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71
content/phdthesis/jabben07_mechat.md
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@ -49,9 +49,12 @@ The noise source has a PSD given by:
\\[ S\_T(f) = 4 k T \text{Re}(Z(f)) \ [V^2/Hz] \\] \\[ S\_T(f) = 4 k T \text{Re}(Z(f)) \ [V^2/Hz] \\]
with \\(k = 1.38 \cdot 10^{-23} \,[J/K]\\) the Boltzmann's constant, \\(T\\) the temperature [K] and \\(Z(f)\\) the frequency dependent impedance of the system. with \\(k = 1.38 \cdot 10^{-23} \,[J/K]\\) the Boltzmann's constant, \\(T\\) the temperature [K] and \\(Z(f)\\) the frequency dependent impedance of the system.
```text <div class="examp">
A kilo Ohm resistor at 20 degree Celsius will show a thermal noise of $0.13 \mu V$ from zero up to one kHz. <div></div>
```
A kilo Ohm resistor at 20 degree Celsius will show a thermal noise of \\(0.13 \mu V\\) from zero up to one kHz.
</div>
**Shot Noise**. **Shot Noise**.
Seen with junctions in a transistor. Seen with junctions in a transistor.
@ -59,9 +62,12 @@ It has a white spectral density:
\\[ S\_S = 2 q\_e i\_{dc} \ [A^2/Hz] \\] \\[ S\_S = 2 q\_e i\_{dc} \ [A^2/Hz] \\]
with \\(q\_e\\) the electronic charge (\\(1.6 \cdot 10^{-19}\, [C]\\)), \\(i\_{dc}\\) the average current [A]. with \\(q\_e\\) the electronic charge (\\(1.6 \cdot 10^{-19}\, [C]\\)), \\(i\_{dc}\\) the average current [A].
```text <div class="examp">
An averable current of 1 A will introduce noise with a STD of $10 \cdot 10^{-9}\,[A]$ from zero up to one kHz. <div></div>
```
An averable current of 1 A will introduce noise with a STD of \\(10 \cdot 10^{-9}\,[A]\\) from zero up to one kHz.
</div>
**Excess Noise** (or \\(1/f\\) noise). **Excess Noise** (or \\(1/f\\) noise).
It results from fluctuating conductivity due to imperfect contact between two materials. It results from fluctuating conductivity due to imperfect contact between two materials.
@ -91,24 +97,28 @@ The corresponding PSD is white up to the Nyquist frequency:
\\[ S\_Q = \frac{q^2}{12 f\_N} \\] \\[ S\_Q = \frac{q^2}{12 f\_N} \\]
with \\(f\_N\\) the Nyquist frequency [Hz]. with \\(f\_N\\) the Nyquist frequency [Hz].
```text <div class="examp">
<div></div>
Let's take the example of a 16 bit ADC which has an electronic noise with a SNR of 80dB. Let's take the example of a 16 bit ADC which has an electronic noise with a SNR of 80dB.
Let's suppose the ADC is used to measure a position over a range of 1 mm. Let's suppose the ADC is used to measure a position over a range of 1 mm.
- ADC quantization noise: it has 16 bots over the 1 mm range.
The standard diviation from the quantization is:
\[ \sigma_{ADq} = \frac{1 \cdot 10^6/2^16}{\sqrt{12}} = 4.4\,[nm] \]
- ADC electronic noise: the RMS value of a sine that covers to full range is $\frac{0.5}{\sqrt{2}} = 0.354\,[mm]$.
With a SNR of 80dB, the electronic noise from the ADC becomes:
\[ \sigma_{ADn} = 35\,[nm] \]
Let's suppose the ADC is used to measure a sensor with an electronic noise having a standard deviation of $\sigma_{sn} = 17\,[nm]$. - ADC quantization noise: it has 16 bots over the 1 mm range.
The standard diviation from the quantization is:
\\[ \sigma\_{ADq} = \frac{1 \cdot 10^6/2^16}{\sqrt{12}} = 4.4\,[nm] \\]
- ADC electronic noise: the RMS value of a sine that covers to full range is \\(\frac{0.5}{\sqrt{2}} = 0.354\,[mm]\\).
