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content/zettels/active_isolation_platforms.md
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| Manufacturer | links | Country |
|--------------|----------------------------------|---------|
| ACE | [link](https://www.ace-ace.com/) | Germany |
<./biblio/references.bib>

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Tags
: [Complementary Filters]({{< relref "complementary_filters" >}})
([Beijen et al. 2019](#orgc359149))
([Beijen et al. 2019](#orgc6f7554))
([Beijen 2018](#org585205d)) (section 6.3.1)
([Beijen 2018](#org8e8fef4)) (section 6.3.1)
## Bibliography {#bibliography}
<a id="org585205d"></a>Beijen, MA. 2018. “Disturbance Feedforward Control for Vibration Isolation Systems: Analysis, Design, and Implementation.” Technische Universiteit Eindhoven.
<a id="org8e8fef4"></a>Beijen, MA. 2018. “Disturbance Feedforward Control for Vibration Isolation Systems: Analysis, Design, and Implementation.” Technische Universiteit Eindhoven.
<a id="orgc359149"></a>Beijen, Michiel A., Marcel F. Heertjes, Hans Butler, and Maarten Steinbuch. 2019. “Mixed Feedback and Feedforward Control Design for Multi-Axis Vibration Isolation Systems.” _Mechatronics_ 61:106–16. <https://doi.org/https://doi.org/10.1016/j.mechatronics.2019.06.005>.
<a id="orgc6f7554"></a>Beijen, Michiel A., Marcel F. Heertjes, Hans Butler, and Maarten Steinbuch. 2019. “Mixed Feedback and Feedforward Control Design for Multi-Axis Vibration Isolation Systems.” _Mechatronics_ 61:106–16. <https://doi.org/https://doi.org/10.1016/j.mechatronics.2019.06.005>.

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For vibration isolation:
- In ([Ito and Schitter 2016](#org4bbf168)), the effect of the actuator stiffness on the attainable vibration isolation is studied ([Notes]({{< relref "ito16_compar_class_high_precis_actuat" >}}))
- In ([Ito and Schitter 2016](#orga71edd4)), the effect of the actuator stiffness on the attainable vibration isolation is studied ([Notes]({{< relref "ito16_compar_class_high_precis_actuat" >}}))
## Brush-less DC Motor {#brush-less-dc-motor}
- ([Yedamale 2003](#org1638958))
- ([Yedamale 2003](#org0ac1a74))
<https://www.electricaltechnology.org/2016/05/bldc-brushless-dc-motor-construction-working-principle.html>
@@ -30,6 +30,6 @@ For vibration isolation:
## Bibliography {#bibliography}
<a id="org4bbf168"></a>Ito, Shingo, and Georg Schitter. 2016. “Comparison and Classification of High-Precision Actuators Based on Stiffness Influencing Vibration Isolation.” _IEEE/ASME Transactions on Mechatronics_ 21 (2):1169–78. <https://doi.org/10.1109/tmech.2015.2478658>.
<a id="orga71edd4"></a>Ito, Shingo, and Georg Schitter. 2016. “Comparison and Classification of High-Precision Actuators Based on Stiffness Influencing Vibration Isolation.” _IEEE/ASME Transactions on Mechatronics_ 21 (2):1169–78. <https://doi.org/10.1109/tmech.2015.2478658>.
<a id="org1638958"></a>Yedamale, Padmaraja. 2003. “Brushless Dc (BLDC) Motor Fundamentals.” _Microchip Technology Inc_ 20:3–15.
<a id="org0ac1a74"></a>Yedamale, Padmaraja. 2003. “Brushless Dc (BLDC) Motor Fundamentals.” _Microchip Technology Inc_ 20:3–15.

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content/zettels/analog_to_digital_converters.md
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+++
title = "Analog to Digital Converters"
author = ["Thomas Dehaeze"]
keywords = ["electronics"]
draft = false
+++
@@ -12,7 +13,7 @@ Tags
<https://dewesoft.com/daq/types-of-adc-converters>
- Delta Sigma ([Baker 2011](#orgb22f10b))
- Delta Sigma ([Baker 2011](#org60f0e22))
- Successive Approximation
@@ -31,9 +32,9 @@ Let's suppose that the ADC is ideal and the only noise comes from the quantizati
Interestingly, the noise amplitude is uniformly distributed.
The quantization noise can take a value between \\(\pm q/2\\), and the probability density function is constant in this range (i.e., it’s a uniform distribution).
Since the integral of the probability density function is equal to one, its value will be \\(1/q\\) for \\(-q/2 < e < q/2\\) (Fig. [1](#org57805de)).
Since the integral of the probability density function is equal to one, its value will be \\(1/q\\) for \\(-q/2 < e < q/2\\) (Fig. [1](#orgee08810)).
<a id="org57805de"></a>
<a id="orgee08810"></a>
{{< figure src="/ox-hugo/probability_density_function_adc.png" caption="Figure 1: Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}}
@@ -88,4 +89,4 @@ The quantization is:
## Bibliography {#bibliography}
<a id="orgb22f10b"></a>Baker, Bonnie. 2011. “How Delta-Sigma Adcs Work, Part.” _Analog Applications_ 7.
<a id="org60f0e22"></a>Baker, Bonnie. 2011. “How Delta-Sigma Adcs Work, Part.” _Analog Applications_ 7.

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:
<a id="org3e05411"></a>
<a id="org67aca6e"></a>
{{< figure src="/ox-hugo/bipolar_transistor_basic_circuits.svg" caption="Figure 1: 5 basic circuits using the bipolar transistor" >}}
<./biblio/references.bib>

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## Software {#software}
- [WireViz](https://github.com/formatc1702/WireViz) is a nice software to easily document cables and wiring harnesses
<./biblio/references.bib>

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## Basic Circuit {#basic-circuit}
Two basic circuits of charge amplifiers are shown in Figure [1](#org45de288) (taken from ([Fleming 2010](#org2341229))) and Figure [2](#org8955723) (taken from ([Schmidt, Schitter, and Rankers 2014](#orgf9a1421)))
Two basic circuits of charge amplifiers are shown in Figure [1](#org7d016e2) (taken from ([Fleming 2010](#org467f88f))) and Figure [2](#orgb83f736) (taken from ([Schmidt, Schitter, and Rankers 2014](#org80f2485)))
<a id="org45de288"></a>
<a id="org7d016e2"></a>
{{< figure src="/ox-hugo/charge_amplifier_circuit.png" caption="Figure 1: Electrical model of a piezoelectric force sensor is shown in gray. The op-amp charge amplifier is shown on the right. The output voltage \\(V\_s\\) equal to \\(-q/C\_s\\)" >}}
<a id="org8955723"></a>
<a id="orgb83f736"></a>
{{< figure src="/ox-hugo/charge_amplifier_circuit_bis.png" caption="Figure 2: A piezoelectric accelerometer with a charge amplifier as signal conditioning element" >}}
The input impedance of the charge amplifier is very small (unlike when using a voltage amplifier).
The gain of the charge amplified (Figure [1](#org45de288)) is equal to:
The gain of the charge amplified (Figure [1](#org7d016e2)) is equal to:
\\[ \frac{V\_s}{q} = \frac{-1}{C\_s} \\]
@@ -50,6 +50,6 @@ The gain of the charge amplified (Figure [1](#org45de288)) is equal to:
## Bibliography {#bibliography}
<a id="org2341229"></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="org467f88f"></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="orgf9a1421"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.
<a id="org80f2485"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.

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## Collocated/Dual actuator and sensor {#collocated-dual-actuator-and-sensor}
According to ([Preumont 2018](#org5d050e8)):
According to ([Preumont 2018](#orgbf8f4c5)):
> A **collocated** control system is a control system where the actuator and the sensor are attached to the same degree of freedom.
>
@@ -19,9 +19,9 @@ According to ([Preumont 2018](#org5d050e8)):
## Nearly Collocated Actuator Sensor Pair {#nearly-collocated-actuator-sensor-pair}
From Figure [1](#org0d605b2), it is clear that at some frequency / for some mode, the actuator and the sensor will not be collocated anymore (here starting with mode 3).
From Figure [1](#org5d460f9), it is clear that at some frequency / for some mode, the actuator and the sensor will not be collocated anymore (here starting with mode 3).
<a id="org0d605b2"></a>
<a id="org5d460f9"></a>
{{< figure src="/ox-hugo/preumont18_nearly_collocated_schematic.png" caption="Figure 1: Mode shapes for a uniform beam. \\(u\\) and \\(y\\) are not collocated actuator and sensor" >}}
@@ -38,6 +38,7 @@ Of course, this will reduce the sensibility.
- [ ] What happens is small pieces of actuators are mixed with small pieces of sensors?
## Bibliography {#bibliography}
<a id="org5d050e8"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.
<a id="orgbf8f4c5"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.

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## Complementary Filters Synthesis {#complementary-filters-synthesis}
The shaping of complementary filters can be done using the \\(\mathcal{H}\_\infty\\) synthesis ([Dehaeze, Vermat, and Christophe 2019](#org0c35169)).
The shaping of complementary filters can be done using the \\(\mathcal{H}\_\infty\\) synthesis ([Dehaeze, Vermat, and Christophe 2019](#org066e272)).
## Bibliography {#bibliography}
<a id="org0c35169"></a>Dehaeze, Thomas, Mohit Vermat, and Collette Christophe. 2019. “Complementary Filters Shaping Using \\(mathcalH\_Infty\\) Synthesis.” In _7th International Conference on Control, Mechatronics and Automation (ICCMA)_, 459–64. <https://doi.org/10.1109/ICCMA46720.2019.8988642>.
<a id="org066e272"></a>Dehaeze, Thomas, Mohit Vermat, and Collette Christophe. 2019. “Complementary Filters Shaping Using \\(mathcalH\_Infty\\) Synthesis.” In _7th International Conference on Control, Mechatronics and Automation (ICCMA)_, 459–64. <https://doi.org/10.1109/ICCMA46720.2019.8988642>.

