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title = "Active Isolation Platforms"
author = ["Thomas Dehaeze"]
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Tags
: [Vibration Isolation]({{< relref "vibration_isolation" >}})
| Manufacturers | Links | Country |
|---------------|------------------------------------------------------------------------|---------|
| TMC | [link](https://www.techmfg.com/) | USA |
| Newport | [link](https://www.newport.com/c/optical-tables-%26-isolation-systems) | USA |
<./biblio/references.bib>

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title = "Granite"
author = ["Thomas Dehaeze"]
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:
<https://www.microplan-group.com/fr/>
<./biblio/references.bib>

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## Review of Absolute (inertial) Position Sensors {#review-of-absolute--inertial--position-sensors}
- Collette, C. et al., Review: inertial sensors for low-frequency seismic vibration measurement <sup id="dd5109075933cf543c7eba0979c0ba50"><a class="reference-link" href="#collette12_review" title="Collette, Janssens, Fernandez-Carmona, , Artoos, Guinchard, Hauviller \&amp; Preumont, Review: Inertial Sensors for Low-Frequency Seismic Vibration Measurement, {Bulletin of the Seismological Society of America}, v(4), 1289-1300 (2012).">(Collette {\it et al.}, 2012)</a></sup>
- Collette, C. et al., Comparison of new absolute displacement sensors <sup id="0b0b67de6dddc4d28031ab2d3b28cd3d"><a class="reference-link" href="#collette12_compar" title="Collette, Janssens, Mokrani, Fueyo-Roza, L, Artoos, Esposito, Fernandez-Carmona, , Guinchard \&amp; Leuxe, Comparison of new absolute displacement sensors, in in: {International Conference on Noise and Vibration Engineering
(ISMA)}, edited by (2012)">(Collette {\it et al.}, 2012)</a></sup>
- Collette, C. et al., Review: inertial sensors for low-frequency seismic vibration measurement ([Collette, Janssens, Fernandez-Carmona, et al. 2012](#org3cd922d))
- Collette, C. et al., Comparison of new absolute displacement sensors ([Collette, Janssens, Mokrani, et al. 2012](#org8b5d5a2))
<a id="org472a92d"></a>
<a id="org1914e49"></a>
{{< figure src="/ox-hugo/collette12_absolute_disp_sensors.png" caption="Figure 1: Dynamic range of several types of inertial sensors; Price versus resolution for several types of inertial sensors" >}}
## Accelerometers {#accelerometers}
| Manufacturers | Links |
|--------------------|---------------------------------------------------------------|
| Micromega Dynamics | [link](https://micromega-dynamics.com/products/) |
| MMF | [link](https://www.mmf.de/seismic%5Faccelerometers.htm) |
| PCB | [link](https://www.pcb.com/products/productfinder.aspx?tx=14) |
| Manufacturers | Links | Country |
|--------------------|---------------------------------------------------------------------------------------------|---------|
| Micromega Dynamics | [link](https://micromega-dynamics.com/products/) | Belgium |
| MMF | [link](https://www.mmf.de/seismic%5Faccelerometers.htm) | Germany |
| PCB | [link](https://www.pcb.com/products/productfinder.aspx?tx=14) | USA |
| Guralp | [link](https://www.guralp.com/products/surface) | UK |
| Nanometric | [link](https://www.nanometrics.ca/products/accelerometers) | Canada |
| Kistler | [link](https://www.kistler.com/fr/produits/composants/accelerometres/?pfv%5Fmetrics=metric) | Swiss |
Wireless Accelerometers
- <https://micromega-dynamics.com/products/recovib/miniature-vibration-recorder/>
<a id="org005935d"></a>
<a id="orgf34c817"></a>
