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title = "Acquisition Systems"
author = ["Dehaeze Thomas"]
draft = false
category = "equipment"
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## Manufacturers {#manufacturers}
<https://dewesoft.com/daq/list-of-data-acquisition-companies>
| Manufacturers | Country |
|----------------------------------------------------------------------------------------------------|----------|
| [Dewesoft](https://dewesoft.com/) | Slovenia |

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{{< youtube b9lxtOJj3yU >}}
Also see (<a href="#citeproc_bib_item_2">Kester 2005</a>).
## Link between required dynamic range and effective number of bits {#link-between-required-dynamic-range-and-effective-number-of-bits}
<a id="figure--fig:dynamic-range-enob"></a>
{{< figure src="/ox-hugo/dynamic_range_enob.png" caption="<span class=\"figure-number\">Figure 2: </span>Relation between Dynamic range and required number of bits (effective)" >}}
## Oversampling {#oversampling}
@@ -92,4 +101,5 @@ The quantization is:
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Baker, Bonnie. 2011. “How Delta-Sigma Adcs Work, Part.” <i>Analog Applications</i> 7.</div>
<div class="csl-entry"><a id="citeproc_bib_item_2"></a>Kester, Walt. 2005. “Taking the Mystery out of the Infamous Formula, $snr = 6.02 N + 1.76 Db$, and Why You Should Care.”</div>
</div>

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title = "Eddy Current Damping"
author = ["Dehaeze Thomas"]
draft = false
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Tags
: [Passive Damping]({{< relref "passive_damping.md" >}})
<https://courses.lumenlearning.com/suny-physics/chapter/23-4-eddy-currents-and-magnetic-damping/>
## Vacuum compatible magnets {#vacuum-compatible-magnets}
<https://www.mceproducts.com/articles/magnets-in-vacuum-applications>
## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
</div>

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title = "Electromagnetism"
draft = false
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Tags
:
## Maxwell equations for magnetics {#maxwell-equations-for-magnetics}
### Gauss law {#gauss-law}
"Magnetic fieldlines are closed loop."
\begin{equation}
\oiint\_S (\bm{B} \cdot \hat{\bm{n}}) dS = 0
\end{equation}
### Faraday's law {#faraday-s-law}
A changing magnetic field causes an electric field over a wire
\begin{equation}
\oint\_L \bm{E} \cdot d\bm{l} = -\frac{d}{dt} \iint\_S(\bm{B} \cdot \bm{n}) dS
\end{equation}
The line-integral of the electrical field over a closed loop L equals the change of the field through the open surface S bounded by the loop L.
This is a voltage source (EMF), where the current is driven in the direction of the electric field.
### Ampère's law {#ampère-s-law}
"Current through a wire gives a magnetic field".
\begin{equation}
\oint\_L \bm{B} \cdot dl = \mu\_0 I
\end{equation}
The line integral of the magnetic field over a closed loop L is proportional to the current through the surface S enclosed by the loop L.
## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
</div>

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title = "Encoders"
author = ["Dehaeze Thomas"]
draft = false
category = "equipment"
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There are two main types of encoders: optical encoders, and magnetic encoders.
## Linear Encoders {#linear-encoders}
## Manufacturers {#manufacturers}
### Manufacturers {#manufacturers}
| Manufacturers | Country |
|---------------------------------------------------------------------------------|---------|
| [Heidenhain](https://www.heidenhain.com/en_US/products/linear-encoders/) | Germany |
| [MicroE Systems](https://www.celeramotion.com/microe/products/linear-encoders/) | USA |
| [Renishaw](https://www.renishaw.com/en/browse-encoder-range--6440) | UK |
| [Celera Motion](https://www.celeramotion.com/microe/) | USA |
<https://www.posic.com/EN/>
<https://www.rls.si/eng/products/rotary-magnetic-encoders>
## Angular Encoders {#angular-encoders}
<https://www.maxongroup.com/maxon/view/category/sensor>
| Manufacturers | Country |
|--------------------------------------------------------------------------|-------------|
| [Heidenhain](https://www.heidenhain.com/en_US/products/linear-encoders/) | Germany |
| [Renishaw](https://www.renishaw.com/en/browse-encoder-range--6440) | UK |
| [Celera Motion](https://www.celeramotion.com/microe/) | USA |
| [Magnescale](https://www.magnescale.com/en/) | Japanese |
| [Posic](https://www.posic.com/EN/) | Switzerland |
| [RLS](https://www.rls.si/eng/products/rotary-magnetic-encoders) | Slovenia |
| [AMO](https://www.amo-gmbh.com/en/) | Australia |
| [NumerikJena](https://www.numerikjena.de/en/) | Germany |
## Bibliography {#bibliography}

