From 8aed6183a9ff19ea7c746dc47713ceade8bceee4 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Wed, 27 Mar 2024 23:02:11 +0100 Subject: [PATCH] Use subfigures when possible --- .gitignore | 2 - figs/test_apa_2dof_comp_frf.pdf | 7485 ---------------- figs/test_apa_2dof_comp_frf.png | Bin 182356 -> 0 bytes figs/test_apa_2dof_comp_frf_enc.pdf | 4668 ++++++++++ figs/test_apa_2dof_comp_frf_enc.png | Bin 0 -> 92874 bytes figs/test_apa_2dof_comp_frf_force.pdf | 4668 ++++++++++ figs/test_apa_2dof_comp_frf_force.png | Bin 0 -> 92874 bytes figs/test_apa_effect_resistance.pdf | Bin 37358 -> 36937 bytes figs/test_apa_effect_resistance.png | Bin 72122 -> 58501 bytes figs/test_apa_frf_encoder.pdf | Bin 546344 -> 544305 bytes figs/test_apa_frf_encoder.png | Bin 110844 -> 90069 bytes figs/test_apa_frf_force.pdf | Bin 522704 -> 521811 bytes figs/test_apa_frf_force.png | Bin 95133 -> 81653 bytes figs/test_apa_identified_damped_plants.pdf | Bin 131657 -> 129661 bytes figs/test_apa_identified_damped_plants.png | Bin 80183 -> 108384 bytes figs/test_apa_iff_root_locus.pdf | Bin 29463 -> 28521 bytes figs/test_apa_iff_root_locus.png | Bin 32300 -> 27296 bytes figs/test_apa_iff_schematic.pdf | Bin 27502 -> 26026 bytes figs/test_apa_iff_schematic.png | Bin 159630 -> 157066 bytes figs/test_apa_iff_schematic.svg | 58 +- figs/test_apa_schematic.pdf | Bin 24769 -> 23351 bytes figs/test_apa_schematic.png | Bin 145551 -> 143097 bytes figs/test_apa_schematic.svg | 57 +- figs/test_apa_super_element_comp_frf.pdf | 7598 ----------------- figs/test_apa_super_element_comp_frf.png | Bin 187291 -> 0 bytes figs/test_apa_super_element_comp_frf_enc.pdf | 4658 ++++++++++ figs/test_apa_super_element_comp_frf_enc.png | Bin 0 -> 94608 bytes .../test_apa_super_element_comp_frf_force.pdf | Bin 0 -> 544217 bytes .../test_apa_super_element_comp_frf_force.png | Bin 0 -> 85503 bytes matlab/src/extractNodes.m | 91 + test-bench-apa.org | 287 +- test-bench-apa.pdf | Bin 8779729 -> 8912276 bytes test-bench-apa.tex | 94 +- 33 files changed, 14339 insertions(+), 15327 deletions(-) delete mode 100644 figs/test_apa_2dof_comp_frf.pdf delete mode 100644 figs/test_apa_2dof_comp_frf.png create mode 100644 figs/test_apa_2dof_comp_frf_enc.pdf create mode 100644 figs/test_apa_2dof_comp_frf_enc.png create mode 100644 figs/test_apa_2dof_comp_frf_force.pdf create mode 100644 figs/test_apa_2dof_comp_frf_force.png delete mode 100644 figs/test_apa_super_element_comp_frf.pdf delete mode 100644 figs/test_apa_super_element_comp_frf.png create mode 100644 figs/test_apa_super_element_comp_frf_enc.pdf create mode 100644 figs/test_apa_super_element_comp_frf_enc.png create mode 100644 figs/test_apa_super_element_comp_frf_force.pdf create mode 100644 figs/test_apa_super_element_comp_frf_force.png create mode 100644 matlab/src/extractNodes.m diff --git a/.gitignore b/.gitignore index f834ecc..0e3ab6a 100644 --- a/.gitignore +++ b/.gitignore @@ -1,5 +1,3 @@ -mat/ -figures/ ltximg/ 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+362,7 @@ Two other similar measurements are performed to measured the bending of the APA #+name: fig:test_apa_meas_setup_modes #+caption: Experimental setup to measured flexible modes of the APA300ML. For the bending in the $X$ direction, the impact point is located at the back of the top measurement point. For the bending in the $Y$ direction, the impact point is located on the back surface of the top interface (on the back of the 2 measurements points). +#+attr_latex: :options [htbp] #+begin_figure #+attr_latex: :caption \subcaption{\label{fig:test_apa_meas_setup_X_bending}$X$ bending} #+attr_latex: :options {0.49\textwidth} @@ -477,7 +468,8 @@ This test bench is shown in Figure ref:fig:test_bench_apa and consists of the AP An encoder is used to measure the relative motion between the two granites (i.e. the displacement of the APA). #+name: fig:test_bench_apa -#+caption: Test bench used to characterize the APA300ML +#+caption: Schematic of the test bench used to estimate the dynamics of the APA300ML +#+attr_latex: :options [htbp] #+begin_figure #+attr_latex: :caption \subcaption{\label{fig:test_apa_bench_picture}Picture of the test bench} #+attr_latex: :options {0.3\textwidth} @@ -762,6 +754,20 @@ The following can be observed: - A lightly damped resonance at $95\,\text{Hz}$ - A "mass line" up to $\approx 800\,\text{Hz}$, above which some resonances appear. These additional resonances might be coming from the limited stiffness of the encoder support or from the limited compliance of the APA support. +The dynamics from $u$ to the measured voltage across the sensor stack $V_s$ is also identified and shown in Figure ref:fig:test_apa_frf_force. + +A lightly damped resonance is observed at $95\,\text{Hz}$ and a lightly damped anti-resonance at $41\,\text{Hz}$. +No additional resonances is present up to at least $2\,\text{kHz}$ indicating at Integral Force Feedback can be applied without stability issues from high frequency flexible modes. + +As illustrated by the Root Locus, the poles of the closed-loop system converges to the zeros of the open-loop plant. +Suppose that a controller with a very high gain is implemented such that the voltage $V_s$ across the sensor stack is zero. +In that case, because of the very high controller gain, no stress and strain is present on the sensor stack (and on the actuator stacks are well, as they are both in series). +Such closed-loop system would therefore virtually corresponds to a system for which the piezoelectric stacks have been removed and just the mechanical shell is kept. +From this analysis, the axial stiffness of the shell can be estimated to be $k_{\text{shell}} = 5.7 \cdot (2\pi \cdot 41)^2 = 0.38\,N/\mu m$. +# TODO - Compare with FEM result + +Such reasoning can lead to very interesting insight into the system just from an open-loop identification. + #+begin_src matlab :exports none %% Plot the FRF from u to de figure; @@ -777,7 +783,7 @@ hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]); hold off; -legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2); +legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2); ylim([1e-8, 1e-3]); ax2 = nexttile; @@ -795,29 +801,10 @@ linkaxes([ax1,ax2],'x'); xlim([10, 2e3]); #+end_src -#+begin_src matlab :tangle no :exports results :results file replace -exportFig('figs/test_apa_frf_encoder.pdf', 'width', 'wide', 'height', 'tall'); +#+begin_src matlab :tangle no :exports results :results file none +exportFig('figs/test_apa_frf_encoder.pdf', 'width', 'half', 'height', 'tall'); #+end_src -#+name: fig:test_apa_frf_encoder -#+caption: Estimated Frequency Response Function from generated voltage $u$ to the encoder displacement $d_e$ for the 6 APA300ML -#+RESULTS: -[[file:figs/test_apa_frf_encoder.png]] - -The dynamics from $u$ to the measured voltage across the sensor stack $V_s$ is also identified and shown in Figure ref:fig:test_apa_frf_force. - -A lightly damped resonance is observed at $95\,\text{Hz}$ and a lightly damped anti-resonance at $41\,\text{Hz}$. -No additional resonances is present up to at least $2\,\text{kHz}$ indicating at Integral Force Feedback can be applied without stability issues from high frequency flexible modes. - -As illustrated by the Root