_dvf_hf(:, :, i) = tfestimate(meas_data_hf{i}.Va, meas_data_hf{i}.de, win, [], [], 1/Ts);
    +end
    +
    +
    + + +
    +

    enc_struts_dvf_frf.png +

    +

    Figure 4: Measured FRF for the DVF plant

    +
    +
    +
    + + +
    +

    2.5 IFF Plant

    +
    +

    +First, let’s compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure 5). +

    + +
    +
    %% Coherence
    +coh_iff_lf = zeros(length(f), 6, 6);
    +coh_iff_hf = zeros(length(f), 6, 6);
    +
    +for i = 1:6
    +    coh_iff_lf(:, :, i) = mscohere(meas_data_lf{i}.Va, meas_data_lf{i}.Vs, win, [], [], 1/Ts);
    +    coh_iff_hf(:, :, i) = mscohere(meas_data_hf{i}.Va, meas_data_hf{i}.Vs, win, [], [], 1/Ts);
    +end
    +
    +
    +
    + + +
    +

    enc_struts_iff_coh.png +

    +

    Figure 5: Obtained coherence for the IFF plant

    +
    + +

    +Then the 6x6 transfer function matrix is estimated (Figure 6). +

    +
    +
    %% IFF Plant
    +G_iff_lf = zeros(length(f), 6, 6);
    +G_iff_hf = zeros(length(f), 6, 6);
    +
    +for i = 1:6
    +    G_iff_lf(:, :, i) = tfestimate(meas_data_lf{i}.Va, meas_data_lf{i}.Vs, win, [], [], 1/Ts);
    +    G_iff_hf(:, :, i) = tfestimate(meas_data_hf{i}.Va, meas_data_hf{i}.Vs, win, [], [], 1/Ts);
    +end
    +
    +
    + + +
    +

    enc_struts_iff_frf.png +

    +

    Figure 6: Measured FRF for the IFF plant

    +
    +
    +
    + +
    +

    2.6 Jacobian

    +
    +
    +
    load('jacobian.mat', 'J');
    +
    +
    + +
    +
    G_dvf_J_lf = G_dvf_lf(i_lf, i, j)
    +
    +
    + +