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## BNC {#bnc}
BNC connectors can have an impedance of 50Ohms or 75Ohms as shown in Figure [1](#orgfe209b2).
BNC connectors can have an impedance of 50Ohms or 75Ohms as shown in Figure [1](#orgd1b23d3).
<a id="orgfe209b2"></a>
<a id="orgd1b23d3"></a>
{{< figure src="/ox-hugo/bnc_50_75_ohms.jpg" caption="Figure 1: 75Ohms and 50Ohms BNC connectors" >}}
<./biblio/references.bib>

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## Special Properties {#special-properties}
Cubic Stewart Platforms can be decoupled provided that (from ([Chen and McInroy 2000](#org0969434)))
Cubic Stewart Platforms can be decoupled provided that (from ([Chen and McInroy 2000](#org2ea9cff)))
> 1. The payload mass-inertia matrix is diagonal
> 2. If a mutually orthogonal geometry has been selected, the payload's center of mass must coincide with the center of the cube formed by the orthogonal struts.
@@ -22,4 +22,4 @@ Cubic Stewart Platforms can be decoupled provided that (from ([Chen and McInroy
## Bibliography {#bibliography}
<a id="org0969434"></a>Chen, Yixin, and J.E. McInroy. 2000. “Identification and Decoupling Control of Flexure Jointed Hexapods.” In _Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)_, nil. <https://doi.org/10.1109/robot.2000.844878>.
<a id="org2ea9cff"></a>Chen, Yixin, and J.E. McInroy. 2000. “Identification and Decoupling Control of Flexure Jointed Hexapods.” In _Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)_, nil. <https://doi.org/10.1109/robot.2000.844878>.

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title = "Decoupled Control"
author = ["Thomas Dehaeze"]
draft = false
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Tags
: [Multivariable Control]({{< relref "multivariable_control" >}})

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:
<./biblio/references.bib>

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content/zettels/dynamic_error_budgeting.md
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Backlinks:
- [Dynamic error budgeting, a design approach]({{< relref "monkhorst04_dynam_error_budget" >}})
- [Systems and Signals Norms]({{< relref "norms" >}})
- [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})
- [The design of high performance mechatronics - 2nd revised edition]({{< relref "schmidt14_desig_high_perfor_mechat_revis_edition" >}})
- [Mechatronic design of a magnetically suspended rotating platform]({{< relref "jabben07_mechat" >}})
Tags
:
A good introduction to Dynamic Error Budgeting is given in ([Monkhorst 2004](#orgce880aa)).
A good introduction to Dynamic Error Budgeting is given in ([Monkhorst 2004](#orgda61e4e)).
## Step by Step process {#step-by-step-process}
Taken from ([Monkhorst 2004](#orgce880aa)): ([Notes]({{< relref "monkhorst04_dynam_error_budget" >}}))
Taken from ([Monkhorst 2004](#orgda61e4e)): ([Notes]({{< relref "monkhorst04_dynam_error_budget" >}}))
> Step by step, the process is as follows:
>
@@ -34,6 +26,7 @@ Taken from ([Monkhorst 2004](#orgce880aa)): ([Notes]({{< relref "monkhorst04_dyn
> Iterate until the error budget is meet.
## Bibliography {#bibliography}
<a id="orgce880aa"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.
<a id="orgda61e4e"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.

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| [Kaman](https://www.kamansensors.com/product/smt-9700/) | USA |
| [Keyence](https://www.keyence.com/ss/products/measure/measurement%5Flibrary/type/inductive/) | USA |
| [Althen](https://www.althensensors.com/sensors/linear-position-sensors/eddy-current-sensors/) | Netherlands |
<./biblio/references.bib>

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content/zettels/electronic_active_filters.md
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@@ -29,14 +29,14 @@ With:
- \\(\omega\_0 = \frac{1}{R\sqrt{C\_1 C\_2}}\\)
- \\(\xi = \frac{C\_2}{C\_1}\\)
<a id="org21a1d35"></a>
<a id="orgb2c3453"></a>
{{< figure src="/ox-hugo/elec_active_second_order_low_pass_filter.png" caption="Figure 1: Second Order Low Pass Filter" >}}
## High Pass Filter {#high-pass-filter}
Same as [1](#org21a1d35) but by exchanging R1 with C1 and R2 with C2
Same as [1](#orgb2c3453) but by exchanging R1 with C1 and R2 with C2
\begin{equation}
\frac{V\_o}{V\_i}(s) = \frac{R^2 C\_1 C\_2 s^2}{R^2 C\_1 C\_2 s^2 + 2 R C\_2 s + 1}
@@ -46,5 +46,3 @@ With:
- \\(\omega\_0 = \frac{1}{R\sqrt{C\_1 C\_2}}\\)
- \\(\xi = \frac{C\_2}{C\_1}\\)
<./biblio/references.bib>

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## First Order Low Pass Filter {#first-order-low-pass-filter}
<a id="orgf718550"></a>
<a id="org1c6b488"></a>
{{< figure src="/ox-hugo/elec_passive_first_order_low_pass_filter.png" caption="Figure 1: First Order Low Pass Filter using an RC circuit" >}}
## First Order High Pass Filter {#first-order-high-pass-filter}
<a id="orgc9b929d"></a>
<a id="orgecf7617"></a>
{{< figure src="/ox-hugo/elec_passive_first_order_high_pass_filter.png" caption="Figure 2: First Order High Pass Filter using an RC circuit" >}}
## Second Order Low Pass Filter {#second-order-low-pass-filter}
<a id="orgb56edb0"></a>
<a id="orgcfc4c15"></a>
{{< figure src="/ox-hugo/elec_passive_second_order_low_pass_filter.png" caption="Figure 3: Second Order Low Pass Filter using an RLC circuit" >}}
## Second Order High Pass Filter {#second-order-high-pass-filter}
<a id="org1bcacc5"></a>
<a id="org0b32ffe"></a>
{{< figure src="/ox-hugo/elec_passive_second_order_high_pass_filter.png" caption="Figure 4: Second Order High Pass Filter using an RLC circuit" >}}
<./biblio/references.bib>

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draft = false
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Backlinks:
- [Charge Amplifiers]({{< relref "charge_amplifiers" >}})
- [Signal Conditioner]({{< relref "signal_conditioner" >}})
- [Analog to Digital Converters]({{< relref "analog_to_digital_converters" >}})
- [Transconductance Amplifiers]({{< relref "transconductance_amplifiers" >}})
- [Digital to Analog Converters]({{< relref "digital_to_analog_converters" >}})
- [The art of electronics - third edition]({{< relref "horowitz15_art_of_elect_third_edition" >}})
- [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})
- [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
- [Transimpedance Amplifiers]({{< relref "transimpedance_amplifiers" >}})
Tags
:
<./biblio/references.bib>

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content/zettels/finite_element_model.md
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Backlinks:
- [Vibration Simulation using Matlab and ANSYS]({{< relref "hatch00_vibrat_matlab_ansys" >}})
Tags
:
@@ -16,17 +12,18 @@ Tags
Some resources:
- ([Hatch 2000](#org4303bb7)) ([Notes]({{< relref "hatch00_vibrat_matlab_ansys" >}}))
- ([Khot and Yelve 2011](#org31239e2))
- ([Kovarac et al. 2015](#org304a9dd))
- ([Hatch 2000](#orgddee845)) ([Notes]({{< relref "hatch00_vibrat_matlab_ansys" >}}))
- ([Khot and Yelve 2011](#orgb0a5955))
- ([Kovarac et al. 2015](#org7660da4))
The idea is to extract reduced state space model from Ansys into Matlab.
## Bibliography {#bibliography}
<a id="org4303bb7"></a>Hatch, Michael R. 2000. _Vibration Simulation Using MATLAB and ANSYS_. CRC Press.
<a id="orgddee845"></a>Hatch, Michael R. 2000. _Vibration Simulation Using MATLAB and ANSYS_. CRC Press.
<a id="org31239e2"></a>Khot, SM, and Nitesh P Yelve. 2011. “Modeling and Response Analysis of Dynamic Systems by Using ANSYS and MATLAB.” _Journal of Vibration and Control_ 17 (6). SAGE Publications Sage UK: London, England:953–58.
<a id="orgb0a5955"></a>Khot, SM, and Nitesh P Yelve. 2011. “Modeling and Response Analysis of Dynamic Systems by Using ANSYS and MATLAB.” _Journal of Vibration and Control_ 17 (6). SAGE Publications Sage UK: London, England:953–58.
<a id="org304a9dd"></a>Kovarac, A, M Zeljkovic, C Mladjenovic, and A Zivkovic. 2015. “Create SISO State Space Model of Main Spindle from ANSYS Model.” In _12th International Scientific Conference, Novi Sad, Serbia_, 37–41.
<a id="org7660da4"></a>Kovarac, A, M Zeljkovic, C Mladjenovic, and A Zivkovic. 2015. “Create SISO State Space Model of Main Spindle from ANSYS Model.” In _12th International Scientific Conference, Novi Sad, Serbia_, 37–41.