Locus, the poles of the closed-loop system converges to the zeros of the open-loop plant. -Suppose that a controller with a very high gain is implemented such that the voltage $V_s$ across the sensor stack is zero. -In that case, because of the very high controller gain, no stress and strain is present on the sensor stack (and on the actuator stacks are well, as they are both in series). -Such closed-loop system would therefore virtually corresponds to a system for which the piezoelectric stacks have been removed and just the mechanical shell is kept. -From this analysis, the axial stiffness of the shell can be estimated to be $k_{\text{shell}} = 5.7 \cdot (2\pi \cdot 41)^2 = 0.38\,N/\mu m$. -# TODO - Compare with FEM result - -Such reasoning can lead to very interesting insight into the system just from an open-loop identification. - #+begin_src matlab :exports none %% Plot the FRF from u to Vs figure; @@ -851,14 +838,27 @@ linkaxes([ax1,ax2],'x'); xlim([10, 2e3]); #+end_src -#+begin_src matlab :tangle no :exports results :results file replace -exportFig('figs/test_apa_frf_force.pdf', 'width', 'wide', 'height', 'tall'); +#+begin_src matlab :tangle no :exports results :results file none +exportFig('figs/test_apa_frf_force.pdf', 'width', 'half', 'height', 'tall'); #+end_src -#+name: fig:test_apa_frf_force -#+caption: Estimated Frequency Response Function from generated voltage $u$ to the sensor stack voltage $V_s$ for the 6 APA300ML -#+RESULTS: +#+name: fig:test_apa_frf_dynamics +#+caption: Measured frequency response function from generated voltage $u$ to the encoder displacement $d_e$ (\subref{fig:test_apa_frf_encoder}) and to the force sensor voltage $V_s$ (\subref{fig:test_apa_frf_force}) for the six APA300ML +#+attr_latex: :options [htbp] +#+begin_figure +#+attr_latex: :caption \subcaption{\label{fig:test_apa_frf_encoder}FRF from $u$ to $d_e$} +#+attr_latex: :options {0.49\textwidth} +#+begin_subfigure +#+attr_latex: :width 0.95\linewidth +[[file:figs/test_apa_frf_encoder.png]] +#+end_subfigure +#+attr_latex: :caption \subcaption{\label{fig:test_apa_frf_force}FRF from $u$ to $V_s$} +#+attr_latex: :options {0.49\textwidth} +#+begin_subfigure +#+attr_latex: :width 0.95\linewidth [[file:figs/test_apa_frf_force.png]] +#+end_subfigure +#+end_figure All the identified dynamics of the six APA300ML (both when looking at the encoder in Figure ref:fig:test_apa_frf_encoder and at the force sensor in Figure ref:fig:test_apa_frf_force) are almost identical, indicating good manufacturing repeatability for the piezoelectric stacks and the mechanical lever. @@ -900,15 +900,15 @@ G_hpf = 0.6*(s/2*pi*f0)/(1 + s/2*pi*f0); #+begin_src matlab :exports none %% Compare the HPF model and the measured FRF figure; -tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); +tiledlayout(2, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); -ax1 = nexttile([2,1]); +ax1 = nexttile(); hold on; plot(f, abs(frf_wo_k), 'DisplayName', 'Without $R$'); plot(f, abs(frf_wi_k), 'DisplayName', 'With $R$'); hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); -ylabel('Amplitude $V_s/u$ [V/V]'); set(gca, 'XTickLabel',[]); +ylabel('Amplitude [V/V]'); set(gca, 'XTickLabel',[]); hold off; ylim([1e-1, 1e0]); legend('location', 'southeast') @@ -921,14 +921,15 @@ hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); hold off; -yticks(-360:45:360); ylim([-45, 90]); +yticks(-360:45:360); ylim([-5, 90]); linkaxes([ax1,ax2],'x'); xlim([0.2, 8]); +xticks([0.2, 0.5, 1, 2, 5]); #+end_src #+begin_src matlab :tangle no :exports results :results file replace -exportFig('figs/test_apa_effect_resistance.pdf', 