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title = "Actuator Fusion"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Complementary Filters]({{< relref "complementary_filters" >}})
<sup id="89b9470055c4d7f0f1957aa4400df9e8"><a href="#beijen19_mixed_feedb_feedf_contr_desig" title="Michiel Beijen, Marcel Heertjes, Hans Butler, \&amp; Maarten Steinbuch, Mixed Feedback and Feedforward Control Design for Multi-Axis Vibration Isolation Systems, Mechatronics, v(), 106 - 116 (2019).">("Michiel Beijen {\it et al.}, 2019)</a></sup>
<sup id="28a270550e13d2c8d045c9e0a9557945"><a href="#beijen18_distur" title="@phdthesis{beijen18_distur,
author = {Beijen, MA},
school = {Technische Universiteit Eindhoven},
title = {Disturbance feedforward control for vibration isolation
systems: analysis, design, and implementation},
year = 2018,
}">@phdthesis{beijen18_distur,
author = {Beijen, MA},
school = {Technische Universiteit Eindhoven},
title = {Disturbance feedforward control for vibration isolation
systems: analysis, design, and implementation},
year = 2018,
}</a></sup> (section 6.3.1)
# Bibliography
<a id="beijen19_mixed_feedb_feedf_contr_desig"></a>Beijen, M. A., Heertjes, M. F., Butler, H., & Steinbuch, M., *Mixed feedback and feedforward control design for multi-axis vibration isolation systems*, Mechatronics, *61()*, 106–116 (2019). http://dx.doi.org/https://doi.org/10.1016/j.mechatronics.2019.06.005 [↩](#89b9470055c4d7f0f1957aa4400df9e8)
<a id="beijen18_distur"></a>Beijen, M., *Disturbance feedforward control for vibration isolation systems: analysis, design, and implementation* (Doctoral dissertation) (2018). Technische Universiteit Eindhoven, . [↩](#28a270550e13d2c8d045c9e0a9557945)
## Backlinks {#backlinks}
- [Sensor Fusion]({{< relref "sensor_fusion" >}})

