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@ -352,7 +352,7 @@ Khac = -5e4 * ... % Gain
* Introduction :ignore: * Introduction :ignore:
This chapter presents an approach to selecting and validating appropriate instrumentation for the Nano Active Stabilization System (NASS), ensuring each component meets specific performance requirements. This chapter presents an approach to select and validate appropriate instrumentation for the Nano Active Stabilization System (NASS), ensuring each component meets specific performance requirements.
Figure ref:fig:detail_instrumentation_plant illustrates the control diagram with all relevant noise sources whose effects on sample position will be evaluated throughout this analysis. Figure ref:fig:detail_instrumentation_plant illustrates the control diagram with all relevant noise sources whose effects on sample position will be evaluated throughout this analysis.
The selection process follows a three-stage methodology. The selection process follows a three-stage methodology.
@ -598,9 +598,7 @@ The DAC, ADC, and amplifier noise are considered uncorrelated, which is a reason
Similarly, the noise sources corresponding to each strut are also assumed to be uncorrelated. Similarly, the noise sources corresponding to each strut are also assumed to be uncorrelated.
This means that the power spectral densities (PSD) of the different noise sources are summed. This means that the power spectral densities (PSD) of the different noise sources are summed.
The system symmetry has been utilized to further simplify the analysis. Since the effect of each strut on the vertical error is identical due to symmetry, only one strut is considered for this analysis, and the total effect of the six struts is calculated as six times the effect of one strut in terms of power, which translates to a factor of $\sqrt{6} \approx 2.5$ for RMS values.
The effect of all struts on the vertical errors is identical, as verified from the extracted sensitivity curves.
Therefore, only one strut is considered for this analysis, and the total effect of the six struts is calculated as six times the effect of one strut in terms of power, which translates to a factor of $\sqrt{6} \approx 2.5$ for RMS values.
In order to derive specifications in terms of noise spectral density for each instrumentation component, a white noise profile is assumed, which is typical for these components. In order to derive specifications in terms of noise spectral density for each instrumentation component, a white noise profile is assumed, which is typical for these components.
@ -655,12 +653,6 @@ save('./mat/instrumentation_requirements.mat', ...
:HEADER-ARGS:matlab+: :tangle matlab/detail_instrumentation_2_choice.m :HEADER-ARGS:matlab+: :tangle matlab/detail_instrumentation_2_choice.m
:END: :END:
<<sec:detail_instrumentation_choice>> <<sec:detail_instrumentation_choice>>
** Introduction :ignore:
The selection of appropriate instrumentation components was based on the noise specifications derived in Section ref:sec:detail_instrumentation_dynamic_error_budgeting and other relevant specifications that will be further developed.
This section presents the evaluation process for ADCs, DACs, voltage amplifiers, and relative positioning sensors, detailing the comparison between different options and justifying the final selections.
** Matlab Init :noexport:ignore: ** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>> <<matlab-dir>>
@ -691,7 +683,7 @@ load('instrumentation_requirements.mat')
**** Introduction :ignore: **** Introduction :ignore:
Several characteristics of piezoelectric voltage amplifiers must be considered for this application. Several characteristics of piezoelectric voltage amplifiers must be considered for this application.
To utilize the full stroke of the piezoelectric actuator, the voltage output should range between $-20$ and $150\,V$. To take advantage of the full stroke of the piezoelectric actuator, the voltage output should range between $-20$ and $150\,V$.
The amplifier should accept an analog input voltage, preferably in the range of $-10$ to $10\,V$, as this is standard for most DACs. The amplifier should accept an analog input voltage, preferably in the range of $-10$ to $10\,V$, as this is standard for most DACs.
**** Small signal Bandwidth and Output Impedance **** Small signal Bandwidth and Output Impedance
@ -983,10 +975,6 @@ The specifications of the considered relative motion sensor, the Renishaw Vionic
:HEADER-ARGS:matlab+: :tangle matlab/detail_instrumentation_3_characterization.m :HEADER-ARGS:matlab+: :tangle matlab/detail_instrumentation_3_characterization.m
:END: :END:
<<sec:detail_instrumentation_characterization>> <<sec:detail_instrumentation_characterization>>
** Introduction :ignore:
Following the procurement of all instrumentation components, individual testing was conducted to verify their compliance with the specified requirements.
** Matlab Init :noexport:ignore: ** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>> <<matlab-dir>>
@ -1308,7 +1296,7 @@ A Femto DLPVA-101-B-S amplifier with adjustable gains from 20dB up to 80dB was s
The first step was to characterize the input[fn:detail_instrumentation_2] noise of the amplifier. The first step was to characterize the input[fn:detail_instrumentation_2] noise of the amplifier.
This was accomplished by short-circuiting its input with a $50\,\Omega$ resistor and measuring the output voltage with the ADC (Figure ref:fig:detail_instrumentation_femto_meas_setup). This was accomplished by short-circuiting its input with a $50\,\Omega$ resistor and measuring the output voltage with the ADC (Figure ref:fig:detail_instrumentation_femto_meas_setup).
