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content/zettels/active_damping.md
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## Backlinks {#backlinks}
Backlinks:
- [A concept of active mount for space applications]({{< relref "souleille18_concep_activ_mount_space_applic" >}})
- [Active isolation and damping of vibrations via stewart platform]({{< relref "hanieh03_activ_stewar" >}})

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content/zettels/actuator_fusion.md
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### Backlinks {#backlinks}
Backlinks:
- [Sensor Fusion]({{< relref "sensor_fusion" >}})
Tags
: [Complementary Filters]({{< relref "complementary_filters" >}})
([Beijen et al. 2019](#orgb647b35))
([Beijen et al. 2019](#orgaff80f9))
([Beijen 2018](#orgb43eced)) (section 6.3.1)
([Beijen 2018](#org35f402d)) (section 6.3.1)
## Bibliography {#bibliography}
<a id="orgb43eced"></a>Beijen, MA. 2018. “Disturbance Feedforward Control for Vibration Isolation Systems: Analysis, Design, and Implementation.” Technische Universiteit Eindhoven.
<a id="org35f402d"></a>Beijen, MA. 2018. “Disturbance Feedforward Control for Vibration Isolation Systems: Analysis, Design, and Implementation.” Technische Universiteit Eindhoven.
<a id="orgb647b35"></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="orgaff80f9"></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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content/zettels/actuators.md
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### Backlinks {#backlinks}
Backlinks:
- [Voice Coil Actuators]({{< relref "voice_coil_actuators" >}})
- [Collocated Control]({{< relref "collocated_control" >}})
- [Comparison and classification of high-precision actuators based on stiffness influencing vibration isolation]({{< relref "ito16_compar_class_high_precis_actuat" >}})
- [Voice Coil Actuators]({{< relref "voice_coil_actuators" >}})
- [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
Tags
@@ -24,18 +24,18 @@ Links to specific actuators:
For vibration isolation:
- In ([Ito and Schitter 2016](#org04f932d)), 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](#org7d0bcd5)), 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](#orge9272fd))
- ([Yedamale 2003](#org87858d4))
<https://www.electricaltechnology.org/2016/05/bldc-brushless-dc-motor-construction-working-principle.html>
## Bibliography {#bibliography}
<a id="org04f932d"></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="org7d0bcd5"></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="orge9272fd"></a>Yedamale, Padmaraja. 2003. “Brushless Dc (BLDC) Motor Fundamentals.” _Microchip Technology Inc_ 20:3–15.
<a id="org87858d4"></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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@@ -23,9 +23,9 @@ 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](#orgf06d261)).
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](#org5848c2b)).
<a id="orgf06d261"></a>
<a id="org5848c2b"></a>
{{< figure src="/ox-hugo/probability_density_function_adc.png" caption="Figure 1: Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}}
@@ -48,7 +48,7 @@ Thus, the two-sided PSD (from \\(\frac{-f\_s}{2}\\) to \\(\frac{f\_s}{2}\\)), we
\int\_{-f\_s/2}^{f\_s/2} \Gamma(f) d f = f\_s \Gamma = \frac{q^2}{12}
\end{equation}
<div class="important">
<div class="bred">
<div></div>
Finally, the Power Spectral Density of the quantization noise of an ADC is equal to:
@@ -62,7 +62,7 @@ Finally, the Power Spectral Density of the quantization noise of an ADC is equal
</div>
<div class="examp">
<div class="bgreen">
<div></div>
Let's take a 18bits ADC with a range of +/-10V and a sample frequency of 10kHz.

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content/zettels/capacitive_sensors.md
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Backlinks:
- [Position Sensors]({{< relref "position_sensors" >}})
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
Description:
## Description of Capacitive Sensors {#description-of-capacitive-sensors}
- <http://www.lionprecision.com/tech-library/technotes/cap-0020-sensor-theory.html>
- <https://www.lionprecision.com/comparing-capacitive-and-eddy-current-sensors>

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content/zettels/collocated_control.md
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## Collocated/Dual actuator and sensor {#collocated-dual-actuator-and-sensor}
According to ([Preumont 2018](#org97812d4)):
According to ([Preumont 2018](#org5d050e8)):
> 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](#org97812d4)):
## Nearly Collocated Actuator Sensor Pair {#nearly-collocated-actuator-sensor-pair}
From Figure [1](#org9754446), 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](#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).
<a id="org9754446"></a>
<a id="org0d605b2"></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" >}}
@@ -40,4 +40,4 @@ Of course, this will reduce the sensibility.
## Bibliography {#bibliography}
<a id="org97812d4"></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="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>.