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Books:
- ([Lobontiu 2002](#orgf96bd1c))
- ([Henein 2003](#org77c1a30))
- ([Smith 2005](#orgdf03b02))
- ([Soemers 2011](#orgc441221))
- ([Cosandier 2017](#orgc637f07))
- ([Lobontiu 2002](#org0e711a7))
- ([Henein 2003](#org4fb65e1))
- ([Smith 2005](#orgbf46163))
- ([Soemers 2011](#orgf482067))
- ([Cosandier 2017](#orgf099485))
## Flexure Joints for Stewart Platforms: {#flexure-joints-for-stewart-platforms}
From ([Chen and McInroy 2000](#org26c43a0)):
From ([Chen and McInroy 2000](#org14378b5)):
> To avoid the extremely non-linear micro-dynamics of joint friction and backlash, these hexapods employ flexure joints.
> A flexure joint bends material to achieve motion, rather than sliding of rolling across two surfaces.
@@ -31,14 +31,14 @@ From ([Chen and McInroy 2000](#org26c43a0)):
## Bibliography {#bibliography}
<a id="org26c43a0"></a>Chen, Yixin, and J.E. McInroy. 2000. “Identification and Decoupling Control of Flexure Jointed Hexapods.” In _Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)_, nil. <https://doi.org/10.1109/robot.2000.844878>.
<a id="org14378b5"></a>Chen, Yixin, and J.E. McInroy. 2000. “Identification and Decoupling Control of Flexure Jointed Hexapods.” In _Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)_, nil. <https://doi.org/10.1109/robot.2000.844878>.
<a id="orgc637f07"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="orgf099485"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="org77c1a30"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="org4fb65e1"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="orgf96bd1c"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="org0e711a7"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="orgdf03b02"></a>Smith, Stuart T. 2005. _Foundations of Ultra-Precision Mechanism Design_. Vol. 2. CRC Press.
<a id="orgbf46163"></a>Smith, Stuart T. 2005. _Foundations of Ultra-Precision Mechanism Design_. Vol. 2. CRC Press.
<a id="orgc441221"></a>Soemers, Herman. 2011. _Design Principles for Precision Mechanisms_. T-Pointprint.
<a id="orgf482067"></a>Soemers, Herman. 2011. _Design Principles for Precision Mechanisms_. T-Pointprint.

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## Materials {#materials}
- ([Smith 2000](#org48aca5d))
- ([Lobontiu 2002](#org45b1d4f))
- ([Henein 2003](#org516fc89))
- ([Cosandier 2017](#orgb511c9e))
- ([Smith 2000](#org903194d))
- ([Lobontiu 2002](#org353b748))
- ([Henein 2003](#org26cb408))
- ([Cosandier 2017](#org684f025))
## Bibliography {#bibliography}
<a id="orgb511c9e"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="org684f025"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="org516fc89"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="org26cb408"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="org45b1d4f"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="org353b748"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="org48aca5d"></a>Smith, Stuart T. 2000. _Flexures: Elements of Elastic Mechanisms_. Crc Press.
<a id="org903194d"></a>Smith, Stuart T. 2000. _Flexures: Elements of Elastic Mechanisms_. Crc Press.

9
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@@ -17,9 +17,9 @@ There are two main technique for force sensors:
The choice between the two is usually based on whether the measurement is static (strain gauge) or dynamics (piezoelectric).
Main differences between the two are shown in Figure [1](#org921c881).
Main differences between the two are shown in Figure [1](#orgd4cde6e).
<a id="org921c881"></a>
<a id="orgd4cde6e"></a>
{{< figure src="/ox-hugo/force_sensor_piezo_vs_strain_gauge.png" caption="Figure 1: Piezoelectric Force sensor VS Strain Gauge Force sensor" >}}
@@ -29,7 +29,7 @@ Main differences between the two are shown in Figure [1](#org921c881).
### 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](#org26fffc0)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
An analysis the dynamics and noise of a piezoelectric force sensor is done in ([Fleming 2010](#org6f75dec)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
### Manufacturers {#manufacturers}
@@ -75,6 +75,7 @@ However, if a charge conditioner is used, the signal will be doubled.
| [Althen](https://www.althensensors.com/sensors/weighing-sensors-load-cells/) | Netherlands |
## Bibliography {#bibliography}
<a id="org26fffc0"></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="org6f75dec"></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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@@ -15,16 +15,16 @@ The documentation for the toolbox is accessible [here](https://fomcon.net/fomcon
Here are the parameters that are used to define the wanted properties of the fractional model:
```matlab
wb = 2*pi*0.1; % Lowest frequency bound
wh = 2*pi*1e3; % Highest frequency bound
n = 8; % Approximation order
r = 0.5; % Wanted slope, The corresponding phase will be pi*r
wb = 2*pi*0.1; % Lowest frequency bound
wh = 2*pi*1e3; % Highest frequency bound
n = 8; % Approximation order
r = 0.5; % Wanted slope, The corresponding phase will be pi*r
```
Then, to create an approximation of a fractional-order operator \\(s^r\\) of order \\(n\\) which is valid in the frequency range \\([\omega\_b\, \omega\_h]\\), the `oustafod` function can be used:
```matlab
G = oustafod(r,n,wb,wh);
G = oustafod(r,n,wb,wh);
```
```text
@@ -37,10 +37,8 @@ G =
Continuous-time transfer function.
```
Few examples of different slopes are shown in Figure [1](#orgaa7c066).
Few examples of different slopes are shown in Figure [1](#org9241d6d).
<a id="orgaa7c066"></a>
<a id="org9241d6d"></a>
{{< figure src="/ox-hugo/approximate_deriv_int.png" caption="Figure 1: Example of fractional approximations" >}}
<./biblio/references.bib>

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@@ -4,38 +4,34 @@ author = ["Thomas Dehaeze"]
draft = false
+++
Backlinks:
- [Vibration Control of Active Structures - Fourth Edition]({{< relref "preumont18_vibrat_contr_activ_struc_fourt_edition" >}})
- [Control of spacecraft and aircraft]({{< relref "bryson93_contr_spacec_aircr" >}})
Tags
:
High-Authority Control/Low-Authority Control
From ([Preumont 2018](#org2917245)):
From ([Preumont 2018](#org4171546)):
> The HAC/LAC approach consist of combining the two approached in a dual-loop control as shown in Figure [1](#org9ce3153). The inner loop uses a set of collocated actuator/sensor pairs for decentralized active damping with guaranteed stability ; the outer loop consists of a non-collocated HAC based on a model of the actively damped structure. This approach has the following advantages:
> The HAC/LAC approach consist of combining the two approached in a dual-loop control as shown in Figure [1](#org5a821d8). The inner loop uses a set of collocated actuator/sensor pairs for decentralized active damping with guaranteed stability ; the outer loop consists of a non-collocated HAC based on a model of the actively damped structure. This approach has the following advantages:
>
> - The active damping extends outside the bandwidth of the HAC and reduces the settling time of the modes which are outsite the bandwidth
> - The active damping makes it easier to gain-stabilize the modes outside the bandwidth of the output loop (improved gain margin)
> - The larger damping of the modes within the controller bandwidth makes them more robust to the parmetric uncertainty (improved phase margin)
<a id="org9ce3153"></a>
<a id="org5a821d8"></a>
{{< figure src="/ox-hugo/hac_lac_control_architecture.png" caption="Figure 1: HAC-LAC Control Architecture" >}}
Nice papers:
- ([Williams and Antsaklis 1989](#orge6af6e6))
- ([Aubrun 1980](#org05dd00f))
- ([Williams and Antsaklis 1989](#orgb65b217))
- ([Aubrun 1980](#org9a935c0))
## Bibliography {#bibliography}
<a id="org05dd00f"></a>Aubrun, J.N. 1980. “Theory of the Control of Structures by Low-Authority Controllers.” _Journal of Guidance and Control_ 3 (5):444–51. <https://doi.org/10.2514/3.56019>.
<a id="org9a935c0"></a>Aubrun, J.N. 1980. “Theory of the Control of Structures by Low-Authority Controllers.” _Journal of Guidance and Control_ 3 (5):444–51. <https://doi.org/10.2514/3.56019>.
<a id="org2917245"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.
<a id="org4171546"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.
<a id="orge6af6e6"></a>Williams, T.W.C., and P.J. Antsaklis. 1989. “Limitations of Vibration Suppression in Flexible Space Structures.” In _Proceedings of the 28th IEEE Conference on Decision and Control_, nil. <https://doi.org/10.1109/cdc.1989.70563>.
<a id="orgb65b217"></a>Williams, T.W.C., and P.J. Antsaklis. 1989. “Limitations of Vibration Suppression in Flexible Space Structures.” In _Proceedings of the 28th IEEE Conference on Decision and Control_, nil. <https://doi.org/10.1109/cdc.1989.70563>.