{{< figure src="/ox-hugo/inertial_sensors_characteristics_accelerometers.png" caption="Figure 2: Characteristics of commercially available accelerometers <sup id=\"642a18d86de4e062c6afb0f5f20501c4\"><a class=\"reference-link\" href=\"#collette11_review\" title=\"Collette, Artoos, Guinchard, Janssens, , Carmona Fernandez \&amp; Hauviller, Review of sensors for low frequency seismic vibration measurement, CERN, (2011).\">(Collette {\it et al.}, 2011)</a></sup>" >}}
## Geophones {#geophones}
## Geophones and Seismometers {#geophones-and-seismometers}
| Manufacturers | Links |
|---------------|----------------------------------------------------------------|
| Sercel | [link](http://www.sercel.com/products/Pages/seismometers.aspx) |
| Wilcoxon | [link](https://wilcoxon.com/) |
| Manufacturers | Links | Country |
|-----------------------|---------------------------------------------------------------------------------------------|---------|
| Sercel | [link](http://www.sercel.com/products/Pages/seismometers.aspx) | France |
| Wilcoxon | [link](https://wilcoxon.com/) | USA |
| Geospace technologies | [link](https://www.geospace.com/sensors/#) | USA |
| Ion | [link](https://www.iongeo.com/technologies/hardware/seismic-equipment/precision-geophones/) | USA |
| Streckeisen | [link](https://streckeisen.swiss/en/products/overview/) | Swiss |
| Guralp | [link](https://www.guralp.com/products/surface) | UK |
| Nanometric | [link](https://www.nanometrics.ca/products/seismometers) | Canada |
<a id="orgd64c709"></a>
<a id="org877de39"></a>
{{< figure src="/ox-hugo/inertial_sensors_characteristics_geophone.png" caption="Figure 3: Characteristics of commercially available geophones <sup id=\"642a18d86de4e062c6afb0f5f20501c4\"><a class=\"reference-link\" href=\"#collette11_review\" title=\"Collette, Artoos, Guinchard, Janssens, , Carmona Fernandez \&amp; Hauviller, Review of sensors for low frequency seismic vibration measurement, CERN, (2011).\">(Collette {\it et al.}, 2011)</a></sup>" >}}
# Bibliography
<a class="bibtex-entry" id="collette12_review">Collette, C., Janssens, S., Fernandez-Carmona, P., Artoos, K., Guinchard, M., Hauviller, C., & Preumont, A., *Review: inertial sensors for low-frequency seismic vibration measurement*, Bulletin of the Seismological Society of America, *102(4)*, 1289–1300 (2012). http://dx.doi.org/10.1785/0120110223</a> [↩](#dd5109075933cf543c7eba0979c0ba50)
<a class="bibtex-entry" id="collette12_compar">Collette, C., Janssens, S., Mokrani, B., Fueyo-Roza, L., Artoos, K., Esposito, M., Fernandez-Carmona, P., …, *Comparison of new absolute displacement sensors*, In , International Conference on Noise and Vibration Engineering (ISMA) (pp. ) (2012). : .</a> [↩](#0b0b67de6dddc4d28031ab2d3b28cd3d)
## Bibliography {#bibliography}
<a class="bibtex-entry" id="collette11_review">Collette, C., Artoos, K., Guinchard, M., Janssens, S., Carmona Fernandez, P., & Hauviller, C., *Review of sensors for low frequency seismic vibration measurement* (2011).</a> [↩](#642a18d86de4e062c6afb0f5f20501c4)
<a id="org3cd922d"></a>Collette, C., S. Janssens, P. Fernandez-Carmona, K. Artoos, M. Guinchard, C. Hauviller, and A. Preumont. 2012. “Review: Inertial Sensors for Low-Frequency Seismic Vibration Measurement.” _Bulletin of the Seismological Society of America_ 102 (4):1289–1300. <https://doi.org/10.1785/0120110223>.
<a id="org8b5d5a2"></a>Collette, C, S Janssens, B Mokrani, L Fueyo-Roza, K Artoos, M Esposito, P Fernandez-Carmona, M Guinchard, and R Leuxe. 2012. “Comparison of New Absolute Displacement Sensors.” In _International Conference on Noise and Vibration Engineering (ISMA)_.