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For vibration isolation:
- In <sup id="aad53368e29e8a519e2f63857044fa46"><a href="#ito16_compar_class_high_precis_actuat" title="Shingo Ito \&amp; Georg Schitter, Comparison and Classification of High-Precision Actuators Based on Stiffness Influencing Vibration Isolation, {IEEE/ASME Transactions on Mechatronics}, v(2), 1169-1178 (2016).">(Shingo Ito \& Georg Schitter, 2016)</a></sup>, the effect of the actuator stiffness on the attainable vibration isolation is studied ([Notes]({{< relref "ito16_compar_class_high_precis_actuat" >}}))
- In <sup id="aad53368e29e8a519e2f63857044fa46"><a class="reference-link" href="#ito16_compar_class_high_precis_actuat" title="Shingo Ito \&amp; Georg Schitter, Comparison and Classification of High-Precision Actuators Based on Stiffness Influencing Vibration Isolation, {IEEE/ASME Transactions on Mechatronics}, v(2), 1169-1178 (2016).">(Shingo Ito \& Georg Schitter, 2016)</a></sup>, the effect of the actuator stiffness on the attainable vibration isolation is studied ([Notes]({{< relref "ito16_compar_class_high_precis_actuat" >}}))
## Piezoelectric {#piezoelectric}
@@ -23,8 +23,29 @@ For vibration isolation:
| PI | [link](https://www.physikinstrumente.com/en/) |
| Piezo System | [link](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/) |
| Noliac | [link](http://www.noliac.com/) |
| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) |
A model of a multi-layer monolithic piezoelectric stack actuator is described in <sup id="c823f68dd2a72b9667a61b3c046b4731"><a href="#fleming10_nanop_system_with_force_feedb" title="Fleming, Nanopositioning System With Force Feedback for High-Performance Tracking and Vibration Control, {IEEE/ASME Transactions on Mechatronics}, v(3), 433-447 (2010).">(Fleming, 2010)</a></sup> ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
A model of a multi-layer monolithic piezoelectric stack actuator is described in <sup id="c823f68dd2a72b9667a61b3c046b4731"><a class="reference-link" href="#fleming10_nanop_system_with_force_feedb" title="Fleming, Nanopositioning System With Force Feedback for High-Performance Tracking and Vibration Control, {IEEE/ASME Transactions on Mechatronics}, v(3), 433-447 (2010).">(Fleming, 2010)</a></sup> ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
### Piezoelectric Stack Actuators {#piezoelectric-stack-actuators}
Typical strain is \\(0.1\%\\).
### Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}
The Amplified Piezo Actuators principle is presented in <sup id="5decd2b31c4a9842b80c58b56f96590a"><a class="reference-link" href="#claeyssen07_amplif_piezoel_actuat" title="Frank Claeyssen, Le Letty, Barillot, \&amp; Sosnicki, Amplified Piezoelectric Actuators: Static \&amp; Dynamic Applications, {Ferroelectrics}, v(1), 3-14 (2007).">(Frank Claeyssen {\it et al.}, 2007)</a></sup>:
> 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 <sup id="849750850d9986ed326e74bd3c448d03"><a class="reference-link" href="#lucinskis16_dynam_charac" title="@misc{lucinskis16_dynam_charac,
author = {R. Lucinskis and C. Mangeot},
title = {Dynamic Characterization of an amplified piezoelectric
actuator},
year = 2016,
}">(Lucinskis \& Mangeot, 2016)</a></sup>.
## Voice Coil {#voice-coil}
@@ -55,16 +76,20 @@ A model of a multi-layer monolithic piezoelectric stack actuator is described in
## Brush-less DC Motor {#brush-less-dc-motor}
- <sup id="d2e68d39d09d7e8e71ff08a6ebd45400"><a href="#yedamale03_brush_dc_bldc_motor_fundam" title="Yedamale, Brushless Dc (BLDC) Motor Fundamentals, {Microchip Technology Inc}, v(), 3--15 (2003).">(Yedamale, 2003)</a></sup>
- <sup id="d2e68d39d09d7e8e71ff08a6ebd45400"><a class="reference-link" href="#yedamale03_brush_dc_bldc_motor_fundam" title="Yedamale, Brushless Dc (BLDC) Motor Fundamentals, {Microchip Technology Inc}, v(), 3--15 (2003).">(Yedamale, 2003)</a></sup>
<https://www.electricaltechnology.org/2016/05/bldc-brushless-dc-motor-construction-working-principle.html>
# Bibliography
<a id="ito16_compar_class_high_precis_actuat"></a>Ito, S., & Schitter, G., *Comparison and classification of high-precision actuators based on stiffness influencing vibration isolation*, IEEE/ASME Transactions on Mechatronics, *21(2)*, 1169–1178 (2016). http://dx.doi.org/10.1109/tmech.2015.2478658 [↩](#aad53368e29e8a519e2f63857044fa46)
<a class="bibtex-entry" id="ito16_compar_class_high_precis_actuat">Ito, S., & Schitter, G., *Comparison and classification of high-precision actuators based on stiffness influencing vibration isolation*, IEEE/ASME Transactions on Mechatronics, *21(2)*, 1169–1178 (2016). http://dx.doi.org/10.1109/tmech.2015.2478658</a> [↩](#aad53368e29e8a519e2f63857044fa46)
<a id="fleming10_nanop_system_with_force_feedb"></a>Fleming, A., *Nanopositioning system with force feedback for high-performance tracking and vibration control*, IEEE/ASME Transactions on Mechatronics, *15(3)*, 433–447 (2010). http://dx.doi.org/10.1109/tmech.2009.2028422 [↩](#c823f68dd2a72b9667a61b3c046b4731)
<a class="bibtex-entry" id="fleming10_nanop_system_with_force_feedb">Fleming, A., *Nanopositioning system with force feedback for high-performance tracking and vibration control*, IEEE/ASME Transactions on Mechatronics, *15(3)*, 433–447 (2010). http://dx.doi.org/10.1109/tmech.2009.2028422</a> [↩](#c823f68dd2a72b9667a61b3c046b4731)
<a id="yedamale03_brush_dc_bldc_motor_fundam"></a>Yedamale, P., *Brushless dc (bldc) motor fundamentals*, Microchip Technology Inc, *20()*, 3–15 (2003). [↩](#d2e68d39d09d7e8e71ff08a6ebd45400)
<a class="bibtex-entry" id="claeyssen07_amplif_piezoel_actuat">Claeyssen, F., Letty, R. L., Barillot, F., & Sosnicki, O., *Amplified piezoelectric actuators: static \& dynamic applications*, Ferroelectrics, *351(1)*, 3–14 (2007). http://dx.doi.org/10.1080/00150190701351865</a> [↩](#5decd2b31c4a9842b80c58b56f96590a)
<a class="bibtex-entry" id="lucinskis16_dynam_charac">Lucinskis, R., & Mangeot, C. (2016). *Dynamic characterization of an amplified piezoelectric actuator*. Retrieved from [](). .</a> [↩](#849750850d9986ed326e74bd3c448d03)
<a class="bibtex-entry" id="yedamale03_brush_dc_bldc_motor_fundam">Yedamale, P., *Brushless dc (bldc) motor fundamentals*, Microchip Technology Inc, *20()*, 3–15 (2003). </a> [↩](#d2e68d39d09d7e8e71ff08a6ebd45400)
## Backlinks {#backlinks}

