1 Test-Bench Description
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+
1 Test-Bench Description
-
+
+
+
+
+
+
+Here are the documentation of the equipment used for this test bench:
@@ -46,12 +56,202 @@ Here are the documentation of the equipment used for this test bench:
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+
+
+
Figure 1: Nano-Hexapod
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+
+
+
Figure 2: Nano-Hexapod and the control electronics
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+
2 Encoders fixed to the Struts
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+
+
+
+
+2.1 Introduction
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+
+
+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 + ++
+
+
+
+
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 ++
+
+
+
Figure 4: Measured FRF for the DVF plant
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+
+
+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 + ++
+
+
+
+
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 ++
+
+
+
Figure 6: Measured FRF for the IFF plant
+
+
2.6 Jacobian
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+
+
+
+load('jacobian.mat', 'J'); ++
+
+
+G_dvf_J_lf = G_dvf_lf(i_lf, i, j) ++
+#+end_src
+
-
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 @@
Created: 2021-06-07 lun. 19:00
+Created: 2021-06-08 mar. 21:51
#+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) +<