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title = "EtherCAT"
author = ["Dehaeze Thomas"]
draft = false
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Tags
:
## Manufacturers {#manufacturers}
General purpose / PLC:
| Manufacturer |
|-------------------------------------------------------------------------------------|
| [Bechoff](https://www.beckhoff.com/fr-fr/products/i-o/ethercat-terminals/) |
| [Wago](https://www.wago.com/global/i-o-systems/fieldbus-coupler-ethercat/p/750-354) |
Acquisition systems:
| Manufacturer |
|----------------------------------------------------------------------------|
| [National Instrument](https://www.ni.com/fr-fr/support/model.ni-9145.html) |
| [Dewesoft](https://dewesoft.com/products/daq-systems) |
## Cycle Time {#cycle-time}
See (<a href="#citeproc_bib_item_1">Robert et al. 2012</a>).
There is a nice [online calculator](https://developer.acontis.com/ethercat-cycle-time-calculator.html).
## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Robert, Jérémy, Jean-Philippe Georges, Eric Rondeau, and Thierry Divoux. 2012. “Minimum Cycle Time Analysis of Ethernet-Based Real-Time protocols.” <i>International Journal of Computers, Communications and Control</i> 7 (4). Agora University of Oradea: 743–57. <a href="https://hal.archives-ouvertes.fr/hal-00714560">https://hal.archives-ouvertes.fr/hal-00714560</a>.</div>
</div>

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title = "Granite"
author = ["Dehaeze Thomas"]
draft = false
category = "equipment"
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## Manufacturers {#manufacturers}
| Manufacturers | Country |
|--------------------------------------------------|---------|
| [Microplan](https://www.microplan-group.com/fr/) | France |
| [Zali](http://zali-precision.it/en/products/) | Italy |
| Manufacturers | Country |
|--------------------------------------------------|-------------|
| [Microplan](https://www.microplan-group.com/fr/) | France |
| [Zali](http://zali-precision.it/en/products/) | Italy |
| [Mytri](https://www.mytri.nl/en) | Netherlands |
## Bibliography {#bibliography}

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title = "Linear Brushless Motor"
author = ["Dehaeze Thomas"]
draft = false
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Tags
:
: [Motors]({{< relref "motors.md" >}})
## Ironcore VS Ironless {#ironcore-vs-ironless}
- Ironcore: more torque/force density
- Ironless: less cogging
## Manufacturesr {#manufacturesr}
@@ -27,6 +29,7 @@ Tags
| [Hiwin](https://www.hiwin.de/fr/Produits/c/3952) | Germany |
| [Baumeuller](https://www.baumueller.com/en/products/motors/linear-motors) | Germany |
| [Rexroth](https://www.boschrexroth.com/en/xc/products/product-groups/electric-drives-and-controls/motors-and-gearboxes/synchronous-linear-motors) | Germany |
| [Kollmorgen](https://www.kollmorgen.com/fr-fr/products/motors/direct-drive/direct-drive-linear/moteurs-lin%C3%A9aires-accouplement-direct/) | Germany |
| [PBA Systems](https://www.pbasystems.com.sg/product-category/precision-robotics/direct-drive-motors/) | Singapore |
| [Akribis](https://www.akribis-sys.de/en/produkte/1/linear-motors/) | Singapore |
| [Chieftek](http://www.chieftek.com/product-lm.asp) | Taiwan |

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title = "Mass Spring Damper Systems"
author = ["Dehaeze Thomas"]
draft = false
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@@ -13,7 +12,7 @@ Tags
Let's consider Figure [1](#figure--fig:mass-spring-damper-system) where:
- \\(m\\) is the mass in [kg]
- \\(ḱ\\) is the spring stiffness in [N/m]
- \\(k\\) is the spring stiffness in [N/m]
- \\(c\\) is the damping coefficient in [N/(m/s)]
- \\(F\\) is the actuator force in [N]
- \\(F\_d\\) is external force applied to the mass in [N]
@@ -42,14 +41,34 @@ with:
- \\(\xi\\) the damping ratio
## Transmissibility {#transmissibility}
## Transfer function {#transfer-function}
### Voice Coil Actuator with flexible guiding {#voice-coil-actuator-with-flexible-guiding}
```matlab
%% Mechanical properties
m = 1; % Mobile mass [kg]
k = 1e6; % stiffness [N/m]
xi = 0.01; % Modal Damping
c = 2*xi*sqrt(k*m);
```
```matlab
%% Transfer function from F [N] to x [m]
G = 1/(m*s^2 + c*s + k);
```
### Transmissibility {#transmissibility}
\begin{equation}
\frac{x}{w}(s) = \frac{1}{\frac{s^2}{\omega\_0^2} + 2 \xi \frac{s}{\omega\_0} + 1}
\end{equation}
## Compliance {#compliance}
### Compliance {#compliance}
\begin{equation}
\frac{x}{F\_d}(s) = \frac{1/k}{\frac{s^2}{\omega\_0^2} + 2 \xi \frac{s}{\omega\_0} + 1}