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

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:
<./biblio/references.bib>
## Description of the Cubic Architecture {#description-of-the-cubic-architecture}
## Special Properties {#special-properties}
Cubic Stewart Platforms can be decoupled provided that (from <sup id="ba05ff213f8e5963d91559d95becfbdb"><a href="#chen00_ident_decoup_contr_flexur_joint_hexap" title="Yixin Chen \&amp; McInroy, Identification and Decoupling Control of Flexure Jointed Hexapods, nil, in in: {Proceedings 2000 ICRA. Millennium Conference. IEEE
International Conference on Robotics and Automation. Symposia
Proceedings (Cat. No.00CH37065)}, edited by (2000)">(Yixin Chen \& McInroy, 2000)</a></sup>)
> 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.
# Bibliography
<a id="chen00_ident_decoup_contr_flexur_joint_hexap"></a>Chen, Y., & McInroy, J., *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) (pp. ) (2000). : . [↩](#ba05ff213f8e5963d91559d95becfbdb)
## Backlinks {#backlinks}
- [Sensors and control of a space-based six-axis vibration isolation system]({{< relref "hauge04_sensor_contr_space_based_six" >}})
- [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}})
- [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" >}})

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title = "Dynamic Error Budgeting"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
:
A good introduction to Dynamic Error Budgeting is given in <sup id="651e626e040250ee71a0847aec41b60c"><a class="reference-link" href="#monkhorst04_dynam_error_budget" title="@phdthesis{monkhorst04_dynam_error_budget,
author = {Wouter Monkhorst},
school = {Delft University},
title = {Dynamic Error Budgeting, a design approach},
year = 2004,
}">@phdthesis{monkhorst04_dynam_error_budget,
author = {Wouter Monkhorst},
school = {Delft University},
title = {Dynamic Error Budgeting, a design approach},
year = 2004,
}</a></sup>.
## Step by Step process {#step-by-step-process}
Taken from <sup id="651e626e040250ee71a0847aec41b60c"><a class="reference-link" href="#monkhorst04_dynam_error_budget" title="@phdthesis{monkhorst04_dynam_error_budget,
author = {Wouter Monkhorst},
school = {Delft University},
title = {Dynamic Error Budgeting, a design approach},
year = 2004,
}">@phdthesis{monkhorst04_dynam_error_budget,
author = {Wouter Monkhorst},
school = {Delft University},
title = {Dynamic Error Budgeting, a design approach},
year = 2004,
}</a></sup>: ([Notes]({{< relref "monkhorst04_dynam_error_budget" >}}))
> Step by step, the process is as follows:
>
> - design a concept system
> - model the concept system, such that the closed loop transfer functions can be determined
> - Identify all significant disturbances.
> Model them with their _Power Spectral Density_
> - Define the performance outputs of the system and simulate the output error.
> Using the theory of _propagation_, the contribution of each disturbance to the output error can be analyzed and the critical disturbance can be pointed out
> - Make changes to the system that are expected to improve the performance level, and simulate the output error again.
> Iterate until the error budget is meet.
# Bibliography
<a class="bibtex-entry" id="monkhorst04_dynam_error_budget">Monkhorst, W., *Dynamic error budgeting, a design approach* (Doctoral dissertation) (2004). Delft University, .</a> [↩](#651e626e040250ee71a0847aec41b60c)
## Backlinks {#backlinks}
- [The design of high performance mechatronics - 2nd revised edition]({{< relref "schmidt14_desig_high_perfor_mechat_revis_edition" >}})
- [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})
- [Mechatronic design of a magnetically suspended rotating platform]({{< relref "jabben07_mechat" >}})
- [Systems and Signals Norms]({{< relref "norms" >}})
- [Dynamic error budgeting, a design approach]({{< relref "monkhorst04_dynam_error_budget" >}})

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## Backlinks {#backlinks}
- [The art of electronics - third edition]({{< relref "horowitz15_art_of_elect_third_edition" >}})
- [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})

