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and find the maximum valu *We need inputs and outputs to be in volts for the NASS plant !* - use 2DoF model of APA and 3 and 4 DoF model of the flexible joints +** TODO [#B] Verify that the specs are correct +[[*Output Voltage Noise][Output Voltage Noise]] + +Are we considering output voltage noise for the specs? + ** DONE [#A] Make schematic with the plant and all the instrumentation CLOSED: [2025-02-27 Thu 14:25] @@ -801,34 +806,36 @@ The most important characteristics are the (small signal) bandwidth > 5 [kHz] an #+caption: Characteristics of the PD200 compared with the specifications #+attr_latex: :environment tabularx :width \linewidth :align Xcccc #+attr_latex: :center t :booktabs t :float t -| *Specification* | *PD200* | WMA-200 | LA75B | E-505 | -|---------------------------------------------------------+------------------------------------------+-------------------------------------------+----------------------+-----------| -| Input Voltage Range: $\pm 10\,V$ | $\pm 10\,V$ | $\pm8.75\,V$ | $-1/7.5\,V$ | | -| Output Voltage Range: $-20/150\,V$ | $-50/150\,V$ | $\pm 175\,V$ | $-20/150\,V$ | -30/130 | -| Gain | 20 | 20 | 20 | 10 | -| Output Current $> 50\,mA$ | $900\,mA$ | $150\,mA$ | $360\,mA$ | $215\,mA$ | -| Slew Rate $> 34\,V/ms$ | $150\,V/\mu s$ | $80\,V/\mu s$ | n/a | n/a | -| Output noise (10uF load) $< 20\,mV\ \text{RMS}$ | $0.7\,mV\,\text{RMS}$ ($10\,\mu F$ load) | $0.05\,mV$ ($10\,\mu F$ load) | $3.4\,mV$ | $0.6\,mV$ | -| Small Signal Bandwidth ($10\,\mu F$ load): $> 5\,kHz$ | $6.4\,kHz$ ($10\,\mu F$ load) | $300\,Hz$[fn:detail_instrumentation_1] | $30\,kHz$ (unloaded) | n/a | -| Output Impedance: $< 3.6\,\Omega$ | n/a | $50\,\Omega$[fn:detail_instrumentation_1] | n/a | n/a | +| *Specification* | *PD200* | WMA-200 | LA75B | E-505 | +|--------------------------------------+-----------------------+-------------------------------------------+--------------+-----------| +| Input Voltage Range: $\pm 10\,V$ | $\pm 10\,V$ | $\pm8.75\,V$ | $-1/7.5\,V$ | | +| Output Voltage Range: $-20/150\,V$ | $-50/150\,V$ | $\pm 175\,V$ | $-20/150\,V$ | -30/130 | +| Gain | 20 | 20 | 20 | 10 | +| Output Current $> 50\,mA$ | $900\,mA$ | $150\,mA$ | $360\,mA$ | $215\,mA$ | +| Slew Rate $> 34\,V/ms$ | $150\,V/\mu s$ | $80\,V/\mu s$ | n/a | n/a | +| Output noise $< 20\,mV\ \text{RMS}$ | $0.7\,mV\,\text{RMS}$ | $0.05\,mV$ | $3.4\,mV$ | $0.6\,mV$ | +| (10uF load) | ($10\,\mu F$ load) | ($10\,\mu F$ load) | | | +| Small Signal Bandwidth $> 5\,kHz$ | $6.4\,kHz$ | $300\,Hz$ | $30\,kHz$ | n/a | +| ($10\,\mu F$ load) | ($10\,\mu F$ load) | [fn:detail_instrumentation_1] | (unloaded) | | +| Output Impedance: $< 3.6\,\Omega$ | n/a | $50\,\Omega$[fn:detail_instrumentation_1] | n/a | n/a | -#+name: fig:detail_instrumentation_pd200_specs -#+caption: Caption with reference to sub figure (\subref{fig:detail_instrumentation_pd200_specs_bandwidth}) -#+attr_latex: :options [htbp] -#+begin_figure -#+attr_latex: :caption \subcaption{\label{fig:detail_instrumentation_pd200_specs_bandwidth}sub caption a} -#+attr_latex: :options {0.48\textwidth} -#+begin_subfigure -#+attr_latex: :width 0.95\linewidth -[[file:figs/detail_instrumentation_pd200_specs_bandwidth.png]] -#+end_subfigure -#+attr_latex: :caption \subcaption{\label{fig:detail_instrumentation_pd200_specs_noise}sub caption b} -#+attr_latex: :options {0.48\textwidth} -#+begin_subfigure -#+attr_latex: :width 0.95\linewidth -[[file:figs/detail_instrumentation_pd200_specs_noise.png]] -#+end_subfigure -#+end_figure +# #+name: fig:detail_instrumentation_pd200_specs +# #+caption: Caption with reference to sub figure (\subref{fig:detail_instrumentation_pd200_specs_bandwidth}) +# #+attr_latex: :options [htbp] +# #+begin_figure +# #+attr_latex: :caption \subcaption{\label{fig:detail_instrumentation_pd200_specs_bandwidth}sub caption a} +# #+attr_latex: :options {0.48\textwidth} +# #+begin_subfigure +# #+attr_latex: :width 0.95\linewidth +# [[file:figs/detail_instrumentation_pd200_specs_bandwidth.png]] +# #+end_subfigure +# #+attr_latex: :caption \subcaption{\label{fig:detail_instrumentation_pd200_specs_noise}sub caption b} +# #+attr_latex: :options {0.48\textwidth} +# #+begin_subfigure +# #+attr_latex: :width 0.95\linewidth +# [[file:figs/detail_instrumentation_pd200_specs_noise.png]] +# #+end_subfigure +# #+end_figure ** ADC and DAC **** Synchronicity and Jitter @@ -1039,15 +1046,15 @@ The specifications are summarized in Table ref:tab:detail_instrumentation_sensor #+name: tab:detail_instrumentation_sensor_specs #+caption: Characteristics of the Vionic compared with the specifications -#+attr_latex: :environment tabularx :width 0.6\linewidth :align Xccc +#+attr_latex: :environment tabularx :width 0.9\linewidth :align Xccc #+attr_latex: :center t :booktabs t :float t -| *Specification* | *Renishaw Vionic* | LION CPL190 | Cedrat ECP500 | -|-----------------------------+-------------------+-------------+---------------| -| Bandwidth $> 5\,\text{kHz}$ | > 500 kHz | 10kHz | 20kHz | -| Noise $< 6\,nm\,\text{RMS}$ | 1.6 nm rms | 4 nm rms | 15 nm rms | -| Range $> 100\,\mu m$ | Ruler length | 250 um | 500um | -| In line measurement | | $\times$ | $\checkmark$ | -| Digital Output | $\times$ | | | +| *Specification* | *Renishaw Vionic* | LION CPL190 | Cedrat ECP500 | +|-----------------------------+---------------------+-------------+---------------| +| Bandwidth $> 5\,\text{kHz}$ | $> 500\,\text{kHz}$ | 10kHz | 20kHz | +| Noise $< 6\,nm\,\text{RMS}$ | 1.6 nm rms | 4 nm rms | 15 nm rms | +| Range $> 100\,\mu m$ | Ruler length | 250 um | 500um | +| In line measurement | | $\times$ | $\times$ | +| Digital Output | $\times$ | | | * Characterization of Instrumentation :PROPERTIES: @@ -1107,6 +1114,8 @@ The ADC noise of the IO131 was simply measured by short-circuiting its input wit Results are shown in Figure ref:fig:detail_instrumentation_adc_noise_measured. The ADC noise is a white noise with an amplitude spectral density of $5.6\,\mu V/\sqrt{Hz}$. +RMS value of 0.4mV. + #+begin_src matlab %% ADC noise adc = load("2023-08-23_15-42_io131_adc_noise.mat"); @@ -1124,6 +1133,11 @@ adc.f = f; % estimated mean ASD sprintf('Mean ASD of the ADC: %.1f uV/sqrt(Hz)', 1e6*sqrt(mean(adc.pxx))) +sprintf('Specifications: %.1f uV/sqrt(Hz)', 1e6*max_adc_asd) + +% estimated RMS +sprintf('RMS of the ADC: %.2f mV RMS', 1e3*rms(detrend(adc.adc_1,0))) +sprintf('RMS specifications: %.2f mV RMS', max_adc_rms) % Estimate quantization noise of the IO318 ADC delta_V = 20; % +/-10 V @@ -1139,8 +1153,8 @@ adc.q_asd = sqrt(adc.q_psd); % Quantization noise Amplitude Spectral Density [V/ %% Measured ADC noise (IO318) figure; hold on; -plot(adc.f, sqrt(adc.pxx), 'color', colors(3,:), 'DisplayName', sprintf('Measured, %.2f mV RMS', 1e3*rms(detrend(adc.adc_1,0)))) -plot([adc.f(2), adc.f(end)], [max_adc_asd, max_adc_asd], '--', 'color', colors(3,:), 'DisplayName', sprintf('Specs, %.2f mV RMS', max_adc_rms)) +plot(adc.f, sqrt(adc.pxx), 'color', colors(3,:), 'DisplayName', '$\Gamma_{q_{ad}}$') +plot([adc.f(2), adc.f(end)], [max_adc_asd, max_adc_asd], '--', 'color', colors(3,:), 'DisplayName', 'Specs') plot([adc.f(2), adc.f(end)], [adc.q_asd, adc.q_asd], 'k--', 'DisplayName', 'Quantization noise (16 bits, $\pm 10\,V$)') hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); @@ -1271,28 +1285,30 @@ hold off; xlabel('Time [s]'); ylabel('Voltage [V]'); leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1); leg.ItemTokenSize(1) = 15; -xlim([0, 50]); +xlim([0, 20]); #+end_src #+begin_src matlab :tangle no :exports results :results file none -exportFig('figs/detail_instrumentation_step_response_force_sensor.pdf', 'width', 500, 'height', 300); +exportFig('figs/detail_instrumentation_step_response_force_sensor.pdf', 'width', 'third', 'height', 300); #+end_src -#+attr_latex: :options [b]{0.48\linewidth} -#+begin_minipage -#+name: fig:detail_instrumentation_step_response_force_sensor -#+caption: Translation Stage -#+attr_latex: :scale 1 :float nil -[[file:figs/detail_instrumentation_step_response_force_sensor.png]] -#+end_minipage -\hfill -#+attr_latex: :options [b]{0.48\linewidth} -#+begin_minipage -#+name: fig:detail_instrumentation_force_sensor_adc -#+caption: Tilt Stage -#+attr_latex: :width 0.95\linewidth :float nil +#+name: fig:detail_instrumentation_force_sensor +#+caption: Electrical schematic of the ADC measuring the piezoelectric force sensor (\subref{fig:detail_instrumentation_force_sensor_adc}). Measured voltage $V_s$ while step voltages are generated for the actuator stacks (\subref{fig:detail_instrumentation_step_response_force_sensor}). +#+attr_latex: :options [htbp] +#+begin_figure +#+attr_latex: :caption \subcaption{\label{fig:detail_instrumentation_force_sensor_adc}Electrical Schematic} +#+attr_latex: :options {0.61\textwidth} +#+begin_subfigure +#+attr_latex: :scale 1 [[file:figs/detail_instrumentation_force_sensor_adc.png]] -#+end_minipage +#+end_subfigure +#+attr_latex: :caption \subcaption{\label{fig:detail_instrumentation_step_response_force_sensor}Signals} +#+attr_latex: :options {0.35\textwidth} +#+begin_subfigure +#+attr_latex: :width 0.95\linewidth +[[file:figs/detail_instrumentation_step_response_force_sensor.png]] +#+end_subfigure +#+end_figure As shown in Figure ref:fig:detail_instrumentation_step_response_force_sensor, the voltage across the Piezoelectric sensor stack shows a constant voltage offset. This can be explained by looking at the electrical model shown in Figure ref:fig:detail_instrumentation_force_sensor_adc (taken from cite:reza06_piezoel_trans_vibrat_contr_dampin). @@ -1382,24 +1398,26 @@ xlim([0, 20]); #+end_src #+begin_src matlab :tangle no :exports results :results file none -exportFig('figs/detail_instrumentation_step_response_force_sensor_R.pdf', 'width', 500, 'height', 300); +exportFig('figs/detail_instrumentation_step_response_force_sensor_R.pdf', 'width', 'third', 'height', 300); #+end_src -#+attr_latex: :options [b]{0.48\linewidth} -#+begin_minipage -#+name: fig:detail_instrumentation_step_response_force_sensor_R -#+caption: Translation Stage -#+attr_latex: :scale 1 :float nil -[[file:figs/detail_instrumentation_step_response_force_sensor_R.png]] -#+end_minipage -\hfill -#+attr_latex: :options [b]{0.48\linewidth} -#+begin_minipage -#+name: fig:detail_instrumentation_force_sensor_adc_R -#+caption: Tilt Stage -#+attr_latex: :width 0.95\linewidth :float nil +#+name: fig:detail_instrumentation_force_sensor_R +#+caption: Effect of an added resistor $R_p$ in parallel to the force sensor. The electrical schematic is shown in (\subref{fig:detail_instrumentation_force_sensor_adc_R}) and the measured signals in (\subref{fig:detail_instrumentation_step_response_force_sensor_R}). +#+attr_latex: :options [htbp] +#+begin_figure +#+attr_latex: :caption \subcaption{\label{fig:detail_instrumentation_force_sensor_adc_R}Electrical Schematic} +#+attr_latex: :options {0.61\textwidth} +#+begin_subfigure +#+attr_latex: :scale 1 [[file:figs/detail_instrumentation_force_sensor_adc_R.png]] -#+end_minipage +#+end_subfigure +#+attr_latex: :caption \subcaption{\label{fig:detail_instrumentation_step_response_force_sensor_R}Signals} +#+attr_latex: :options {0.35\textwidth} +#+begin_subfigure +#+attr_latex: :width 0.95\linewidth +[[file:figs/detail_instrumentation_step_response_force_sensor_R.png]] +#+end_subfigure +#+end_figure ** Instrumentation Amplifier @@ -1421,6 +1439,8 @@ The maximum amplifier gain of 80dB (i.e. 10000) is used. The measured voltage is then divided by 10000 to obtain the equivalent noise at the input of the voltage amplifier. In that case, the noise of the ADC is negligible, thanks to the high gain used. +It was also verified that the bandwidth of the instrumentation amplifier is much larger than 5kHz such that not phase drop are added by the use of the amplifier in the frequency band of interest. + #+begin_src latex :file detail_instrumentation_femto_meas_setup.pdf \begin{tikzpicture} \node[block={0.6cm}{0.6cm}] (const) {$0$}; @@ -1488,18 +1508,19 @@ hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); xlabel('Frequency [Hz]'); ylabel('ASD [$V/\sqrt{Hz}$]'); legend('location', 'northeast'); -xlim([1, 5e3]); ylim([1e-10, 4e-4]); -xticks([1e0, 1e1, 1e2, 1e3]) +xlim([1, 5e3]); ylim([2e-10, 1e-7]); +xticks([1e0, 1e1, 1e2, 1e3]); +yticks([1e-9, 1e-8]); #+end_src #+begin_src matlab :tangle no :exports results :results file none -exportFig('figs/detail_instrumentation_femto_input_noise.pdf', 'width', 'half', 'height', 'normal'); +exportFig('figs/detail_instrumentation_femto_input_noise.pdf', 'width', 'half', 'height', 350); #+end_src #+attr_latex: :options [b]{0.48\linewidth} #+begin_minipage #+name: fig:detail_instrumentation_femto_meas_setup -#+caption: Translation Stage +#+caption: Measurement of the instrumentation amplifier input voltage noise #+attr_latex: :scale 1 :float nil [[file:figs/detail_instrumentation_femto_meas_setup.png]] #+end_minipage @@ -1507,14 +1528,12 @@ exportFig('figs/detail_instrumentation_femto_input_noise.pdf', 'width', 'half', #+attr_latex: :options [b]{0.48\linewidth} #+begin_minipage #+name: fig:detail_instrumentation_femto_input_noise -#+caption: Tilt Stage +#+caption: Obtained ASD of the instrumentation amplifier input voltage noise #+attr_latex: :scale 1 :float nil [[file:figs/detail_instrumentation_femto_input_noise.png]] #+end_minipage ** Digital to Analog Converters -**** Noise Measurement - In order not to have any quantization noise and only measure the output voltage noise of the DAC, we "ask" the DAC to output a zero voltage. The measurement setup is schematically represented in Figure ref:fig:detail_instrumentation_dac_setup. @@ -1583,7 +1602,7 @@ And it is verified that the Amplitude Spectral Density of $n_{da}$ is much large #+end_src #+name: fig:detail_instrumentation_dac_setup -#+caption: Figure caption +#+caption: Measurement of the DAC output voltage noise. A pre-amplifier with a gain of 1000 is used before measuring the signal with the ADC. #+RESULTS: [[file:figs/detail_instrumentation_dac_setup.png]] @@ -1604,6 +1623,14 @@ Noverlap = floor(Nfft/2); dac.pxx = pxx(f<=5e3); dac.f = f(f<=5e3); + +% Estimated mean ASD +sprintf('Mean ASD of the DAC: %.1f uV/sqrt(Hz)', 1e6*sqrt(mean(dac.pxx))) +sprintf('Specifications: %.1f uV/sqrt(Hz)', 1e6*max_dac_asd) + +% Estimated RMS +sprintf('RMS of the DAC: %.2f mV RMS', 1e3*rms(dac.Vn)) +sprintf('RMS specifications: %.2f mV RMS', max_dac_rms) #+end_src The obtained Amplitude Spectral Density of the DAC's output voltage is shown in Figure ref:fig:detail_instrumentation_dac_output_noise. @@ -1611,20 +1638,22 @@ It is