    +#+end_src

    +

    Author: Dehaeze Thomas

    -

    Created: 2021-06-07 lun. 19:00

    +

    Created: 2021-06-08 mar. 21:51

    diff --git a/test-bench-nano-hexapod.org b/test-bench-nano-hexapod.org index 6eed63a..79856a6 100644 --- a/test-bench-nano-hexapod.org +++ b/test-bench-nano-hexapod.org @@ -46,6 +46,7 @@
    #+end_export +* Introduction :ignore: * Test-Bench Description #+begin_note @@ -56,3 +57,425 @@ Here are the documentation of the equipment used for this test bench: - Encoder: Renishaw [[file:doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf][Vionic]] and used [[file:doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf][Ruler]] - Interferometers: Attocube #+end_note + +#+name: fig:picture_bench_granite_nano_hexapod +#+caption: Nano-Hexapod +[[file:figs/IMG_20210608_152917.jpg]] + +#+name: fig:picture_bench_granite_overview +#+caption: Nano-Hexapod and the control electronics +[[file:figs/IMG_20210608_154722.jpg]] + +* Encoders fixed to the Struts +** 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) +<> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes +<> +#+end_src + +#+begin_src matlab :tangle no +addpath('./matlab/mat/'); +addpath('./matlab/src/'); +addpath('./matlab/'); +#+end_src + +#+begin_src matlab :eval no +addpath('./mat/'); +addpath('./src/'); +#+end_src + +** Load Data +#+begin_src matlab +meas_data_lf = {}; + +for i = 1:6 + meas_data_lf(i) = {load(sprintf('mat/frf_data_exc_strut_%i_noise_lf.mat', i), 't', 'Va', 'Vs', 'de')}; + meas_data_hf(i) = {load(sprintf('mat/frf_data_exc_strut_%i_noise_hf.mat', i), 't', 'Va', 'Vs', 'de')}; +end +#+end_src + +** Spectral Analysis - Setup +#+begin_src matlab +% Sampling Time [s] +Ts = (meas_data_lf{1}.t(end) - (meas_data_lf{1}.t(1)))/(length(meas_data_lf{1}.t)-1); + +% Sampling Frequency [Hz] +Fs = 1/Ts; + +% Hannning Windows +win = hanning(ceil(1*Fs)); +#+end_src + +And we get the frequency vector. +#+begin_src matlab +[~, f] = tfestimate(meas_data_lf{1}.Va, meas_data_lf{1}.de, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab +i_lf = f < 250; % Points for low frequency excitation +i_hf = f > 250; % Points for high frequency excitation +#+end_src + +** DVF Plant +First, let's compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure [[fig:enc_struts_dvf_coh]]). + +#+begin_src matlab +%% Coherence +coh_dvf_lf = zeros(length(f), 6, 6); +coh_dvf_hf = zeros(length(f), 6, 6); + +for i = 1:6 + coh_dvf_lf(:, :, i) = mscohere(meas_data_lf{i}.Va, meas_data_lf{i}.de, win, [], [], 1/Ts); + coh_dvf_hf(:, :, i) = mscohere(meas_data_hf{i}.Va, meas_data_hf{i}.de, win, [], [], 1/Ts); +end + +#+end_src + +#+begin_src matlab :exports none +figure; +hold on; +for i = 1:5 + for j = i+1:6 + plot(f(i_lf), coh_dvf_lf(i_lf, i, j), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); + plot(f(i_hf), coh_dvf_hf(i_hf, i, j), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); + end +end +for i =1:6 + set(gca,'ColorOrderIndex',i) + plot(f(i_lf), coh_dvf_lf(i_lf,i, i), ... + 'DisplayName', sprintf('$G_{dvf}(%i,%i)$', i, i)); + set(gca,'ColorOrderIndex',i) + plot(f(i_hf), coh_dvf_hf(i_hf,i, i), ... + 'HandleVisibility', 'off'); +end +plot(f(i_lf), coh_dvf_lf(i_lf, 1, 2), 'color', [0, 0, 0, 0.2], ... + 'DisplayName', '$G_{dvf}(i,j)$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Coherence [-]'); +xlim([20, 2e3]); ylim([0, 1]); +legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 3); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/enc_struts_dvf_coh.