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content/zettels/complementary_filters.md
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## Backlinks {#backlinks}
Backlinks:
- [Advances in internal model control technique: a review and future prospects]({{< relref "saxena12_advan_inter_model_contr_techn" >}})
- [Actuator Fusion]({{< relref "actuator_fusion" >}})

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content/zettels/cubic_architecture.md
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### Backlinks {#backlinks}
Backlinks:
- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
- [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}})
@@ -19,7 +19,7 @@ Tags
## Special Properties {#special-properties}
Cubic Stewart Platforms can be decoupled provided that (from ([Chen and McInroy 2000](#org916c010)))
Cubic Stewart Platforms can be decoupled provided that (from ([Chen and McInroy 2000](#org4014064)))
> 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.
@@ -27,4 +27,4 @@ Cubic Stewart Platforms can be decoupled provided that (from ([Chen and McInroy
## Bibliography {#bibliography}
<a id="org916c010"></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="org4014064"></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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content/zettels/current_amplifier.md
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Backlinks:
- [Voice Coil Actuators]({{< relref "voice_coil_actuators" >}})
Tags
: [Electronics]({{< relref "electronics" >}}), [Voice Coil Actuators]({{< relref "voice_coil_actuators" >}})

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content/zettels/dynamic_error_budgeting.md
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### Backlinks {#backlinks}
Backlinks:
- [Dynamic error budgeting, a design approach]({{< relref "monkhorst04_dynam_error_budget" >}})
- [Systems and Signals Norms]({{< relref "norms" >}})
@@ -15,12 +15,12 @@ draft = false
Tags
:
A good introduction to Dynamic Error Budgeting is given in ([Monkhorst 2004](#org9c3cf08)).
A good introduction to Dynamic Error Budgeting is given in ([Monkhorst 2004](#orgce880aa)).
## Step by Step process {#step-by-step-process}
Taken from ([Monkhorst 2004](#org9c3cf08)): ([Notes]({{< relref "monkhorst04_dynam_error_budget" >}}))
Taken from ([Monkhorst 2004](#orgce880aa)): ([Notes]({{< relref "monkhorst04_dynam_error_budget" >}}))
> Step by step, the process is as follows:
>
@@ -36,4 +36,4 @@ Taken from ([Monkhorst 2004](#org9c3cf08)): ([Notes]({{< relref "monkhorst04_dyn
## Bibliography {#bibliography}
<a id="org9c3cf08"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.
<a id="orgce880aa"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.

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content/zettels/eddy_current_sensors.md
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Backlinks:
- [Position Sensors]({{< relref "position_sensors" >}})
Tags
: [Position Sensors]({{< relref "position_sensors" >}})

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content/zettels/electronics.md
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## Backlinks {#backlinks}
Backlinks:
- [Signal Conditioner]({{< relref "signal_conditioner" >}})
- [Analog to Digital Converters]({{< relref "analog_to_digital_converters" >}})
- [Digital to Analog Converters]({{< relref "digital_to_analog_converters" >}})
- [The art of electronics - third edition]({{< relref "horowitz15_art_of_elect_third_edition" >}})
- [Current Amplifier]({{< relref "current_amplifier" >}})
- [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})
- [Voltage Amplifier]({{< relref "voltage_amplifier" >}})

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content/zettels/finite_element_model.md
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### Backlinks {#backlinks}
Backlinks:
- [Vibration Simulation using Matlab and ANSYS]({{< relref "hatch00_vibrat_matlab_ansys" >}})
@@ -16,17 +16,17 @@ Tags
Some resources:
- ([Hatch 2000](#org7219756)) ([Notes]({{< relref "hatch00_vibrat_matlab_ansys" >}}))
- ([Khot and Yelve 2011](#org9158163))
- ([Kovarac et al. 2015](#orga16f226))
- ([Hatch 2000](#org4303bb7)) ([Notes]({{< relref "hatch00_vibrat_matlab_ansys" >}}))
- ([Khot and Yelve 2011](#org31239e2))
- ([Kovarac et al. 2015](#org304a9dd))
The idea is to extract reduced state space model from Ansys into Matlab.
## Bibliography {#bibliography}
<a id="org7219756"></a>Hatch, Michael R. 2000. _Vibration Simulation Using MATLAB and ANSYS_. CRC Press.
<a id="org4303bb7"></a>Hatch, Michael R. 2000. _Vibration Simulation Using MATLAB and ANSYS_. CRC Press.
<a id="org9158163"></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="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="orga16f226"></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="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.