'width', 'wide', 'height', 'tall'); +exportFig('figs/test_apa_effect_resistance.pdf', 'width', 'wide', 'height', 600); #+end_src #+name: fig:test_apa_effect_resistance @@ -1032,7 +1033,7 @@ To estimate how the dynamics of the APA changes when the Integral Force Feedback The transfer function from the "damped" plant input $u\prime$ to the encoder displacement $d_e$ is identified for several IFF controller gains $g$. #+name: fig:test_apa_iff_schematic -#+caption: Figure caption +#+caption: Implementation of Integral Force Feedback in the Speedgoat. The damped plant has a new input $u\prime$ [[file:figs/test_apa_iff_schematic.png]] #+begin_src matlab @@ -1064,6 +1065,13 @@ The identified dynamics are then fitted by second order transfer functions. The comparison between the identified damped dynamics and the fitted second order transfer functions is done in Figure ref:fig:test_apa_identified_damped_plants for different gains $g$. It is clear that large amount of damping is added when the gain is increased and that the frequency of the pole is shifted to lower frequencies. + +The evolution of the pole in the complex plane as a function of the controller gain $g$ (i.e. the "root locus") is computed: +- using the IFF plant model eqref:eq:test_apa_iff_manual_fit and the implemented controller eqref:eq:test_apa_Kiff_formula +- from the fitted transfer functions of the damped plants experimentally identified for several controller gains + +The two obtained root loci are compared in Figure ref:fig:test_apa_iff_root_locus and are in good agreement considering that the damped plants were only fitted using a second order transfer function. + #+begin_src matlab %% Fit the data with 2nd order transfer function using vectfit3 opts = struct(); @@ -1114,21 +1122,10 @@ xlim([10, 1e3]); legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1); #+end_src -#+begin_src matlab :tangle no :exports results :results file replace -exportFig('figs/test_apa_identified_damped_plants.pdf', 'width', 'wide', 'height', 'normal'); +#+begin_src matlab :tangle no :exports results :results file none +exportFig('figs/test_apa_identified_damped_plants.pdf', 'width', 'normal', 'height', 'tall'); #+end_src -#+name: fig:test_apa_identified_damped_plants -#+caption: Identified dynamics (solid lines) and fitted transfer functions (dashed lines) from $u\prime$ to $d_e$ for different IFF gains -#+RESULTS: -[[file:figs/test_apa_identified_damped_plants.png]] - -The evolution of the pole in the complex plane as a function of the controller gain $g$ (i.e. the "root locus") is computed: -- using the IFF plant model eqref:eq:test_apa_iff_manual_fit and the implemented controller eqref:eq:test_apa_Kiff_formula -- from the fitted transfer functions of the damped plants experimentally identified for several controller gains - -The two obtained root loci are compared in Figure ref:fig:test_apa_iff_root_locus and are in good agreement considering that the damped plants were only fitted using a second order transfer function. - #+begin_src matlab :exports none :results none %% Root Locus of the APA300ML with Integral Force Feedback % Comparison between the computed root locus from the plant model and the root locus estimated from the damped plant pole identification @@ -1155,22 +1152,36 @@ end for i = 1:length(i_kept) plot(real(pole(G_dL_id{i})), imag(pole(G_dL_id{i})), 'x', 'color', [colors(i,:), 1], 'DisplayName', sprintf('g = %1.f', data.gains(i_kept(i)))); end -ylim([0, 700]); -xlim([-600,100]); xlabel('Real Part') ylabel('Imaginary Part') -axis square -legend('location', 'northwest'); +axis equal +ylim([0, 