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title = "Motor Commutation"
draft = false
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Tags
: [Motors]({{< relref "motors.md" >}})
## Sensors {#sensors}
- Hall effect sensors
- [Encoders]({{< relref "encoders.md" >}})
## Electrical Commutation {#electrical-commutation}
For a 3 phase motor (linear or angular), the force constant is a function of the position.
The motor can be designed in such a way that the relation is close to a sinusoidal function of a trapezoidal function.
### "Hard" commutation {#hard-commutation}
<a id="figure--fig:motor-hard-commutation"></a>
{{< figure src="/ox-hugo/motor_hard_commutation.png" caption="<span class=\"figure-number\">Figure 1: </span>By changing the direction of the current at the zero force positions of each coil (dashed), an almost constant force-constant of the total actuator is obtained." >}}
### Sinusoidal Commutation {#sinusoidal-commutation}
<a id="figure--fig:motor-sin-commutation"></a>
{{< figure src="/ox-hugo/motor_sin_commutation.png" caption="<span class=\"figure-number\">Figure 2: </span>Three phase commutation with a sinusoidal control of the currents in each coil segment (\\(I\_R, I\_S, I\_T\\)) in phase with their spatial sinusoidal force-constant \\(B l = k\\) values (\\(k\_R, k\_S, k\_T\\)) results in a force per segment with a spatial frequency that is double the original spatial frequency of the coils. The resulting total force of the three coil segments is the sum of the values of the force in each segment and is independent of the position." >}}
## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
</div>

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title = "Motors"
author = ["Dehaeze Thomas"]
draft = false
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@@ -14,24 +13,19 @@ Reviews:
## Linear Motors {#linear-motors}
### Short Stroke {#short-stroke}
[Piezoelectric Actuators]({{< relref "piezoelectric_actuators.md" >}})
### Long Stroke {#long-stroke}
[Voice Coil Actuators]({{< relref "voice_coil_actuators.md" >}})
- [Piezoelectric Actuators]({{< relref "piezoelectric_actuators.md" >}})
- [Voice Coil Actuators]({{< relref "voice_coil_actuators.md" >}})
- [Linear Brushless Motor]({{< relref "linear_brushless_motor.md" >}})
## Angular Motors {#angular-motors}
[Stepper Motor]({{< relref "stepper_motor.md" >}})
- [Stepper Motor]({{< relref "stepper_motor.md" >}})
- [Torque Motor]({{< relref "torque_motor.md" >}})
## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Murugesan, S. 1981. “An Overview of Electric Motors for Space Applications.” <i>Ieee Transactions on Industrial Electronics and Control Instrumentation</i> IECI-28 (4): 260–65. doi:<a href="https://doi.org/10.1109/TIECI.1981.351050">10.1109/TIECI.1981.351050</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Murugesan, S. 1981. “An Overview of Electric Motors for Space Applications.” <i>IEEE Transactions on Industrial Electronics and Control Instrumentation</i> IECI-28 (4): 260–65. doi:<a href="https://doi.org/10.1109/TIECI.1981.351050">10.1109/TIECI.1981.351050</a>.</div>
</div>

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@@ -165,21 +165,21 @@ This is due to the fact that voltage amplifier has a limitation on the deliverab
<a id="figure--fig:piezoelectric-capacitance-voltage-max"></a>
{{< figure src="/ox-hugo/piezoelectric_capacitance_voltage_max.png" caption="<span class=\"figure-number\">Figure 2: </span>Maximum sin-wave amplitude as a function of frequency for several piezoelectric capacitance" >}}
{{< figure src="/ox-hugo/piezoelectric_capacitance_voltage_max.png" caption="<span class=\"figure-number\">Figure 1: </span>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](#figure--fig:piezoelectric-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 [1](#figure--fig:piezoelectric-mass-load)).
<a id="figure--fig:piezoelectric-mass-load"></a>
{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="<span class=\"figure-number\">Figure 3: </span>Motion of a piezoelectric stack actuator under external constant force" >}}
{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="<span class=\"figure-number\">Figure 1: </span>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](#figure--fig:piezoelectric-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 [1](#figure--fig:piezoelectric-spring-load)):
\begin{equation}
\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
@@ -187,16 +187,16 @@ Then the piezoelectric actuator is in contact with a spring load \\(k\_e\\), its
<a id="figure--fig:piezoelectric-spring-load"></a>
{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="<span class=\"figure-number\">Figure 4: </span>Motion of a piezoelectric stack actuator in contact with a stiff environment" >}}
{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="<span class=\"figure-number\">Figure 1: </span>Motion of a piezoelectric stack actuator in contact with a stiff environment" >}}
For piezo actuators, force and displacement are inversely related (Figure [5](#figure--fig:piezoelectric-force-displ-relation)).
For piezo actuators, force and displacement are inversely related (Figure [1](#figure--fig:piezoelectric-force-displ-relation)).
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="figure--fig:piezoelectric-force-displ-relation"></a>
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="<span class=\"figure-number\">Figure 5: </span>Relation between the maximum force and displacement" >}}
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="<span class=\"figure-number\">Figure 1: </span>Relation between the maximum force and displacement" >}}
## Piezoelectric stiffness - Electrical Boundaries {#piezoelectric-stiffness-electrical-boundaries}
@@ -211,13 +211,14 @@ Therefore, if the piezoelectric actuator is driven by a charge amplifier (i.e. h
Piezoelectric actuators can be driven either using a voltage to charge converter or a [Voltage Amplifier]({{< relref "voltage_amplifier.md" >}}).
Limitations of the electronics is discussed in [Design, modeling and control of nanopositioning systems]({{< relref "fleming14_desig_model_contr_nanop_system.md" >}}).
Also see (<a href="#citeproc_bib_item_4">Liu et al. 2007</a>).
## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static &#38; Dynamic Applications.” <i>Ferroelectrics</i> 351 (1): 3–14. doi:<a href="https://doi.org/10.1080/00150190701351865">10.1080/00150190701351865</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_2"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” <i>Ieee/Asme Transactions on Mechatronics</i> 15 (3): 433–47. doi:<a href="https://doi.org/10.1109/tmech.2009.2028422">10.1109/tmech.2009.2028422</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_2"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” <i>IEEE/ASME Transactions on Mechatronics</i> 15 (3): 433–47. doi:<a href="https://doi.org/10.1109/tmech.2009.2028422">10.1109/tmech.2009.2028422</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_3"></a>Ling, Mingxiang, Junyi Cao, Minghua Zeng, Jing Lin, and Daniel J Inman. 2016. “Enhanced Mathematical Modeling of the Displacement Amplification Ratio for Piezoelectric Compliant Mechanisms.” <i>Smart Materials and Structures</i> 25 (7): 075022. doi:<a href="https://doi.org/10.1088/0964-1726/25/7/075022">10.1088/0964-1726/25/7/075022</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_4"></a>Liu, W. Q., Z. H. Feng, R. B. Liu, and J. Zhang. 2007. “The Influence of Preamplifiers on the Piezoelectric Sensor’s Dynamic Property.” <i>Review of Scientific Instruments</i> 78 (12): 125107. doi:<a href="https://doi.org/10.1063/1.2825404">10.1063/1.2825404</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_5"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”</div>