almost white noise with an ASD of 0.6uV/sqrt(Hz). There is a little bit of 50Hz, and some low frequency noise (thermal noise?) which are not foreseen to be an issue as it will be inside the bandwidth. #+begin_src matlab :exports none -colors = get(gca,'colororder'); - figure; +tiledlayout(1, 1, 'TileSpacing', 'compact', 'Padding', 'None'); + +ax1 = nexttile(); hold on; plot(femto.f, sqrt(femto.pxx), 'color', colors(5,:), 'DisplayName', '$\Gamma_{n_a}$'); plot(dac.f, sqrt(dac.pxx), 'color', colors(1,:), 'DisplayName', '$\Gamma_{n_{da}}$'); +plot([dac.f(2), dac.f(end)], [max_dac_asd, max_dac_asd], '--', 'color', colors(1,:), 'DisplayName', 'DAC specs') plot(adc.f, sqrt(adc.pxx)./dac.notes.pre_amp.gain, 'color', colors(3,:), 'DisplayName', '$\Gamma_{q_{ad}}/|G_a|$') hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); xlabel('Frequency [Hz]'); ylabel('ASD [$V/\sqrt{Hz}$]'); -leg = legend('location', 'east', 'FontSize', 8, 'NumColumns', 1); +leg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1); leg.ItemTokenSize(1) = 15; -xlim([1, 5e3]); ylim([1e-10, 4e-4]); -xticks([1e0, 1e1, 1e2, 1e3]) +xlim([1, 5e3]); ylim([2e-10, 4e-4]); +xticks([1e0, 1e1, 1e2, 1e3]); #+end_src #+begin_src matlab :tangle no :exports results :results file none @@ -1680,7 +1709,7 @@ ylim([-200, 20]) linkaxes([ax1,ax2],'x'); xlim([1, 5e3]); -xticks([1e0, 1e1, 1e2, 1e3]) +xticks([1e0, 1e1, 1e2, 1e3]); #+end_src #+begin_src matlab :tangle no :exports results :results file replace @@ -1688,16 +1717,16 @@ exportFig('figs/detail_instrumentation_dac_adc_tf.pdf', 'width', 'half', 'height #+end_src #+name: fig:detail_instrumentation_dac -#+caption: Measure transfer function from DAC to ADC - It fits a pure "1-sample" delay (\subref{fig:fig_label_a}) +#+caption: Measurement of the output voltage noise of the ADC (\subref{fig:detail_instrumentation_dac_output_noise}) and measured transfer function from DAC to ADC (\subref{fig:detail_instrumentation_dac_adc_tf}) which corresponds to a "1-sample" delay. #+attr_latex: :options [htbp] #+begin_figure -#+attr_latex: :caption \subcaption{\label{fig:detail_instrumentation_dac_output_noise}sub caption a} +#+attr_latex: :caption \subcaption{\label{fig:detail_instrumentation_dac_output_noise}Output noise of the DAC} #+attr_latex: :options {0.48\textwidth} #+begin_subfigure #+attr_latex: :width 0.95\linewidth [[file:figs/detail_instrumentation_dac_output_noise.png]] #+end_subfigure -#+attr_latex: :caption \subcaption{\label{fig:detail_instrumentation_dac_adc_tf}sub caption b} +#+attr_latex: :caption \subcaption{\label{fig:detail_instrumentation_dac_adc_tf}Transfer function from DAC to ADC} #+attr_latex: :options {0.48\textwidth} #+begin_subfigure #+attr_latex: :width 0.95\linewidth @@ -1768,56 +1797,11 @@ Two piezoelectric stacks of the APA95ML are connected to the PD200 output to hav #+end_src #+name: fig:detail_instrumentation_pd200_setup -#+caption: Sources of noise in the experimental setup +#+caption: Setup used to measured the output voltage noise of the PD200 voltage amplifier. A gain $G_a = 1000$ was used for the instrumentation amplifier. #+RESULTS: [[file:figs/detail_instrumentation_pd200_setup.png]] -#+begin_src matlab :exports none -%% PD200 Input Voltage Noise -% Load all the measurements -pd200w = load('noise_PD200_4_3uF.mat', 't', 'Vn', 'notes'); -% Take into account the pre-amplifier gain and PD200 Gain -pd200w.Vn = pd200w.Vn/pd200w.notes.pre_amp.gain/20; -#+end_src - -The measured low frequency (<20Hz) *output* noise of one of the PD200 amplifiers is shown in Figure ref:fig:pd200_noise_time_lpf. -It is very similar to the one specified in the datasheet in Figure ref:fig:pd200_expected_noise. - -#+begin_src matlab :exports none -% Compute the low frequency noise -G_lpf = 1/(1 + s/2/pi/20); -t_max = 40; - -figure; -hold on; -plot(pd200w.t(1:t_max/Ts), 20*lsim(G_lpf, 1e3*pd200w.Vn(1:t_max/Ts), pd200w.t(1:t_max/Ts))) -hold off; -xlabel('Time [s]'); -ylabel('Voltage [mV]'); -ylim([-3, 3]); -#+end_src - -#+begin_src matlab :tangle no :exports results :results file replace -exportFig('figs/pd200_noise_time_lpf.pdf', 'width', 'wide', 'height', 'normal'); -#+end_src - -#+name: fig:pd200_noise_time_lpf -#+caption: Measured low frequency noise of the PD200 from 0.01Hz to 20Hz -#+RESULTS: -[[file:figs/pd200_noise_time_lpf.png]] - -The obtained RMS and peak to peak values of the measured *output* noise are shown in Table ref:tab:rms_pkp_noise and found to be very similar to the specified ones. - -| | *RMS [$\mu V$]* | *Peak to Peak [$mV$]* | -|-----------------------------+-----------------+-----------------------| -| Specification [$10\,\mu F$] | 714.0 | 4.3 | -| PD200 1 | 565.1 | 3.7 | -| PD200 2 | 767.6 | 3.5 | -| PD200 3 | 479.9 | 3.0 | -| PD200 4 | 615.7 | 3.5 | -| PD200 5 | 651.0 | 2.4 | -| PD200 6 | 473.2 | 2.7 | -| PD200 7 | 423.1 | 2.3 | +# Can say that measurements are found to be very close to the one specified in the documentation. The Amplitude Spectral Density $\Gamma_n(\omega)$ of the measured signal by the ADC is computed. The Amplitude Spectral Density of the input voltage noise of the PD200 amplifier $n_p$ is then computed taking into account the gain of the pre-amplifier and the gain of the PD200 amplifier: @@ -1831,16 +1815,16 @@ And we verify that we are indeed measuring the noise of the PD200 and not the no \end{equation} #+begin_src matlab :exports none -%% PD200 Input Voltage Noise +%% PD200 Output Voltage Noise % Load all the measurements pd200 = {}; for i = 1:6 pd200(i) = {load(['mat/noise_PD200_' num2str(i) '_10uF.mat'], 't', 'Vout', 'notes')}; end -% Take into account the pre-amplifier gain and PD200 Gain +% Take into account the pre-amplifier gain for i = 1:6 - pd200{i}.Vout = pd200{i}.Vout/pd200{i}.notes.pre_amp.gain/20; + pd200{i}.Vout = pd200{i}.Vout/pd200{i}.notes.pre_amp.gain; end % Sampling time / frequency @@ -1857,9 +1841,13 @@ for i = 1:6 pd200{i}.pxx = pxx(f<=5e3); pd200{i}.f = f(f<=5e3); end + +% Estimated RMS +sprintf('RMS of the PD200: %.2f mV RMS', 1e3*rms(detrend(pd200{1}.Vout,0))) +sprintf('RMS specifications: %.2f mV RMS', max_amp_rms) #+end_src -The Amplitude Spectral Density of the measured *input* noise is computed and shown in Figure ref:fig:asd_noise_pd200_10uF. +The Amplitude Spectral Density of the measured *input* noise is computed and shown in Figure ref:fig:detail_instrumentation_pd200_noise. It is verified that the contribution of the PD200 noise is much larger than the contribution of the pre-amplifier noise of the quantization noise. @@ -1930,7 +1918,10 @@ end Gp = 20/(1 + s/2/pi/25e3); #+end_src -The obtained transfer functions from $V_{in}$ to $V_{out}$ are shown in Figure ref:fig:pd200_small_signal_tf. +We can see the very well matching between all the 7 amplifiers. +The amplitude is constant over a wide frequency band and the phase drop is limited to less than 1 degree up to 500Hz. + +The identified dynamics in Figure ref:fig:detail_instrumentation_pd200_tf can very well be modeled this dynamics with a first order low pass filter (even a constant could work fine). #+begin_src matlab :exports none figure; @@ -1938,27 +1929,25 @@ tiledlayout(3, 1, 'TileSpacing', 'compact', 'Padding', 'None'); ax1 = nexttile([2,1]); hold on; -for i = 1:length(pd200) - plot(pd200{i}.f, abs(pd200{i}.tf), 'color', [colors(2,:), 0.5]) -end -plot(pd200{1}.f, abs(squeeze(freqresp(Gp, pd200{1}.f, 'Hz'))), 'k--') +plot(pd200{1}.f, abs(pd200{1}.tf), '-', 'color', [colors(2,:), 0.5], 'linewidth', 2.5, 'DisplayName', 'Measurement') +plot(pd200{1}.f, abs(squeeze(freqresp(Gp, pd200{1}.f, 'Hz'))), '--', 'color', colors(2,:), 'DisplayName', 'Model') hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); -ylabel('Amplitude $V_{out}/V_{in}$ [V/V]'); set(gca, 'XTickLabel',[]); +ylabel('Magnitude [V/V]'); set(gca, 'XTickLabel',[]); hold off; ylim([1, 1e2]); +leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1); +leg.ItemTokenSize(1) = 15; ax2 = nexttile; hold on; -for i = 1:length(pd200) - plot(pd200{i}.f, 180/pi*unwrap(angle(pd200{i}.tf)), 'color', [colors(2,:), 0.5]) -end -plot(pd200{1}.f, 180/pi*unwrap(angle(squeeze(freqresp(Gp, pd200{1}.f, 'Hz')))), 'k--') +plot(pd200{1}.f, 180/pi*unwrap(angle(pd200{1}.tf)), '-', 'color', [colors(2,:), 0.5], 'linewidth', 2.5) +plot(pd200{1}.f, 180/pi*unwrap(angle(squeeze(freqresp(Gp, pd200{1}.f, 'Hz')))), '--', 'color', colors(2,:)) set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); hold off; -yticks(-360:5:360); -ylim([-45, 5]); +yticks(-360:2:360); +ylim([-13, 1]); linkaxes([ax1,ax2],'x'); xlim([1, 5e3]); @@ -1973,11 +1962,6 @@ exportFig('figs/detail_instrumentation_pd200_tf.pdf', 'width', 'wide', 'height', #+RESULTS: [[file:figs/detail_instrumentation_pd200_tf.png]] -We can see the very well matching between all the 7 amplifiers. -The amplitude is constant over a wide frequency band and the phase drop is limited to less than 1 degree up to 500Hz. - -The identified dynamics in Figure ref:fig:pd200_small_signal_tf can very well be modeled this dynamics with a first order low pass filter (even a constant could work fine). - **** Output Impedance The goal of this experimental setup is to estimate the output impedance $R_\text{out}$ of the PD200 voltage amplifiers. @@ -2023,20 +2007,19 @@ f0 = 1./(R_out*Cp) #+name: tab:table_name #+caption: Measured characteristics, Manual characterstics and specified ones -#+attr_latex: :environment tabularx :width \linewidth :align lXXX +#+attr_latex: :environment tabularx :width \linewidth :align Xcc #+attr_latex: :center t :booktabs t :float t -| | | | | -| *Characteristics* | *Measurement* | *Manual* | *Specification* | -|-------------------------------------+---------------+--------------+-----------------| -| Input Voltage Range | - | +/- 10 [V] | +/- 10 [V] | -| Output Voltage Range | - | -50/150 [V] | -20/150 [V] | -| Gain | | 20 [V/V] | - | -| Maximum RMS current | | 0.9 [A] | > 50 [mA] | -| Maximum Pulse current | | 10 [A] | - | -| Slew Rate | | 150 [V/us] | - | -| Noise (10uF load) | | 0.7 [mV RMS] | < 2 [mV rms] | -| Small Signal Bandwidth (10uF load) | | 7.4 [kHz] | > 5 [kHz] | -| Large Signal Bandwidth (150V, 10uF) | | 300 [Hz] | - | +| *Characteristics* | *Specification* | *Measurement* | +|-------------------------------------+-----------------+---------------| +| Input Voltage Range | +/- 10 [V] | - | +| Output Voltage Range | -20/150 [V] | - | +| Gain | 20 | 20 | +| Maximum RMS current | > 50 [mA] | | +| Maximum Pulse current | - | | +| Slew Rate | - | | +| Noise (10uF load) | < 2 [mV rms] | | +| Small Signal Bandwidth (10uF load) | > 5 [kHz] | | +| Large Signal Bandwidth (150V, 10uF) | - | | ** Noise of the full setup with 16bits DAC :noexport: @@ -2135,15 +2118,15 @@ Then, the measured signal $y_m$ corresponds to the noise $n$. The measurement bench is shown in Figures ref:fig:meas_bench_top_view and ref:fig:meas_bench_side_view. Note that the bench is then covered with a "plastic bubble sheet" in order to keep disturbances as small as possible. -#+name: fig:meas_bench_top_view -#+caption: Top view picture of the measurement bench -#+attr_latex: :width 0.8\linewidth -[[file:figs/IMG_20210211_170554.jpg]] +# #+name: fig:meas_bench_top_view +# #+caption: Top view picture of the measurement bench +# #+attr_latex: :width 0.8\linewidth +# [[file:figs/IMG_20210211_170554.jpg]] -#+name: fig:meas_bench_side_view -#+caption: Side view picture of the measurement bench -#+attr_latex: :width 0.8\linewidth -[[file:figs/IMG_20210211_170607.jpg]] +# #+name: fig:meas_bench_side_view +# #+caption: Side view picture of the measurement bench +# #+attr_latex: :width 0.8\linewidth +# [[file:figs/IMG_20210211_170607.jpg]] Then, and for all the 7 encoders, we record the measured motion during 100s with a sampling frequency of 20kHz. @@ -2178,7 +2161,9 @@ xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]'); xlim([1, 5e3]); ylim([1e-12, 1e-8]); #+end_src -** External Metrology +** TODO External Metrology :noexport: + +Should this be included here? [[file:~/Cloud/work-projects/ID31-NASS/matlab/test-bench-attocube/test-bench-attocube.org][test-bench-attocube]] @@ -2192,51 +2177,78 @@ For the final tests, QuDIS were used. ** Conclusion #+begin_src matlab +%% Estimate the resulting errors induced by noise of instruments f = dac.f; -length(dac.pxx) -length(adc.pxx) -length(pd200{1}.pxx) -length(enc{1}.pxx) - +% Vertical direction psd_z_dac = 6*(abs(squeeze(freqresp(Gd('z', 'nda1' ), f, 'Hz'))).^2).*dac.pxx; psd_z_adc = 6*(abs(squeeze(freqresp(Gd('z', 'nad1' ), f, 'Hz'))).^2).*adc.pxx; psd_z_amp = 6*(abs(squeeze(freqresp(Gd('z', 'namp1'), f, 'Hz'))).^2).*pd200{1}.pxx; psd_z_enc = 6*(abs(squeeze(freqresp(Gd('z', 'ddL1' ), f, 'Hz'))).^2).*enc{1}.pxx; psd_z_tot = psd_z_dac + psd_z_adc + psd_z_amp + psd_z_enc; +rms_z_dac = sqrt(trapz(f, psd_z_dac)); +rms_z_adc = sqrt(trapz(f, psd_z_adc)); +rms_z_amp = sqrt(trapz(f, psd_z_amp)); +rms_z_enc = sqrt(trapz(f, psd_z_enc)); rms_z_tot = sqrt(trapz(f, psd_z_tot)); + +% Lateral direction +psd_y_dac = 6*(abs(squeeze(freqresp(Gd('y', 'nda1' ), f, 'Hz'))).^2).*dac.pxx; +psd_y_adc = 6*(abs(squeeze(freqresp(Gd('y', 'nad1' ), f, 'Hz'))).^2).*adc.pxx; +psd_y_amp = 6*(abs(squeeze(freqresp(Gd('y', 'namp1'), f, 'Hz'))).^2).*pd200{1}.pxx; +psd_y_enc = 6*(abs(squeeze(freqresp(Gd('y', 'ddL1' ), f, 'Hz'))).^2).*enc{1}.pxx; +psd_y_tot = psd_y_dac + psd_y_adc + psd_y_amp + psd_y_enc; + +rms_y_tot = sqrt(trapz(f, psd_y_tot)); #+end_src - [ ] Compare with measurement noise? or effect of measurement noise => higher so it's OK? -- [ ] Or compare with specifications? +- [ ] Or compare with specifications? (but we don't have specifications for ASD, only RMS) +- [ ] Or maybe put the ASD of the measured vibration in simulation (or noise budget based on disturbances) => show that we are bellow disturbances so it should not be limited From all the measured noises, compute the obtained PSD error in Y and Z (show PSD of individual + Sum + Cumulative?) #+begin_src matlab :exports none :results none -%% Measured output voltage noise of the PD200 amplifiers +%% Closed-loop noise budgeting using measured noise of instrumentation figure; hold on; -plot(f, sqrt(psd_z_tot), 'k-', 'linewidth', 2, 'DisplayName', sprintf('Total: %.1f nm RMS', 1e9*rms_z_tot)); -plot(f, sqrt(psd_z_amp), 'color', colors(2, :), 'DisplayName', 'PD200'); -plot(f, sqrt(psd_z_dac), 'color', colors(1,:), 'DisplayName', 'DAC') -plot(f, sqrt(psd_z_adc), 'color', colors(3,:), 'DisplayName', 'ADC') -plot(f, sqrt(psd_z_enc), 'color', colors(5,:), 'DisplayName', 'ENC') +plot(f, sqrt(psd_z_amp), 'color', [colors(2,:)], 'linewidth', 2.5, 'DisplayName', 'PD200'); +plot(f, sqrt(psd_z_dac), 'color', [colors(1,:)], 'linewidth', 2.5, 'DisplayName', 'DAC') +plot(f, sqrt(psd_z_adc), 'color', [colors(3,:)], 'linewidth', 2.5, 'DisplayName', 'ADC') +plot(f, sqrt(psd_z_tot), 'k-', 'DisplayName', sprintf('Total: %.1f nm RMS', 1e9*rms_z_tot)); hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]'); leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1); leg.ItemTokenSize(1) = 15; -xlim([1, 5e3]); -xticks([1e0, 1e1, 1e2, 1e3]) +xlim([1, 5e3]); ylim([1e-14, 1e-9]); +xticks([1e0, 1e1, 1e2, 1e3]); #+end_src +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/detail_instrumentation_cl_noise_budget.