## Backlinks {#backlinks}
- [Sensors]({{< relref "sensors" >}})
- [Collocated Control]({{< relref "collocated_control" >}})
- [Position Sensors]({{< relref "position_sensors" >}})

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Books:
- <sup id="88712982e0649b89da706b6abbcbc6c2"><a href="#higham17_matlab" title="Higham, MATLAB guide, Society for Industrial and Applied Mathematics (2017).">(Higham, 2017)</a></sup>
- <sup id="15f4380b6ce8a647387d3ccea25711f1"><a href="#attaway18_matlab" title="Attaway, MATLAB : a practical introduction to programming and problem solving, Butterworth-Heinemann (2018).">(Attaway, 2018)</a></sup>
- <sup id="e770e23b0d222a65eb74f036227b13b2"><a href="#overflow18_matlab_notes_profes" title="Stack OverFlow, MATLAB Notes for Professionals, GoalKicker.com (2018).">(Stack OverFlow, 2018)</a></sup>
- <sup id="87b279fa5b4ec9b1a73abed2d00b313f"><a href="#johnson10_matlab" title="Johnson, The elements of MATLAB style, Cambridge University Press (2010).">(Johnson, 2010)</a></sup>
- <sup id="1b4159c36c5367ee0c92139fb403e7e1"><a href="#hahn16_essen_matlab" title="Hahn \&amp; Valentine, Essential MATLAB for engineers and scientists, Academic Press (2016).">(Hahn \& Valentine, 2016)</a></sup>
- ([Higham 2017](#org80aac16))
- ([Attaway 2018](#org689a4e6))
- ([OverFlow 2018](#org6480d2d))
- ([Johnson 2010](#org657d51a))
- ([Hahn and Valentine 2016](#org23bf05a))
## Useful Commands {#useful-commands}
@@ -54,13 +54,28 @@ hold off;
legend('Location', 'northeast');
```
# Bibliography
<a id="higham17_matlab"></a>Higham, D., *Matlab guide* (2017), Philadelphia: Society for Industrial and Applied Mathematics. [↩](#88712982e0649b89da706b6abbcbc6c2)
<a id="attaway18_matlab"></a>Attaway, S., *Matlab : a practical introduction to programming and problem solving* (2018), Amsterdam: Butterworth-Heinemann. [↩](#15f4380b6ce8a647387d3ccea25711f1)
## Installation {#installation}
<a id="overflow18_matlab_notes_profes"></a>OverFlow, S., *Matlab notes for professionals* (2018), : GoalKicker.com. [↩](#e770e23b0d222a65eb74f036227b13b2)
If a single user is using the Matlab installation on the machine:
<a id="johnson10_matlab"></a>Johnson, R. K., *The elements of matlab style* (2010), : Cambridge University Press. [↩](#87b279fa5b4ec9b1a73abed2d00b313f)
```bash
sudo chown -R $LOGNAME: /usr/local/MATLAB/R2017b
```
<a id="hahn16_essen_matlab"></a>Hahn, B., & Valentine, D. T., *Essential matlab for engineers and scientists* (2016), : Academic Press. [↩](#1b4159c36c5367ee0c92139fb403e7e1)
Then, Toolboxes can be installed by the user without any problem.
To install Toolboxes, the best is to Download the Matlab installer from mathworks and just select the wanted toolboxes.
## Bibliography {#bibliography}
<a id="org689a4e6"></a>Attaway, Stormy. 2018. _MATLAB : a Practical Introduction to Programming and Problem Solving_. Amsterdam: Butterworth-Heinemann.
<a id="org23bf05a"></a>Hahn, Brian, and Daniel T Valentine. 2016. _Essential MATLAB for Engineers and Scientists_. Academic Press.
<a id="org80aac16"></a>Higham, Desmond. 2017. _MATLAB Guide_. Philadelphia: Society for Industrial and Applied Mathematics.
<a id="org657d51a"></a>Johnson, Richard K. 2010. _The Elements of MATLAB Style_. Cambridge University Press.