The maximum amplifier gain of 80dB (equivalent to 10000) was utilized for this measurement. The maximum amplifier gain of 80dB (equivalent to 10000) was used for this measurement.
The measured voltage $n$ was then divided by 10000 to determine the equivalent noise at the input of the voltage amplifier $n_a$. The measured voltage $n$ was then divided by 10000 to determine the equivalent noise at the input of the voltage amplifier $n_a$.
In this configuration, the noise contribution from the ADC $q_{ad}$ is rendered negligible due to the high gain employed. In this configuration, the noise contribution from the ADC $q_{ad}$ is rendered negligible due to the high gain employed.
@ -1818,7 +1806,7 @@ exportFig('figs/detail_instrumentation_pd200_tf.pdf', 'width', 'wide', 'height',
** Linear Encoders ** Linear Encoders
To measure the noise of the encoder, the head and ruler were rigidly fixed together to ensure that no actual motion would be detected. To measure the noise of the encoder, the head and ruler were rigidly fixed together to ensure that no relative motion would be detected.
Under these conditions, any measured signal would correspond solely to the encoder noise. Under these conditions, any measured signal would correspond solely to the encoder noise.
The measurement setup is shown in Figure ref:fig:detail_instrumentation_vionic_bench. The measurement setup is shown in Figure ref:fig:detail_instrumentation_vionic_bench.
@ -1948,7 +1936,7 @@ exportFig('figs/detail_instrumentation_cl_noise_budget.pdf', 'width', 'wide', 'h
<<sec:detail_instrumentation_conclusion>> <<sec:detail_instrumentation_conclusion>>
This section has presented a comprehensive approach to the selection and characterization of instrumentation for the nano active stabilization system. This section has presented a comprehensive approach to the selection and characterization of instrumentation for the nano active stabilization system.
The multi-body model developed earlier proved invaluable for incorporating instrumentation components and their associated noise sources into the system analysis. The multi-body model created earlier served as a key tool for embedding instrumentation components and their associated noise sources within the system analysis.
From the most stringent requirement (i.e. the specification on vertical sample motion limited to 15 nm RMS), detailed specifications for each noise source were methodically derived through dynamic error budgeting. From the most stringent requirement (i.e. the specification on vertical sample motion limited to 15 nm RMS), detailed specifications for each noise source were methodically derived through dynamic error budgeting.
Based on these specifications, appropriate instrumentation components were selected for the system. Based on these specifications, appropriate instrumentation components were selected for the system.
@ -1960,7 +1948,7 @@ Initial measurements of the ADC system revealed an issue with force sensor reado
All components were found to meet or exceed their respective specifications. The ADC demonstrated noise levels of $5.6\,\mu V/\sqrt{\text{Hz}}$ (versus the $11\,\mu V/\sqrt{\text{Hz}}$ specification), the DAC showed $0.6\,\mu V/\sqrt{\text{Hz}}$ (versus $14\,\mu V/\sqrt{\text{Hz}}$ required), the voltage amplifiers exhibited noise well below the $280\,\mu V/\sqrt{\text{Hz}}$ limit, and the encoders achieved $1\,\text{nm RMS}$ noise (versus the $6\,\text{nm RMS}$ specification). All components were found to meet or exceed their respective specifications. The ADC demonstrated noise levels of $5.6\,\mu V/\sqrt{\text{Hz}}$ (versus the $11\,\mu V/\sqrt{\text{Hz}}$ specification), the DAC showed $0.6\,\mu V/\sqrt{\text{Hz}}$ (versus $14\,\mu V/\sqrt{\text{Hz}}$ required), the voltage amplifiers exhibited noise well below the $280\,\mu V/\sqrt{\text{Hz}}$ limit, and the encoders achieved $1\,\text{nm RMS}$ noise (versus the $6\,\text{nm RMS}$ specification).
Finally, the measured noise characteristics of all instrumentation components were incorporated into the multi-body model to predict the actual system performance. Finally, the measured noise characteristics of all instrumentation components were included into the multi-body model to predict the actual system performance.
The combined effect of all noise sources was estimated to induce vertical sample vibrations of only $1.5\,\text{nm RMS}$, which is substantially below the $15\,\text{nm RMS}$ requirement. The combined effect of all noise sources was estimated to induce vertical sample vibrations of only $1.5\,\text{nm RMS}$, which is substantially below the $15\,\text{nm RMS}$ requirement.
This rigorous methodology spanning requirement formulation, component selection, and experimental characterization validates the instrumentation's ability to fulfill the nano active stabilization system's demanding performance specifications. This rigorous methodology spanning requirement formulation, component selection, and experimental characterization validates the instrumentation's ability to fulfill the nano active stabilization system's demanding performance specifications.