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:detail_instrumentation_cl_noise_budget +#+caption: Closed-loop noise budgeting using measured noise of instrumentation +#+RESULTS: +[[file:figs/detail_instrumentation_cl_noise_budget.png]] + * Conclusion :PROPERTIES: :UNNUMBERED: t :END: <> +- thanks to multi-body model in which it is easy to include instrumentation and noise sources + From specification on the sample's vertical motion (most stringent requirement), specification for each noise source was extracted. +- based on those specifications, adequate instrumentation were chosen. + for some instrumentation, it was difficult to choose only based on data-sheets are manufacturers often don't share relevant information for noise budgets, such as amplitude spectral densities +- then, the instrumentation was procured and tested individually. + All were found to comply with the requirements. + Finally, based on the measured noise of all instrumentation, the expected sample's vibration induced by all the noise sources was estimated and found to comply with the requirements. + * Bibliography :ignore: #+latex: \printbibliography[heading=bibintoc,title={Bibliography}] diff --git a/nass-instrumentation.pdf b/nass-instrumentation.pdf index 9d6a328..4caca40 100644 Binary files a/nass-instrumentation.pdf and b/nass-instrumentation.pdf differ diff --git a/nass-instrumentation.tex b/nass-instrumentation.tex index c40236e..100b018 100644 --- a/nass-instrumentation.tex +++ b/nass-instrumentation.tex @@ -1,4 +1,4 @@ -% Created 2025-03-14 Fri 22:33 +% Created 2025-03-15 Sat 10:44 % Intended LaTeX compiler: pdflatex \documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt} @@ -43,6 +43,7 @@ The received instrumentation are characterized in Section \ref{sec:detail_instru \end{figure} \chapter{Dynamic Error Budgeting} +\label{sec:org5318a4e} \label{sec:detail_instrumentation_dynamic_error_budgeting} \textbf{Goal}: \begin{itemize} @@ -66,6 +67,7 @@ As the voltage amplifier gain will impact how the DAC noise will be amplified, s \item Assumption of voltage amplifier with gain 20 \end{itemize} \section{Closed-Loop Sensitivity to Instrumentation Disturbances} +\label{sec:org0921bec} The following noise sources are considered (Figure \ref{fig:detail_instrumentation_plant}): \begin{itemize} @@ -87,6 +89,7 @@ The lateral error was also considered, but the specifications are less stringent \end{figure} \section{Estimation of maximum instrumentation noise} +\label{sec:orgd3ab02f} From previous analysis, we know how the noise of the instrumentation will affect the vertical error of the sample. Now, we want to determine specifications for each instrumentation such that the effect on the vertical error of the sample is within specifications. @@ -147,6 +150,7 @@ RMS Noise & \(0.8\,mV\,\text{RMS}\) & \(1\,mV\,\text{RMS}\) & \(20\,mV\,\text{RM If the Amplitude Spectral Density of the noise of the ADC, DAC and voltage amplifiers are all below the specified maximum noises, then the induced vertical error will be below 15nmRMS. \chapter{Choice of Instrumentation} +\label{sec:orge67db89} \label{sec:detail_instrumentation_choice} In previous section: noise characteristics. In this section, other characteristics (range, bandwidth, etc\ldots{}) @@ -161,12 +165,14 @@ In this section, also tell which instrumentation has been bought, and different \item[{$\square$}] block diagram of the model of the amplifier \end{itemize} \section{Piezoelectric Voltage Amplifier} +\label{sec:org584716c} There are several characteristics of the piezoelectric voltage amplifiers that should be considered. To be able to use the full stroke of the piezoelectric actuator, the voltage output should be between -20 and 150V. It should accept an analog input voltage, preferably between -10 and 10V. \paragraph{Small signal Bandwidth and Output Impedance} +\label{sec:orgf100305} There are two bandwidth that should be considered for a piezoelectric voltage amplifier: large signal bandwidth and small signal bandwidth. Large signal bandwidth are linked to the output current capacities of the amplifier and will be discussed next. @@ -193,6 +199,7 @@ As the capacitance load of the two piezoelectric stacks correspond to a capacita If a small signal bandwidth of \(f_0 = \frac{\omega_0}{2\pi} = 5\,kHz\) is wanted, it corresponds to a maximum output impedance of \(R_0 = 3.6\,\Omega\). \paragraph{Large signal Bandwidth} +\label{sec:orga060611} Large signal bandwidth are linked to the maximum output capabilities of the amplifiers in terms of amplitude as a function of frequency \cite{spengen16_high_voltag_amplif}. @@ -211,6 +218,7 @@ In order to reach high voltage at high frequency, the required current that the \end{itemize} \paragraph{Output voltage noise} +\label{sec:orga1946e3} As discussed in Section \ref{sec:detail_instrumentation_dynamic_error_budgeting}, the output noise of the voltage amplifier should be smaller than \(20\,mV\,\text{RMS}\). @@ -220,6 +228,7 @@ Therefore, when comparing noise of different voltage amplifiers, it should be no Here, the output noise should be smaller than 20mVRMS for a load of 8.8uF. \paragraph{Choice of voltage amplifier} +\label{sec:org3c7c558} The specifications as well as the amplifier characteristics as shown in the datasheet are summarized in Table \ref{tab:pd200_characteristics}. @@ -249,31 +258,20 @@ Output Voltage Range: \(-20/150\,V\) & \(-50/150\,V\) & \(\pm 175\,V\) & \(-20/1 Gain & 20 & 20 & 20 & 10\\ Output Current \(> 50\,mA\) & \(900\,mA\) & \(150\,mA\) & \(360\,mA\) & \(215\,mA\)\\ Slew Rate \(> 34\,V/ms\) & \(150\,V/\mu s\) & \(80\,V/\mu s\) & n/a & n/a\\ -Output noise (10uF load) \(< 20\,mV\ \text{RMS}\) & \(0.7\,mV\,\text{RMS}\) (\(10\,\mu F\) load) & \(0.05\,mV\) (\(10\,\mu F\) load) & \(3.4\,mV\) & \(0.6\,mV\)\\ -Small Signal Bandwidth (\(10\,\mu F\) load): \(> 5\,kHz\) & \(6.4\,kHz\) (\(10\,\mu F\) load) & \(300\,Hz\)\footnotemark & \(30\,kHz\) (unloaded) & n/a\\ -Output Impedance: \(< 3.6\,\Omega\) & n/a & \(50\,\Omega\)\textsuperscript{\ref{org9c934eb}} & n/a & n/a\\ +Output noise \(< 20\,mV\ \text{RMS}\) & \(0.7\,mV\,\text{RMS}\) & \(0.05\,mV\) & \(3.4\,mV\) & \(0.6\,mV\)\\ +(10uF load) & (\(10\,\mu F\) load) & (\(10\,\mu F\) load) & & \\ +Small Signal Bandwidth \(> 5\,kHz\) & \(6.4\,kHz\) & \(300\,Hz\) & \(30\,kHz\) & n/a\\ +(\(10\,\mu F\) load) & (\(10\,\mu F\) load) & \footnotemark & (unloaded) & \\ +Output Impedance: \(< 3.6\,\Omega\) & n/a & \(50\,\Omega\)\textsuperscript{\ref{org28ed3ea}} & n/a & n/a\\ \bottomrule \end{tabularx} -\end{table}\footnotetext[1]{\label{org9c934eb}The manufacturer proposed to remove the \(50\,\Omega\) output resistor to improve to small signal