<a id="org6480d2d"></a>OverFlow, Stack. 2018. _MATLAB Notes for Professionals_. GoalKicker.com.

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### Manufacturers {#manufacturers}
| Manufacturers | Links |
|---------------------|----------------------------------------------------------------------------------------------------------------|
| Cedrat | [link](http://www.cedrat-technologies.com/) |
| PI | [link](https://www.physikinstrumente.com/en/) |
| Piezo System | [link](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/) |
| Noliac | [link](http://www.noliac.com/) |
| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) |
| PiezoDrive | [link](https://www.piezodrive.com/actuators/) |
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/10.html) |
| CoreMorrow | [link](http://www.coremorrow.com/en/pro-9-1.html) |
| PiezoData | [link](https://www.piezodata.com/piezo-stack-actuator-2/) |
| Queensgate | [link](https://www.nanopositioning.com/product-category/nanopositioning/nanopositioning-actuators-translators) |
| Manufacturers | Links | Country |
|---------------------|----------------------------------------------------------------------------------------------------------------|-----------|
| Cedrat | [link](http://www.cedrat-technologies.com/) | France |
| PI | [link](https://www.physikinstrumente.com/en/) | USA |
| Piezo System | [link](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/) | Germany |
| Noliac | [link](http://www.noliac.com/) | Denmark |
| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA |
| PiezoDrive | [link](https://www.piezodrive.com/actuators/) | Australia |
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/10.html) | Japan |
| CoreMorrow | [link](http://www.coremorrow.com/en/pro-9-1.html) | China |
| PiezoData | [link](https://www.piezodata.com/piezo-stack-actuator-2/) | China |
| Queensgate | [link](https://www.nanopositioning.com/product-category/nanopositioning/nanopositioning-actuators-translators) | UK |
| Matsusada Precision | [link](https://www.matsusada.com/product/pz/) | Japan |
### Model {#model}
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#org7ef2e50)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#org1025f36)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel.
@@ -44,27 +45,27 @@ with:
## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#orgc110fa4)):
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#org4de69d6)):
> The displacement amplification effect is related in a first approximation to the ratio of the shell long axis length to the short axis height.
> The flatter is the actuator, the higher is the amplification.
A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#orge1d2714)).
A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org2278a86)).
<a id="org5a5d286"></a>
<a id="org220f472"></a>
{{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="Figure 1: Topology of several types of compliant mechanisms <sup id=\"d9e8b33774f1e65d16bd79114db8ac64\"><a class=\"reference-link\" href=\"#ling16_enhan_mathem_model_displ_amplif\" title=\"Mingxiang Ling, Junyi Cao, Minghua Zeng, Jing Lin, \&amp; Daniel J Inman, Enhanced Mathematical Modeling of the Displacement Amplification Ratio for Piezoelectric Compliant Mechanisms, {Smart Materials and Structures}, v(7), 075022 (2016).\">(Mingxiang Ling {\it et al.}, 2016)</a></sup>" >}}
| Manufacturers | Links |
|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| Cedrat | [link](https://www.cedrat-technologies.com/en/products/actuators/amplified-piezo-actuators.html) |
| PiezoDrive | [link](https://www.piezodrive.com/actuators/ap-series-amplified-piezoelectric-actuators/) |
| Dynamic-Structures | [link](https://www.dynamic-structures.com/category/piezo-actuators-stages) |
| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) |
| Noliac | [link](http://www.noliac.com/products/actuators/amplified-actuators/) |
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F5.html), [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F3.html), [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5Fmtkk.html) |
| CoreMorrow | [link](http://www.coremorrow.com/en/pro-13-1.html) |
| PiezoData | [link](https://www.piezodata.com/piezoelectric-actuator-amplifier/) |
| **Manufacturers** | **Links** | **Country** |
|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------|
| Cedrat | [link](https://www.cedrat-technologies.com/en/products/actuators/amplified-piezo-actuators.html) | France |
| PiezoDrive | [link](https://www.piezodrive.com/actuators/ap-series-amplified-piezoelectric-actuators/) | Australia |
| Dynamic-Structures | [link](https://www.dynamic-structures.com/category/piezo-actuators-stages) | USA |
| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA |
| Noliac | [link](http://www.noliac.com/products/actuators/amplified-actuators/) | Denmark |
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F5.html), [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F3.html), [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5Fmtkk.html) | Japan |
| CoreMorrow | [link](http://www.coremorrow.com/en/pro-13-1.html) | China |
| PiezoData | [link](https://www.piezodata.com/piezoelectric-actuator-amplifier/) | China |
## Specifications {#specifications}
@@ -143,54 +144,54 @@ For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolut
### Electrical Capacitance {#electrical-capacitance}
The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#orgebd19c2)).