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:enc_struts_dvf_coh +#+caption: Obtained coherence for the DVF plant +#+RESULTS: +[[file:figs/enc_struts_dvf_coh.png]] + +Then the 6x6 transfer function matrix is estimated (Figure [[fig:enc_struts_dvf_frf]]). +#+begin_src matlab +%% DVF Plant +G_dvf_lf = zeros(length(f), 6, 6); +G_dvf_hf = zeros(length(f), 6, 6); + +for i = 1:6 + G_dvf_lf(:, :, i) = tfestimate(meas_data_lf{i}.Va, meas_data_lf{i}.de, win, [], [], 1/Ts); + G_dvf_hf(:, :, i) = tfestimate(meas_data_hf{i}.Va, meas_data_hf{i}.de, win, [], [], 1/Ts); +end +#+end_src + +#+begin_src matlab :exports none +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:5 + for j = i+1:6 + plot(f(i_lf), abs(G_dvf_lf(i_lf, i, j)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); + plot(f(i_hf), abs(G_dvf_hf(i_hf, i, j)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); + end +end +for i =1:6 + set(gca,'ColorOrderIndex',i) + plot(f(i_lf), abs(G_dvf_lf(i_lf,i, i)), ... + 'DisplayName', sprintf('$G_{dvf}(%i,%i)$', i, i)); + set(gca,'ColorOrderIndex',i) + plot(f(i_hf), abs(G_dvf_hf(i_hf,i, i)), ... + 'HandleVisibility', 'off'); +end +plot(f(i_lf), abs(G_dvf_lf(i_lf, 1, 2)), 'color', [0, 0, 0, 0.2], ... + 'DisplayName', '$G_{dvf}(i,j)$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]); +ylim([1e-9, 1e-3]); +legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 3); + +ax2 = nexttile; +hold on; +for i =1:6 + set(gca,'ColorOrderIndex',i) + plot(f(i_lf), 180/pi*angle(G_dvf_lf(i_lf,i, i))); + set(gca,'ColorOrderIndex',i) + plot(f(i_hf), 180/pi*angle(G_dvf_hf(i_hf,i, i))); +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); + +linkaxes([ax1,ax2],'x'); +xlim([20, 2e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/enc_struts_dvf_frf.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:enc_struts_dvf_frf +#+caption: Measured FRF for the DVF plant +#+RESULTS: +[[file:figs/enc_struts_dvf_frf.png]] + + +** IFF Plant +First, let's compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure [[fig:enc_struts_iff_coh]]). + +#+begin_src matlab +%% Coherence +coh_iff_lf = zeros(length(f), 6, 6); +coh_iff_hf = zeros(length(f), 6, 6); + +for i = 1:6 + coh_iff_lf(:, :, i) = mscohere(meas_data_lf{i}.Va, meas_data_lf{i}.Vs, win, [], [], 1/Ts); + coh_iff_hf(:, :, i) = mscohere(meas_data_hf{i}.Va, meas_data_hf{i}.Vs, win, [], [], 1/Ts); +end + +#+end_src + +#+begin_src matlab :exports none +figure; +hold on; +for i = 1:5 + for j = i+1:6 + plot(f(i_lf), coh_iff_lf(i_lf, i, j), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); + plot(f(i_hf), coh_iff_hf(i_hf, i, j), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); + end +end +for i =1:6 + set(gca,'ColorOrderIndex',i) + plot(f(i_lf), coh_iff_lf(i_lf,i, i), ... + 'DisplayName', sprintf('$G_{iff}(%i,%i)$', i, i)); + set(gca,'ColorOrderIndex',i) + plot(f(i_hf), coh_iff_hf(i_hf,i, i), ... + 'HandleVisibility', 'off'); +end +plot(f(i_lf), coh_iff_lf(i_lf, 1, 2), 'color', [0, 0, 0, 0.2], ... + 'DisplayName', '$G_{iff}(i,j)$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Coherence [-]'); +xlim([20, 2e3]); ylim([0, 1]); +legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 3); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/enc_struts_iff_coh.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:enc_struts_iff_coh +#+caption: Obtained coherence for the IFF plant +#+RESULTS: +[[file:figs/enc_struts_iff_coh.png]] + +Then the 6x6 transfer function matrix is estimated (Figure [[fig:enc_struts_iff_frf]]). +#+begin_src matlab +%% IFF Plant +G_iff_lf = zeros(length(f), 6, 6); +G_iff_hf = zeros(length(f), 6, 6); + +for i = 1:6 + G_iff_lf(:, :, i) = tfestimate(meas_data_lf{i}.Va, meas_data_lf{i}.Vs, win, [], [], 1/Ts); + G_iff_hf(:, :, i) = tfestimate(meas_data_hf{i}.Va, meas_data_hf{i}.Vs, win, [], [], 1/Ts); +end +#+end_src + +#+begin_src matlab :exports none +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:5 + for j = i+1:6 + plot(f(i_lf), abs(G_iff_lf(i_lf, i, j)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); + plot(f(i_hf), abs(G_iff_hf(i_hf, i, j)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); + end +end +for i =1:6 + set(gca,'ColorOrderIndex',i) + plot(f(i_lf), abs(G_iff_lf(i_lf,i, i)), ... + 'DisplayName', sprintf('$G_{iff}(%i,%i)$', i, i)); + set(gca,'ColorOrderIndex',i) + plot(f(i_hf), abs(G_iff_hf(i_hf,i, i)), ... + 