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@@ -10,10 +10,10 @@ Tags
## 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 ([Collette, Janssens, Fernandez-Carmona, et al. 2012](#orge266e77))
- Collette, C. et al., Comparison of new absolute displacement sensors ([Collette, Janssens, Mokrani, et al. 2012](#orga0b31ea))
- Collette, C. et al., Review: inertial sensors for low-frequency seismic vibration measurement ([Collette, Janssens, Fernandez-Carmona, et al. 2012](#orga092f9a))
- Collette, C. et al., Comparison of new absolute displacement sensors ([Collette, Janssens, Mokrani, et al. 2012](#orgef1075b))
<a id="orgaa8be44"></a>
<a id="org9a5fa73"></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" >}}
@@ -35,7 +35,7 @@ Wireless Accelerometers
- <https://micromega-dynamics.com/products/recovib/miniature-vibration-recorder/>
<a id="org47441e2"></a>
<a id="org1693047"></a>
{{< figure src="/ox-hugo/inertial_sensors_characteristics_accelerometers.png" caption="Figure 2: Characteristics of commercially available accelerometers <sup id=\"642a18d86de4e062c6afb0f5f20501c4\"><a href=\"#collette11_review\" title=\"Collette, Artoos, Guinchard, Janssens, , Carmona Fernandez \&amp; Hauviller, Review of sensors for low frequency seismic vibration measurement, CERN, (2011).\">collette11_review</a></sup>" >}}
@@ -52,7 +52,7 @@ Wireless Accelerometers
| [Guralp](https://www.guralp.com/products/surface) | UK |
| [Nanometric](https://www.nanometrics.ca/products/seismometers) | Canada |
<a id="orga5e26ab"></a>
<a id="org6d70737"></a>
{{< figure src="/ox-hugo/inertial_sensors_characteristics_geophone.png" caption="Figure 3: Characteristics of commercially available geophones <sup id=\"642a18d86de4e062c6afb0f5f20501c4\"><a href=\"#collette11_review\" title=\"Collette, Artoos, Guinchard, Janssens, , Carmona Fernandez \&amp; Hauviller, Review of sensors for low frequency seismic vibration measurement, CERN, (2011).\">collette11_review</a></sup>" >}}
@@ -60,6 +60,6 @@ Wireless Accelerometers
## Bibliography {#bibliography}
<a id="orge266e77"></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="orga092f9a"></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="orga0b31ea"></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)_.
<a id="orgef1075b"></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)_.

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Tags
: [Active Damping]({{< relref "active_damping" >}})
<./biblio/references.bib>

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## Effect of Refractive Index - Environmental Units {#effect-of-refractive-index-environmental-units}
The measured distance is proportional to the refractive index of the air that depends on several quantities as shown in Table [1](#table--tab:index-air) (Taken from ([Thurner et al. 2015](#org1b86993))).
The measured distance is proportional to the refractive index of the air that depends on several quantities as shown in Table [1](#table--tab:index-air) (Taken from ([Thurner et al. 2015](#org90df4b2))).
<a id="table--tab:index-air"></a>
<div class="table-caption">
@@ -59,16 +59,16 @@ Typical characteristics of commercial environmental units are shown in Table [2]
## Interferometer Precision {#interferometer-precision}
Figure [1](#org3490ef0) shows the expected precision as a function of the measured distance due to change of refractive index of the air (taken from ([Jang and Kim 2017](#org3b0a481))).
Figure [1](#org195a5db) shows the expected precision as a function of the measured distance due to change of refractive index of the air (taken from ([Jang and Kim 2017](#org4c766f1))).
<a id="org3490ef0"></a>
<a id="org195a5db"></a>
{{< figure src="/ox-hugo/position_sensor_interferometer_precision.png" caption="Figure 1: Expected precision of interferometer as a function of measured distance" >}}
## Sources of uncertainty {#sources-of-uncertainty}
Sources of error in laser interferometry are well described in ([Ducourtieux 2018](#org588696d)).
Sources of error in laser interferometry are well described in ([Ducourtieux 2018](#org08e49c8)).
It includes:
@@ -78,10 +78,10 @@ It includes:
- Pressure: \\(K\_P \approx 0.27 ppm hPa^{-1}\\)
- Humidity: \\(K\_{HR} \approx 0.01 ppm \% RH^{-1}\\)
- These errors can partially be compensated using an environmental unit.
- Air turbulence (Figure [2](#orgceb0667))
- Air turbulence (Figure [2](#org7f738e4))
- Non linearity
<a id="orgceb0667"></a>
<a id="org7f738e4"></a>
{{< figure src="/ox-hugo/interferometers_air_turbulence.png" caption="Figure 2: Effect of air turbulences on measurement stability" >}}
@@ -89,8 +89,8 @@ It includes:
## Bibliography {#bibliography}
<a id="org588696d"></a>Ducourtieux, Sebastien. 2018. “Toward High Precision Position Control Using Laser Interferometry: Main Sources of Error.” <https://doi.org/10.13140/rg.2.2.21044.35205>.
<a id="org08e49c8"></a>Ducourtieux, Sebastien. 2018. “Toward High Precision Position Control Using Laser Interferometry: Main Sources of Error.” <https://doi.org/10.13140/rg.2.2.21044.35205>.
<a id="org3b0a481"></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="org4c766f1"></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="org1b86993"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” _Applied Optics_ 54 (10). Optical Society of America:3051–63.
<a id="org90df4b2"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” _Applied Optics_ 54 (10). Optical Society of America:3051–63.

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>
> The primary disadvantage of FIR filters is that they often require a much higher filter order than IIR filters to achieve a given level of performance. Correspondingly, the delay of these filters is often much greater than for an equal performance IIR filter.
From ([Shaw and Srinivasan 1990](#orge62ce0f))
From ([Shaw and Srinivasan 1990](#org82fbcc5))
> The FIR are capable of realizing filters with linear phase shift characteristics and furthermore are less susceptible to signal input and filter coefficient quantization effects.
> However, their computational demands are excessively large because of the large number of multiplications and additions to be performed at each sampling interval.
@@ -52,4 +52,4 @@ From <https://dsp.stackexchange.com/a/30999>
## Bibliography {#bibliography}
<a id="orge62ce0f"></a>Shaw, F.R., and K. Srinivasan. 1990. “Bandwidth Enhancement of Position Measurements Using Measured Acceleration.” _Mechanical Systems and Signal Processing_ 4 (1):23–38. <https://doi.org/10.1016/0888-3270(90)>90038-m.
<a id="org82fbcc5"></a>Shaw, F.R., and K. Srinivasan. 1990. “Bandwidth Enhancement of Position Measurements Using Measured Acceleration.” _Mechanical Systems and Signal Processing_ 4 (1):23–38. <https://doi.org/10.1016/0888-3270(90)>90038-m.

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| [Micro-Epsilon](https://www.micro-epsilon.com/displacement-position-sensors/inductive-sensor-lvdt/) | Germany |
| [Keyence](https://www.keyence.eu/products/measure/contact-distance-lvdt/gt2/index.jsp) | USA |
| [Althen](https://www.althensensors.com/sensors/linear-position-sensors/lvdt-sensors/) | Netherlands |
<./biblio/references.bib>

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## Actuated Mass Spring Damper System {#actuated-mass-spring-damper-system}
Let's consider Figure [1](#orga358a0b) where:
Let's consider Figure [1](#orgbf5f22b) where:
- \\(m\\) is the mass in [kg]
- \\(ḱ\\) is the spring stiffness in [N/m]
@@ -20,7 +20,7 @@ Let's consider Figure [1](#orga358a0b) where:
- \\(w\\) is ground motion
- \\(x\\) is the absolute mass motion
<a id="orga358a0b"></a>
<a id="orgbf5f22b"></a>
{{< figure src="/ox-hugo/mass_spring_damper_system.png" caption="Figure 1: Mass Spring Damper System" >}}

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Books:
- ([Higham 2017](#org68f863c))
- ([Attaway 2018](#org3441bfb))
- ([OverFlow 2018](#org8e0ff2b))
- ([Johnson 2010](#org019531d))
- ([Hahn and Valentine 2016](#orgbeacac3))
- ([Higham 2017](#org28e00d3))
- ([Attaway 2018](#org46f9de5))
- ([OverFlow 2018](#orgfac8ed6))
- ([Johnson 2010](#org9e4fa10))
- ([Hahn and Valentine 2016](#org56f31fb))
## Useful Commands {#useful-commands}
@@ -108,12 +108,12 @@ Nice functions:
## Bibliography {#bibliography}
<a id="org3441bfb"></a>Attaway, Stormy. 2018. _MATLAB : a Practical Introduction to Programming and Problem Solving_. Amsterdam: Butterworth-Heinemann.
<a id="org46f9de5"></a>Attaway, Stormy. 2018. _MATLAB : a Practical Introduction to Programming and Problem Solving_. Amsterdam: Butterworth-Heinemann.
<a id="orgbeacac3"></a>Hahn, Brian, and Daniel T Valentine. 2016. _Essential MATLAB for Engineers and Scientists_. Academic Press.
<a id="org56f31fb"></a>Hahn, Brian, and Daniel T Valentine. 2016. _Essential MATLAB for Engineers and Scientists_. Academic Press.
<a id="org68f863c"></a>Higham, Desmond. 2017. _MATLAB Guide_. Philadelphia: Society for Industrial and Applied Mathematics.
<a id="org28e00d3"></a>Higham, Desmond. 2017. _MATLAB Guide_. Philadelphia: Society for Industrial and Applied Mathematics.
<a id="org019531d"></a>Johnson, Richard K. 2010. _The Elements of MATLAB Style_. Cambridge University Press.
<a id="org9e4fa10"></a>Johnson, Richard K. 2010. _The Elements of MATLAB Style_. Cambridge University Press.
<a id="org8e0ff2b"></a>OverFlow, Stack. 2018. _MATLAB Notes for Professionals_. GoalKicker.com.
<a id="orgfac8ed6"></a>OverFlow, Stack. 2018. _MATLAB Notes for Professionals_. GoalKicker.com.

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draft = false
+++
Backlinks:
- [Advanced motion control for precision mechatronics: control, identification, and learning of complex systems]({{< relref "oomen18_advan_motion_contr_precis_mechat" >}})
Tags
:
<./biblio/references.bib>

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Tags
: [Norms]({{< relref "norms" >}})
A very nice book about Multivariable Control is ([Skogestad and Postlethwaite 2007](#org2f5ed44))
A very nice book about Multivariable Control is ([Skogestad and Postlethwaite 2007](#org94735a9))
## Bibliography {#bibliography}
<a id="org2f5ed44"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="org94735a9"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.