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content/zettels/flexible_joints.md
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### Backlinks {#backlinks}
Backlinks:
- [Identification and decoupling control of flexure jointed hexapods]({{< relref "chen00_ident_decoup_contr_flexur_joint_hexap" >}})
- [Dynamic modeling and experimental analyses of stewart platform with flexible hinges]({{< relref "jiao18_dynam_model_exper_analy_stewar" >}})
@@ -14,6 +14,7 @@ draft = false
- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
- [Dynamic modeling of flexure jointed hexapods for control purposes]({{< relref "mcinroy99_dynam" >}})
- [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}})
- [Flexures]({{< relref "flexures" >}})
Tags
:
@@ -23,16 +24,16 @@ Tags
Books:
- ([Lobontiu 2002](#orgf8c62f3))
- ([Henein 2003](#org4dba0af))
- ([Smith 2005](#orgeb2cb93))
- ([Soemers 2011](#org7d2ccfb))
- ([Cosandier 2017](#org4a2f5bd))
- ([Lobontiu 2002](#org74b9989))
- ([Henein 2003](#org1491e2e))
- ([Smith 2005](#orgcdbef5f))
- ([Soemers 2011](#org9626592))
- ([Cosandier 2017](#org9b28dc9))
## Flexure Joints for Stewart Platforms: {#flexure-joints-for-stewart-platforms}
From ([Chen and McInroy 2000](#orga69dc7b)):
From ([Chen and McInroy 2000](#org4bbdddf)):
> 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.
@@ -41,14 +42,14 @@ From ([Chen and McInroy 2000](#orga69dc7b)):
## Bibliography {#bibliography}
<a id="orga69dc7b"></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="org4bbdddf"></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="org4a2f5bd"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="org9b28dc9"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="org4dba0af"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="org1491e2e"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="orgf8c62f3"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="org74b9989"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="orgeb2cb93"></a>Smith, Stuart T. 2005. _Foundations of Ultra-Precision Mechanism Design_. Vol. 2. CRC Press.
<a id="orgcdbef5f"></a>Smith, Stuart T. 2005. _Foundations of Ultra-Precision Mechanism Design_. Vol. 2. CRC Press.
<a id="org7d2ccfb"></a>Soemers, Herman. 2011. _Design Principles for Precision Mechanisms_. T-Pointprint.
<a id="org9626592"></a>Soemers, Herman. 2011. _Design Principles for Precision Mechanisms_. T-Pointprint.

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## Materials {#materials}
- ([Smith 2000](#org0c6025e))
- ([Lobontiu 2002](#org42ce68f))
- ([Henein 2003](#org59d412b))
- ([Cosandier 2017](#org637114f))
- ([Smith 2000](#org48aca5d))
- ([Lobontiu 2002](#org45b1d4f))
- ([Henein 2003](#org516fc89))
- ([Cosandier 2017](#orgb511c9e))
## Bibliography {#bibliography}
<a id="org637114f"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="orgb511c9e"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="org59d412b"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="org516fc89"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="org42ce68f"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="org45b1d4f"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="org0c6025e"></a>Smith, Stuart T. 2000. _Flexures: Elements of Elastic Mechanisms_. Crc Press.
<a id="org48aca5d"></a>Smith, Stuart T. 2000. _Flexures: Elements of Elastic Mechanisms_. Crc Press.

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content/zettels/force_sensors.md
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@@ -8,9 +8,10 @@ Backlinks:
- [Signal Conditioner]({{< relref "signal_conditioner" >}})
- [Sensors]({{< relref "sensors" >}})
- [Position Sensors]({{< relref "position_sensors" >}})
- [Nanopositioning system with force feedback for high-performance tracking and vibration control]({{< relref "fleming10_nanop_system_with_force_feedb" >}})
- [Collocated Control]({{< relref "collocated_control" >}})
- [Instrumented Hammer]({{< relref "instrumented_hammer" >}})
- [Position Sensors]({{< relref "position_sensors" >}})
Tags
: [Signal Conditioner]({{< relref "signal_conditioner" >}}), [Modal Analysis]({{< relref "modal_analysis" >}})
@@ -21,7 +22,7 @@ Tags
### 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](#orga926d58)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
An analysis the dynamics and noise of a piezoelectric force sensor is done in ([Fleming 2010](#org9ffb699)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
### Manufacturers {#manufacturers}
@@ -54,4 +55,4 @@ However, if a charge conditioner is used, the signal will be doubled.
## Bibliography {#bibliography}
<a id="orga926d58"></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="org9ffb699"></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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### Backlinks {#backlinks}
Backlinks:
- [Guidelines for the selection of weighting functions for h-infinity control]({{< relref "bibel92_guidel_h" >}})