610]); +xlim([-300,0]); +legend('location', 'southwest'); #+end_src -#+begin_src matlab :tangle no :exports results :results file replace -exportFig('figs/test_apa_iff_root_locus.pdf', 'width', 'wide', 'height', 'tall'); +#+begin_src matlab :tangle no :exports results :results file none +exportFig('figs/test_apa_iff_root_locus.pdf', 'width', 'half', 'height', 'tall'); #+end_src -#+name: fig:test_apa_iff_root_locus -#+caption: Root Locus of the APA300ML with Integral Force Feedback - Comparison between the computed root locus from the plant model (black line) and the root locus estimated from the damped plant pole identification (colorful crosses) -#+RESULTS: +#+name: fig:test_apa_iff +#+caption: Experimental results of applying Integral Force Feedback to the APA300ML. Obtained damped plant (\subref{fig:test_apa_identified_damped_plants}) and Root Locus (\subref{fig:test_apa_iff_root_locus}) +#+attr_latex: :options [htbp] +#+begin_figure +#+attr_latex: :caption \subcaption{\label{fig:test_apa_identified_damped_plants}Measured frequency response functions of damped plants for several IFF gains (solid lines). Identified 2nd order plants to match the experimental data (dashed lines)} +#+attr_latex: :options {0.59\textwidth} +#+begin_subfigure +#+attr_latex: :height 8cm +[[file:figs/test_apa_identified_damped_plants.png]] +#+end_subfigure +#+attr_latex: :caption \subcaption{\label{fig:test_apa_iff_root_locus}Root Locus plot using the plant model (black) and poles of the identified damped plants (color crosses)} +#+attr_latex: :options {0.39\textwidth} +#+begin_subfigure +#+attr_latex: :height 8cm [[file:figs/test_apa_iff_root_locus.png]] +#+end_subfigure +#+end_figure + ** Conclusion :ignore: @@ -1231,6 +1242,9 @@ clear io; io_i = 1; io(io_i) = linio([mdl, '/u'], 1, 'openinput'); io_i = io_i + 1; % DAC Voltage io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage io(io_i) = linio([mdl, '/de'], 1, 'openoutput'); io_i = io_i + 1; % Encoder + +%% Frequency vector for analysis +freqs = 5*logspace(0, 3, 1000); #+end_src ** Two Degrees of Freedom APA Model @@ -1367,7 +1381,7 @@ The obtained parameters of the model shown in Figure ref:fig:test_apa_2dof_model The dynamics of the 2DoF APA300ML model is now extracted using optimized parameters (listed in Table ref:tab:test_apa_2dof_parameters) from the Simscape model. It is compared with the experimental data in Figure ref:fig:test_apa_2dof_comp_frf. -A good match can be observed between the model and the experimental data, both for the encoder and for the force sensor. +A good match can be observed between the model and the experimental data, both for the encoder (Figure ref:fig:test_apa_2dof_comp_frf_enc) and for the force sensor (Figure ref:fig:test_apa_2dof_comp_frf_force). This indicates that this model represents well the axial dynamics of the APA300ML. #+begin_src matlab @@ -1393,9 +1407,8 @@ G_2dof.OutputName = {'Vs', 'de'}; #+begin_src matlab :exports none %% Comparison of the measured FRF and the optimized 2DoF model of the APA300ML -freqs = 5*logspace(0, 3, 1000); figure; -tiledlayout(3, 2, 'TileSpacing', 'Compact', 'Padding', 'None'); +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); ax1 = nexttile([2,1]); hold on; @@ -1411,7 +1424,32 @@ hold off; ylim([1e-8, 1e-3]); legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1); -ax1b = nexttile([2,1]); +ax2 = nexttile; +hold on; +for i = 1:length(apa_nums) + plot(f, 180/pi*angle(enc_frf(:, i)), 'color', [0,0,0,0.2]); +end +plot(freqs, 180/pi*angle(squeeze(freqresp(G_2dof('de', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:)) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); ylim([-180, 