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title = "Signal to Noise Ratio"
author = ["Dehaeze Thomas"]
draft = false
+++
@@ -15,7 +14,7 @@ From (<a href="#citeproc_bib_item_2">Jabben 2007</a>) (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.
> The noise performance of components like sensors, amplifiers, converters, etc., is often specified in terms of a **Signal to Noise Ratio** (SNR).
> The SNR gives the ratio of the RMS value of a sine that covers the full range of the channel through which the signal is propagating over the RMS value of the electrical noise.
> The SNR gives the **ratio of the RMS value of a sine that covers the full range** of the channel through which the signal is propagating **over the RMS value of the electrical noise**.
>
> Usually, the SNR is specified up to a certain cut-off frequency.
> If no information on the colouring of the noise is available, then the corresponding **PSD can be assumed to be white up to the cut-off frequency** \\(f\_c\\):
@@ -95,6 +94,6 @@ The peak-to-peak noise will be approximately \\(6 \sigma = 1.7 nm\\)
## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” <i>Ieee/Asme Transactions on Mechatronics</i> 15 (3): 433–47. doi:<a href="https://doi.org/10.1109/tmech.2009.2028422">10.1109/tmech.2009.2028422</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” <i>IEEE/ASME Transactions on Mechatronics</i> 15 (3): 433–47. doi:<a href="https://doi.org/10.1109/tmech.2009.2028422">10.1109/tmech.2009.2028422</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_2"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.</div>
</div>

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title = "Torque Motor"
draft = false
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Tags
: [Motors]({{< relref "motors.md" >}})
## Manufacturers {#manufacturers}
| Manufacturers | Country |
|--------------------------------------------------------------------------------------------------------------------|-------------|
| [Tecnotion](https://www.tecnotion.com/product-category/torque-motors/) | Netherlands |
| [MagneticInnovations](https://www.magneticinnovations.com/direct-drive-electric-motors/torque-motor-direct-drive/) | Netherlands |
| [Etel](https://www.etel.ch/torque-motors/overview/) | Switzerland |
| [TDS](https://www.tds-pp.com/en/products/torque-motors/) | Switzerland |
| [Aerotech](https://www.aerotech.com/product/motors/s-series-brushless-frameless-torque-motor/) | USA |
| [ThinGap](https://www.thingap.com/) | USA |
| [CeleraMotion](https://www.celeramotion.com/applimotion/products/direct-drive-frameless-rotary-motors/) | |
## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
</div>