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@ -1,4 +1,4 @@
% Created 2025-03-17 Mon 22:15 % Created 2025-04-06 Sun 18:12
% Intended LaTeX compiler: pdflatex % Intended LaTeX compiler: pdflatex
\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt} \documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
@ -13,7 +13,7 @@
pdftitle={Nano Active Stabilization System - Instrumentation}, pdftitle={Nano Active Stabilization System - Instrumentation},
pdfkeywords={}, pdfkeywords={},
pdfsubject={}, pdfsubject={},
pdfcreator={Emacs 29.4 (Org mode 9.6)}, pdfcreator={Emacs 30.1 (Org mode 9.7.26)},
pdflang={English}} pdflang={English}}
\usepackage{biblatex} \usepackage{biblatex}
@ -23,8 +23,7 @@
\tableofcontents \tableofcontents
\clearpage \clearpage
This chapter presents an approach to select and validate appropriate instrumentation for the Nano Active Stabilization System (NASS), ensuring each component meets specific performance requirements.
This chapter presents an approach to selecting and validating appropriate instrumentation for the Nano Active Stabilization System (NASS), ensuring each component meets specific performance requirements.
Figure \ref{fig:detail_instrumentation_plant} illustrates the control diagram with all relevant noise sources whose effects on sample position will be evaluated throughout this analysis. Figure \ref{fig:detail_instrumentation_plant} illustrates the control diagram with all relevant noise sources whose effects on sample position will be evaluated throughout this analysis.
The selection process follows a three-stage methodology. The selection process follows a three-stage methodology.
@ -43,7 +42,6 @@ The measured noise characteristics are then incorporated into the multi-body mod
\includegraphics[scale=1]{figs/detail_instrumentation_plant.png} \includegraphics[scale=1]{figs/detail_instrumentation_plant.png}
\caption{\label{fig:detail_instrumentation_plant}Block diagram of the NASS with considered instrumentation. The RT controller is a Speedgoat machine.} \caption{\label{fig:detail_instrumentation_plant}Block diagram of the NASS with considered instrumentation. The RT controller is a Speedgoat machine.}
\end{figure} \end{figure}
\chapter{Dynamic Error Budgeting} \chapter{Dynamic Error Budgeting}
\label{sec:detail_instrumentation_dynamic_error_budgeting} \label{sec:detail_instrumentation_dynamic_error_budgeting}
The primary goal of this analysis is to establish specifications for the maximum allowable noise levels of the instrumentation used for the NASS (ADC, DAC, and voltage amplifier) that would result in acceptable vibration levels in the system. The primary goal of this analysis is to establish specifications for the maximum allowable noise levels of the instrumentation used for the NASS (ADC, DAC, and voltage amplifier) that would result in acceptable vibration levels in the system.
@ -69,7 +67,6 @@ The transfer functions from these three noise sources (for one strut) to the ver
\includegraphics[scale=1]{figs/detail_instrumentation_noise_sensitivities.png} \includegraphics[scale=1]{figs/detail_instrumentation_noise_sensitivities.png}
\caption{\label{fig:detail_instrumentation_noise_sensitivities}Transfer function from noise sources to vertical motion errors, in closed-loop with the implemented HAC-LAC strategy.} \caption{\label{fig:detail_instrumentation_noise_sensitivities}Transfer function from noise sources to vertical motion errors, in closed-loop with the implemented HAC-LAC strategy.}
\end{figure} \end{figure}
\section{Estimation of maximum instrumentation noise} \section{Estimation of maximum instrumentation noise}
\label{ssec:detail_instrumentation_max_noise_specs} \label{ssec:detail_instrumentation_max_noise_specs}
@ -80,9 +77,7 @@ The DAC, ADC, and amplifier noise are considered uncorrelated, which is a reason
Similarly, the noise sources corresponding to each strut are also assumed to be uncorrelated. Similarly, the noise sources corresponding to each strut are also assumed to be uncorrelated.
This means that the power spectral densities (PSD) of the different noise sources are summed. This means that the power spectral densities (PSD) of the different noise sources are summed.
The system symmetry has been utilized to further simplify the analysis. Since the effect of each strut on the vertical error is identical due to symmetry, only one strut is considered for this analysis, and the total effect of the six struts is calculated as six times the effect of one strut in terms of power, which translates to a factor of \(\sqrt{6} \approx 2.5\) for RMS values.
The effect of all struts on the vertical errors is identical, as verified from the extracted sensitivity curves.
Therefore, only one strut is considered for this analysis, and the total effect of the six struts is calculated as six times the effect of one strut in terms of power, which translates to a factor of \(\sqrt{6} \approx 2.5\) for RMS values.
In order to derive specifications in terms of noise spectral density for each instrumentation component, a white noise profile is assumed, which is typical for these components. In order to derive specifications in terms of noise spectral density for each instrumentation component, a white noise profile is assumed, which is typical for these components.