With a SNR of 80dB, the electronic noise from the ADC becomes:
\\[ \sigma\_{ADn} = 35\,[nm] \\]
Let's suppose the ADC is used to measure a sensor with an electronic noise having a standard deviation of \\(\sigma\_{sn} = 17\,[nm]\\).
The PSD of this digitalized sensor noise is: The PSD of this digitalized sensor noise is:
\[ \sigma_s = \sqrt{\sigma_{sn}^2 + \sigma_{ADq}^2 + \sigma_{ADn}^2} = 39\,[nm]\] \\[ \sigma\_s = \sqrt{\sigma\_{sn}^2 + \sigma\_{ADq}^2 + \sigma\_{ADn}^2} = 39\,[nm]\\]
from which the PSD of the total sensor noise $S_s$ is calculated: from which the PSD of the total sensor noise \\(S\_s\\) is calculated:
\[ S_s = \frac{\sigma_s^2}{f_N} = 1.55\,[nm^2/Hz] \] \\[ S\_s = \frac{\sigma\_s^2}{f\_N} = 1.55\,[nm^2/Hz] \\]
with $f_N$ is the Nyquist frequency of 1kHz. with \\(f\_N\\) is the Nyquist frequency of 1kHz.
```
</div>
#### Acoustic Noise {#acoustic-noise} #### Acoustic Noise {#acoustic-noise}
@ -119,9 +129,12 @@ The disturbance force acting on a body, is the **difference of pressure between
To have a pressure difference, the body must have a certain minimum dimension, depending on the wave length of the sound. To have a pressure difference, the body must have a certain minimum dimension, depending on the wave length of the sound.
For a body of typical dimensions of 100mm, only frequencies above 800 Hz have a significant disturbance contribution. For a body of typical dimensions of 100mm, only frequencies above 800 Hz have a significant disturbance contribution.
```text <div class="examp">
Consider a cube with a rib size of 100 mm located in a room with a sound level of 80dB, distributed between one and ten kHz, then the force disturbance PSD equal $2.2 \cdot 10^{-2}\,[N^2/Hz]$ <div></div>
```
Consider a cube with a rib size of 100 mm located in a room with a sound level of 80dB, distributed between one and ten kHz, then the force disturbance PSD equal \\(2.2 \cdot 10^{-2}\,[N^2/Hz]\\)
</div>
#### Brownian Noise {#brownian-noise} #### Brownian Noise {#brownian-noise}
@ -148,21 +161,21 @@ Three factors influence the performance:
The DEB helps identifying which disturbance is the limiting factor, and it should be investigated if the controller can deal with this disturbance before re-designing the plant. The DEB helps identifying which disturbance is the limiting factor, and it should be investigated if the controller can deal with this disturbance before re-designing the plant.
The modelling of disturbance as stochastic variables, is by excellence suitable for the optimal stochastic control framework. The modelling of disturbance as stochastic variables, is by excellence suitable for the optimal stochastic control framework.
In Figure [1](#org30a4301), the generalized plant maps the disturbances to the performance channels. In Figure [1](#orga43f7f1), the generalized plant maps the disturbances to the performance channels.
By minimizing the \\(\mathcal{H}\_2\\) system norm of the generalized plant, the variance of the performance channels is minimized. By minimizing the \\(\mathcal{H}\_2\\) system norm of the generalized plant, the variance of the performance channels is minimized.
<a id="org30a4301"></a> <a id="orga43f7f1"></a>
{{< figure src="/ox-hugo/jabben07_general_plant.png" caption="Figure 1: Control system with the generalized plant \\(G\\). The performance channels are stacked in \\(z\\), while the controller input is denoted with \\(y\\)" >}} {{< figure src="/ox-hugo/jabben07_general_plant.png" caption="Figure 1: Control system with the generalized plant \\(G\\). The performance channels are stacked in \\(z\\), while the controller input is denoted with \\(y\\)" >}}
#### Using Weighting Filters for Disturbance Modelling {#using-weighting-filters-for-disturbance-modelling} #### Using Weighting Filters for Disturbance Modelling {#using-weighting-filters-for-disturbance-modelling}
Since disturbances are generally not white, the system of Figure [1](#org30a4301) needs to be augmented with so called **disturbance weighting filters**. Since disturbances are generally not white, the system of Figure [1](#orga43f7f1) needs to be augmented with so called **disturbance weighting filters**.