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draft = false
+++
Backlinks:
- [Automated markerless full field hard x-ray microscopic tomography at sub-50 nm 3-dimension spatial resolution]({{< relref "wang12_autom_marker_full_field_hard" >}})
- [An instrument for 3d x-ray nano-imaging]({{< relref "holler12_instr_x_ray_nano_imagin" >}})
- [Interferometric characterization of rotation stages for x-ray nanotomography]({{< relref "stankevic17_inter_charac_rotat_stages_x_ray_nanot" >}})
Tags
:
<./biblio/references.bib>

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## Resources {#resources}
- [Slotine Lectures on Nonlinear Systems](http://web.mit.edu/nsl/www/videos/lectures.html)
<./biblio/references.bib>

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:
Lecture about Nonlinear Systems at MIT ([link](http://web.mit.edu/nsl/www/videos/lectures.html)).
<./biblio/references.bib>

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Resources:
- ([Skogestad and Postlethwaite 2007](#org4c8b20e))
- ([Toivonen 2002](#org81db503))
- ([Zhang 2011](#orgc4d2be1))
- ([Skogestad and Postlethwaite 2007](#orga6846b3))
- ([Toivonen 2002](#org300cd1c))
- ([Zhang 2011](#org037ea69))
## Definition {#definition}
@@ -176,7 +176,7 @@ In terms of signals, the \\(\mathcal{H}\_\infty\\) norm can be interpreted as fo
The \\(\mathcal{H}\_2\\) is very useful when combined to [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}}).
As explained in ([Monkhorst 2004](#orgc401feb)), the \\(\mathcal{H}\_2\\) norm has a stochastic interpretation:
As explained in ([Monkhorst 2004](#org16354b5)), the \\(\mathcal{H}\_2\\) norm has a stochastic interpretation:
> The squared \\(\mathcal{H}\_2\\) norm can be interpreted as the output variance of a system with zero mean white noise input.
@@ -184,10 +184,10 @@ As explained in ([Monkhorst 2004](#orgc401feb)), the \\(\mathcal{H}\_2\\) norm h
## Bibliography {#bibliography}
<a id="orgc401feb"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.
<a id="org16354b5"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.
<a id="org4c8b20e"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="orga6846b3"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="org81db503"></a>Toivonen, Hannu T. 2002. “Robust Control Methods.” Abo Akademi University.
<a id="org300cd1c"></a>Toivonen, Hannu T. 2002. “Robust Control Methods.” Abo Akademi University.
<a id="orgc4d2be1"></a>Zhang, Weidong. 2011. _Quantitative Process Control Theory_. CRC Press.
<a id="org037ea69"></a>Zhang, Weidong. 2011. _Quantitative Process Control Theory_. CRC Press.

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### Model {#model}
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#org8e467ce)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orga50fca3)) ([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.
@@ -56,14 +56,14 @@ Some manufacturers propose "raw" plate actuators that can be used as actuator /
## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#org5363d27)):
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#orgc2229f2)):
> 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](#org6963733)).
A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org661d95e)).
<a id="org050f47d"></a>
<a id="org8c43728"></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 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>" >}}
@@ -155,43 +155,43 @@ 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](#org8857f21)).
The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#org538bacc)).
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="org8857f21"></a>
<a id="org538bacc"></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](#org35eead3)).
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](#org8d008aa)).
<a id="org35eead3"></a>
<a id="org8d008aa"></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](#orgf00c960)):
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](#orgf006168)):
\begin{equation}
\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
\end{equation}
<a id="orgf00c960"></a>
<a id="orgf006168"></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](#orgb6392e0)).
For piezo actuators, force and displacement are inversely related (Figure [5](#org4b9d568)).
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="orgb6392e0"></a>
<a id="org4b9d568"></a>
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
@@ -201,10 +201,11 @@ When an external load is applied, the stiffness of the load (\\(k\_e\\)) determi
Piezoelectric actuators can be driven either using a voltage to charge converter or a [Voltage Amplifier]({{< relref "voltage_amplifier" >}}).
## Bibliography {#bibliography}
<a id="org5363d27"></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="orgc2229f2"></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="org8e467ce"></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="orga50fca3"></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="org6963733"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
<a id="org661d95e"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”

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## 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](#org0cb5981)) ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
- Fleming, A. J., A review of nanometer resolution position sensors: operation and performance ([Fleming 2013](#orgbadb097)) ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
<a id="table--tab:characteristics-relative-sensor"></a>
<div class="table-caption">
@@ -57,11 +57,12 @@ High precision positioning sensors include:
Capacitive Sensors and Eddy-Current sensors are compare [here](https://www.lionprecision.com/comparing-capacitive-and-eddy-current-sensors/).
<a id="org12bd001"></a>
<a id="org2b23cef"></a>
{{< figure src="/ox-hugo/position_sensors_thurner15.png" caption="Figure 1: Overview of range and precision of different position displacement sensors. Taken from <sup id=\"53230532ada812541a7cd984b3aa2662\"><a href=\"#thurner15_fiber_based_distan_sensin_inter\" title=\"Thurner, Quacquarelli, Braun, Pierre-Fran\ccois, Dal Savio, Karrai \&amp; Khaled, Fiber-Based Distance Sensing Interferometry, {Applied optics}, v(10), 3051--3063 (2015).\">thurner15_fiber_based_distan_sensin_inter</a></sup>" >}}
## Bibliography {#bibliography}
<a id="org0cb5981"></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="orgbadb097"></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>.

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Tutorial about Power Spectral Density is accessible [here](https://research.tdehaeze.xyz/spectral-analysis/).
A good article about how to use the `pwelch` function with Matlab ([Schmid 2012](#org6fb2cbe)).
A good article about how to use the `pwelch` function with Matlab ([Schmid 2012](#org7c6692c)).
## Bibliography {#bibliography}
<a id="org6fb2cbe"></a>Schmid, Hanspeter. 2012. “How to Use the FFT and Matlab’s Pwelch Function for Signal and Noise Simulations and Measurements.” _Institute of Microelectronics_.
<a id="org7c6692c"></a>Schmid, Hanspeter. 2012. “How to Use the FFT and Matlab’s Pwelch Function for Signal and Noise Simulations and Measurements.” _Institute of Microelectronics_.

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draft = false
+++
Backlinks:
- [Vibration Control of Active Structures - Fourth Edition]({{< relref "preumont18_vibrat_contr_activ_struc_fourt_edition" >}})
- [Multivariable feedback control: analysis and design]({{< relref "skogestad07_multiv_feedb_contr" >}})
- [Modal testing: theory, practice and application]({{< relref "ewins00_modal" >}})
- [The art of electronics - third edition]({{< relref "horowitz15_art_of_elect_third_edition" >}})
- [The design of high performance mechatronics - 2nd revised edition]({{< relref "schmidt14_desig_high_perfor_mechat_revis_edition" >}})
- [Parallel robots : mechanics and control]({{< relref "taghirad13_paral" >}})
Tags
:
## Here are my favorite books {#here-are-my-favorite-books}
([Steinbuch and Oomen 2016](#org662d0f5))
([Taghirad 2013](#orgcce6317))
([Lurie 2012](#org52a8951))
([Skogestad and Postlethwaite 2007](#orgaf2a97d))
([Schmidt, Schitter, and Rankers 2014](#org8465a79))
([Preumont 2018](#org43a3abb))
([Leach 2014](#org974f416))
([Ewins 2000](#org89be7f5))
([Leach and Smith 2018](#org7904c40))
([Horowitz 2015](#orga618168))
([Steinbuch and Oomen 2016](#orgf417be1))
([Taghirad 2013](#org5d52649))
([Lurie 2012](#org55fc1e1))
([Skogestad and Postlethwaite 2007](#orgc1de88b))
([Schmidt, Schitter, and Rankers 2014](#orgb0fd6be))
([Preumont 2018](#orgf335f1e))
([Leach 2014](#orgcac846b))
([Ewins 2000](#orgff1b332))
([Leach and Smith 2018](#orga27fe16))
([Horowitz 2015](#orgf44e740))
## Bibliography {#bibliography}
<a id="org89be7f5"></a>Ewins, DJ. 2000. _Modal Testing: Theory, Practice and Application_. _Research Studies Pre, 2nd Ed., ISBN-13_. Baldock, Hertfordshire, England Philadelphia, PA: Wiley-Blackwell.
<a id="orgff1b332"></a>Ewins, DJ. 2000. _Modal Testing: Theory, Practice and Application_. _Research Studies Pre, 2nd Ed., ISBN-13_. Baldock, Hertfordshire, England Philadelphia, PA: Wiley-Blackwell.
<a id="orga618168"></a>Horowitz, Paul. 2015. _The Art of Electronics - Third Edition_. New York, NY, USA: Cambridge University Press.
<a id="orgf44e740"></a>Horowitz, Paul. 2015. _The Art of Electronics - Third Edition_. New York, NY, USA: Cambridge University Press.
<a id="org974f416"></a>Leach, Richard. 2014. _Fundamental Principles of Engineering Nanometrology_. Elsevier. <https://doi.org/10.1016/c2012-0-06010-3>.
<a id="orgcac846b"></a>Leach, Richard. 2014. _Fundamental Principles of Engineering Nanometrology_. Elsevier. <https://doi.org/10.1016/c2012-0-06010-3>.
<a id="org7904c40"></a>Leach, Richard, and Stuart T. Smith. 2018. _Basics of Precision Engineering - 1st Edition_. CRC Press.
<a id="orga27fe16"></a>Leach, Richard, and Stuart T. Smith. 2018. _Basics of Precision Engineering - 1st Edition_. CRC Press.
<a id="org52a8951"></a>Lurie, B. J. 2012. _Classical Feedback Control : with MATLAB and Simulink_. Boca Raton, FL: CRC Press.
<a id="org55fc1e1"></a>Lurie, B. J. 2012. _Classical Feedback Control : with MATLAB and Simulink_. Boca Raton, FL: CRC Press.
<a id="org43a3abb"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.
<a id="orgf335f1e"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.
<a id="org8465a79"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.
<a id="orgb0fd6be"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.
<a id="orgaf2a97d"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="orgc1de88b"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="org662d0f5"></a>Steinbuch, Maarten, and Tom Oomen. 2016. “Model-Based Control for High-Tech Mechatronics Systems.” CRC Press/Taylor & Francis.
<a id="orgf417be1"></a>Steinbuch, Maarten, and Tom Oomen. 2016. “Model-Based Control for High-Tech Mechatronics Systems.” CRC Press/Taylor & Francis.
<a id="orgcce6317"></a>Taghirad, Hamid. 2013. _Parallel Robots : Mechanics and Control_. Boca Raton, FL: CRC Press.
<a id="org5d52649"></a>Taghirad, Hamid. 2013. _Parallel Robots : Mechanics and Control_. Boca Raton, FL: CRC Press.