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title = "Transconductance Amplifiers"
author = ["Dehaeze Thomas"]
draft = false
category = "equipment"
+++
@@ -18,46 +17,6 @@ Such a converter is called a voltage-to-current converter, also named a voltage-
Such amplifier is used to control motors (e.g. voice coil, BLDC, stepper motors, ...).
## Specifications {#specifications}
### Noise {#noise}
```matlab
BL = 20; % [N/A]
m = 1; % [kg]
```
```matlab
freq = logspace(0,4,1000); % [Hz]
%% Current noise of the amplifier
I_asd = 1e-6*ones(size(freq)); % [A/sqrt(Hz)]
```
```matlab
x_asd = I_asd*(BL/m)./(2*pi*freq).^2;
```
```matlab
figure;
plot(freq, x_asd)
xlabel("Frequency [Hz]");
ylabel("ASD [$m/\sqrt{Hz}$]");
set(gca, 'Xscale', 'log');
set(gca, 'Yscale', 'log');
```
```matlab
figure;
plot(freq, sqrt(flip(-cumtrapz(flip(freq), flip(x_asd.^2)))))
xlabel("Frequency [Hz]");
ylabel("Cumulative Amplitude Spectrum [m rms]");
set(gca, 'Xscale', 'log');
set(gca, 'Yscale', 'log');
```
## Manufacturers {#manufacturers}
<a id="table--tab:table-name"></a>
@@ -71,9 +30,8 @@ set(gca, 'Yscale', 'log');
| [Apogee](https://prodrive-technologies.com/motion/products/servo-drives/apogee-kepler-series/) | Prodrive | PWM | 1 to 3 | +/-10V 16bits | Encoder | 7kHz | 1e-6 |
| [S3-400/8](https://prodrive-technologies.com/motion/products/servo-drives/cygnus-series/) | Prodrive | PWM | 1 | +/-10V | Encoder | 1kHz | 1e-4 |
| [LWM7S](https://www.maccon.co.uk/linear-servo-amplifier.html) | Macon | Linear | 1 | | Encoder/Hall | | |
| [Soloist ML](https://www.aerotech.com/product/motion-control-platforms/soloist-ml-controller-and-linear-digital-drive/) | Aerotech | Linear | 1 | +/-10V 16bits | Encoder/Hall | | |
| [Automation1 XL4s](https://www.aerotech.com/product/motion-control-platforms/automation1-xl4s-high-performance-voice-coil-drive/) | Aerotech | Linear | 1 (voice coil) | +/-10V 16bits | ? | | |
| [Automation1 XL2e](https://www.aerotech.com/product/motion-control-platforms/automation1-xl4s-high-performance-voice-coil-drive/) | Aerotech | Linear | 1 | +/-10V 16bits | Encoder/Hall | 2.5kHz | |
| [Automation1 XL4s](https://www.aerotech.com/product/motion-control-platforms/automation1-xl4s-high-performance-voice-coil-drive/) | Aerotech | Linear | 1 (voice coil) | +/-10V 16bits | ? | | |
| [EM-356B](https://electromen.com/en/products/item/motor-controllers/brushless-dc-motor/EM-356B) | Electromen | PWM | 1 | 0-10V | Hall | | |
| [azbh10a4](https://www.a-m-c.com/product/azbh10a4/) | AMC | PWM | 1 | +/-10V | Hall | | |
| [X-MCC](https://www.zaber.com/products/controllers-joysticks/X-MCC) | Zaber | ?? | 1 to 4 | | | | |
@@ -88,14 +46,276 @@ set(gca, 'Yscale', 'log');
| Model | Manufacturer | Linear / PWM | Axes | Interfaces | Current Bandwidth | Max Current | ASD at 1kHz [A/sqrt(Hz)] |
|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------|--------------|------------------------|------------|-------------------|-------------|--------------------------|
| [LA300](https://varedan.com/product/analog-linear-servo-amplifiers/la-300-analog-linear-servo-amplifier/) | Varedan | Linear | 3 | +/-10V | 10kHz | 4A | |
| [LA24](https://www.cedrat-technologies.com/en/technologies/actuators/magnetic-actuators-motors.html) | Cedrat | Linear | 3 | +/-10V | 35kHz | 1.5A | |
| [CMAu10](https://www.cedrat-technologies.com/en/products/magnetic-controllers/oem-amplifiers.html) | Cedrat | Linear | 1 | +/-10V | 5kHz | 0.5A | |
| [TA115](https://www.trustautomation.com/products/linear-drives/ta115-linear-drive/) and [TA105](https://www.trustautomation.com/products/linear-drives/ta105-linear-drive/) | TrustAutomation | Linear | 1 | +/-10V | 5kHz | | 1e-6 |
| [SMA6520](https://www.glentek.com/shop/?swoof=1&product_cat=linear-brushless-series&really_curr_tax=21-product_cat) | Glentek | Linear | 1 Brushless (3 phases) | +/-10V | 10kHz | | |
| [SMA5005](https://www.glentek.com/shop/?swoof=1&product_cat=linear-brush-series&really_curr_tax=21-product_cat) | Glentek | Linear | 1 | +/-10V | 10kHz | | |
## Required properties {#required-properties}
Main required properties are (taken from (<a href="#citeproc_bib_item_1">Schmidt, Schitter, and Rankers 2020</a>)):