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content/zettels/hac_hac.md
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### Backlinks {#backlinks}
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" >}})
@@ -14,28 +14,28 @@ Tags
High-Authority Control/Low-Authority Control
From ([Preumont 2018](#org8496b17)):
From ([Preumont 2018](#org2917245)):
> The HAC/LAC approach consist of combining the two approached in a dual-loop control as shown in Figure [1](#orgf651b12). 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](#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 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="orgf651b12"></a>
<a id="org9ce3153"></a>
{{< figure src="/ox-hugo/hac_lac_control_architecture.png" caption="Figure 1: HAC-LAC Control Architecture" >}}
Nice papers:
- ([Williams and Antsaklis 1989](#org457e1df))
- ([Aubrun 1980](#org0d91759))
- ([Williams and Antsaklis 1989](#orge6af6e6))
- ([Aubrun 1980](#org05dd00f))
## Bibliography {#bibliography}
<a id="org0d91759"></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="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="org8496b17"></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="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="org457e1df"></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="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>.

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## Review of Absolute (inertial) Position Sensors {#review-of-absolute--inertial--position-sensors}
- Collette, C. et al., Review: inertial sensors for low-frequency seismic vibration measurement ([Collette, Janssens, Fernandez-Carmona, et al. 2012](#orgc31d4ec))
- Collette, C. et al., Comparison of new absolute displacement sensors ([Collette, Janssens, Mokrani, et al. 2012](#org79555eb))
- Collette, C. et al., Review: inertial sensors for low-frequency seismic vibration measurement ([Collette, Janssens, Fernandez-Carmona, et al. 2012](#orgb478ab9))
- Collette, C. et al., Comparison of new absolute displacement sensors ([Collette, Janssens, Mokrani, et al. 2012](#org83cb971))
<a id="orgf5b5084"></a>
<a id="org57bff9f"></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" >}}
@@ -41,7 +41,7 @@ Wireless Accelerometers
- <https://micromega-dynamics.com/products/recovib/miniature-vibration-recorder/>
<a id="orgaedbdbc"></a>
<a id="orgcf3bc21"></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>" >}}
@@ -58,13 +58,13 @@ Wireless Accelerometers
| Guralp | [link](https://www.guralp.com/products/surface) | UK |
| Nanometric | [link](https://www.nanometrics.ca/products/seismometers) | Canada |
<a id="orgcf4f484"></a>
<a id="orgde66251"></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>" >}}
## Bibliography {#bibliography}
<a id="orgc31d4ec"></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="orgb478ab9"></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="org79555eb"></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="org83cb971"></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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draft = false
+++
Backlinks:
- [Position Sensors]({{< relref "position_sensors" >}})
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
@@ -38,16 +42,16 @@ Tags
## Interferometer Precision {#interferometer-precision}
([Jang and Kim 2017](#org95c0093))
([Jang and Kim 2017](#orgc0eaaa4))
<a id="org69d5980"></a>
<a id="orge2a3743"></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](#orgd56bef1)).
Sources of error in laser interferometry are well described in ([Ducourtieux 2018](#org2c23555)).
It includes:
@@ -57,16 +61,16 @@ 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](#org0f5db6f))
- Air turbulence (Figure [2](#org92b4926))
- Non linearity
<a id="org0f5db6f"></a>
<a id="org92b4926"></a>
{{< figure src="/ox-hugo/interferometers_air_turbulence.png" caption="Figure 2: Effect of air turbulences on measurement stability" >}}
## Bibliography {#bibliography}
<a id="orgd56bef1"></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="org2c23555"></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="org95c0093"></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="orgc0eaaa4"></a>Jang, Yoon-Soo, and Seung-Woo Kim. 2017. “Compensation of the Refractive Index of Air in Laser Interferometer for Distance Measurement: A Review.” _International Journal of Precision Engineering and Manufacturing_ 18 (12):1881–90. <https://doi.org/10.1007/s12541-017-0217-y>.