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|--------------------------------------------------------|---------|
| [Huber](https://www.xhuber.com/en/) | Germany |
| [LAB Motion System](http://www.leuvenairbearings.com/) | Belgium |
<./biblio/references.bib>

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draft = false
+++
Backlinks:
- [Nanopositioning with multiple sensors: a case study in data storage]({{< relref "sebastian12_nanop_with_multip_sensor" >}})
- [Sensor fusion for active vibration isolation in precision equipment]({{< relref "tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip" >}})
- [Nanopositioning system with force feedback for high-performance tracking and vibration control]({{< relref "fleming10_nanop_system_with_force_feedb" >}})
- [Vibration control of flexible structures using fusion of inertial sensors and hyper-stable actuator-sensor pairs]({{< relref "collette14_vibrat" >}})
- [Sensor fusion methods for high performance active vibration isolation systems]({{< relref "collette15_sensor_fusion_method_high_perfor" >}})
- [Position Sensors]({{< relref "position_sensors" >}})
Tags
: [Actuator Fusion]({{< relref "actuator_fusion" >}}), [Complementary Filters]({{< relref "complementary_filters" >}}), [Sensors]({{< relref "sensors" >}})
<./biblio/references.bib>

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Measuring the noise level of inertial sensors is not easy as the seismic motion is usually much larger than the sensor's noise level.
A technique to estimate the sensor noise in such case is proposed in ([Barzilai, VanZandt, and Kenny 1998](#org4702c9a)) and well explained in ([Poel 2010](#orgeaef46f)) (Section 6.1.3).
A technique to estimate the sensor noise in such case is proposed in ([Barzilai, VanZandt, and Kenny 1998](#org65ed433)) and well explained in ([Poel 2010](#org02bd600)) (Section 6.1.3).
The idea is to mount two inertial sensors closely together such that they should measure the same quantity.
This is represented in Figure [1](#org030f5c0) where two identical sensors are measuring the same motion \\(x(t)\\).
This is represented in Figure [1](#orgbc58a8d) where two identical sensors are measuring the same motion \\(x(t)\\).
<a id="org030f5c0"></a>
<a id="orgbc58a8d"></a>
{{< figure src="/ox-hugo/huddle_test_setup.png" caption="Figure 1: Schematic representation of the setup for measuring the noise of inertial sensors." >}}
@@ -76,7 +76,7 @@ Now suppose that:
- sensor noises are modelled as input noises \\(n\_1(t)\\) and \\(n\_2(s)\\)
- sensor noises are uncorrelated and each are uncorrelated with \\(x(t)\\)
Then, the system can be represented by the block diagram in Figure [2](#orgec7c79b), and we can write:
Then, the system can be represented by the block diagram in Figure [2](#org1dabfe7), and we can write:
\begin{align}
P\_{y\_1y\_1}(\omega) &= |H\_1(\omega)|^2 ( P\_{x}(\omega) + P\_{n\_1}(\omega) ) \\\\\\
@@ -90,7 +90,7 @@ And the CSD between \\(y\_1(t)\\) and \\(y\_2(t)\\) is:
\gamma^2\_{y\_1y\_2}(\omega) = \frac{|C\_{y\_1y\_2}(j\omega)|^2}{P\_{y\_1}(\omega) P\_{y\_2}(\omega)}
\end{equation}
<a id="orgec7c79b"></a>
<a id="org1dabfe7"></a>
{{< figure src="/ox-hugo/huddle_test_block_diagram.png" caption="Figure 2: Huddle test block diagram" >}}
@@ -116,6 +116,6 @@ If we assume the two sensor dynamics to be the same \\(H\_1(s) \approx H\_2(s)\\
## Bibliography {#bibliography}
<a id="org4702c9a"></a>Barzilai, Aaron, Tom VanZandt, and Tom Kenny. 1998. “Technique for Measurement of the Noise of a Sensor in the Presence of Large Background Signals.” _Review of Scientific Instruments_ 69 (7):2767–72. <https://doi.org/10.1063/1.1149013>.
<a id="org65ed433"></a>Barzilai, Aaron, Tom VanZandt, and Tom Kenny. 1998. “Technique for Measurement of the Noise of a Sensor in the Presence of Large Background Signals.” _Review of Scientific Instruments_ 69 (7):2767–72. <https://doi.org/10.1063/1.1149013>.
<a id="orgeaef46f"></a>Poel, Gerrit Wijnand van der. 2010. “An Exploration of Active Hard Mount Vibration Isolation for Precision Equipment.” University of Twente. <https://doi.org/10.3990/1.9789036530163>.
<a id="org02bd600"></a>Poel, Gerrit Wijnand van der. 2010. “An Exploration of Active Hard Mount Vibration Isolation for Precision Equipment.” University of Twente. <https://doi.org/10.3990/1.9789036530163>.

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| [YMC](http://www.chinaymc.com/product/showproduct.php?id=78&lang=en) | China |
| [Vibration Research](https://vibrationresearch.com/shakers/) | USA |
| [Sentek Dynamics](https://www.sentekdynamics.com/) | USA |
<./biblio/references.bib>

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## SNR to Noise PSD {#snr-to-noise-psd}
From ([Jabben 2007](#orgf2f4e47)) (Section 3.3.2):
From ([Jabben 2007](#org55bd4a6)) (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.
@@ -78,7 +78,7 @@ 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](#orgf17a758)):
From ([Fleming 2010](#org65ccddc)):
\\[ \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\\).
@@ -96,8 +96,9 @@ The peak-to-peak noise will be approximately \\(6 \sigma = 1.7 nm\\)
</div>
## Bibliography {#bibliography}
<a id="orgf17a758"></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="org65ccddc"></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="orgf2f4e47"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.
<a id="org55bd4a6"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.

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## SVD of a MIMO system {#svd-of-a-mimo-system}
This is taken from ([Skogestad and Postlethwaite 2007](#orga80f5ed)).
This is taken from ([Skogestad and Postlethwaite 2007](#org8e4f47e)).
We are interested by the physical interpretation of the SVD when applied to the frequency response of a MIMO system \\(G(s)\\) with \\(m\\) inputs and \\(l\\) outputs.
@@ -43,7 +43,7 @@ Then is follows that:
## SVD to pseudo inverse rectangular matrices {#svd-to-pseudo-inverse-rectangular-matrices}
This is taken from ([Preumont 2018](#orgb521567)).
This is taken from ([Preumont 2018](#org6d4589f)).
The **Singular Value Decomposition** (SVD) is a generalization of the eigenvalue decomposition of a rectangular matrix:
\\[ J = U \Sigma V^T = \sum\_{i=1}^r \sigma\_i u\_i v\_i^T \\]
@@ -63,8 +63,9 @@ When \\(c(J)\\) becomes large, the most straightforward way to handle the ill-co
This will have usually little impact of the fitting error while reducing considerably the actuator inputs \\(v\\).
## Bibliography {#bibliography}
<a id="orgb521567"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.
<a id="org6d4589f"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.
<a id="orga80f5ed"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="org8e4f47e"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.