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title = "Finite Element Model"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
:
## Matlab State Space Model from FEM on Ansys {#matlab-state-space-model-from-fem-on-ansys}
Some resources:
- <sup id="484c4fad309f6b0e866a7cacf4653d74"><a class="reference-link" href="#hatch00_vibrat_matlab_ansys" title="Hatch, Vibration simulation using MATLAB and ANSYS, CRC Press (2000).">(Hatch, 2000)</a></sup> ([Notes]({{< relref "hatch00_vibrat_matlab_ansys" >}}))
- <sup id="961d4331bc9da7f553368ca6a06cb743"><a class="reference-link" href="#khot11_model_respon_analy_dynam_system" title="Khot \&amp; Yelve, Modeling and Response Analysis of Dynamic Systems By Using ANSYS{\copyright} and MATLAB{\copyright}, {Journal of Vibration and Control}, v(6), 953--958 (2011).">(Khot \& Yelve, 2011)</a></sup>
- <sup id="326e544dd573b7069b69e0ec90fad499"><a class="reference-link" href="#kosarac15_creat_siso_ansys" title="Ko\vsarac, Zeljkovi\'c, , Mla\djenovi\'c \&amp; \vZivkovi\'c, Create SISO state space model of main spindle from ANSYS model, 37--41, in in: {12th International Scientific Conference, Novi Sad, Serbia}, edited by (2015)">(Ko\vsarac {\it et al.}, 2015)</a></sup>
The idea is to extract reduced state space model from Ansys into Matlab.
# Bibliography
<a class="bibtex-entry" id="hatch00_vibrat_matlab_ansys">Hatch, M. R., *Vibration simulation using matlab and ansys* (2000), : CRC Press.</a> [↩](#484c4fad309f6b0e866a7cacf4653d74)
<a class="bibtex-entry" id="khot11_model_respon_analy_dynam_system">Khot, S., & Yelve, N. P., *Modeling and response analysis of dynamic systems by using ansys\copyright and matlab\copyright*, Journal of Vibration and Control, *17(6)*, 953–958 (2011). </a> [↩](#961d4331bc9da7f553368ca6a06cb743)
<a class="bibtex-entry" id="kosarac15_creat_siso_ansys">Ko\vsarac, A, Zeljkovi\'c, M, Mla\djenovi\'c, C, & \vZivkovi\'c, A, *Create siso state space model of main spindle from ansys model*, In , 12th International Scientific Conference, Novi Sad, Serbia (pp. 37–41) (2015). : .</a> [↩](#326e544dd573b7069b69e0ec90fad499)
## Backlinks {#backlinks}
- [Vibration simulation using matlab and ansys]({{< relref "hatch00_vibrat_matlab_ansys" >}})