- **Power delivery capability**
- **Dynamic properties**
- **Linearity**
- **Voltage or current drive**
- **Efficiency**
- **Four quadrant operation**
## Four Quadrant Operation {#four-quadrant-operation}
The self-inductance of an electromagnetic actuator also causes another problem when the actuator is driven with a period signal, because for a sinusoidal signal the current is out of phase with the voltage.
In the extreme case of a purely reactive load, the maximum current needs to be delivered at zero voltage, while at a quarter of the period a positive current is delivered with a negative voltage and another quarter it is just the other way around.
In mechatronic positioning systems with a high moving mass, the real problem is caused by the kinetic energy that is involved.
At acceleration, the motion voltage of the actuator increases in phase with the current and electric power is inserted in the system and converted into kinetic energy.
The deceleration phase is however completely the opposite.
While the motion voltage still has the same sign as during constant motion, the current needs to be reversed in order to reverse the energy flow.
This means that the full amount of kinetic energy has to be absorbed by the amplifier.
## How to size a linear drive? {#how-to-size-a-linear-drive}
### Why it is important to properly choose a linear drive? {#why-it-is-important-to-properly-choose-a-linear-drive}
From a TrustAutomation [white paper](https://www.trustautomation.com/resources/engineering-blog/how-to-size-a-linear-drive-for-precision-positioning-applications/):
> The price you'll pay for the improved precision (i.e. thanks to the linear drive as compared to a PWM one) will mostly come in the form of heat.
> Linear drive typically maintain small amounts of power inside the drive circuits, increasing heat.
> **Excess voltage not needed by the motor is also dissipated as heat**.
### Determine required currents and voltages {#determine-required-currents-and-voltages}
In order to properly choose a linear amplifier, it is important to determine the voltage and torque that has to be generated.
The required current is based on the force (resp. torque) constant \\(K\_f\\) and peak force (resp. torque).
The required voltage is based on the back EMF constant \\(K\_u\\), peak velocity \\(v\_\text{peak}\\), peak current \\(I\_\text{peak}\\) and winding resistance \\(R\\).
<div class="exampl">
Consider a linear brushless motor with a force constant \\(K\_f\\) equal to 30 N/A, a BEMF constant \\(K\_u\\) equal to \\(18\\,\frac{Vrms}{m/s}\\) (i.e. \\(25\\,\frac{V}{m/s}\\)) and a electrical resistance \\(R\\) of \\(20\\,\Omega\\).
The peak velocity \\(v\_\max\\) is 1 mm/s and the wanted applied peak force \\(F\_\text{peak}\\) is 50 N.
The peak current required is:
\\[ I\_\text{peak} = F\_\text{peak}/K\_f \\]
And we obtain a peak current of 1.7 A.
The peak voltage is:
\\[ V\_\text{peak} = K\_u \cdot v\_\text{peak} + R \cdot I\_\text{peak} + V\_\text{margin} \\]
With \\(V\_\text{margin}\\) of 10 V, we obtain \\(V\_\text{peak} = 45\\,V\\).
From this simple calculation, it is possible to obtain the required capability of the amplifier.
</div>
### Determine safe operating area {#determine-safe-operating-area}
There are two danger scenarios: a stalled motor and a dynamic stopping motion
#### Stalled motor {#stalled-motor}
Consider the voltage supply to the drive \\(V\_\text{supply}\\) and the peak current \\(V\_\text{peak}\\).
Now suppose the motor is pushing against a hard stop, the power \\(W\_\text{drive}\\) that the drive must dissipate is equal to:
\\[ W\_\text{drive} = I\_\text{peak} \cdot V\_\text{drive} \\]
with:
\\[ V\_\text{drive} = V\_\text{supply} - I\_\text{peak} R \\]
<div class="exampl">
For our current application, \\(V\_\text{supply} = 45\\,V\\), \\(R = 20\\,\Omega\\) and \\(I\_\text{peak} = 1.7\\,A\\) which gives:
\\[ W\_\text{drive} = 19\\,W \\]
Then, it should be checked that the amplifier can dissipate this amount of power.
</div>
#### Dynamic Stopping. {#dynamic-stopping-dot}
With a linear drive, the kinetic energy is absorbed by the drive itself, but must be dissipated as heat.
This energy must be added to the energy required by the drive to stop all motion.