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| Manufacturers | Country |
|-----------------------------------|---------|
| [Moflon](https://www.moflon.com/) | China |
<./biblio/references.bib>

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title = "Spillover Effect"
author = ["Thomas Dehaeze"]
draft = false
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:

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Papers by J.E. McInroy:
- ([O’Brien et al. 1998](#org413fc20))
- ([McInroy, O’Brien, and Neat 1999](#orgc5005e3))
- ([McInroy 1999](#orgb4c311e))
- ([McInroy and Hamann 2000](#org8285ab1))
- ([Chen and McInroy 2000](#org709b3d5))
- ([McInroy 2002](#org349aaf8))
- ([Li, Hamann, and McInroy 2001](#orgaa83268))
- ([Lin and McInroy 2003](#org055e9ff))
- ([Jafari and McInroy 2003](#org26e42d2))
- ([Chen and McInroy 2004](#orgd92590e))
- ([O’Brien et al. 1998](#orgf349082))
- ([McInroy, O’Brien, and Neat 1999](#org5767dd1))
- ([McInroy 1999](#org2c21b8d))
- ([McInroy and Hamann 2000](#org4297441))
- ([Chen and McInroy 2000](#org8bb7a6a))
- ([McInroy 2002](#org9b28444))
- ([Li, Hamann, and McInroy 2001](#orgf3f89be))
- ([Lin and McInroy 2003](#org950f17b))
- ([Jafari and McInroy 2003](#orge2968a9))
- ([Chen and McInroy 2004](#org5ac50ad))
## Bibliography {#bibliography}
<a id="orgd92590e"></a>Chen, Y., and J.E. McInroy. 2004. “Decoupled Control of Flexure-Jointed Hexapods Using Estimated Joint-Space Mass-Inertia Matrix.” _IEEE Transactions on Control Systems Technology_ 12 (3):413–21. <https://doi.org/10.1109/tcst.2004.824339>.
<a id="org5ac50ad"></a>Chen, Y., and J.E. McInroy. 2004. “Decoupled Control of Flexure-Jointed Hexapods Using Estimated Joint-Space Mass-Inertia Matrix.” _IEEE Transactions on Control Systems Technology_ 12 (3):413–21. <https://doi.org/10.1109/tcst.2004.824339>.
<a id="org709b3d5"></a>Chen, Yixin, and J.E. McInroy. 2000. “Identification and Decoupling Control of Flexure Jointed Hexapods.” In _Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)_, nil. <https://doi.org/10.1109/robot.2000.844878>.
<a id="org8bb7a6a"></a>Chen, Yixin, and J.E. McInroy. 2000. “Identification and Decoupling Control of Flexure Jointed Hexapods.” In _Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)_, nil. <https://doi.org/10.1109/robot.2000.844878>.
<a id="org26e42d2"></a>Jafari, F., and J.E. McInroy. 2003. “Orthogonal Gough-Stewart Platforms for Micromanipulation.” _IEEE Transactions on Robotics and Automation_ 19 (4). Institute of Electrical and Electronics Engineers (IEEE):595–603. <https://doi.org/10.1109/tra.2003.814506>.
<a id="orge2968a9"></a>Jafari, F., and J.E. McInroy. 2003. “Orthogonal Gough-Stewart Platforms for Micromanipulation.” _IEEE Transactions on Robotics and Automation_ 19 (4). Institute of Electrical and Electronics Engineers (IEEE):595–603. <https://doi.org/10.1109/tra.2003.814506>.
<a id="org055e9ff"></a>Lin, Haomin, and J.E. McInroy. 2003. “Adaptive Sinusoidal Disturbance Cancellation for Precise Pointing of Stewart Platforms.” _IEEE Transactions on Control Systems Technology_ 11 (2):267–72. <https://doi.org/10.1109/tcst.2003.809248>.
<a id="org950f17b"></a>Lin, Haomin, and J.E. McInroy. 2003. “Adaptive Sinusoidal Disturbance Cancellation for Precise Pointing of Stewart Platforms.” _IEEE Transactions on Control Systems Technology_ 11 (2):267–72. <https://doi.org/10.1109/tcst.2003.809248>.
<a id="orgaa83268"></a>Li, Xiaochun, Jerry C. Hamann, and John E. McInroy. 2001. “Simultaneous Vibration Isolation and Pointing Control of Flexure Jointed Hexapods.” In _Smart Structures and Materials 2001: Smart Structures and Integrated Systems_, nil. <https://doi.org/10.1117/12.436521>.
<a id="orgf3f89be"></a>Li, Xiaochun, Jerry C. Hamann, and John E. McInroy. 2001. “Simultaneous Vibration Isolation and Pointing Control of Flexure Jointed Hexapods.” In _Smart Structures and Materials 2001: Smart Structures and Integrated Systems_, nil. <https://doi.org/10.1117/12.436521>.
<a id="orgb4c311e"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In _Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)_, nil. <https://doi.org/10.1109/cca.1999.806694>.
<a id="org2c21b8d"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In _Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)_, nil. <https://doi.org/10.1109/cca.1999.806694>.
<a id="org349aaf8"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” _IEEE/ASME Transactions on Mechatronics_ 7 (1):95–99. <https://doi.org/10.1109/3516.990892>.
<a id="org9b28444"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” _IEEE/ASME Transactions on Mechatronics_ 7 (1):95–99. <https://doi.org/10.1109/3516.990892>.
<a id="org8285ab1"></a>McInroy, J.E., and J.C. Hamann. 2000. “Design and Control of Flexure Jointed Hexapods.” _IEEE Transactions on Robotics and Automation_ 16 (4):372–81. <https://doi.org/10.1109/70.864229>.
<a id="org4297441"></a>McInroy, J.E., and J.C. Hamann. 2000. “Design and Control of Flexure Jointed Hexapods.” _IEEE Transactions on Robotics and Automation_ 16 (4):372–81. <https://doi.org/10.1109/70.864229>.
<a id="orgc5005e3"></a>McInroy, J.E., J.F. O’Brien, and G.W. Neat. 1999. “Precise, Fault-Tolerant Pointing Using a Stewart Platform.” _IEEE/ASME Transactions on Mechatronics_ 4 (1):91–95. <https://doi.org/10.1109/3516.752089>.
<a id="org5767dd1"></a>McInroy, J.E., J.F. O’Brien, and G.W. Neat. 1999. “Precise, Fault-Tolerant Pointing Using a Stewart Platform.” _IEEE/ASME Transactions on Mechatronics_ 4 (1):91–95. <https://doi.org/10.1109/3516.752089>.
<a id="org413fc20"></a>O’Brien, J.F., J.E. McInroy, D. Bodtke, M. Bruch, and J.C. Hamann. 1998. “Lessons Learned in Nonlinear Systems and Flexible Robots Through Experiments on a 6 Legged Platform.” In _Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)_, nil. <https://doi.org/10.1109/acc.1998.703532>.
<a id="orgf349082"></a>O’Brien, J.F., J.E. McInroy, D. Bodtke, M. Bruch, and J.C. Hamann. 1998. “Lessons Learned in Nonlinear Systems and Flexible Robots Through Experiments on a 6 Legged Platform.” In _Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)_, nil. <https://doi.org/10.1109/acc.1998.703532>.

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@@ -4,11 +4,5 @@ author = ["Thomas Dehaeze"]
draft = false
+++
Backlinks:
- [Modal testing: theory, practice and application]({{< relref "ewins00_modal" >}})
Tags
: [Modal Analysis]({{< relref "modal_analysis" >}})
<./biblio/references.bib>

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@@ -78,13 +78,13 @@ Sed aliquam
Here is a list of links to:
- Figure [3](#orgcbf9e46)
- Figure [3](#org4ea4248)
- Table [3](#table--tab:table-with-equations)
- Listing [1](#code-snippet--lst:matlab-figure)
- Specific line of code
- Equation \eqref{eq:numbered}
- Section
- Bibliographic Reference ([Stanisic and Legrand 2014](#org0ed95e1)), and ([Schulte and Davison 2011](#org7b9fb79); [Dominik 2010](#org4f5b6d0); [Stanisic and Legrand 2014](#org0ed95e1))
- Bibliographic Reference ([Stanisic and Legrand 2014](#org09d50a0)), and ([Schulte and Davison 2011](#org166e681); [Dominik 2010](#orge1088ab); [Stanisic and Legrand 2014](#org09d50a0))
### Maths {#maths}
@@ -157,7 +157,7 @@ Some text.
## Headlines {#headlines}
<a id="org94d8c54"></a>
<a id="orgff62b8e"></a>
### Second level Headline with tags {#second-level-headline-with-tags}
@@ -304,7 +304,7 @@ Cras non mauris ex. Morbi ut eros eu tellus egestas dapibus et et est. Aenean so
xlabel('Time [s]'); ylabel('Voltage [V]');
```
<a id="org75ab154"></a>
<a id="org5984071"></a>
{{< figure src="figs/matlab_fig_example.png" caption="Figure 1: Matlab Figure" >}}
@@ -375,7 +375,7 @@ Moreover, we can link to specific bode blocks (Listing [1](#code-snippet--lst:ma
Code to produce a nice contour plot
</div>
<a id="orgfcd383d"></a>
<a id="org1543d5a"></a>
{{< figure src="figs/matlab_logo.png" caption="Figure 2: Obtained Contour Plot" >}}
@@ -450,7 +450,7 @@ Numbering can be continued by using `+n` option as shown below.
### Normal Image {#normal-image}
Figure [3](#orgcbf9e46) shows the results of the Tikz code of listing [4](#code-snippet--lst:tikz-test).
Figure [3](#org4ea4248) shows the results of the Tikz code of listing [4](#code-snippet--lst:tikz-test).
<a id="code-snippet--lst:tikz-test"></a>
```latex
@@ -477,10 +477,10 @@ Figure [3](#orgcbf9e46) shows the results of the Tikz code of listing [4](#code-
<div class="src-block-caption">
<span class="src-block-number"><a href="#code-snippet--lst:tikz-test">Code Snippet 4</a></span>:
Tikz code that is used to generate Figure <a href="#orgcbf9e46">3</a>
Tikz code that is used to generate Figure <a href="#org4ea4248">3</a>
</div>
<a id="orgcbf9e46"></a>
<a id="org4ea4248"></a>
{{< figure src="figs/general_control_names.png" caption="Figure 3: General Control Configuration" >}}
@@ -493,7 +493,7 @@ Figure [3](#orgcbf9e46) shows the results of the Tikz code of listing [4](#code-
### Wrap Image {#wrap-image}
<a id="orge97a9ba"></a>
<a id="orgf642771"></a>
{{< figure src="figs/general_control_names.png" caption="Figure 4: General Control Configuration" >}}
@@ -509,7 +509,7 @@ Fusce blandit mauris dui, sed lobortis sapien tincidunt ac. Maecenas vitae moles
[[file:figs/general_control_names.png]]
```
<a id="org669836c"></a>
<a id="orgf69ab28"></a>
{{< figure src="figs/general_control_names.png" caption="Figure 5: General Control Configuration" >}}
@@ -518,7 +518,7 @@ Fusce blandit mauris dui, sed lobortis sapien tincidunt ac. Maecenas vitae moles
### Sub Images {#sub-images}
Link to subfigure [2](#org0dc182a).
Link to subfigure [2](#org8a50ede).
```md
#+name: fig:subfigure
@@ -536,7 +536,7 @@ Link to subfigure [2](#org0dc182a).
| ![](figs/general_control_names.png) | ![](figs/general_control_names.png) |
|--------------------------------------------|--------------------------------------------|
| <a id="org0dc182a"></a> sub figure caption | <a id="org5fce826"></a> sub figure caption |
| <a id="org8a50ede"></a> sub figure caption | <a id="org65296f2"></a> sub figure caption |
## Tables {#tables}
@@ -647,11 +647,11 @@ It is approximately **12,742 km**
## Bibliography {#bibliography}
<a id="org4f5b6d0"></a>Dominik, Carsten. 2010. _The Org Mode 7 Reference Manual-Organize Your Life with GNU Emacs_. Network Theory Ltd.
<a id="orge1088ab"></a>Dominik, Carsten. 2010. _The Org Mode 7 Reference Manual-Organize Your Life with GNU Emacs_. Network Theory Ltd.
<a id="org7b9fb79"></a>Schulte, Eric, and Dan Davison. 2011. “Active Documents with Org-Mode.” _Computing in Science & Engineering_ 13 (3). IEEE Computer Society:66–73.
<a id="org166e681"></a>Schulte, Eric, and Dan Davison. 2011. “Active Documents with Org-Mode.” _Computing in Science & Engineering_ 13 (3). IEEE Computer Society:66–73.
<a id="org0ed95e1"></a>Stanisic, Luka, and Arnaud Legrand. 2014. “Effective Reproducible Research with Org-Mode and Git.” In _European Conference on Parallel Processing_, 475–86. Springer.
<a id="org09d50a0"></a>Stanisic, Luka, and Arnaud Legrand. 2014. “Effective Reproducible Research with Org-Mode and Git.” In _European Conference on Parallel Processing_, 475–86. Springer.
[^fn:1]: A long foot note. Lorem ipsum dolor sit amet, consectetur adipiscing elit. With a reference to Figure [3](#orgcbf9e46).
[^fn:1]: A long foot note. Lorem ipsum dolor sit amet, consectetur adipiscing elit. With a reference to Figure [3](#org4ea4248).
[^fn:2]: An other footnote.