A disturbance weighting filter gives the disturbance PSD when white noise as input is applied. A disturbance weighting filter gives the disturbance PSD when white noise as input is applied.
This is illustrated in Figure [2](#org3b94947) where a vector of white noise time signals \\(\underbar{w}(t)\\) is filtered through a weighting filter to obtain the colored physical disturbances \\(w(t)\\) with the desired PSD \\(S\_w\\) . This is illustrated in Figure [2](#org906705e) where a vector of white noise time signals \\(\underbar{w}(t)\\) is filtered through a weighting filter to obtain the colored physical disturbances \\(w(t)\\) with the desired PSD \\(S\_w\\) .
The generalized plant framework also allows to include **weighting filters for the performance channels**. The generalized plant framework also allows to include **weighting filters for the performance channels**.
This is useful for three reasons: This is useful for three reasons:
@ -171,7 +184,7 @@ This is useful for three reasons:
- some performance channels may be of more importance than others - some performance channels may be of more importance than others
- by using dynamic weighting filters, one can emphasize the performance in a certain frequency range - by using dynamic weighting filters, one can emphasize the performance in a certain frequency range
<a id="org3b94947"></a> <a id="org906705e"></a>
{{< figure src="/ox-hugo/jabben07_weighting_functions.png" caption="Figure 2: Control system with the generalized plant \\(G\\) and weighting functions" >}} {{< figure src="/ox-hugo/jabben07_weighting_functions.png" caption="Figure 2: Control system with the generalized plant \\(G\\) and weighting functions" >}}
@ -196,9 +209,9 @@ So, to obtain feasible controllers, the performance channel is a combination of
By choosing suitable weighting filters for \\(y\\) and \\(u\\), the performance can be optimized while keeping the controller effort limited: By choosing suitable weighting filters for \\(y\\) and \\(u\\), the performance can be optimized while keeping the controller effort limited:
\\[ \\|z\\|\_{rms}^2 = \left\\| \begin{bmatrix} y \\ \alpha u \end{bmatrix} \right\\|\_{rms}^2 = \\|y\\|\_{rms}^2 + \alpha^2 \\|u\\|\_{rms}^2 \\] \\[ \\|z\\|\_{rms}^2 = \left\\| \begin{bmatrix} y \\ \alpha u \end{bmatrix} \right\\|\_{rms}^2 = \\|y\\|\_{rms}^2 + \alpha^2 \\|u\\|\_{rms}^2 \\]
By calculation \\(\mathcal{H}\_2\\) optimal controllers for increasing \\(\alpha\\) and plotting the performance \\(\\|y\\|\\) vs the controller effort \\(\\|u\\|\\), the curve as depicted in Figure [3](#orgb0b1e78) is obtained. By calculation \\(\mathcal{H}\_2\\) optimal controllers for increasing \\(\alpha\\) and plotting the performance \\(\\|y\\|\\) vs the controller effort \\(\\|u\\|\\), the curve as depicted in Figure [3](#org58a8c87) is obtained.