@ -93,17 +88,12 @@ Based on this analysis, the obtained maximum noise levels are as follows: DAC ma
In terms of RMS noise, these translate to less than \(1\,\text{mV RMS}\) for the DAC, less than \(20\,\text{mV RMS}\) for the voltage amplifier, and less than \(0.8\,\text{mV RMS}\) for the ADC. In terms of RMS noise, these translate to less than \(1\,\text{mV RMS}\) for the DAC, less than \(20\,\text{mV RMS}\) for the voltage amplifier, and less than \(0.8\,\text{mV RMS}\) for the ADC.
If the Amplitude Spectral Density of the noise of the ADC, DAC, and voltage amplifiers all remain below these specified maximum levels, then the induced vertical error will be maintained below 15nm RMS. If the Amplitude Spectral Density of the noise of the ADC, DAC, and voltage amplifiers all remain below these specified maximum levels, then the induced vertical error will be maintained below 15nm RMS.
\chapter{Choice of Instrumentation} \chapter{Choice of Instrumentation}
\label{sec:detail_instrumentation_choice} \label{sec:detail_instrumentation_choice}
The selection of appropriate instrumentation components was based on the noise specifications derived in Section \ref{sec:detail_instrumentation_dynamic_error_budgeting} and other relevant specifications that will be further developed.
This section presents the evaluation process for ADCs, DACs, voltage amplifiers, and relative positioning sensors, detailing the comparison between different options and justifying the final selections.
\section{Piezoelectric Voltage Amplifier} \section{Piezoelectric Voltage Amplifier}
Several characteristics of piezoelectric voltage amplifiers must be considered for this application. Several characteristics of piezoelectric voltage amplifiers must be considered for this application.
To utilize the full stroke of the piezoelectric actuator, the voltage output should range between \(-20\) and \(150\,V\). To take advantage of the full stroke of the piezoelectric actuator, the voltage output should range between \(-20\) and \(150\,V\).
The amplifier should accept an analog input voltage, preferably in the range of \(-10\) to \(10\,V\), as this is standard for most DACs. The amplifier should accept an analog input voltage, preferably in the range of \(-10\) to \(10\,V\), as this is standard for most DACs.
\paragraph{Small signal Bandwidth and Output Impedance} \paragraph{Small signal Bandwidth and Output Impedance}
Small signal bandwidth is particularly important for feedback applications as it can limit the overall bandwidth of the complete feedback system. Small signal bandwidth is particularly important for feedback applications as it can limit the overall bandwidth of the complete feedback system.
@ -126,7 +116,6 @@ When combined with the piezoelectric load (represented as a capacitance \(C_p\))
Consequently, the small signal bandwidth depends on the load capacitance and decreases as the load capacitance increases. Consequently, the small signal bandwidth depends on the load capacitance and decreases as the load capacitance increases.
For the APA300ML, the capacitive load of the two piezoelectric stacks corresponds to \(C_p = 8.8\,\mu F\). For the APA300ML, the capacitive load of the two piezoelectric stacks corresponds to \(C_p = 8.8\,\mu F\).
If a small signal bandwidth of \(f_0 = \frac{\omega_0}{2\pi} = 5\,\text{kHz}\) is desired, the voltage amplifier output impedance should be less than \(R_0 = 3.6\,\Omega\). If a small signal bandwidth of \(f_0 = \frac{\omega_0}{2\pi} = 5\,\text{kHz}\) is desired, the voltage amplifier output impedance should be less than \(R_0 = 3.6\,\Omega\).
\paragraph{Large signal Bandwidth} \paragraph{Large signal Bandwidth}
Large signal bandwidth relates to the maximum output capabilities of the amplifier in terms of amplitude as a function of frequency. Large signal bandwidth relates to the maximum output capabilities of the amplifier in terms of amplitude as a function of frequency.
@ -144,7 +133,6 @@ The maximum required current can be calculated as \(I_{\text{max}} = 2 \cdot V_{
\end{enumerate} \end{enumerate}
Therefore, ideally, a voltage amplifier capable of providing \(0.3\,A\) of current would be interesting for scanning applications. Therefore, ideally, a voltage amplifier capable of providing \(0.3\,A\) of current would be interesting for scanning applications.
\paragraph{Output voltage noise} \paragraph{Output voltage noise}
As established in Section \ref{sec:detail_instrumentation_dynamic_error_budgeting}, the output noise of the voltage amplifier should be below \(20\,\text{mV RMS}\). As established in Section \ref{sec:detail_instrumentation_dynamic_error_budgeting}, the output noise of the voltage amplifier should be below \(20\,\text{mV RMS}\).
@ -153,7 +141,6 @@ It should be noted that the load capacitance of the piezoelectric stack filters
Therefore, when comparing noise specifications from different voltage amplifier datasheets, it is essential to verify the capacitance of the load used during the measurement \cite{spengen20_high_voltag_amplif}. Therefore, when comparing noise specifications from different voltage amplifier datasheets, it is essential to verify the capacitance of the load used during the measurement \cite{spengen20_high_voltag_amplif}.