bandwidth above \(10\,kHz\)} +\end{table}\footnotetext[1]{\label{org28ed3ea}The manufacturer proposed to remove the \(50\,\Omega\) output resistor to improve to small signal bandwidth above \(10\,kHz\)} -\begin{figure}[htbp] -\begin{subfigure}{0.48\textwidth} -\begin{center} -\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_instrumentation_pd200_specs_bandwidth.png} -\end{center} -\subcaption{\label{fig:detail_instrumentation_pd200_specs_bandwidth}sub caption a} -\end{subfigure} -\begin{subfigure}{0.48\textwidth} -\begin{center} -\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_instrumentation_pd200_specs_noise.png} -\end{center} -\subcaption{\label{fig:detail_instrumentation_pd200_specs_noise}sub caption b} -\end{subfigure} -\caption{\label{fig:detail_instrumentation_pd200_specs}Caption with reference to sub figure (\subref{fig:detail_instrumentation_pd200_specs_bandwidth})} -\end{figure} \section{ADC and DAC} +\label{sec:org80ca7dd} \paragraph{Synchronicity and Jitter} +\label{sec:orge597a56} For control systems, it is very important that the inputs and outputs are sampled synchronously with the controller and with low jitter \cite{abramovitch22_pract_method_real_world_contr_system,abramovitch23_tutor_real_time_comput_issues_contr_system}. @@ -285,6 +283,7 @@ Therefore, the ADC and DAC: \end{itemize} \paragraph{Sampling Frequency, Bandwidth and delays} +\label{sec:org41d5214} Several requirements that may appear the same but are different: \begin{itemize} @@ -300,6 +299,7 @@ Therefore, Sigma-Delta ADC are very well used for signal acquisition, but has li Therefore, for real time control applications, SAR-ADC (Successive approximation ADCs) is still the mostly applied type because of its single sample latency. \paragraph{ADC Noise} +\label{sec:org323f222} From the dynamical error budget in Section \ref{sec:detail_instrumentation_dynamic_error_budgeting} Measurement noise ASD should be bellow 11uV/sqrt(Hz), 0.8mV RMS @@ -364,11 +364,13 @@ The minimum number of bits so that the quantization noise is above some define v With a sampling frequency \(F_s = 10\,kHz\), a full range of \(\Delta V = 20\,V\) and a maximum allowed ASD \(\Phi_{\text{max}} = 11\,\mu V/\sqrt{Hz}\), the minimum number of bits is \(n_{\text{min}} = 12.4\), which is easily satisfied. \paragraph{DAC Output voltage noise} +\label{sec:org30caf00} Similarly, the DAC output voltage noise ASD should be below \(14\,\mu V/\sqrt{Hz}\), 1mV RMS. This corresponds to a 13bits +/-10V DAC. \paragraph{Choice of the ADC and DAC Board} +\label{sec:org1df7a52} Based on the above analysis, the choice of ADC and DAC is quite simple. @@ -394,6 +396,7 @@ Noise is not specified, but as it has 16 bits resolution, it should be well belo It will be experimentally measured in Section \ref{sec:detail_instrumentation_characterization}. \section{Relative Displacement Sensors} +\label{sec:org2dd10f4} Specifications: \begin{itemize} @@ -464,20 +467,21 @@ The specifications are summarized in Table \ref{tab:detail_instrumentation_senso \begin{table}[htbp] \caption{\label{tab:detail_instrumentation_sensor_specs}Characteristics of the Vionic compared with the specifications} \centering -\begin{tabularx}{0.6\linewidth}{Xccc} +\begin{tabularx}{0.9\linewidth}{Xccc} \toprule \textbf{Specification} & \textbf{Renishaw Vionic} & LION CPL190 & Cedrat ECP500\\ \midrule -Bandwidth \(> 5\,\text{kHz}\) & > 500 kHz & 10kHz & 20kHz\\ +Bandwidth \(> 5\,\text{kHz}\) & \(> 500\,\text{kHz}\) & 10kHz & 20kHz\\ Noise \(< 6\,nm\,\text{RMS}\) & 1.6 nm rms & 4 nm rms & 15 nm rms\\ Range \(> 100\,\mu m\) & Ruler length & 250 um & 500um\\ -In line measurement & & \(\times\) & \(\checkmark\)\\ +In line measurement & & \(\times\) & \(\times\)\\ Digital Output & \(\times\) & & \\ \bottomrule \end{tabularx} \end{table} \chapter{Characterization of Instrumentation} +\label{sec:org3c1dd2e} \label{sec:detail_instrumentation_characterization} All the instrumentation was then procured and tested individually to verify whether is fulfils the specifications or not. @@ -494,14 +498,18 @@ blue & DAC\\ \item[{$\square$}] Make sure that at some point I talk about twisted pairs etc.. Maybe use the nice schematic? \end{itemize} \section{Analog to Digital Converters} +\label{sec:orga04d2a2} Internally uses the AD7609 ADC from Analog Devices. 200kSPS, 16 bits, +/-10V \paragraph{Measured Noise} +\label{sec:org485cf0d} The ADC noise of the IO131 was simply measured by short-circuiting its input with a 50 Ohm resistor. Results are shown in Figure \ref{fig:detail_instrumentation_adc_noise_measured}. The ADC noise is a white noise with an amplitude spectral density of \(5.6\,\mu V/\sqrt{Hz}\). +RMS value of 0.4mV. + \begin{figure}[htbp] \centering \includegraphics[scale=1]{figs/detail_instrumentation_adc_noise_measured.png} @@ -519,6 +527,7 @@ This works because the noise can be approximated by a white noise and the amplit \paragraph{Reading of piezoelectric force sensor} +\label{sec:org05565b5} There are few other things to consider when measuring the voltage generated by a piezoelectric stack. @@ -542,19 +551,21 @@ With the capacitance being \(C_p = 4.4 \mu F\), the internal impedance of the Sp It is close to the specified value of \(1\,M\Omega\) found in the datasheet -\begin{minipage}[b]{0.48\linewidth} +\begin{figure}[htbp] +\begin{subfigure}{0.61\textwidth} \begin{center} -\includegraphics[scale=1,scale=1]{figs/detail_instrumentation_step_response_force_sensor.png} -\captionof{figure}{\label{fig:detail_instrumentation_step_response_force_sensor}Translation Stage} +\includegraphics[scale=1,scale=1]{figs/detail_instrumentation_force_sensor_adc.png} \end{center} -\end{minipage} -\hfill -\begin{minipage}[b]{0.48\linewidth} +\subcaption{\label{fig:detail_instrumentation_force_sensor_adc}Electrical Schematic} +\end{subfigure} +\begin{subfigure}{0.35\textwidth} \begin{center} -\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_instrumentation_force_sensor_adc.png} -\captionof{figure}{\label{fig:detail_instrumentation_force_sensor_adc}Tilt Stage} +\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_instrumentation_step_response_force_sensor.png} \end{center} -\end{minipage} +\subcaption{\label{fig:detail_instrumentation_step_response_force_sensor}Signals} +\end{subfigure} +\caption{\label{fig:detail_instrumentation_force_sensor}Electrical schematic of the ADC measuring the piezoelectric force sensor (\subref{fig:detail_instrumentation_force_sensor_adc}). Measured voltage \(V_s\) while step voltages are generated for the actuator stacks (\subref{fig:detail_instrumentation_step_response_force_sensor}).