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:
<./biblio/references.bib>
## Resources {#resources}
Books:
- <sup id="7d07367ac4d34d56738dbfe0eb53371f"><a href="#lobontiu02_compl" title="Lobontiu, Compliant mechanisms: design of flexure hinges, CRC press (2002).">(Lobontiu, 2002)</a></sup>
- <sup id="53d819004fa64ee1fe2e715469c5991f"><a href="#henein03_concep_guidag_flexib" title="Henein, Conception des Guidages Flexibles, Presses polytechniques et universitaires romandes (2003).">(Henein, 2003)</a></sup>
- <sup id="ccc31a1054040cbdbbb28ba9e590af72"><a href="#smith05_found" title="Smith, Foundations of ultra-precision mechanism design, CRC Press (2005).">(Smith, 2005)</a></sup>
- <sup id="13540f4d4ba6bb415fdc21c85dde63cc"><a href="#soemers11_desig_princ" title="Soemers, Design Principles for precision mechanisms, T-Pointprint (2011).">(Soemers, 2011)</a></sup>
- <sup id="880641d23cd52fb47b40104731883e32"><a href="#cosandier17_flexur_mechan_desig" title="Cosandier, Flexure Mechanism Design, Distributed by CRC Press, 2017EOFL Press (2017).">(Cosandier, 2017)</a></sup>
## Flexure Joints for Stewart Platforms: {#flexure-joints-for-stewart-platforms}
From <sup id="ba05ff213f8e5963d91559d95becfbdb"><a href="#chen00_ident_decoup_contr_flexur_joint_hexap" title="Yixin Chen \&amp; McInroy, Identification and Decoupling Control of Flexure Jointed Hexapods, nil, in in: {Proceedings 2000 ICRA. Millennium Conference. IEEE
International Conference on Robotics and Automation. Symposia
Proceedings (Cat. No.00CH37065)}, edited by (2000)">(Yixin Chen \& McInroy, 2000)</a></sup>:
> 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.
> This does eliminate friction and backlash, but adds spring dynamics and limits the workspace.
# Bibliography
<a id="lobontiu02_compl"></a>Lobontiu, N., *Compliant mechanisms: design of flexure hinges* (2002), : CRC press. [↩](#7d07367ac4d34d56738dbfe0eb53371f)
<a id="henein03_concep_guidag_flexib"></a>Henein, S., *Conception des guidages flexibles* (2003), Lausanne, Suisse: Presses polytechniques et universitaires romandes. [↩](#53d819004fa64ee1fe2e715469c5991f)
<a id="smith05_found"></a>Smith, S. T., *Foundations of ultra-precision mechanism design* (2005), : CRC Press. [↩](#ccc31a1054040cbdbbb28ba9e590af72)
<a id="soemers11_desig_princ"></a>Soemers, H., *Design principles for precision mechanisms* (2011), : T-Pointprint. [↩](#13540f4d4ba6bb415fdc21c85dde63cc)
<a id="cosandier17_flexur_mechan_desig"></a>Cosandier, F., *Flexure Mechanism Design* (2017), Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press. [↩](#880641d23cd52fb47b40104731883e32)
<a id="chen00_ident_decoup_contr_flexur_joint_hexap"></a>Chen, Y., & McInroy, J., *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) (pp. ) (2000). : . [↩](#ba05ff213f8e5963d91559d95becfbdb)
## Backlinks {#backlinks}
- [A six-axis single-stage active vibration isolator based on stewart platform]({{< relref "preumont07_six_axis_singl_stage_activ" >}})
- [Nanometre-cutting machine using a stewart-platform parallel mechanism]({{< relref "furutani04_nanom_cuttin_machin_using_stewar" >}})
- [Dynamic modeling and experimental analyses of stewart platform with flexible hinges]({{< relref "jiao18_dynam_model_exper_analy_stewar" >}})
- [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}})
- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
- [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" >}})
- [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}})
- [Dynamic modeling of flexure jointed hexapods for control purposes]({{< relref "mcinroy99_dynam" >}})
- [Identification and decoupling control of flexure jointed hexapods]({{< relref "chen00_ident_decoup_contr_flexur_joint_hexap" >}})

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# Bibliography
<a id="fleming10_nanop_system_with_force_feedb"></a>Fleming, A., *Nanopositioning system with force feedback for high-performance tracking and vibration control*, IEEE/ASME Transactions on Mechatronics, *15(3)*, 433–447 (2010). http://dx.doi.org/10.1109/tmech.2009.2028422 [↩](#c823f68dd2a72b9667a61b3c046b4731)
## Backlinks {#backlinks}
- [Nanopositioning system with force feedback for high-performance tracking and vibration control]({{< relref "fleming10_nanop_system_with_force_feedb" >}})
- [Position Sensors]({{< relref "position_sensors" >}})