<a id="orgb0b1e78"></a> <a id="org58a8c87"></a>
{{< figure src="/ox-hugo/jabben07_pareto_curve_H2.png" caption="Figure 3: An illustration of a Pareto curve. Each point of the curve represents the performance obtained with an optimal controller. The curve is obtained by varying \\(\alpha\\) and calculating an \\(\mathcal{H}\_2\\) optimal controller for each \\(\alpha\\)." >}} {{< figure src="/ox-hugo/jabben07_pareto_curve_H2.png" caption="Figure 3: An illustration of a Pareto curve. Each point of the curve represents the performance obtained with an optimal controller. The curve is obtained by varying \\(\alpha\\) and calculating an \\(\mathcal{H}\_2\\) optimal controller for each \\(\alpha\\)." >}}

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content/zettels/connectors.md
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@ -10,9 +10,9 @@ Tags
## Manufacturers {#manufacturers} ## Manufacturers {#manufacturers}
| Manufacturers | Links | | Manufacturers | Links | Country |
|---------------|-------------------------------------------------| |---------------|-------------------------------------------------|-------------|
| LEMO | [link](https://www.lemo.com/en) | | LEMO | [link](https://www.lemo.com/en) | Switzerland |
| Fischer | [link](https://www.fischerconnectors.com/uk/en) | | Fischer | [link](https://www.fischerconnectors.com/uk/en) | Switzerland |
<./biblio/references.bib> <./biblio/references.bib>

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content/zettels/force_sensors.md
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@ -4,13 +4,13 @@ author = ["Thomas Dehaeze"]
draft = false draft = false
+++ +++
### Backlinks {#backlinks} Backlinks:
- [Signal Conditioner]({{< relref "signal_conditioner" >}})
- [Sensors]({{< relref "sensors" >}}) - [Sensors]({{< relref "sensors" >}})
- [Nanopositioning system with force feedback for high-performance tracking and vibration control]({{< relref "fleming10_nanop_system_with_force_feedb" >}}) - [Nanopositioning system with force feedback for high-performance tracking and vibration control]({{< relref "fleming10_nanop_system_with_force_feedb" >}})
- [Collocated Control]({{< relref "collocated_control" >}}) - [Collocated Control]({{< relref "collocated_control" >}})
- [Position Sensors]({{< relref "position_sensors" >}}) - [Position Sensors]({{< relref "position_sensors" >}})
- [Signal Conditioner]({{< relref "signal_conditioner" >}})
Tags Tags
: :
@ -21,7 +21,7 @@ Tags
### Dynamics and Noise of a piezoelectric force sensor {#dynamics-and-noise-of-a-piezoelectric-force-sensor} ### Dynamics and Noise of a piezoelectric force sensor {#dynamics-and-noise-of-a-piezoelectric-force-sensor}
An analysis the dynamics and noise of a piezoelectric force sensor is done in ([Fleming 2010](#org82df6e1)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})). An analysis the dynamics and noise of a piezoelectric force sensor is done in ([Fleming 2010](#org25f6243)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
### Manufacturers {#manufacturers} ### Manufacturers {#manufacturers}
@ -36,17 +36,10 @@ An analysis the dynamics and noise of a piezoelectric force sensor is done in ([
### Signal Conditioner {#signal-conditioner} ### Signal Conditioner {#signal-conditioner}
The voltage generated by the piezoelectric material generally needs to be amplified. The voltage generated by the piezoelectric material generally needs to be amplified using a [Signal Conditioner]({{< relref "signal_conditioner" >}}).
Either **charge** amplifiers or **voltage** amplifiers can be used. Either **charge** amplifiers or **voltage** amplifiers can be used.
| Manufacturers | Links | Country |
|---------------|------------------------------------------------------------------------------------|---------|
| PCB | [link](https://www.pcb.com/products?m=482c15) | USA |
| HBM | [link](https://www.hbm.com/en/2660/paceline-cma-charge-amplifier-analogamplifier/) | Germany |
| Kistler | [link](https://www.kistler.com/fr/produits/composants/conditionnement-de-signal/) | Swiss |
| MMF | [link](https://www.mmf.de/signal%5Fconditioners.htm) | Germany |
### Effect of using multiple Stacks in series of parallels {#effect-of-using-multiple-stacks-in-series-of-parallels} ### Effect of using multiple Stacks in series of parallels {#effect-of-using-multiple-stacks-in-series-of-parallels}
@ -60,4 +53,4 @@ However, if a charge conditioner is used, the signal will be doubled.
## Bibliography {#bibliography} ## Bibliography {#bibliography}
<a id="org82df6e1"></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="org25f6243"></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>.