For this application, the output noise must remain below \(20\,\text{mV RMS}\) with a load of \(8.8\,\mu F\) and a bandwidth exceeding \(5\,\text{kHz}\). For this application, the output noise must remain below \(20\,\text{mV RMS}\) with a load of \(8.8\,\mu F\) and a bandwidth exceeding \(5\,\text{kHz}\).
\paragraph{Choice of voltage amplifier} \paragraph{Choice of voltage amplifier}
The specifications are summarized in Table \ref{tab:detail_instrumentation_amp_choice}. The specifications are summarized in Table \ref{tab:detail_instrumentation_amp_choice}.
@ -188,19 +175,16 @@ Small Signal Bandwidth \(> 5\,kHz\) & \(6.4\,kHz\) & \(300\,Hz\) & \(30\,kHz\)
Output Impedance: \(< 3.6\,\Omega\) & n/a & \(50\,\Omega\) & n/a & n/a\\ Output Impedance: \(< 3.6\,\Omega\) & n/a & \(50\,\Omega\) & n/a & n/a\\
\bottomrule \bottomrule
\end{tabularx} \end{tabularx}
\end{table}\footnotetext[1]{\label{orge65a0e3}The manufacturer proposed to remove the \(50\,\Omega\) output resistor to improve to small signal bandwidth above \(10\,kHz\)} \end{table}\footnotetext[1]{\label{org835cd7f}The manufacturer proposed to remove the \(50\,\Omega\) output resistor to improve to small signal bandwidth above \(10\,kHz\)}
\section{ADC and DAC} \section{ADC and DAC}
Analog-to-digital converters and digital-to-analog converters play key roles in the system, serving as the interface between the digital RT controller and the analog physical plant. Analog-to-digital converters and digital-to-analog converters play key roles in the system, serving as the interface between the digital RT controller and the analog physical plant.
The proper selection of these components is critical for system performance. The proper selection of these components is critical for system performance.
\paragraph{Synchronicity and Jitter} \paragraph{Synchronicity and Jitter}
For control systems, synchronous sampling of inputs and outputs of the real-time controller and minimal jitter are essential requirements \cite{abramovitch22_pract_method_real_world_contr_system,abramovitch23_tutor_real_time_comput_issues_contr_system}. For control systems, synchronous sampling of inputs and outputs of the real-time controller and minimal jitter are essential requirements \cite{abramovitch22_pract_method_real_world_contr_system,abramovitch23_tutor_real_time_comput_issues_contr_system}.
Therefore, the ADC and DAC must be well interfaced with the Speedgoat real-time controller and triggered synchronously with the computation of the control signals. Therefore, the ADC and DAC must be well interfaced with the Speedgoat real-time controller and triggered synchronously with the computation of the control signals.
Based on this requirement, priority was given to ADC and DAC components specifically marketed by Speedgoat to ensure optimal integration. Based on this requirement, priority was given to ADC and DAC components specifically marketed by Speedgoat to ensure optimal integration.
\paragraph{Sampling Frequency, Bandwidth and delays} \paragraph{Sampling Frequency, Bandwidth and delays}
Several requirements that may initially appear similar are actually distinct in nature. Several requirements that may initially appear similar are actually distinct in nature.
@ -214,7 +198,6 @@ Typically, the latency can reach 20 times the sampling period \cite[, chapt. 8.4
Consequently, while Sigma-Delta ADCs are widely used for signal acquisition applications, they have limited utility in real-time control scenarios where latency is a critical factor. Consequently, while Sigma-Delta ADCs are widely used for signal acquisition applications, they have limited utility in real-time control scenarios where latency is a critical factor.
For real-time control applications, SAR-ADCs (Successive Approximation ADCs) remain the predominant choice due to their single-sample latency characteristics. For real-time control applications, SAR-ADCs (Successive Approximation ADCs) remain the predominant choice due to their single-sample latency characteristics.
\paragraph{ADC Noise} \paragraph{ADC Noise}
Based on the dynamic error budget established in Section \ref{sec:detail_instrumentation_dynamic_error_budgeting}, the measurement noise ASD should not exceed \(11\,\mu V/\sqrt{\text{Hz}}\). Based on the dynamic error budget established in Section \ref{sec:detail_instrumentation_dynamic_error_budgeting}, the measurement noise ASD should not exceed \(11\,\mu V/\sqrt{\text{Hz}}\).
@ -257,12 +240,10 @@ From a specified noise amplitude spectral density \(\Gamma_{\text{max}}\), the m
\end{equation} \end{equation}
With a sampling frequency \(F_s = 10\,\text{kHz}\), an input range \(\Delta V = 20\,V\) and a maximum allowed ASD \(\Gamma_{\text{max}} = 11\,\mu V/\sqrt{Hz}\), the minimum number of bits is \(n_{\text{min}} = 12.4\), which is readily achievable with commercial ADCs. With a sampling frequency \(F_s = 10\,\text{kHz}\), an input range \(\Delta V = 20\,V\) and a maximum allowed ASD \(\Gamma_{\text{max}} = 11\,\mu V/\sqrt{Hz}\), the minimum number of bits is \(n_{\text{min}} = 12.4\), which is readily achievable with commercial ADCs.