'HandleVisibility', 'off'); +end +plot(f(i_lf), abs(G_iff_lf(i_lf, 1, 2)), 'color', [0, 0, 0, 0.2], ... + 'DisplayName', '$G_{iff}(i,j)$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]); +legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 3); +ylim([1e-3, 1e2]); + +ax2 = nexttile; +hold on; +for i =1:6 + set(gca,'ColorOrderIndex',i) + plot(f(i_lf), 180/pi*angle(G_iff_lf(i_lf,i, i))); + set(gca,'ColorOrderIndex',i) + plot(f(i_hf), 180/pi*angle(G_iff_hf(i_hf,i, i))); +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); + +linkaxes([ax1,ax2],'x'); +xlim([20, 2e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/enc_struts_iff_frf.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:enc_struts_iff_frf +#+caption: Measured FRF for the IFF plant +#+RESULTS: +[[file:figs/enc_struts_iff_frf.png]] + +** Jacobian +#+begin_src matlab +load('jacobian.mat', 'J'); +#+end_src +*** DVF Plant +#+begin_src matlab +G_dvf_J_lf = permute(pagemtimes(inv(J), pagemtimes(permute(G_dvf_lf, [2 3 1]), inv(J'))), [3 1 2]); +G_dvf_J_hf = permute(pagemtimes(inv(J), pagemtimes(permute(G_dvf_hf, [2 3 1]), inv(J'))), [3 1 2]); +#+end_src + +#+begin_src matlab :exports none +labels = {'$D_x/F_{x}$', '$D_y/F_{y}$', '$D_z/F_{z}$', '$R_{x}/M_{x}$', '$R_{y}/M_{y}$', '$R_{R}/M_{z}$'}; + +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:5 + for j = i+1:6 + plot(f(i_lf), abs(G_dvf_J_lf(i_lf, i, j)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); + plot(f(i_hf), abs(G_dvf_J_hf(i_hf, i, j)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); + end +end +for i =1:6 + set(gca,'ColorOrderIndex',i) + plot(f(i_lf), abs(G_dvf_J_lf(i_lf,i, i)), ... + 'DisplayName', labels{i}); + set(gca,'ColorOrderIndex',i) + plot(f(i_hf), abs(G_dvf_J_hf(i_hf,i, i)), ... + 'HandleVisibility', 'off'); +end +plot(f(i_lf), abs(G_dvf_J_lf(i_lf, 1, 2)), 'color', [0, 0, 0, 0.2], ... + 'DisplayName', '$D_i/F_j$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]); +ylim([1e-7, 1e-1]); +legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 3); + +ax2 = nexttile; +hold on; +for i =1:6 + set(gca,'ColorOrderIndex',i) + plot(f(i_lf), 180/pi*angle(G_dvf_J_lf(i_lf,i, i))); + set(gca,'ColorOrderIndex',i) + plot(f(i_hf), 180/pi*angle(G_dvf_J_hf(i_hf,i, i))); +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); + +linkaxes([ax1,ax2],'x'); +xlim([20, 2e3]); +#+end_src + +*** IFF Plant +#+begin_src matlab +G_iff_J_lf = permute(pagemtimes(inv(J), pagemtimes(permute(G_iff_lf, [2 3 1]), inv(J'))), [3 1 2]); +G_iff_J_hf = permute(pagemtimes(inv(J), pagemtimes(permute(G_iff_hf, [2 3 1]), inv(J'))), [3 1 2]); +#+end_src + +#+begin_src matlab :exports none +labels = {'$F_{m,x}/F_{x}$', '$F_{m,y}/F_{y}$', '$F_{m,z}/F_{z}$', '$M_{m,x}/M_{x}$', '$M_{m,y}/M_{y}$', '$M_{m,z}/M_{z}$'}; + +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:5 + for j = i+1:6 + plot(f(i_lf), abs(G_iff_J_lf(i_lf, i, j)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); + plot(f(i_hf), abs(G_iff_J_hf(i_hf, i, j)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); + end +end +for i =1:6 + set(gca,'ColorOrderIndex',i) + plot(f(i_lf), abs(G_iff_J_lf(i_lf,i, i)), ... + 'DisplayName', labels{i}); + set(gca,'ColorOrderIndex',i) + plot(f(i_hf), abs(G_iff_J_hf(i_hf,i, i)), ... + 'HandleVisibility', 'off'); +end +plot(f(i_lf), abs(G_iff_J_lf(i_lf, 1, 2)), 'color', [0, 0, 0, 0.2], ... + 'DisplayName', '$D_i/F_j$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]); +ylim([1e-7, 1e-1]); +legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 3); + +ax2 = nexttile; +hold on; +for i =1:6 + set(gca,'ColorOrderIndex',i) + plot(f(i_lf), 180/pi*angle(G_iff_J_lf(i_lf,i, i))); + set(gca,'ColorOrderIndex',i) + plot(f(i_hf), 180/pi*angle(G_iff_J_hf(i_hf,i, i))); +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); 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