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content/zettels/piezoelectric_actuators.md
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@ -4,7 +4,7 @@ author = ["Thomas Dehaeze"]
draft = false draft = false
+++ +++
### Backlinks {#backlinks} Backlinks:
- [Actuators]({{< relref "actuators" >}}) - [Actuators]({{< relref "actuators" >}})
- [Voltage Amplifier]({{< relref "voltage_amplifier" >}}) - [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
@ -35,7 +35,7 @@ Tags
### Model {#model} ### Model {#model}
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgdda2743)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})). A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgf8860c8)) ([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. Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel.
@ -50,27 +50,27 @@ with:
## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators} ## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#orga200a60)): The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#org98162bd)):
> 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 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. > The flatter is the actuator, the higher is the amplification.
A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org46de525)). A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org47bb392)).
<a id="orgeed82ad"></a> <a id="orgeb77af2"></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>" >}} {{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="Figure 1: Topology of several types of compliant mechanisms <sup id=\"d9e8b33774f1e65d16bd79114db8ac64\"><a 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).\">ling16_enhan_mathem_model_displ_amplif</a></sup>" >}}
| **Manufacturers** | **Links** | **Country** | | Manufacturers | Links | Country |
|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------| |---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------|
| Cedrat | [link](https://www.cedrat-technologies.com/en/products/actuators/amplified-piezo-actuators.html) | France | | 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 | | 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 | | 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 | | Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA |
| Noliac | [link](http://www.noliac.com/products/actuators/amplified-actuators/) | Denmark | | 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 | | 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 | | CoreMorrow | [link](http://www.coremorrow.com/en/pro-13-1.html) | China |
| PiezoData | [link](https://www.piezodata.com/piezoelectric-actuator-amplifier/) | China | | PiezoData | [link](https://www.piezodata.com/piezoelectric-actuator-amplifier/) | China |
## Specifications {#specifications} ## Specifications {#specifications}
@ -149,51 +149,51 @@ For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolut
### Electrical Capacitance {#electrical-capacitance} ### 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](#org9c97b26)). The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#org297ca75)).
This is due to the fact that voltage amplifier has a limitation on the deliverable current. 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. [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="org9c97b26"></a> <a id="org297ca75"></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" >}} {{< 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} ## 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](#org6172e71)). 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](#org481d529)).
<a id="org6172e71"></a> <a id="org481d529"></a>
{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="Figure 3: Motion of a piezoelectric stack actuator under external constant force" >}} {{< 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} ## 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](#org802b6e3)): 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](#orgf063765)):
\begin{equation} \begin{equation}
\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e} \Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
\end{equation} \end{equation}
<a id="org802b6e3"></a> <a id="orgf063765"></a>
{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="Figure 4: Motion of a piezoelectric stack actuator in contact with a stiff environment" >}} {{< 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](#orga68d9e2)). For piezo actuators, force and displacement are inversely related (Figure [5](#org82b8a4e)).
Maximum, or blocked, force (\\(F\_b\\)) occurs when there is no displacement. 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. 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. 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="orga68d9e2"></a> <a id="org82b8a4e"></a>
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}} {{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
## Bibliography {#bibliography} ## Bibliography {#bibliography}
<a id="orga200a60"></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="org98162bd"></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="orgdda2743"></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="orgf8860c8"></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="org46de525"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.” <a id="org47bb392"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”