} +\end{figure} As shown in Figure \ref{fig:detail_instrumentation_step_response_force_sensor}, the voltage across the Piezoelectric sensor stack shows a constant voltage offset. This can be explained by looking at the electrical model shown in Figure \ref{fig:detail_instrumentation_force_sensor_adc} (taken from \cite{reza06_piezoel_trans_vibrat_contr_dampin}). @@ -585,21 +596,24 @@ After the resistor is added, the same steps response is performed. And indeed, we obtain a much smaller offset voltage (\(V_{\text{off}} = 0.15\,V\)) and a much faster time constant (\(\tau = 0.45\,s\)). This validates the model of the ADC and the effectiveness of the added resistor. -\begin{minipage}[b]{0.48\linewidth} +\begin{figure}[htbp] +\begin{subfigure}{0.61\textwidth} \begin{center} -\includegraphics[scale=1,scale=1]{figs/detail_instrumentation_step_response_force_sensor_R.png} -\captionof{figure}{\label{fig:detail_instrumentation_step_response_force_sensor_R}Translation Stage} +\includegraphics[scale=1,scale=1]{figs/detail_instrumentation_force_sensor_adc_R.png} \end{center} -\end{minipage} -\hfill -\begin{minipage}[b]{0.48\linewidth} +\subcaption{\label{fig:detail_instrumentation_force_sensor_adc_R}Electrical Schematic} +\end{subfigure} +\begin{subfigure}{0.35\textwidth} \begin{center} -\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_instrumentation_force_sensor_adc_R.png} -\captionof{figure}{\label{fig:detail_instrumentation_force_sensor_adc_R}Tilt Stage} +\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_instrumentation_step_response_force_sensor_R.png} \end{center} -\end{minipage} +\subcaption{\label{fig:detail_instrumentation_step_response_force_sensor_R}Signals} +\end{subfigure} +\caption{\label{fig:detail_instrumentation_force_sensor_R}Effect of an added resistor \(R_p\) in parallel to the force sensor. The electrical schematic is shown in (\subref{fig:detail_instrumentation_force_sensor_adc_R}) and the measured signals in (\subref{fig:detail_instrumentation_step_response_force_sensor_R}).} +\end{figure} \section{Instrumentation Amplifier} +\label{sec:org4ed7494} Because the ADC noise may be too large to measure noise of other instruments (anything below \(5.6\,\mu V/\sqrt{Hz}\) cannot be distinguish from the noise of the ADC itself), a low noise instrumentation amplifier can be used. @@ -623,23 +637,24 @@ The maximum amplifier gain of 80dB (i.e. 10000) is used. The measured voltage is then divided by 10000 to obtain the equivalent noise at the input of the voltage amplifier. In that case, the noise of the ADC is negligible, thanks to the high gain used. +It was also verified that the bandwidth of the instrumentation amplifier is much larger than 5kHz such that not phase drop are added by the use of the amplifier in the frequency band of interest. + \begin{minipage}[b]{0.48\linewidth} \begin{center} \includegraphics[scale=1,scale=1]{figs/detail_instrumentation_femto_meas_setup.png} -\captionof{figure}{\label{fig:detail_instrumentation_femto_meas_setup}Translation Stage} +\captionof{figure}{\label{fig:detail_instrumentation_femto_meas_setup}Measurement of the instrumentation amplifier input voltage noise} \end{center} \end{minipage} \hfill \begin{minipage}[b]{0.48\linewidth} \begin{center} \includegraphics[scale=1,scale=1]{figs/detail_instrumentation_femto_input_noise.png} -\captionof{figure}{\label{fig:detail_instrumentation_femto_input_noise}Tilt Stage} +\captionof{figure}{\label{fig:detail_instrumentation_femto_input_noise}Obtained ASD of the instrumentation amplifier input voltage noise} \end{center} \end{minipage} \section{Digital to Analog Converters} -\paragraph{Noise Measurement} - +\label{sec:org7adcab5} In order not to have any quantization noise and only measure the output voltage noise of the DAC, we ``ask'' the DAC to output a zero voltage. The measurement setup is schematically represented in Figure \ref{fig:detail_instrumentation_dac_setup}. @@ -659,7 +674,7 @@ And it is verified that the Amplitude Spectral Density of \(n_{da}\) is much lar \begin{figure}[htbp] \centering \includegraphics[scale=1]{figs/detail_instrumentation_dac_setup.png} -\caption{\label{fig:detail_instrumentation_dac_setup}Figure caption} +\caption{\label{fig:detail_instrumentation_dac_setup}Measurement of the DAC output voltage noise. A pre-amplifier with a gain of 1000 is used before measuring the signal with the ADC.} \end{figure} The obtained Amplitude Spectral Density of the DAC's output voltage is shown in Figure \ref{fig:detail_instrumentation_dac_output_noise}. @@ -675,21 +690,23 @@ It corresponds to 1 sample delay (Figure \ref{fig:detail_instrumentation_dac_adc \begin{center} \includegraphics[scale=1,width=0.95\linewidth]{figs/detail_instrumentation_dac_output_noise.png} \end{center} -\subcaption{\label{fig:detail_instrumentation_dac_output_noise}sub caption a} +\subcaption{\label{fig:detail_instrumentation_dac_output_noise}Output noise of the DAC} \end{subfigure} \begin{subfigure}{0.48\textwidth} \begin{center} \includegraphics[scale=1,width=0.95\linewidth]{figs/detail_instrumentation_dac_adc_tf.png} \end{center} -\subcaption{\label{fig:detail_instrumentation_dac_adc_tf}sub caption b} +\subcaption{\label{fig:detail_instrumentation_dac_adc_tf}Transfer function from DAC to ADC} \end{subfigure} -\caption{\label{fig:detail_instrumentation_dac}Measure transfer function from DAC to ADC - It fits a pure ``1-sample'' delay (\subref{fig:fig_label_a})} +\caption{\label{fig:detail_instrumentation_dac}Measurement of the output voltage noise of the ADC (\subref{fig:detail_instrumentation_dac_output_noise}) and measured transfer function from DAC to ADC (\subref{fig:detail_instrumentation_dac_adc_tf}) which corresponds to a ``1-sample'' delay.} \end{figure} \section{Piezoelectric Voltage Amplifier} +\label{sec:orgd93524f} \paragraph{Output Voltage Noise} +\label{sec:orgc975b4b} The measurement setup is shown in Figure \ref{fig:detail_instrumentation_pd200_setup}. The input of the PD200 amplifier is shunted with a 50 Ohm resistor such that there in no voltage input expected the PD200 input voltage noise. The gain of the pre-amplifier is increased in order to measure a signal much larger than the quantization noise of the ADC. @@ -699,35 +716,9 @@ Two piezoelectric stacks of the APA95ML are connected to the PD200 output to hav \begin{figure}[htbp] \centering \includegraphics[scale=1]{figs/detail_instrumentation_pd200_setup.png} -\caption{\label{fig:detail_instrumentation_pd200_setup}Sources of noise in the experimental setup} +\caption{\label{fig:detail_instrumentation_pd200_setup}Setup used to measured the output voltage noise of the PD200 voltage amplifier. A gain \(G_a = 1000\) was used for the instrumentation amplifier.} \end{figure} -The measured low frequency (<20Hz) \textbf{output} noise of one of the PD200 amplifiers is shown in Figure \ref{fig:pd200_noise_time_lpf}. -It is very similar to the one specified in the datasheet in Figure \ref{fig:pd200_expected_noise}. - -\begin{figure}[htbp] -\centering -\includegraphics[scale=1]{figs/pd200_noise_time_lpf.png} -\caption{\label{fig:pd200_noise_time_lpf}Measured low frequency noise of the PD200 from 0.01Hz to 20Hz} -\end{figure} - -The obtained RMS and peak to peak values of the measured \textbf{output} noise are shown in Table \ref{tab:rms_pkp_noise} and found to be very similar to the specified ones. - -\begin{center} -\begin{tabular}{lrr} - & \textbf{RMS [\(\mu V\)]} & \textbf{Peak to Peak [\(mV\)]}\\ -\hline -Specification [\(10\,\mu F\)] & 714.0 & 4.3\\ -PD200 1 & 565.1 & 3.7\\ -PD200 2 & 767.6 & 3.5\\ -PD200 3 & 479.9 & 3.0\\ -PD200 4 & 615.7 & 3.5\\ -PD200 5 & 651.0 & 2.4\\ -PD200 6 & 473.2 & 2.7\\ -PD200 7 & 423.1 & 2.3\\ -\end{tabular} -\end{center} - The Amplitude Spectral Density \(\Gamma_n(\omega)\) of the measured signal by the ADC is computed. The Amplitude Spectral Density of the input voltage noise of the PD200 amplifier \(n_p\) is then computed taking into account the gain of the pre-amplifier and the gain