\paragraph{DAC Output voltage noise} \paragraph{DAC Output voltage noise}
Similar to the ADC requirements, the DAC output voltage noise ASD should not exceed \(14\,\mu V/\sqrt{\text{Hz}}\). Similar to the ADC requirements, the DAC output voltage noise ASD should not exceed \(14\,\mu V/\sqrt{\text{Hz}}\).
This specification corresponds to a \(\pm 10\,V\) DAC with 13-bit resolution, which is easily attainable with current technology. This specification corresponds to a \(\pm 10\,V\) DAC with 13-bit resolution, which is easily attainable with current technology.
\paragraph{Choice of the ADC and DAC Board} \paragraph{Choice of the ADC and DAC Board}
Based on the preceding analysis, the selection of suitable ADC and DAC components is straightforward. Based on the preceding analysis, the selection of suitable ADC and DAC components is straightforward.
@ -273,7 +254,6 @@ The board also includes 8 analog outputs based on the AD5754R with 16-bit resolu
Although noise specifications are not explicitly provided in the datasheet, the 16-bit resolution should ensure performance well below the established requirements. Although noise specifications are not explicitly provided in the datasheet, the 16-bit resolution should ensure performance well below the established requirements.
This will be experimentally verified in Section \ref{sec:detail_instrumentation_characterization}. This will be experimentally verified in Section \ref{sec:detail_instrumentation_characterization}.
\section{Relative Displacement Sensors} \section{Relative Displacement Sensors}
The specifications for the relative displacement sensors include sufficient compactness for integration within each strut, noise levels below \(6\,\text{nm RMS}\) (derived from the \(15\,\text{nm RMS}\) vertical error requirement for the system divided by the contributions of six struts), and a measurement range exceeding \(100\,\mu m\). The specifications for the relative displacement sensors include sufficient compactness for integration within each strut, noise levels below \(6\,\text{nm RMS}\) (derived from the \(15\,\text{nm RMS}\) vertical error requirement for the system divided by the contributions of six struts), and a measurement range exceeding \(100\,\mu m\).
@ -345,10 +325,8 @@ Digital Output & \(\times\) & & \\
\bottomrule \bottomrule
\end{tabularx} \end{tabularx}
\end{table} \end{table}
\chapter{Characterization of Instrumentation} \chapter{Characterization of Instrumentation}
\label{sec:detail_instrumentation_characterization} \label{sec:detail_instrumentation_characterization}
Following the procurement of all instrumentation components, individual testing was conducted to verify their compliance with the specified requirements.
\section{Analog to Digital Converters} \section{Analog to Digital Converters}
\paragraph{Measured Noise} \paragraph{Measured Noise}
@ -367,7 +345,6 @@ This approach is effective because the noise approximates white noise and its am
\includegraphics[scale=1]{figs/detail_instrumentation_adc_noise_measured.png} \includegraphics[scale=1]{figs/detail_instrumentation_adc_noise_measured.png}
\caption{\label{fig:detail_instrumentation_adc_noise_measured}Measured ADC noise (IO318)} \caption{\label{fig:detail_instrumentation_adc_noise_measured}Measured ADC noise (IO318)}
\end{figure} \end{figure}
\paragraph{Reading of piezoelectric force sensor} \paragraph{Reading of piezoelectric force sensor}
To further validate the ADC's capability to effectively measure voltage generated by a piezoelectric stack, a test was conducted using the APA95ML. To further validate the ADC's capability to effectively measure voltage generated by a piezoelectric stack, a test was conducted using the APA95ML.
@ -436,7 +413,6 @@ These results validate both the model of the ADC and the effectiveness of the ad
\end{subfigure} \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}).} \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} \end{figure}
\section{Instrumentation Amplifier} \section{Instrumentation Amplifier}
Because the ADC noise may be too low to measure the noise of other instruments (anything below \(5.6\,\mu V/\sqrt{\text{Hz}}\) cannot be distinguished from the noise of the ADC itself), a low noise instrumentation amplifier was employed. Because the ADC noise may be too low to measure the noise of other instruments (anything below \(5.6\,\mu V/\sqrt{\text{Hz}}\) cannot be distinguished from the noise of the ADC itself), a low noise instrumentation amplifier was employed.
@ -444,7 +420,7 @@ A Femto DLPVA-101-B-S amplifier with adjustable gains from 20dB up to 80dB was s
The first step was to characterize the input\footnote{For variable gain amplifiers, it is usual to refer to the input noise rather than the output noise, as the input referred noise is almost independent on the chosen gain.} noise of the amplifier. The first step was to characterize the input\footnote{For variable gain amplifiers, it is usual to refer to the input noise rather than the output noise, as the input referred noise is almost independent on the chosen gain.} noise of the amplifier.