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content/zettels/position_sensors.md
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@ -18,7 +18,7 @@ Tags
## Reviews of Relative Position Sensors {#reviews-of-relative-position-sensors} ## Reviews of Relative Position Sensors {#reviews-of-relative-position-sensors}
- Fleming, A. J., A review of nanometer resolution position sensors: operation and performance ([Fleming 2013](#org1ee8f98)) ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}})) - Fleming, A. J., A review of nanometer resolution position sensors: operation and performance ([Fleming 2013](#org81e91f9)) ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
<a id="table--tab:characteristics-relative-sensor"></a> <a id="table--tab:characteristics-relative-sensor"></a>
<div class="table-caption"> <div class="table-caption">
@ -76,7 +76,7 @@ Description:
## Inductive Sensor (Eddy Current) {#inductive-sensor--eddy-current} ## Inductive Sensor (Eddy Current) {#inductive-sensor--eddy-current}
| Manufacturers | Links | | | Manufacturers | Links | Country |
|----------------|-------------------------------------------------------------------------------------------|---------| |----------------|-------------------------------------------------------------------------------------------|---------|
| Micro-Epsilon | [link](https://www.micro-epsilon.com/displacement-position-sensors/eddy-current-sensor/) | Germany | | Micro-Epsilon | [link](https://www.micro-epsilon.com/displacement-position-sensors/eddy-current-sensor/) | Germany |
| Lion Precision | [link](https://www.lionprecision.com/products/eddy-current-sensors) | USA | | Lion Precision | [link](https://www.lionprecision.com/products/eddy-current-sensors) | USA |
@ -117,9 +117,9 @@ Description:
| Renishaw | 0.2 | 1 | 6 | 1 | | Renishaw | 0.2 | 1 | 6 | 1 |
| Picoscale | 0.2 | 2 | 2 | 1 | | Picoscale | 0.2 | 2 | 2 | 1 |
([Jang and Kim 2017](#org3ee30b7)) ([Jang and Kim 2017](#org64791e2))
<a id="org9edecbb"></a> <a id="org75192f1"></a>
{{< figure src="/ox-hugo/position_sensor_interferometer_precision.png" caption="Figure 1: Expected precision of interferometer as a function of measured distance" >}} {{< figure src="/ox-hugo/position_sensor_interferometer_precision.png" caption="Figure 1: Expected precision of interferometer as a function of measured distance" >}}
@ -136,6 +136,6 @@ Description:
## Bibliography {#bibliography} ## Bibliography {#bibliography}
<a id="org1ee8f98"></a>Fleming, Andrew J. 2013. “A Review of Nanometer Resolution Position Sensors: Operation and Performance.” _Sensors and Actuators a: Physical_ 190 (nil):106–26. <https://doi.org/10.1016/j.sna.2012.10.016>. <a id="org81e91f9"></a>Fleming, Andrew J. 2013. “A Review of Nanometer Resolution Position Sensors: Operation and Performance.” _Sensors and Actuators a: Physical_ 190 (nil):106–26. <https://doi.org/10.1016/j.sna.2012.10.016>.
<a id="org3ee30b7"></a>Jang, Yoon-Soo, and Seung-Woo Kim. 2017. “Compensation of the Refractive Index of Air in Laser Interferometer for Distance Measurement: A Review.” _International Journal of Precision Engineering and Manufacturing_ 18 (12):1881–90. <https://doi.org/10.1007/s12541-017-0217-y>. <a id="org64791e2"></a>Jang, Yoon-Soo, and Seung-Woo Kim. 2017. “Compensation of the Refractive Index of Air in Laser Interferometer for Distance Measurement: A Review.” _International Journal of Precision Engineering and Manufacturing_ 18 (12):1881–90. <https://doi.org/10.1007/s12541-017-0217-y>.

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content/zettels/shaker.md
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draft = false draft = false
+++ +++
### Backlinks {#backlinks} Backlinks:
- [Modal Analysis]({{< relref "modal_analysis" >}}) - [Modal Analysis]({{< relref "modal_analysis" >}})
@ -14,8 +14,6 @@ Tags
## Manufacturers {#manufacturers} ## Manufacturers {#manufacturers}
<https://www.bksv.com/en/products/shakers-and-exciters/LDS-shaker-systems/permanent-magnet-shakers/V201>
| Manufacturers | Links | Country | | Manufacturers | Links | Country |
|--------------------|----------------------------------------------------------------------------------|-----------| |--------------------|----------------------------------------------------------------------------------|-----------|
| Labsen | [link](http://labsentec.com.au/category/products/vibrationshock/) | Australia | | Labsen | [link](http://labsentec.com.au/category/products/vibrationshock/) | Australia |

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content/zettels/signal_conditioner.md
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draft = false draft = false
+++ +++
### Backlinks {#backlinks} Backlinks:
- [Position Sensors]({{< relref "position_sensors" >}}) - [Position Sensors]({{< relref "position_sensors" >}})
Tags Tags
: [Force Sensors]({{< relref "force_sensors" >}}) : [Force Sensors]({{< relref "force_sensors" >}}), [Sensors]({{< relref "sensors" >}}), [Electronics]({{< relref "electronics" >}})
Most sensors needs some signal conditioner electronics before digitize the signal. Most sensors needs some signal conditioner electronics before digitize the signal.