The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#org4b5f8bd)).
This is due to the fact that voltage amplifier has a limitation on the deliverable current.
[Voltage Amplifier]({{< relref "voltage_amplifier" >}}) with high maximum output current should be used if either high bandwidth is wanted or piezoelectric stacks with high capacitance are to be used.
<a id="orgebd19c2"></a>
<a id="org4b5f8bd"></a>
{{< figure src="/ox-hugo/piezoelectric_capacitance_voltage_max.png" caption="Figure 2: Maximum sin-wave amplitude as a function of frequency for several piezoelectric capacitance" >}}
## Piezoelectric actuator experiencing a mass load {#piezoelectric-actuator-experiencing-a-mass-load}
When the piezoelectric actuator is supporting a payload, it will experience a static deflection due to its finite stiffness \\(\Delta l\_n = \frac{mg}{k\_p}\\), but its stroke will remain unchanged (Figure [3](#orgb64bc37)).
When the piezoelectric actuator is supporting a payload, it will experience a static deflection due to its finite stiffness \\(\Delta l\_n = \frac{mg}{k\_p}\\), but its stroke will remain unchanged (Figure [3](#org6e4c8b2)).
<a id="orgb64bc37"></a>
<a id="org6e4c8b2"></a>
{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="Figure 3: Motion of a piezoelectric stack actuator under external constant force" >}}
## Piezoelectric actuator in contact with a spring load {#piezoelectric-actuator-in-contact-with-a-spring-load}
Then the piezoelectric actuator is in contact with a spring load \\(k\_e\\), its maximum stroke \\(\Delta L\\) is less than its free stroke \\(\Delta L\_f\\) (Figure [4](#org944d760)):
Then the piezoelectric actuator is in contact with a spring load \\(k\_e\\), its maximum stroke \\(\Delta L\\) is less than its free stroke \\(\Delta L\_f\\) (Figure [4](#orgadae726)):
\begin{equation}
\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
\end{equation}
<a id="org944d760"></a>
<a id="orgadae726"></a>
{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="Figure 4: Motion of a piezoelectric stack actuator in contact with a stiff environment" >}}
For piezo actuators, force and displacement are inversely related (Figure [5](#org0a60bcb)).
For piezo actuators, force and displacement are inversely related (Figure [5](#org51f52cb)).
Maximum, or blocked, force (\\(F\_b\\)) occurs when there is no displacement.
Likewise, at maximum displacement, or free stroke, (\\(\Delta L\_f\\)) no force is generated.
When an external load is applied, the stiffness of the load (\\(k\_e\\)) determines the displacement (\\(\Delta L\_A\\)) and force (\\(\Delta F\_A\\)) that can be produced.
<a id="org0a60bcb"></a>
<a id="org51f52cb"></a>
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
## Bibliography {#bibliography}
<a id="orgc110fa4"></a>Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” _Ferroelectrics_ 351 (1):3–14. <https://doi.org/10.1080/00150190701351865>.
<a id="org4de69d6"></a>Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” _Ferroelectrics_ 351 (1):3–14. <https://doi.org/10.1080/00150190701351865>.
<a id="org7ef2e50"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.
<a id="org1025f36"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.