180]); + +linkaxes([ax1,ax2],'x'); +xlim([10, 2e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file none +exportFig('figs/test_apa_2dof_comp_frf_enc.pdf', 'width', 'half', 'height', 'tall'); +#+end_src + +#+begin_src matlab :exports none +%% Comparison of the measured FRF and the optimized 2DoF model of the APA300ML +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); hold on; plot(f, abs(iff_frf(:, 1)), 'color', [0,0,0,0.2], 'DisplayName', 'Identified'); for i = 2:length(apa_nums) @@ -1427,18 +1465,6 @@ legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1); ax2 = nexttile; hold on; -for i = 1:length(apa_nums) - plot(f, 180/pi*angle(enc_frf(:, i)), 'color', [0,0,0,0.2]); -end -plot(freqs, 180/pi*angle(squeeze(freqresp(G_2dof('de', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:)) -hold off; -set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); -xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); -hold off; -yticks(-360:90:360); ylim([-180, 180]); - -ax2b = nexttile; -hold on; for i = 1:length(apa_nums) plot(f, 180/pi*angle(iff_frf(:, i)), 'color', [0,0,0,0.2]); end @@ -1449,18 +1475,31 @@ xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); hold off; yticks(-360:90:360); ylim([-180, 180]); -linkaxes([ax1,ax2,ax1b,ax2b],'x'); +linkaxes([ax1,ax2],'x'); xlim([10, 2e3]); #+end_src -#+begin_src matlab :tangle no :exports results :results file replace -exportFig('figs/test_apa_2dof_comp_frf.pdf', 'width', 'full', 'height', 'tall'); +#+begin_src matlab :tangle no :exports results :results file none +exportFig('figs/test_apa_2dof_comp_frf_force.pdf', 'width', 'half', 'height', 'tall'); #+end_src #+name: fig:test_apa_2dof_comp_frf -#+caption: Comparison of the measured FRF and the optimized 2DoF model of the APA300ML -#+RESULTS: -[[file:figs/test_apa_2dof_comp_frf.png]] +#+caption: Comparison of the measured frequency response functions and the identified dynamics from the 2DoF model of the APA300ML. Both for the dynamics from $u$ to $d_e$ (\subref{fig:test_apa_2dof_comp_frf_enc}) (\subref{fig:test_apa_2dof_comp_frf_force}) and from $u$ to $V_s$ (\subref{fig:test_apa_2dof_comp_frf_force}) +#+attr_latex: :options [htbp] +#+begin_figure +#+attr_latex: :caption \subcaption{\label{fig:test_apa_2dof_comp_frf_enc}from $u$ to $d_e$} +#+attr_latex: :options {0.49\textwidth} +#+begin_subfigure +#+attr_latex: :width 0.95\linewidth +[[file:figs/test_apa_2dof_comp_frf_enc.png]] +#+end_subfigure +#+attr_latex: :caption \subcaption{\label{fig:test_apa_2dof_comp_frf_force}from $u$ to $V_s$} +#+attr_latex: :options {0.49\textwidth} +#+begin_subfigure +#+attr_latex: :width 0.95\linewidth +[[file:figs/test_apa_2dof_comp_frf_force.png]] +#+end_subfigure +#+end_figure ** Conclusion :ignore: @@ -1516,6 +1555,9 @@ clear io; io_i = 1; io(io_i) = linio([mdl, '/u'], 1, 'openinput'); io_i = io_i + 1; % DAC Voltage io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage io(io_i) = linio([mdl, '/de'], 1, 'openoutput'); io_i = io_i + 1; % Encoder + +%% Frequency vector for analysis +freqs = 5*logspace(0, 3, 1000); #+end_src ** Extraction of the super-element @@ -1643,9 +1685,8 @@ G_flex.OutputName = {'Vs', 'de'}; #+begin_src matlab :exports none %% Comparison of the measured FRF and the "Flexible" model of the APA300ML -freqs = 5*logspace(0, 3, 1000); figure; -tiledlayout(3, 2, 'TileSpacing', 'Compact', 'Padding', 'None'); +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); ax1 = nexttile([2,1]); hold on; @@ -1661,7 +1702,32 @@ hold off; ylim([1e-8, 1e-3]); legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1); -ax1b = nexttile([2,1]); +ax2 = nexttile; +hold on; +for i = 1:length(apa_nums) + plot(f, 180/pi*angle(enc_frf(:, i)), 'color', [0,0,0,0.2]); +end +plot(freqs, 180/pi*angle(squeeze(freqresp(G_flex('de', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:)) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); ylim([-180, 180]); + +linkaxes([ax1,ax2],'x'); +xlim([10, 2e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file none +exportFig('figs/test_apa_super_element_comp_frf_enc.pdf', 'width', 'half', 'height', 'tall'); +#+end_src + +#+begin_src matlab :exports none +%% Comparison of the measured FRF and the "Flexible" model of the APA300ML +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); hold on; plot(f, abs(iff_frf(:, 1)), 'color', [0,0,0,0.2], 'DisplayName', 'Identified'); for i = 2:length(apa_nums) @@ -1677,18 +1743,6 @@ legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1); ax2 = nexttile; hold on; -for i = 1:length(apa_nums) - plot(f, 180/pi*angle(enc_frf(:, i)), 'color', [0,0,0,0.2]); -end -plot(freqs, 180/pi*angle(squeeze(freqresp(G_flex('de', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:)) -hold off; -set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); -xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); -hold off; -yticks(-360:90:360); ylim([-180, 180]); - -ax2b = nexttile; -hold on; for i = 1:length(apa_nums) plot(f, 180/pi*angle(iff_frf(:, i)), 'color', [0,0,0,0.2]); end @@ -1699,18 +1753,31 @@ xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); hold off; yticks(-360:90:360); ylim([-180, 180]); -linkaxes([ax1,ax2,ax1b,ax2b],'x'); +linkaxes([ax1,ax2],'x'); xlim([10, 2e3]); #+end_src -#+begin_src matlab :tangle no :exports results :results file replace -exportFig('figs/test_apa_super_element_comp_frf.pdf', 'width', 'full', 'height', 'tall'); +#+begin_src matlab :tangle no :exports results :results file none +exportFig('figs/test_apa_super_element_comp_frf_force.pdf', 'width', 'half', 'height', 'tall'); #+end_src #+name: fig:test_apa_super_element_comp_frf -#+caption: Comparison of the measured FRF and the "Flexible" model of the APA300ML -#+RESULTS: -[[file:figs/test_apa_super_element_comp_frf.png]] +#+caption: Comparison of the measured frequency response functions and the identified dynamics from the "flexible" model of the APA300ML. Both for the dynamics from $u$ to $d_e$ (\subref{fig:test_apa_2dof_comp_frf_enc}) (\subref{fig:test_apa_2dof_comp_frf_force}) and from $u$ to $V_s$ (\subref{fig:test_apa_2dof_comp_frf_force}) +#+attr_latex: :options [htbp] +#+begin_figure +#+attr_latex: :caption \subcaption{\label{fig:test_apa_super_element_comp_frf_enc}from $u$ to $d_e$} +#+attr_latex: :options {0.49\textwidth} +#+begin_subfigure +#+attr_latex: :width 0.95\linewidth +[[file:figs/test_apa_super_element_comp_frf_enc.png]] +#+end_subfigure +#+attr_latex: :caption \subcaption{\label{fig:test_apa_super_element_comp_frf_force}from $u$ to $V_s$} +#+attr_latex: :options {0.49\textwidth} +#+begin_subfigure +#+attr_latex: :width 0.95\linewidth +[[file:figs/test_apa_super_element_comp_frf_force.png]] +#+end_subfigure +#+end_figure ** Conclusion :ignore: @@ -1945,6 +2012,6 @@ actuator.cs = args.cs; % Damping of one stack [N/m] [fn:6]Polytec controller 3001 with sensor heads OFV512 [fn:5]Note that this is not fully correct as it was shown in Section ref:ssec:test_apa_stiffness that the electrical boundaries of the piezoelectric stack impacts its stiffness and that the sensor stack is almost open-circuited while the actuator stacks are almost short-circuited. 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