The kinetic energy \\(E\_K\\) is (expressed in Joules):
\\[ E\_K = \frac{1}{2} m v\_\text{peak}^2 \\]
with \\(m\\) the payload mass.
During the linear deceleration phase, the power \\(W\_d\\) that has to be dissipate by the drive is:
\\[ W\_d = \frac{E\_K}{t\_\text{dec}} \\]
with \\(t\_\text{dec}\\) the deceleration time.
<div class="exampl">
Consider a mass of 5 kg with a peak velocity of 1 mm/s and a deceleration time of 0.1s, the power to be dissipated in the drive is:
\\[ W\_d = 25\\,\mu W \\]
which is quite negligible.
If a velocity of 1 m/s is considered instead, we obtain \\(W\_d = 25\\,W\\).
</div>
### Matlab Script to size a linear drive {#matlab-script-to-size-a-linear-drive}
```matlab
%% Motor properties
Kt = 28; % Force constant [N/A] or Torque constant [Nm/A]
Ku = 28; % BEMF in [V/(m/s)] or in [V/(rad/s)]
R = 8.5; % Winding resistance [Ohm]
%% Motion property
Fp = 100; % Peak force [N] or Peak torque [Nm]
vp = 10e-3; % Peak Velocity [m/s] or peak rotation [rad/s]
m = 5; % Mass of the payload [kg]
td = 0.1; % Deceleration time [s]
```
```matlab
%% Driver wanted properties
V_margin = 10; % Power supply margin [V]
Imax = Fp / Kt; % Peak current to be supplied by the driver [A]
Vmax = vp * Ku + R * Imax + V_margin; % Peak voltage to be generated by the driver [V]
```
```text
Imax = 3.6 [A], Vmax = 41 [V]
```
```matlab
%% Stalled Motor
W_stalled = Imax * (Vmax - Imax * R); % [W]
```
```text
W_stalled = 37 [W]
```
```matlab
%% Dynamic Stopping
W_stop = 0.5*m*vp^2 / t_dec; % [W]
```
```text
W_stop = 0.0025 [W]
```
## Estimation of the required current noise {#estimation-of-the-required-current-noise}
### Voice Coil Actuator with flexible guiding {#voice-coil-actuator-with-flexible-guiding}
```matlab
%% Frequency vector used for the analysis
freqs = logspace(0, 4, 1000); % [Hz]
%% Motor properties
Kt = 28; % Force constant [N/A]
%% Amplifier Noise
In = 1e-6.*ones(size(freqs)); % Current noise density [A/sqrt(Hz)]
%% DAC Noise
Vn = (20/2^20)^2/12*1e4*ones(size(freqs)); % DAC output noise in [V/sqrt(Hz)]
Vn = 3e-8
Gi = 0.2; % Amplifier Gain [A/V]
%% Mechanical properties
m = 200e-3; % Mobile mass [kg]
k = 1e3; % Guiding stiffness [N/m]
xi = 0.05; % Modal Damping
```
```matlab
%% Transfer function from F [N] to x [m]
Gx = 1/(m*s^2);
```
```matlab
%% Transfer function from I [A] to x [m]
x_asd_i = In.*abs(squeeze(freqresp(Gx*Kt, freqs, 'Hz')))';
x_asd_v = Vn.*abs(squeeze(freqresp(Gx*Gi*Kt, freqs, 'Hz')))';
%% Cumulative amplitude spectrum
figure;
tiledlayout(1, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
nexttile();
hold on;
plot(freqs, sqrt(flip(-cumtrapz(flip(freqs), flip(x_asd_i.^2)))) , '-');
plot(freqs, sqrt(flip(-cumtrapz(flip(freqs), flip(x_asd_v.^2)))) , '-');
plot(freqs, ex , '-');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude'); xlabel('Frequency [Hz]');
xlim([0, 1e3]);
```
### Approximate analytical formula {#approximate-analytical-formula}
Parameters:
- `Kt`: motor force constant in N/A
- `In`: current noise density of the amplifier in \\(A/\sqrt{Hz}\\)
- `m`: mass in kg
- `fb`: the feedback bandwidth in Hz
We have that the residual motion when the feedback controller is closed is approximately equal to:
\begin{equation}
\epsilon\_x = \sqrt{\int\_\infty^{f\_b} \left(\frac{K\_t I\_n}{m \omega^2}\right)^2 d\omega}
\end{equation}
\begin{equation}
\epsilon\_x = \frac{K\_t I\_n}{m (2\pi)^2} \sqrt{\frac{1}{3 f\_b^3}}
\end{equation}
Therefore, this formula can be used to:
-
<!--listend-->
```matlab
%% Estimate the position stability from the current noise and system parameters
m = 1; % [kg]
In = 1e-6; % [A/sqrt(Hz)]
Kt = 10; % [N/A]
fb = 10; % [Hz]
ex = In*Kt/m/(2*pi)^2*sqrt(1./(3*fb^3));
```
```text
epsilon x = 4.6 [nm RMS]
```
-
<!--listend-->
```matlab
%% Estimate the required current noise from the wanted position stability and the parameters of the system
m = 1; % [kg]
Kt = 10; % [N/A]
fb = 50; % [Hz]
ex = 1e-9; % [m RMS]
In = ex*m*(2*pi)^2/Kt * sqrt(3*fb^3);
```
```text
In = 2.4e-06 [A/sqrt(Hz)]
```
## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2020. <i>The Design of High Performance Mechatronics - Third Revised Edition</i>. Ios Press.</div>
</div>