Few examples are: Few examples are:
@ -29,22 +29,28 @@ The signal conditioning electronics can have different functions:
## Charge Amplifier {#charge-amplifier} ## Charge Amplifier {#charge-amplifier}
| Manufacturers | Links | | Manufacturers | Links | Country |
|---------------|---------------------------------------------------------------------------------------------------------------------| |---------------|---------------------------------------------------------------------------------------------------------------------|---------|
| PCB | [link](https://www.pcb.com/sensors-for-test-measurement/electronics/line-powered-multi-channel-signal-conditioners) | | PCB | [link](https://www.pcb.com/sensors-for-test-measurement/electronics/line-powered-multi-channel-signal-conditioners) | USA |
| HBM | [link](https://www.hbm.com/en/2660/paceline-cma-charge-amplifier-analogamplifier/) | Germany |
| Kistler | [link](https://www.kistler.com/fr/produits/composants/conditionnement-de-signal/) | Swiss |
| MMF | [link](https://www.mmf.de/signal%5Fconditioners.htm) | Germany |
## Voltage Amplifier {#voltage-amplifier} ## Voltage Amplifier {#voltage-amplifier}
| Manufacturers | Links | | Manufacturers | Links | Country |
|---------------|------------------------------------------------------------------| |---------------|------------------------------------------------------------------------------------|---------|
| Femto | [link](https://www.femto.de/en/products/voltage-amplifiers.html) | | Femto | [link](https://www.femto.de/en/products/voltage-amplifiers.html) | Germany |
| HBM | [link](https://www.hbm.com/en/2660/paceline-cma-charge-amplifier-analogamplifier/) | Germany |
| Kistler | [link](https://www.kistler.com/fr/produits/composants/conditionnement-de-signal/) | Swiss |
| MMF | [link](https://www.mmf.de/signal%5Fconditioners.htm) | Germany |
## Current Amplifier {#current-amplifier} ## Current Amplifier {#current-amplifier}
| Manufacturers | Links | | Manufacturers | Links | Country |
|---------------|------------------------------------------------------------------| |---------------|------------------------------------------------------------------|---------|
| Femto | [link](https://www.femto.de/en/products/current-amplifiers.html) | | Femto | [link](https://www.femto.de/en/products/current-amplifiers.html) | Germany |
<./biblio/references.bib> <./biblio/references.bib>

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content/zettels/slip_rings.md
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draft = false draft = false
+++ +++
Backlinks:
- [Rotation Stage]({{< relref "rotation_stage" >}})
Tags Tags
: :
| Manufacturers | Links |
|---------------|---------------------------------| ## Manufacturers {#manufacturers}
| Moflon | [link](https://www.moflon.com/) |
| Manufacturers | Links | Country |
|---------------|---------------------------------|---------|
| Moflon | [link](https://www.moflon.com/) | China |
<./biblio/references.bib> <./biblio/references.bib>

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content/zettels/vibration_isolation.md
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## Vibration Isolating Pads {#vibration-isolating-pads} ## Vibration Isolating Pads {#vibration-isolating-pads}
| Manufacturer | links | | Manufacturer | links | Country |
|--------------|----------------------------------| |--------------|----------------------------------|---------|
| ACE | [link](https://www.ace-ace.com/) | | ACE | [link](https://www.ace-ace.com/) | Germany |
## Vibration Isolation Tables {#vibration-isolation-tables} ## Vibration Isolation Tables {#vibration-isolation-tables}
| Manufacturer | links | | Manufacturer | links | Country |
|-------------------|----------------------------------------------------------------------------------| |-------------------|----------------------------------------------------------------------------------|-------------|