<a id="orge1d2714"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
<a id="org2278a86"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
## Backlinks {#backlinks}

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## Manufacturers {#manufacturers}
| Manufacturers | Links |
|---------------|-------------------------------------------------------------------|
| Labsen | [link](http://labsentec.com.au/category/products/vibrationshock/) |
| Manufacturers | Links |
|-----------------|----------------------------------------------------------------------------------|
| Labsen | [link](http://labsentec.com.au/category/products/vibrationshock/) |
| The Modal Shop | [link](http://www.modalshop.com/excitation/Electrodynamic-Exciter-Family?ID=243) |
| Deweshop | [link](https://dewesoft.com/fr/products/interfaces-and-sensors/shakers) |
| Bruel and Kjaer | [link](https://www.bksv.com/en/products/shakers-and-exciters/LDS-shaker-systems) |
| YMC | [link](http://www.chinaymc.com/product/showproduct.php?id=78&lang=en) |
<./biblio/references.bib>

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## SNR to Noise PSD {#snr-to-noise-psd}
From ([Jabben 2007](#orgd8e3764)) (Section 3.3.2):
From ([Jabben 2007](#org05d266b)) (Section 3.3.2):
> Electronic equipment does most often not come with detailed electric schemes, in which case the PSD should be determined from measurements.
> In the design phase however, one has to rely on information provided by specification sheets from the manufacturer.
@@ -77,13 +77,13 @@ Let's say the wanted noise is \\(1 mV, \text{rms}\\) for a full range of \\(20 V
## Noise Density to RMS noise {#noise-density-to-rms-noise}
From ([Fleming 2010](#org68e05a9)):
From ([Fleming 2010](#org8235840)):
\\[ \text{RMS noise} = \sqrt{2 \times \text{bandwidth}} \times \text{noise density} \\]
If the noise is normally distributed, the RMS value is also the standard deviation \\(\sigma\\).
The peak to peak amplitude is then approximatively \\(6 \sigma\\).
<div class="exampl">
<div class="examp">
<div></div>
- noise density = \\(20 pm/\sqrt{Hz}\\)
@@ -97,13 +97,15 @@ The peak-to-peak noise will be approximately \\(6 \sigma = 1.7 nm\\)
## Bibliography {#bibliography}
<a id="org68e05a9"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.
<a id="org8235840"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.
<a id="orgd8e3764"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.
<a id="org05d266b"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.
## Backlinks {#backlinks}
- [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
- [Power Spectral Density]({{< relref "power_spectral_density" >}})
- [Position Sensors]({{< relref "position_sensors" >}})
- [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
- [Voltage Amplifier]({{< relref "voltage_amplifier" >}})

54
content/zettels/voltage_amplifier.md
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@@ -15,9 +15,9 @@ Tags
The piezoelectric stack can be represented as a capacitance.
Let's take a capacitance driven by a voltage amplifier (Figure [1](#org0d9f468)).
Let's take a capacitance driven by a voltage amplifier (Figure [1](#orgcab6e6f)).
<a id="org0d9f468"></a>
<a id="orgcab6e6f"></a>
{{< figure src="/ox-hugo/voltage_amplifier_capacitance.png" caption="Figure 1: Piezoelectric actuator model with a voltage source" >}}
@@ -37,7 +37,7 @@ Thus, for a specified maximum current \\(I\_\text{max}\\), the "power bandwidth"
- Above \\(\omega\_{0, \text{max}}\\), the maximum current \\(I\_\text{max}\\) is reached and the maximum voltage that can be applied decreases with frequency:
\\[ U\_\text{max} = \frac{I\_\text{max}}{\omega C} \\]
The maximum voltage as a function of frequency is shown in Figure [2](#org8625e7c).
The maximum voltage as a function of frequency is shown in Figure [2](#org1475933).