of the PD200 amplifier: \begin{equation} @@ -739,7 +730,7 @@ And we verify that we are indeed measuring the noise of the PD200 and not the no \Gamma_{n_p}(\omega) |G_p(j\omega)| \ll \Gamma_{n_a} \end{equation} -The Amplitude Spectral Density of the measured \textbf{input} noise is computed and shown in Figure \ref{fig:asd_noise_pd200_10uF}. +The Amplitude Spectral Density of the measured \textbf{input} noise is computed and shown in Figure \ref{fig:detail_instrumentation_pd200_noise}. It is verified that the contribution of the PD200 noise is much larger than the contribution of the pre-amplifier noise of the quantization noise. @@ -753,6 +744,7 @@ It is not clear yet what causes such peaks and if these peaks have high influenc \end{figure} \paragraph{Small Signal Bandwidth} +\label{sec:orgff5c292} Here the small signal dynamics of all the PD200 amplifiers are identified. @@ -762,20 +754,19 @@ The output voltage of the PD200 amplifier is measured thanks to the monitor volt The input voltage of the PD200 amplifier (the generated voltage by the DAC) is measured with another ADC of the Speedgoat. This way, the time delay related to the ADC will not be apparent in the results. -The obtained transfer functions from \(V_{in}\) to \(V_{out}\) are shown in Figure \ref{fig:pd200_small_signal_tf}. - -\begin{figure}[htbp] -\centering -\includegraphics[scale=1]{figs/pd200_small_signal_tf.png} -\caption{\label{fig:pd200_small_signal_tf}Identified dynamics from input voltage to output voltage} -\end{figure} - We can see the very well matching between all the 7 amplifiers. The amplitude is constant over a wide frequency band and the phase drop is limited to less than 1 degree up to 500Hz. -The identified dynamics in Figure \ref{fig:pd200_small_signal_tf} can very well be modeled this dynamics with a first order low pass filter (even a constant could work fine). +The identified dynamics in Figure \ref{fig:detail_instrumentation_pd200_tf} can very well be modeled this dynamics with a first order low pass filter (even a constant could work fine). + +\begin{figure}[htbp] +\centering +\includegraphics[scale=1]{figs/detail_instrumentation_pd200_tf.png} +\caption{\label{fig:detail_instrumentation_pd200_tf}Identified dynamics from input voltage to output voltage} +\end{figure} \paragraph{Output Impedance} +\label{sec:orgb2297c8} The goal of this experimental setup is to estimate the output impedance \(R_\text{out}\) of the PD200 voltage amplifiers. A DAC with a constant output voltage (here 0.1V) is connected to the input of the PD200 amplifier. @@ -800,28 +791,30 @@ With the capacitive load \(C_p = 8.8\,\mu F\), the output resistor of the amplif We get a corner frequency around \(10\,\text{kHz}\) which is not far from the specified \(7.4\,\text{kHz}\). \paragraph{Conclusion} +\label{sec:org1118cdb} \begin{table}[htbp] \caption{\label{tab:table_name}Measured characteristics, Manual characterstics and specified ones} \centering -\begin{tabularx}{\linewidth}{lXXX} +\begin{tabularx}{\linewidth}{Xcc} \toprule -\textbf{Characteristics} & \textbf{Measurement} & \textbf{Manual} & \textbf{Specification}\\ +\textbf{Characteristics} & \textbf{Specification} & \textbf{Measurement}\\ \midrule -Input Voltage Range & - & +/- 10 [V] & +/- 10 [V]\\ -Output Voltage Range & - & -50/150 [V] & -20/150 [V]\\ -Gain & & 20 [V/V] & -\\ -Maximum RMS current & & 0.9 [A] & > 50 [mA]\\ -Maximum Pulse current & & 10 [A] & -\\ -Slew Rate & & 150 [V/us] & -\\ -Noise (10uF load) & & 0.7 [mV RMS] & < 2 [mV rms]\\ -Small Signal Bandwidth (10uF load) & & 7.4 [kHz] & > 5 [kHz]\\ -Large Signal Bandwidth (150V, 10uF) & & 300 [Hz] & -\\ +Input Voltage Range & +/- 10 [V] & -\\ +Output Voltage Range & -20/150 [V] & -\\ +Gain & 20 & 20\\ +Maximum RMS current & > 50 [mA] & \\ +Maximum Pulse current & - & \\ +Slew Rate & - & \\ +Noise (10uF load) & < 2 [mV rms] & \\ +Small Signal Bandwidth (10uF load) & > 5 [kHz] & \\ +Large Signal Bandwidth (150V, 10uF) & - & \\ \bottomrule \end{tabularx} \end{table} \section{Linear Encoders} +\label{sec:orgddea30b} To measure the noise \(n\) of the encoder, one can rigidly fix the head and the ruler together such that no motion should be measured. Then, the measured signal \(y_m\) corresponds to the noise \(n\). @@ -829,39 +822,38 @@ Then, the measured signal \(y_m\) corresponds to the noise \(n\). The measurement bench is shown in Figures \ref{fig:meas_bench_top_view} and \ref{fig:meas_bench_side_view}. Note that the bench is then covered with a ``plastic bubble sheet'' in order to keep disturbances as small as possible. -\begin{figure}[htbp] -\centering -\includegraphics[scale=1,width=0.8\linewidth]{figs/IMG_20210211_170554.jpg} -\caption{\label{fig:meas_bench_top_view}Top view picture of the measurement bench} -\end{figure} - -\begin{figure}[htbp] -\centering -\includegraphics[scale=1,width=0.8\linewidth]{figs/IMG_20210211_170607.jpg} -\caption{\label{fig:meas_bench_side_view}Side view picture of the measurement bench} -\end{figure} - Then, and for all the 7 encoders, we record the measured motion during 100s with a sampling frequency of 20kHz. -\section{External Metrology} - -\href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/test-bench-attocube/test-bench-attocube.org}{test-bench-attocube} - -Different options: -\begin{itemize} -\item Attocube: issue of non-linearity estimated from the encoders -\item Smaract -\item QuDIS -\end{itemize} - -For the final tests, QuDIS were used. - \section{Conclusion} +\label{sec:orgc63ce3f} + +\begin{itemize} +\item[{$\square$}] Compare with measurement noise? or effect of measurement noise => higher so it's OK? +\item[{$\square$}] Or compare with specifications? (but we don't have specifications for ASD, only RMS) +\item[{$\square$}] Or maybe put the ASD of the measured vibration in simulation (or noise budget based on disturbances) => show that we are bellow disturbances so it should not be limited +\end{itemize} From all the measured noises, compute the obtained PSD error in Y and Z (show PSD of individual + Sum + Cumulative?) +\begin{figure}[htbp] +\centering +\includegraphics[scale=1]{figs/detail_instrumentation_cl_noise_budget.png} +\caption{\label{fig:detail_instrumentation_cl_noise_budget}Closed-loop noise budgeting using measured noise of instrumentation} +\end{figure} + \chapter*{Conclusion} +\label{sec:org9929878} \label{sec:detail_instrumentation_conclusion} +\begin{itemize} +\item thanks to multi-body model in which it is easy to include instrumentation and noise sources +From specification on the sample's vertical motion (most stringent requirement), specification for each noise source was extracted. +\item based on those specifications, adequate instrumentation were chosen. +for some instrumentation, it was difficult to choose only based on data-sheets are manufacturers often don't share relevant information for noise budgets, such as amplitude spectral densities +\item then, the instrumentation was procured and tested individually. +All were found to comply with the requirements. +Finally, based on the measured noise of all instrumentation, the expected sample's vibration induced by all the noise sources was estimated and found to comply with the requirements. +\end{itemize} + \printbibliography[heading=bibintoc,title={Bibliography}] \end{document}