| TMC | [link](https://www.techmfg.com/products/stacis/stacisiii) | | TMC | [link](https://www.techmfg.com/products/stacis/stacisiii) | USA |
| Newport | [link](https://www.newport.com/f/guardian-active-isolation-workstations) | | Newport | [link](https://www.newport.com/f/guardian-active-isolation-workstations) | USA |
| Thorlabs | [link](https://www.thorlabs.com/navigation.cfm?guide%5FID=42) | | Thorlabs | [link](https://www.thorlabs.com/navigation.cfm?guide%5FID=42) | USA |
| IDE | [link](https://www.ideworld.com/en/active%5Fvibration%5Fisolation.html) | | IDE | [link](https://www.ideworld.com/en/active%5Fvibration%5Fisolation.html) | Germany |
| Harvard Apparatus | [link](https://www.warneronline.com/labmate-vibraplane-workstations-9100-series) | | Harvard Apparatus | [link](https://www.warneronline.com/labmate-vibraplane-workstations-9100-series) | USA |
| Herzan | [link](https://www.herzan.com/products/active-vibration-control/avi-series.html) | | Herzan | [link](https://www.herzan.com/products/active-vibration-control/avi-series.html) | USA |
| Standa | [link](http://www.standa.lt/products/catalog/optical%5Ftables?item=335) | | Standa | [link](http://www.standa.lt/products/catalog/optical%5Ftables?item=335) | Lithuania |
| Table Stable | [link](http://www.tablestable.com/en/products/list/2/) | | Table Stable | [link](http://www.tablestable.com/en/products/list/2/) | Switzerland |
| Accurion | [link](https://www.halcyonics.com/active-vibration-isolation-products) | | Accurion | [link](https://www.halcyonics.com/active-vibration-isolation-products) | Germany |
| Vibiso | [link](https://vibiso.com/?page%5Fid=3433) | | Vibiso | [link](https://vibiso.com/?page%5Fid=3433) | USA |
<./biblio/references.bib> <./biblio/references.bib>

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content/zettels/voice_coil_actuators.md
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draft = false draft = false
+++ +++
### Backlinks {#backlinks} Backlinks:
- [Actuators]({{< relref "actuators" >}}) - [Actuators]({{< relref "actuators" >}})
- [Shaker]({{< relref "shaker" >}}) - [Shaker]({{< relref "shaker" >}})
- [Current Amplifier]({{< relref "current_amplifier" >}})
Tags Tags
: [Actuators]({{< relref "actuators" >}}) : [Actuators]({{< relref "actuators" >}})
@ -15,20 +16,23 @@ Tags
## Manufacturers {#manufacturers} ## Manufacturers {#manufacturers}
| Manufacturers | Links | | Manufacturers | Links | Country |
|----------------------|----------------------------------------------| |----------------------|----------------------------------------------|-------------|
| Geeplus | [link](https://www.geeplus.com/) | | Geeplus | [link](https://www.geeplus.com/) | UK |
| Maccon | [link](https://www.maccon.de/en.html) | | Maccon | [link](https://www.maccon.de/en.html) | Germany |
| TDS PP | [link](https://www.tds-pp.com/en/) | | TDS PP | [link](https://www.tds-pp.com/en/) | Switzerland |
| H2tech | [link](https://www.h2wtech.com/) | | H2tech | [link](https://www.h2wtech.com/) | USA |
| PBA Systems | [link](http://www.pbasystems.com.sg/) | | PBA Systems | [link](http://www.pbasystems.com.sg/) | Singapore |
| Celera Motion | [link](https://www.celeramotion.com/) | | Celera Motion | [link](https://www.celeramotion.com/) | USA |
| Beikimco | [link](http://www.beikimco.com/) | | Beikimco | [link](http://www.beikimco.com/) | USA |
| Electromate | [link](https://www.electromate.com/) | | Electromate | [link](https://www.electromate.com/) | Canada |
| Magnetic Innovations | [link](https://www.magneticinnovations.com/) | | Magnetic Innovations | [link](https://www.magneticinnovations.com/) | Netherlands |
| Monticont | [link](http://www.moticont.com/) | | Monticont | [link](http://www.moticont.com/) | USA |
## Typical Specifications {#typical-specifications} ## Typical Specifications {#typical-specifications}
## Model of a Voice Coil Actuator {#model-of-a-voice-coil-actuator}
<./biblio/references.bib> <./biblio/references.bib>