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>
> 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](#org99d8f66))
From ([Shaw and Srinivasan 1990](#org5be9a82))
> 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.
@@ -51,4 +51,4 @@ From <https://dsp.stackexchange.com/a/30999>
## Bibliography {#bibliography}
<a id="org99d8f66"></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="org5be9a82"></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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draft = false
+++
Backlinks:
- [Position Sensors]({{< relref "position_sensors" >}})
Tags
: [Position Sensors]({{< relref "position_sensors" >}})

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Backlinks:
- [Simulink]({{< relref "simulink" >}})
Tags
: [Simulink]({{< relref "simulink" >}})
@@ -12,11 +16,11 @@ Tags
Books:
- ([Higham 2017](#org706fce9))
- ([Attaway 2018](#org83f2c16))
- ([OverFlow 2018](#orgc00fab5))
- ([Johnson 2010](#org6262ff7))
- ([Hahn and Valentine 2016](#org0601633))
- ([Higham 2017](#org11a6efd))
- ([Attaway 2018](#org88197da))
- ([OverFlow 2018](#org403ccdc))
- ([Johnson 2010](#org2c4f5cd))
- ([Hahn and Valentine 2016](#org45a0e18))
## Useful Commands {#useful-commands}
@@ -101,12 +105,12 @@ Nice functions:
## Bibliography {#bibliography}
<a id="org83f2c16"></a>Attaway, Stormy. 2018. _MATLAB : a Practical Introduction to Programming and Problem Solving_. Amsterdam: Butterworth-Heinemann.
<a id="org88197da"></a>Attaway, Stormy. 2018. _MATLAB : a Practical Introduction to Programming and Problem Solving_. Amsterdam: Butterworth-Heinemann.
<a id="org0601633"></a>Hahn, Brian, and Daniel T Valentine. 2016. _Essential MATLAB for Engineers and Scientists_. Academic Press.
<a id="org45a0e18"></a>Hahn, Brian, and Daniel T Valentine. 2016. _Essential MATLAB for Engineers and Scientists_. Academic Press.
<a id="org706fce9"></a>Higham, Desmond. 2017. _MATLAB Guide_. Philadelphia: Society for Industrial and Applied Mathematics.
<a id="org11a6efd"></a>Higham, Desmond. 2017. _MATLAB Guide_. Philadelphia: Society for Industrial and Applied Mathematics.
<a id="org6262ff7"></a>Johnson, Richard K. 2010. _The Elements of MATLAB Style_. Cambridge University Press.
<a id="org2c4f5cd"></a>Johnson, Richard K. 2010. _The Elements of MATLAB Style_. Cambridge University Press.
<a id="orgc00fab5"></a>OverFlow, Stack. 2018. _MATLAB Notes for Professionals_. GoalKicker.com.
<a id="org403ccdc"></a>OverFlow, Stack. 2018. _MATLAB Notes for Professionals_. GoalKicker.com.

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## Backlinks {#backlinks}
Backlinks:
- [Fundamental principles of engineering nanometrology]({{< relref "leach14_fundam_princ_engin_nanom" >}})

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draft = false
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## Backlinks {#backlinks}
Backlinks:
- [Instrumented Hammer]({{< relref "instrumented_hammer" >}})
- [Modal testing: theory, practice and application]({{< relref "ewins00_modal" >}})
- [Force Sensors]({{< relref "force_sensors" >}})
- [Instrumented Hammer]({{< relref "instrumented_hammer" >}})
- [System Identification]({{< relref "system_identification" >}})
Tags
: [Inertial Sensors]({{< relref "inertial_sensors" >}}), [Shaker]({{< relref "shaker" >}})

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title = "Model Predictive Control"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
:
<./biblio/references.bib>

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## Backlinks {#backlinks}
Backlinks:
- [Advanced motion control for precision mechatronics: control, identification, and learning of complex systems]({{< relref "oomen18_advan_motion_contr_precis_mechat" >}})

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Tags
: [Norms]({{< relref "norms" >}})
A very nice book about Multivariable Control is ([Skogestad and Postlethwaite 2007](#org12cc089))
A very nice book about Multivariable Control is ([Skogestad and Postlethwaite 2007](#orgd6dd02e))
## Bibliography {#bibliography}
<a id="org12cc089"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="orgd6dd02e"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.