25
content/zettels/tuned_mass_damper.md
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@@ -19,6 +19,17 @@ The TMD then has large internal damping such that the energy is dissipated (i.e.
{{< youtube qDzGCgLu59A >}}
## How to properly apply a TMD? {#how-to-properly-apply-a-tmd}
Few questions:
- What damping mechanism to use?
Eddy current damping?
Viscous damping?
- How to optimize parameters of the TMD (i.e. mass, stiffness and damping)?
- Where to fix the TMD to the structure?
## Tuned Mass Damper Optimization {#tuned-mass-damper-optimization}
The optimal parameters of the tuned mass damper can be roughly estimated as follows:
@@ -100,18 +111,18 @@ The following mass ratios are tested:
mus = [0.01, 0.02, 0.05, 0.1];
```
The obtained transfer functions are shown in Figure [3](#figure--fig:tuned-mass-damper-mass-effect).
The obtained transfer functions are shown in Figure [1](#figure--fig:tuned-mass-damper-mass-effect).
<a id="figure--fig:tuned-mass-damper-mass-effect"></a>
{{< figure src="/ox-hugo/tuned_mass_damper_mass_effect.png" caption="<span class=\"figure-number\">Figure 3: </span>Effect of the TMD mass on its efficiency" >}}
{{< figure src="/ox-hugo/tuned_mass_damper_mass_effect.png" caption="<span class=\"figure-number\">Figure 1: </span>Effect of the TMD mass on its efficiency" >}}
The maximum amplification (i.e. \\(\mathcal{H}\_\infty\\) norm) of the transmissibility as a function of the mass ratio is shown in Figure [4](#figure--fig:tuned-mass-damper-effect-mass-ratio).
The maximum amplification (i.e. \\(\mathcal{H}\_\infty\\) norm) of the transmissibility as a function of the mass ratio is shown in Figure [1](#figure--fig:tuned-mass-damper-effect-mass-ratio).
This relation can help to determine the minimum mass of the TMD that will give acceptable results.
<a id="figure--fig:tuned-mass-damper-effect-mass-ratio"></a>
{{< figure src="/ox-hugo/tuned_mass_damper_effect_mass_ratio.png" caption="<span class=\"figure-number\">Figure 4: </span>Maximum amplification due to resonance as a function of the mass ratio" >}}
{{< figure src="/ox-hugo/tuned_mass_damper_effect_mass_ratio.png" caption="<span class=\"figure-number\">Figure 1: </span>Maximum amplification due to resonance as a function of the mass ratio" >}}
## Manufacturers {#manufacturers}
@@ -126,7 +137,11 @@ This relation can help to determine the minimum mass of the TMD that will give a
Possible damping sources:
- Magnetic (eddy current)
- Viscous
- Viscous fluid
| Fuild | Reference |
|----------------------|---------------------------------------------------|
| Rocol Kilopoise 0868 | (<a href="#citeproc_bib_item_2">Verbaan 2015</a>) |
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Elias, Said, and Vasant Matsagar. 2017. “Research Developments in Vibration Control of Structures Using Passive Tuned Mass Dampers.” <i>Annual Reviews in Control</i> 44 (nil): 129–56. doi:<a href="https://doi.org/10.1016/j.arcontrol.2017.09.015">10.1016/j.arcontrol.2017.09.015</a>.</div>

30
content/zettels/voice_coil_actuators.md
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@@ -27,20 +27,18 @@ As the force is proportional to the current, a [Transconductance Amplifiers]({{<
## Manufacturers {#manufacturers}
| Manufacturers | Country |
|-------------------------------------------------------------------------------------------------------------------------------------|-------------|
| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=14116) | |
| [Geeplus](https://www.geeplus.com/) | UK |
| [Maccon](https://www.maccon.de/en.html) | Germany |
| [TDS PP](https://www.tds-pp.com/en/product/linear-voice-coil-actuators-avm/) | Switzerland |
| [PBA Systems](https://www.pbasystems.com.sg/product/circular-voice-coil-motor-cvc/) | Singapore |
| [Magnetic Innovations](https://www.magneticinnovations.com/) | Netherlands |
| [H2tech](https://www.h2wtech.com/) | USA |
| [Beikimco](http://www.beikimco.com/) | USA |
| [Monticont](http://www.moticont.com/) | USA |
| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=14116) | USA |
| [Akribis](https://akribis-sys.com/products/voice-coil-motors/avm-series) | USA |
| [Celera](https://www.celeramotion.com/applimotion/products/direct-drive-frameless-linear-motors/voice-coil/juke-series-round-body/) | |
| Manufacturers | Country |
|-------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------|
| [Akribis](https://akribis-sys.com/products/voice-coil-motors/avm-series) | Singapore (european distributors: [Maccon](https://www.maccon.de/en.html), [TDS PP](https://www.tds-pp.com/en/product/linear-voice-coil-actuators-avm/)) |
| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=14116) | |
| [Geeplus](https://www.geeplus.com/) | UK |
| [PBA Systems](https://www.pbasystems.com.sg/product/circular-voice-coil-motor-cvc/) | Singapore |
| [Magnetic Innovations](https://www.magneticinnovations.com/) | Netherlands |
| [H2tech](https://www.h2wtech.com/) | USA |
| [Beikimco](http://www.beikimco.com/) | USA |
| [Monticont](http://www.moticont.com/) | USA |
| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=14116) | USA |
| [Celera](https://www.celeramotion.com/applimotion/products/direct-drive-frameless-linear-motors/voice-coil/juke-series-round-body/) | |
## Voice Coil Stages {#voice-coil-stages}
@@ -135,11 +133,11 @@ Dg = m * g ./ k; % [m]
<a id="figure--fig:voice-coil-resonance-fct-stroke"></a>
{{< figure src="/ox-hugo/voice_coil_resonance_fct_stroke.png" caption="<span class=\"figure-number\">Figure 3: </span>Resonance frequency and deflection due to gravity as a function of the wanted stroke (Max voice coil force is 50N and payload mass is 5kg)" >}}
{{< figure src="/ox-hugo/voice_coil_resonance_fct_stroke.png" caption="<span class=\"figure-number\">Figure 1: </span>Resonance frequency and deflection due to gravity as a function of the wanted stroke (Max voice coil force is 50N and payload mass is 5kg)" >}}
<a id="figure--fig:voice-coil-stiffness-fct-stroke"></a>
{{< figure src="/ox-hugo/voice_coil_stiffness_fct_stroke.png" caption="<span class=\"figure-number\">Figure 4: </span>Resonance frequency and deflection due to gravity as a function of the wanted stroke (Max voice coil force is 50N and payload mass is 5kg)" >}}
{{< figure src="/ox-hugo/voice_coil_stiffness_fct_stroke.png" caption="<span class=\"figure-number\">Figure 1: </span>Resonance frequency and deflection due to gravity as a function of the wanted stroke (Max voice coil force is 50N and payload mass is 5kg)" >}}
## Bibliography {#bibliography}