2
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@@ -19,5 +19,3 @@ Tags
| [Hamamatsu](https://www.hamamatsu.com/eu/en/product/optical-components/mems-mirror/index.html) | Japan |
| [Maradin](http://www.maradin.co.il/products/mar1100-mems-2d-laser-scanning-mirror/) | Israel |
| [Opus](http://www.opusmicro.com/mems%5Fen.html) | Taiwan |
<./biblio/references.bib>

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@@ -23,5 +23,3 @@ It is generally used to interface a sensor which outputs a current proportional
| [MMF](https://www.mmf.de/signal%5Fconditioners.htm) | Germany |
| [Femto](https://www.femto.de/en/products/current-amplifiers.html) | Germany |
| [FMB Oxford](https://www.fmb-oxford.com/products/controls-2/control-modules/i404-quad-current-integrator/) | UK |
<./biblio/references.bib>

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draft = false
+++
Backlinks:
- [Element and system design for active and passive vibration isolation]({{< relref "zuo04_elemen_system_desig_activ_passiv_vibrat_isolat" >}})
- [A six-axis single-stage active vibration isolator based on stewart platform]({{< relref "preumont07_six_axis_singl_stage_activ" >}})
- [Investigation on active vibration isolation of a stewart platform with piezoelectric actuators]({{< relref "wang16_inves_activ_vibrat_isolat_stewar" >}})
- [Active isolation and damping of vibrations via stewart platform]({{< relref "hanieh03_activ_stewar" >}})
- [Modeling and control of vibration in mechanical systems]({{< relref "du10_model_contr_vibrat_mechan_system" >}})
- [Vibration Control of Active Structures - Fourth Edition]({{< relref "preumont18_vibrat_contr_activ_struc_fourt_edition" >}})
- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
- [Sensor fusion for active vibration isolation in precision equipment]({{< relref "tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip" >}})
- [An intelligent control system for multiple degree-of-freedom vibration isolation]({{< relref "geng95_intel_contr_system_multip_degree" >}})
- [A soft 6-axis active vibration isolator]({{< relref "spanos95_soft_activ_vibrat_isolat" >}})
- [Six dof active vibration control using stewart platform with non-cubic configuration]({{< relref "zhang11_six_dof" >}})
- [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}})
- [Comparison and classification of high-precision actuators based on stiffness influencing vibration isolation]({{< relref "ito16_compar_class_high_precis_actuat" >}})
- [Vibration control of flexible structures using fusion of inertial sensors and hyper-stable actuator-sensor pairs]({{< relref "collette14_vibrat" >}})
- [Review of active vibration isolation strategies]({{< relref "collette11_review_activ_vibrat_isolat_strat" >}})
- [Force feedback versus acceleration feedback in active vibration isolation]({{< relref "preumont02_force_feedb_versus_accel_feedb" >}})
- [Active Isolation Platforms]({{< relref "active_isolation_platforms" >}})
- [Simultaneous vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_vibrat_isolat_point_contr" >}})
- [Sensors and control of a space-based six-axis vibration isolation system]({{< relref "hauge04_sensor_contr_space_based_six" >}})
- [An exploration of active hard mount vibration isolation for precision equipment]({{< relref "poel10_explor_activ_hard_mount_vibrat" >}})
- [Sensor fusion methods for high performance active vibration isolation systems]({{< relref "collette15_sensor_fusion_method_high_perfor" >}})
Tags
:
<./biblio/references.bib>

6
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@@ -4,11 +4,5 @@ author = ["Thomas Dehaeze"]
draft = false
+++
Backlinks:
- [Advances in internal model control technique: a review and future prospects]({{< relref "saxena12_advan_inter_model_contr_techn" >}})
Tags
:
<./biblio/references.bib>

5
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@@ -16,7 +16,7 @@ Tags
## Model of a Voice Coil Actuator {#model-of-a-voice-coil-actuator}
([Schmidt, Schitter, and Rankers 2014](#org8334379))
([Schmidt, Schitter, and Rankers 2014](#orgc4c6d58))
## Driving Electronics {#driving-electronics}
@@ -40,6 +40,7 @@ As the force is proportional to the current, a [Transconductance Amplifiers]({{<
| [Monticont](http://www.moticont.com/) | USA |
## Bibliography {#bibliography}
<a id="org8334379"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.
<a id="orgc4c6d58"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.

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@@ -33,9 +33,9 @@ Tags
The piezoelectric stack can be represented as a capacitance.
Let's take a capacitance driven by a voltage amplifier (Figure [1](#org811725e)).
Let's take a capacitance driven by a voltage amplifier (Figure [1](#org14569de)).
<a id="org811725e"></a>
<a id="org14569de"></a>
{{< figure src="/ox-hugo/voltage_amplifier_capacitance.png" caption="Figure 1: Piezoelectric actuator model with a voltage source" >}}
@@ -55,7 +55,7 @@ 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](#org8c7858f).
The maximum voltage as a function of frequency is shown in Figure [2](#orga5b5a57).
```matlab
Vpkp = 170; % [V]
@@ -69,7 +69,7 @@ The maximum voltage as a function of frequency is shown in Figure [2](#org8c7858
56.172
```
<a id="org8c7858f"></a>
<a id="orga5b5a57"></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\\)" >}}
@@ -105,7 +105,7 @@ This can pose several problems:
### Noise {#noise}
Sources of noise in a system comprising a voltage amplifier and a capactive load are discussed in ([Spengen 2020](#org2123c0f)).
Sources of noise in a system comprising a voltage amplifier and a capactive load are discussed in ([Spengen 2020](#org8deb271)).
Proper enclosures and cabling are necessary to protect the system from capacitive and inductive interferance.
@@ -117,13 +117,14 @@ The **input** impedance of voltage amplifiers are generally set to \\(50 \Omega\
The **output** (or internal) impedance of voltage amplifier is generally wanted small in order to have a small voltage drop when large current are drawn.
However, for stability reasons and to avoid overshoot (due to the internal negative feedback loop), this impedance can be chosen quite large.
This is discussed in ([Spengen 2017](#orgc500938)).
This is discussed in ([Spengen 2017](#org22b2168)).
## Bibliography {#bibliography}
<a id="org66151a2"></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>.
<a id="org6dde1c6"></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>.
<a id="orgc500938"></a>Spengen, W. Merlijn van. 2017. “High Voltage Amplifiers and the Ubiquitous 50 Ohms: Caveats and Benefits.” Falco Systems.
<a id="org22b2168"></a>Spengen, W. Merlijn van. 2017. “High Voltage Amplifiers and the Ubiquitous 50 Ohms: Caveats and Benefits.” Falco Systems.
<a id="org2123c0f"></a>———. 2020. “High Voltage Amplifiers: So You Think You Have Noise!” Falco Systems.
<a id="org8deb271"></a>———. 2020. “High Voltage Amplifiers: So You Think You Have Noise!” Falco Systems.