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draft = false
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## Backlinks {#backlinks}
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" >}})

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Resources:
- ([Skogestad and Postlethwaite 2007](#org352385f))
- ([Toivonen 2002](#orga84ee63))
- ([Zhang 2011](#org74fd92c))
- ([Skogestad and Postlethwaite 2007](#org44811fa))
- ([Toivonen 2002](#orgfbd38d8))
- ([Zhang 2011](#orgc3b14cc))
## Definition {#definition}
@@ -178,17 +178,17 @@ 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](#org50a92a2)), the \\(\mathcal{H}\_2\\) norm has a stochastic interpretation:
As explained in ([Monkhorst 2004](#orgc4a9d92)), 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.
## Bibliography {#bibliography}
<a id="org50a92a2"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.
<a id="orgc4a9d92"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.
<a id="org352385f"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="org44811fa"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="orga84ee63"></a>Toivonen, Hannu T. 2002. “Robust Control Methods.” Abo Akademi University.
<a id="orgfbd38d8"></a>Toivonen, Hannu T. 2002. “Robust Control Methods.” Abo Akademi University.
<a id="org74fd92c"></a>Zhang, Weidong. 2011. _Quantitative Process Control Theory_. CRC Press.
<a id="orgc3b14cc"></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](#org43d4aea)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#org340217c)) ([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.
@@ -60,14 +60,14 @@ 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](#org9dfeb24)):
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#orge216fed)):
> 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](#org6e94433)).
A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org58c76c8)).
<a id="org7dbc771"></a>
<a id="org149ff7f"></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>" >}}
@@ -159,51 +159,51 @@ 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](#orgb5bc7ee)).
The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#org3fa87dc)).
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="orgb5bc7ee"></a>
<a id="org3fa87dc"></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](#orgc323a64)).
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](#org8acd580)).
<a id="orgc323a64"></a>
<a id="org8acd580"></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](#org1b3fdc7)):
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](#org2781d4a)):
\begin{equation}
\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
\end{equation}
<a id="org1b3fdc7"></a>
<a id="org2781d4a"></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](#org9677b03)).
For piezo actuators, force and displacement are inversely related (Figure [5](#org79cc909)).
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="org9677b03"></a>
<a id="org79cc909"></a>
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
## Bibliography {#bibliography}
<a id="org9dfeb24"></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="orge216fed"></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="org43d4aea"></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="org340217c"></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="org6e94433"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
<a id="org58c76c8"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”

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- [Inertial Sensors]({{< relref "inertial_sensors" >}})
- [Sensors]({{< relref "sensors" >}})
- [Collocated Control]({{< relref "collocated_control" >}})
- [Capacitive Sensors]({{< relref "capacitive_sensors" >}})
- [Encoders]({{< relref "encoders" >}})
- [Eddy Current Sensors]({{< relref "eddy_current_sensors" >}})
- [Linear variable differential transformers]({{< relref "linear_variable_differential_transformers" >}})
- [Interferometers]({{< relref "interferometers" >}})
- [Capacitive Sensors]({{< relref "capacitive_sensors" >}})
Tags
: [Inertial Sensors]({{< relref "inertial_sensors" >}}), [Force Sensors]({{< relref "force_sensors" >}}), [Sensor Fusion]({{< relref "sensor_fusion" >}}), [Signal Conditioner]({{< relref "signal_conditioner" >}}), [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})
@@ -33,7 +33,7 @@ High precision positioning sensors include:
## 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](#orga8fba50)) ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
- Fleming, A. J., A review of nanometer resolution position sensors: operation and performance ([Fleming 2013](#orge209c43)) ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
<a id="table--tab:characteristics-relative-sensor"></a>
<div class="table-caption">
@@ -72,4 +72,4 @@ Capacitive Sensors and Eddy-Current sensors are compare [here](https://www.lionp
## Bibliography {#bibliography}
<a id="orga8fba50"></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="orge209c43"></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://tdehaeze.github.io/spectral-analysis/).
A good article about how to use the `pwelch` function with Matlab ([Schmid 2012](#org28534e1)).
A good article about how to use the `pwelch` function with Matlab ([Schmid 2012](#org5137183)).
## Bibliography {#bibliography}
<a id="org28534e1"></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="org5137183"></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 {#backlinks}
Backlinks:
- [Basics of precision engineering - 1st edition]({{< relref "leach18_basic_precis_engin_edition" >}})
- [Design for precision: current status and trends]({{< relref "schellekens98_desig_precis" >}})