This was accomplished by short-circuiting its input with a \(50\,\Omega\) resistor and measuring the output voltage with the ADC (Figure \ref{fig:detail_instrumentation_femto_meas_setup}). This was accomplished by short-circuiting its input with a \(50\,\Omega\) resistor and measuring the output voltage with the ADC (Figure \ref{fig:detail_instrumentation_femto_meas_setup}).
The maximum amplifier gain of 80dB (equivalent to 10000) was utilized for this measurement. The maximum amplifier gain of 80dB (equivalent to 10000) was used for this measurement.
The measured voltage \(n\) was then divided by 10000 to determine the equivalent noise at the input of the voltage amplifier \(n_a\). The measured voltage \(n\) was then divided by 10000 to determine the equivalent noise at the input of the voltage amplifier \(n_a\).
In this configuration, the noise contribution from the ADC \(q_{ad}\) is rendered negligible due to the high gain employed. In this configuration, the noise contribution from the ADC \(q_{ad}\) is rendered negligible due to the high gain employed.
@ -463,7 +439,6 @@ The resulting amplifier noise amplitude spectral density \(\Gamma_{n_a}\) and th
\captionof{figure}{\label{fig:detail_instrumentation_femto_input_noise}Obtained ASD of the instrumentation amplifier input voltage noise} \captionof{figure}{\label{fig:detail_instrumentation_femto_input_noise}Obtained ASD of the instrumentation amplifier input voltage noise}
\end{center} \end{center}
\end{minipage} \end{minipage}
\section{Digital to Analog Converters} \section{Digital to Analog Converters}
\paragraph{Output Voltage Noise} \paragraph{Output Voltage Noise}
To measure the output noise of the DAC, the setup schematically represented in Figure \ref{fig:detail_instrumentation_dac_setup} was utilized. To measure the output noise of the DAC, the setup schematically represented in Figure \ref{fig:detail_instrumentation_dac_setup} was utilized.
@ -481,7 +456,6 @@ It should be noted that all DAC channels demonstrated similar performance, so on
\includegraphics[scale=1]{figs/detail_instrumentation_dac_setup.png} \includegraphics[scale=1]{figs/detail_instrumentation_dac_setup.png}
\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.} \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} \end{figure}
\paragraph{Delay from ADC to DAC} \paragraph{Delay from ADC to DAC}
To measure the transfer function from DAC to ADC and verify that the bandwidth and latency of both instruments is sufficient, a direct connection was established between the DAC output and the ADC input. To measure the transfer function from DAC to ADC and verify that the bandwidth and latency of both instruments is sufficient, a direct connection was established between the DAC output and the ADC input.
A white noise signal was generated by the DAC, and the ADC response was recorded. A white noise signal was generated by the DAC, and the ADC response was recorded.
@ -504,7 +478,6 @@ The observed frequency response function corresponds to exactly one sample delay
\end{subfigure} \end{subfigure}
\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.} \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} \end{figure}
\section{Piezoelectric Voltage Amplifier} \section{Piezoelectric Voltage Amplifier}
\paragraph{Output Voltage Noise} \paragraph{Output Voltage Noise}
The measurement setup for evaluating the PD200 amplifier noise is illustrated in Figure \ref{fig:detail_instrumentation_pd200_setup}. The measurement setup for evaluating the PD200 amplifier noise is illustrated in Figure \ref{fig:detail_instrumentation_pd200_setup}.
@ -537,7 +510,6 @@ While the exact cause of these peaks is not fully understood, their amplitudes r
\includegraphics[scale=1]{figs/detail_instrumentation_pd200_noise.png} \includegraphics[scale=1]{figs/detail_instrumentation_pd200_noise.png}
\caption{\label{fig:detail_instrumentation_pd200_noise}Measured output voltage noise of the PD200 amplifiers} \caption{\label{fig:detail_instrumentation_pd200_noise}Measured output voltage noise of the PD200 amplifiers}
\end{figure} \end{figure}
\paragraph{Small Signal Bandwidth} \paragraph{Small Signal Bandwidth}
The small signal dynamics of all six PD200 amplifiers were characterized through frequency response measurements. The small signal dynamics of all six PD200 amplifiers were characterized through frequency response measurements.
@ -555,10 +527,9 @@ The identified dynamics shown in Figure \ref{fig:detail_instrumentation_pd200_tf
\includegraphics[scale=1]{figs/detail_instrumentation_pd200_tf.png} \includegraphics[scale=1]{figs/detail_instrumentation_pd200_tf.png}
\caption{\label{fig:detail_instrumentation_pd200_tf}Identified dynamics from input voltage to output voltage of the PD200 voltage amplifier} \caption{\label{fig:detail_instrumentation_pd200_tf}Identified dynamics from input voltage to output voltage of the PD200 voltage amplifier}
\end{figure} \end{figure}
\section{Linear Encoders} \section{Linear Encoders}
To measure the noise of the encoder, the head and ruler were rigidly fixed together to ensure that no actual motion would be detected. To measure the noise of the encoder, the head and ruler were rigidly fixed together to ensure that no relative motion would be detected.