```matlab
Vpkp = 170; % [V]
@@ -51,7 +51,7 @@ C = 1e-6; % [F]
56.172
```
<a id="org8625e7c"></a>
<a id="org1475933"></a>
{{< figure src="/ox-hugo/voltage_amplifier_max_V_piezo.png" caption="Figure 2: Maximum voltage as a function of the frequency for \\(C = 1 \mu F\\), \\(I\_\text{max} = 30mA\\) and \\(V\_{pkp} = 170 V\\)" >}}
@@ -63,6 +63,19 @@ If driven at \\(\Delta U = 100V\\), \\(C = 1 \mu F\\) and \\(I\_\text{max} = 1 A
\\[ t\_c = \frac{100 \cdot 10^{-6}}{1} = 0.1 ms \\]
### Bandwidth limitation (small signals) {#bandwidth-limitation--small-signals}
This is takken from Chapter 14 of ([Fleming and Leang 2014](#org01aad4a)).
```matlab
L = 250e-9; % Cable inductance [H]
Cp = 10e-6; % Driving capacitance [F]
Rs = 10; % Source impedance [Ohm]
G = 1/(L*Cp)/(s^2 + Rs/L*s + 1/(L*Cp));
```
### Amplifiers for Low Voltage PZT {#amplifiers-for-low-voltage-pzt}
Piezoelectric Stack Actuators are behaving like capacitor for the Amplifiers.
@@ -75,21 +88,26 @@ Specifications are usually:
The bandwidth can be estimated from the Maximum Current and the Capacitance of the Piezoelectric Actuator.
| Manufacturers | Links |
|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------|
| Piezo Drive | [link](https://www.piezodrive.com/drivers/) |
| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=13630) |
| PI | [link](https://www.pi-usa.us/en/products/controllers-drivers-motion-control-software/piezo-drivers-controllers-power-supplies-high-voltage-amplifiers/) |
| Micromega Dynamics | |
| Lab Systems | [link](https://www.lab-systems.com/products/amplifier/amplifier.html) |
| Falco System | [link](https://www.falco-systems.com/products.html) |
| Piezomechanics | [link](https://www.piezomechanik.com/products/) |
| Cedrat Technologies | [link](https://www.cedrat-technologies.com/en/products/piezo-controllers/electronic-amplifier-boards.html) |
| acal | [link](https://www.acalbfi.com/nl/Electronic-test-and-measurement/High-voltage-amplifiers/c/CAT-06-03) |
| Trek | [link](https://www.trekinc.com/products/HV%5FAmp.asp) |
| Madcitylabs | [link](http://www.madcitylabs.com/piezoactuators.html) |
| Manufacturers | Links | Country |
|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------|-------------|
| Piezo Drive | [link](https://www.piezodrive.com/drivers/) | Australia |
| Thorlabs | [link](https://www.thorlabs.com/navigation.cfm?guide%5FID=2085) | USA |
| PI | [link](https://www.pi-usa.us/en/products/controllers-drivers-motion-control-software/piezo-drivers-controllers-power-supplies-high-voltage-amplifiers/) | USA |
| Micromega Dynamics | | Belgium |
| Lab Systems | [link](https://www.lab-systems.com/products/amplifier/amplifier.html) | Isreal |
| Falco System | [link](https://www.falco-systems.com/products.html) | Netherlands |
| Piezomechanics | [link](https://www.piezomechanik.com/products/) | Germany |
| Cedrat Technologies | [link](https://www.cedrat-technologies.com/en/products/piezo-controllers/electronic-amplifier-boards.html) | France |
| Trek | [link](https://www.trekinc.com/products/HV%5FAmp.asp) | USA |
| Madcitylabs | [link](http://www.madcitylabs.com/piezoactuators.html) | USA |
| Piezosystem | [link](https://www.piezosystem.com/products/controller/) | Germany |
| Matsusada Precision | [link](https://www.matsusada.com/product/pz/) | Japan |
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/08.html) | Japan |
<./biblio/references.bib>
## Bibliography {#bibliography}
<a id="org01aad4a"></a>Fleming, Andrew J., and Kam K. Leang. 2014. _Design, Modeling and Control of Nanopositioning Systems_. Advances in Industrial Control. Springer International Publishing. <https://doi.org/10.1007/978-3-319-06617-2>.
## Backlinks {#backlinks}