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## Here are my favorite books {#here-are-my-favorite-books}
([Steinbuch and Oomen 2016](#org9c65473))
([Taghirad 2013](#orgcd6d01b))
([Lurie 2012](#org6d15976))
([Skogestad and Postlethwaite 2007](#org19459a0))
([Schmidt, Schitter, and Rankers 2014](#org44678d0))
([Preumont 2018](#org0fc3a2c))
([Leach 2014](#orge863e61))
([Ewins 2000](#org5455809))
([Leach and Smith 2018](#org3c0b64d))
([Horowitz 2015](#org6083f7f))
([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))
## Bibliography {#bibliography}
<a id="org5455809"></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="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="org6083f7f"></a>Horowitz, Paul. 2015. _The Art of Electronics - Third Edition_. New York, NY, USA: Cambridge University Press.
<a id="orga618168"></a>Horowitz, Paul. 2015. _The Art of Electronics - Third Edition_. New York, NY, USA: Cambridge University Press.
<a id="orge863e61"></a>Leach, Richard. 2014. _Fundamental Principles of Engineering Nanometrology_. Elsevier. <https://doi.org/10.1016/c2012-0-06010-3>.
<a id="org974f416"></a>Leach, Richard. 2014. _Fundamental Principles of Engineering Nanometrology_. Elsevier. <https://doi.org/10.1016/c2012-0-06010-3>.
<a id="org3c0b64d"></a>Leach, Richard, and Stuart T. Smith. 2018. _Basics of Precision Engineering - 1st Edition_. CRC Press.
<a id="org7904c40"></a>Leach, Richard, and Stuart T. Smith. 2018. _Basics of Precision Engineering - 1st Edition_. CRC Press.
<a id="org6d15976"></a>Lurie, B. J. 2012. _Classical Feedback Control : with MATLAB and Simulink_. Boca Raton, FL: CRC Press.
<a id="org52a8951"></a>Lurie, B. J. 2012. _Classical Feedback Control : with MATLAB and Simulink_. Boca Raton, FL: CRC Press.
<a id="org0fc3a2c"></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="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="org44678d0"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.
<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="org19459a0"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="orgaf2a97d"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="org9c65473"></a>Steinbuch, Maarten, and Tom Oomen. 2016. “Model-Based Control for High-Tech Mechatronics Systems.” CRC Press/Taylor & Francis.
<a id="org662d0f5"></a>Steinbuch, Maarten, and Tom Oomen. 2016. “Model-Based Control for High-Tech Mechatronics Systems.” CRC Press/Taylor & Francis.
<a id="orgcd6d01b"></a>Taghirad, Hamid. 2013. _Parallel Robots : Mechanics and Control_. Boca Raton, FL: CRC Press.
<a id="orgcce6317"></a>Taghirad, Hamid. 2013. _Parallel Robots : Mechanics and Control_. Boca Raton, FL: CRC Press.

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Backlinks:
- [Slip Rings]({{< relref "slip_rings" >}})
Tags
: [Slip Rings]({{< relref "slip_rings" >}})

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## Backlinks {#backlinks}
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" >}})

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draft = false
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## Backlinks {#backlinks}
Backlinks:
- [Signal Conditioner]({{< relref "signal_conditioner" >}})
- [Sensor Fusion]({{< relref "sensor_fusion" >}})
Tags

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Backlinks:
- [Position Sensors]({{< relref "position_sensors" >}})
- [Force Sensors]({{< relref "force_sensors" >}})
- [Position Sensors]({{< relref "position_sensors" >}})
Tags
: [Force Sensors]({{< relref "force_sensors" >}}), [Sensors]({{< relref "sensors" >}}), [Electronics]({{< relref "electronics" >}})

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## SNR to Noise PSD {#snr-to-noise-psd}
From ([Jabben 2007](#org87840a5)) (Section 3.3.2):
From ([Jabben 2007](#orgae2d3e0)) (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.
@@ -84,7 +84,7 @@ 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](#orgc255675)):
From ([Fleming 2010](#org1022284)):
\\[ \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\\).
@@ -104,6 +104,6 @@ The peak-to-peak noise will be approximately \\(6 \sigma = 1.7 nm\\)
## Bibliography {#bibliography}
<a id="orgc255675"></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="org1022284"></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="org87840a5"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.
<a id="orgae2d3e0"></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](#org4953f60)).
This is taken from ([Skogestad and Postlethwaite 2007](#orga80f5ed)).
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](#org6558f35)).
This is taken from ([Preumont 2018](#orgb521567)).
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 \\]
@@ -65,6 +65,6 @@ This will have usually little impact of the fitting error while reducing conside
## Bibliography {#bibliography}
<a id="org6558f35"></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="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="org4953f60"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<a id="orga80f5ed"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.