Under these conditions, any measured signal would correspond solely to the encoder noise. Under these conditions, any measured signal would correspond solely to the encoder noise.
The measurement setup is shown in Figure \ref{fig:detail_instrumentation_vionic_bench}. The measurement setup is shown in Figure \ref{fig:detail_instrumentation_vionic_bench}.
@ -580,7 +551,6 @@ The noise profile exhibits characteristics of white noise with an amplitude of a
\captionof{figure}{\label{fig:detail_instrumentation_vionic_asd}Measured Amplitude Spectral Density of the encoder noise} \captionof{figure}{\label{fig:detail_instrumentation_vionic_asd}Measured Amplitude Spectral Density of the encoder noise}
\end{center} \end{center}
\end{minipage} \end{minipage}
\section{Noise budgeting from measured instrumentation noise} \section{Noise budgeting from measured instrumentation noise}
After characterizing all instrumentation components individually, their combined effect on the sample's vibration was assessed using the multi-body model developed earlier. After characterizing all instrumentation components individually, their combined effect on the sample's vibration was assessed using the multi-body model developed earlier.
@ -595,12 +565,11 @@ This confirms that the selected instrumentation, with its measured noise charact
\includegraphics[scale=1]{figs/detail_instrumentation_cl_noise_budget.png} \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} \caption{\label{fig:detail_instrumentation_cl_noise_budget}Closed-loop noise budgeting using measured noise of instrumentation}
\end{figure} \end{figure}
\chapter*{Conclusion} \chapter*{Conclusion}
\label{sec:detail_instrumentation_conclusion} \label{sec:detail_instrumentation_conclusion}
This section has presented a comprehensive approach to the selection and characterization of instrumentation for the nano active stabilization system. This section has presented a comprehensive approach to the selection and characterization of instrumentation for the nano active stabilization system.
The multi-body model developed earlier proved invaluable for incorporating instrumentation components and their associated noise sources into the system analysis. The multi-body model created earlier served as a key tool for embedding instrumentation components and their associated noise sources within the system analysis.
From the most stringent requirement (i.e. the specification on vertical sample motion limited to 15 nm RMS), detailed specifications for each noise source were methodically derived through dynamic error budgeting. From the most stringent requirement (i.e. the specification on vertical sample motion limited to 15 nm RMS), detailed specifications for each noise source were methodically derived through dynamic error budgeting.
Based on these specifications, appropriate instrumentation components were selected for the system. Based on these specifications, appropriate instrumentation components were selected for the system.
@ -612,9 +581,8 @@ Initial measurements of the ADC system revealed an issue with force sensor reado
All components were found to meet or exceed their respective specifications. The ADC demonstrated noise levels of \(5.6\,\mu V/\sqrt{\text{Hz}}\) (versus the \(11\,\mu V/\sqrt{\text{Hz}}\) specification), the DAC showed \(0.6\,\mu V/\sqrt{\text{Hz}}\) (versus \(14\,\mu V/\sqrt{\text{Hz}}\) required), the voltage amplifiers exhibited noise well below the \(280\,\mu V/\sqrt{\text{Hz}}\) limit, and the encoders achieved \(1\,\text{nm RMS}\) noise (versus the \(6\,\text{nm RMS}\) specification). All components were found to meet or exceed their respective specifications. The ADC demonstrated noise levels of \(5.6\,\mu V/\sqrt{\text{Hz}}\) (versus the \(11\,\mu V/\sqrt{\text{Hz}}\) specification), the DAC showed \(0.6\,\mu V/\sqrt{\text{Hz}}\) (versus \(14\,\mu V/\sqrt{\text{Hz}}\) required), the voltage amplifiers exhibited noise well below the \(280\,\mu V/\sqrt{\text{Hz}}\) limit, and the encoders achieved \(1\,\text{nm RMS}\) noise (versus the \(6\,\text{nm RMS}\) specification).
Finally, the measured noise characteristics of all instrumentation components were incorporated into the multi-body model to predict the actual system performance. Finally, the measured noise characteristics of all instrumentation components were included into the multi-body model to predict the actual system performance.
The combined effect of all noise sources was estimated to induce vertical sample vibrations of only \(1.5\,\text{nm RMS}\), which is substantially below the \(15\,\text{nm RMS}\) requirement. The combined effect of all noise sources was estimated to induce vertical sample vibrations of only \(1.5\,\text{nm RMS}\), which is substantially below the \(15\,\text{nm RMS}\) requirement.
This rigorous methodology spanning requirement formulation, component selection, and experimental characterization validates the instrumentation's ability to fulfill the nano active stabilization system's demanding performance specifications. This rigorous methodology spanning requirement formulation, component selection, and experimental characterization validates the instrumentation's ability to fulfill the nano active stabilization system's demanding performance specifications.
\printbibliography[heading=bibintoc,title={Bibliography}] \printbibliography[heading=bibintoc,title={Bibliography}]
\end{document} \end{document}