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Papers by J.E. McInroy:
- ([O’Brien et al. 1998](#orgb1b8013))
- ([McInroy, O’Brien, and Neat 1999](#org06dafcc))
- ([McInroy 1999](#orga04f28d))
- ([McInroy and Hamann 2000](#org61fde10))
- ([Chen and McInroy 2000](#org4b76086))
- ([McInroy 2002](#orgc3f19a5))
- ([Li, Hamann, and McInroy 2001](#org469fdd4))
- ([Lin and McInroy 2003](#org52d73bd))
- ([Jafari and McInroy 2003](#orga8e7146))
- ([Chen and McInroy 2004](#org97f0e30))
- ([O’Brien et al. 1998](#org604163d))
- ([McInroy, O’Brien, and Neat 1999](#orgeab0f36))
- ([McInroy 1999](#orga8f456c))
- ([McInroy and Hamann 2000](#orga3c9d81))
- ([Chen and McInroy 2000](#orgf8f0bf1))
- ([McInroy 2002](#org5e8fb03))
- ([Li, Hamann, and McInroy 2001](#org2ed87b9))
- ([Lin and McInroy 2003](#orgdd8e380))
- ([Jafari and McInroy 2003](#org777ce71))
- ([Chen and McInroy 2004](#orgcc43b30))
## Bibliography {#bibliography}
<a id="org97f0e30"></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="orgcc43b30"></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="org4b76086"></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="orgf8f0bf1"></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="orga8e7146"></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="org777ce71"></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="org52d73bd"></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="orgdd8e380"></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="org469fdd4"></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="org2ed87b9"></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="orga04f28d"></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="orga8f456c"></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="orgc3f19a5"></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="org5e8fb03"></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="org61fde10"></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="orga3c9d81"></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="org06dafcc"></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="orgeab0f36"></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="orgb1b8013"></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="org604163d"></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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title = "Trainings"
author = ["Dehaeze Thomas"]
author = ["Thomas Dehaeze"]
draft = false
+++

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## Backlinks {#backlinks}
Backlinks:
- [Advances in internal model control technique: a review and future prospects]({{< relref "saxena12_advan_inter_model_contr_techn" >}})

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The piezoelectric stack can be represented as a capacitance.
Let's take a capacitance driven by a voltage amplifier (Figure [1](#org81a4c8c)).
Let's take a capacitance driven by a voltage amplifier (Figure [1](#orgbf6bfad)).
<a id="org81a4c8c"></a>
<a id="orgbf6bfad"></a>
{{< figure src="/ox-hugo/voltage_amplifier_capacitance.png" caption="Figure 1: Piezoelectric actuator model with a voltage source" >}}
@@ -60,7 +60,7 @@ 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](#orgc5c0812).
The maximum voltage as a function of frequency is shown in Figure [2](#org29f059d).
```matlab
Vpkp = 170; % [V]
@@ -74,7 +74,7 @@ C = 1e-6; % [F]
56.172
```
<a id="orgc5c0812"></a>
<a id="org29f059d"></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\\)" >}}
@@ -110,7 +110,7 @@ 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](#org48e03fb)).
Sources of noise in a system comprising a voltage amplifier and a capactive load are discussed in ([Spengen 2020](#orge9a57bd)).
Proper enclosures and cabling are necessary to protect the system from capacitive and inductive interferance.
@@ -122,13 +122,13 @@ 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](#org9c0a539)).
This is discussed in ([Spengen 2017](#orge194af0)).
## Bibliography {#bibliography}
<a id="orge4d11f6"></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="org892a333"></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="org9c0a539"></a>Spengen, W. Merlijn van. 2017. “High Voltage Amplifiers and the Ubiquitous 50 Ohms: Caveats and Benefits.” Falco Systems.
<a id="orge194af0"></a>Spengen, W. Merlijn van. 2017. “High Voltage Amplifiers and the Ubiquitous 50 Ohms: Caveats and Benefits.” Falco Systems.
<a id="org48e03fb"></a>———. 2020. “High Voltage Amplifiers: So You Think You Have Noise!” Falco Systems.
<a id="orge9a57bd"></a>———. 2020. “High Voltage Amplifiers: So You Think You Have Noise!” Falco Systems.