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High-Authority Control/Low-Authority Control
From <sup id="454500a3af67ef66a7a754d1f2e1bd4a"><a href="#preumont18_vibrat_contr_activ_struc_fourt_edition" title="Andre Preumont, Vibration Control of Active Structures - Fourth Edition, Springer International Publishing (2018).">(Andre Preumont, 2018)</a></sup>:
From <sup id="454500a3af67ef66a7a754d1f2e1bd4a"><a class="reference-link" href="#preumont18_vibrat_contr_activ_struc_fourt_edition" title="Andre Preumont, Vibration Control of Active Structures - Fourth Edition, Springer International Publishing (2018).">(Andre Preumont, 2018)</a></sup>:
> The HAC/LAC approach consist of combining the two approached in a dual-loop control as shown in Figure [1](#org2e37874). 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](#org21fb08d). 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="org2e37874"></a>
<a id="org21fb08d"></a>
{{< figure src="/ox-hugo/hac_lac_control_architecture.png" caption="Figure 1: HAC-LAC Control Architecture" >}}
Nice papers:
- <sup id="ef357e45dadd8cc8869beda6e463777b"><a class="reference-link" href="#williams89_limit" title="Williams \&amp; Antsaklis, Limitations of vibration suppression in flexible space structures, nil, in in: {Proceedings of the 28th IEEE Conference on Decision and
Control}, edited by (1989)">(Williams \& Antsaklis, 1989)</a></sup>
- <sup id="df6fde1eeef81966b2c7fb5421adbe8d"><a class="reference-link" href="#aubrun80_theor_contr_struc_by_low_author_contr" title="Aubrun, Theory of the Control of Structures By Low-Authority Controllers, {Journal of Guidance and Control}, v(5), 444-451 (1980).">(Aubrun, 1980)</a></sup>
# Bibliography
<a id="preumont18_vibrat_contr_activ_struc_fourt_edition"></a>Preumont, A., *Vibration control of active structures - fourth edition* (2018), : Springer International Publishing. [↩](#454500a3af67ef66a7a754d1f2e1bd4a)
<a class="bibtex-entry" id="preumont18_vibrat_contr_activ_struc_fourt_edition">Preumont, A., *Vibration control of active structures - fourth edition* (2018), : Springer International Publishing.</a> [↩](#454500a3af67ef66a7a754d1f2e1bd4a)
<a class="bibtex-entry" id="williams89_limit">Williams, T., & Antsaklis, P., *Limitations of vibration suppression in flexible space structures*, In , Proceedings of the 28th IEEE Conference on Decision and Control (pp. ) (1989). : .</a> [↩](#ef357e45dadd8cc8869beda6e463777b)
<a class="bibtex-entry" id="aubrun80_theor_contr_struc_by_low_author_contr">Aubrun, J., *Theory of the control of structures by low-authority controllers*, Journal of Guidance and Control, *3(5)*, 444–451 (1980). http://dx.doi.org/10.2514/3.56019</a> [↩](#df6fde1eeef81966b2c7fb5421adbe8d)
## Backlinks {#backlinks}
- [Control of spacecraft and aircraft]({{< relref "bryson93_contr_spacec_aircr" >}})
- [Vibration Control of Active Structures - Fourth Edition]({{< relref "preumont18_vibrat_contr_activ_struc_fourt_edition" >}})

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@@ -25,7 +25,7 @@ Wireless Accelerometers
- <https://micromega-dynamics.com/products/recovib/miniature-vibration-recorder/>
<a id="orgdad9a09"></a>
<a id="org868d283"></a>
{{< figure src="/ox-hugo/inertial_sensors_characteristics_accelerometers.png" caption="Figure 1: 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).\">(Collette {\it et al.}, 2011)</a></sup>" >}}
@@ -37,7 +37,7 @@ Wireless Accelerometers
| Sercel | [link](http://www.sercel.com/products/Pages/seismometers.aspx) |
| Wilcoxon | [link](https://wilcoxon.com/) |
<a id="org8c39d2f"></a>
<a id="orgbf3a5fe"></a>
{{< figure src="/ox-hugo/inertial_sensors_characteristics_geophone.png" caption="Figure 2: 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).\">(Collette {\it et al.}, 2011)</a></sup>" >}}
@@ -45,3 +45,8 @@ Wireless Accelerometers
<a id="collette12_review"></a>Collette, C., Janssens, S., Fernandez-Carmona, P., Artoos, K., Guinchard, M., Hauviller, C., & Preumont, A., *Review: inertial sensors for low-frequency seismic vibration measurement*, Bulletin of the Seismological Society of America, *102(4)*, 1289–1300 (2012). http://dx.doi.org/10.1785/0120110223 [↩](#dd5109075933cf543c7eba0979c0ba50)
<a id="collette11_review"></a>Collette, C., Artoos, K., Guinchard, M., Janssens, S., Carmona Fernandez, P., & Hauviller, C., *Review of sensors for low frequency seismic vibration measurement* (2011). [↩](#642a18d86de4e062c6afb0f5f20501c4)
## Backlinks {#backlinks}
- [Position Sensors]({{< relref "position_sensors" >}})

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title = "IRR and FIR Filters"
author = ["Thomas Dehaeze"]
draft = false
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Tags
:
<div class="table-caption">
<span class="table-number">Table 1</span>:
Comparison of IRR and FIR Filters
</div>
| | **IIR** | **FIR** |
|-----------|--------------------------------------------|---------------------------------------|
| Phase | No particular phase | Linear phase possible |
| Stability | Can be unstable | Always stable (feedback not involved) |
| Analog | Derived from analog filter | Cannot simulate analog response |
| Linearity | Used for applications which are not linear | Linear-phase characteristic |
| num/den | Both numerator and denominator | Only has numerators |
> Digital filters with finite-duration impulse response (all-zero, or FIR filters) have both advantages and disadvantages compared to infinite-duration impulse response (IIR) filters.
>
> FIR filters have the following primary advantages:
>
> - They can have exactly linear phase.
> - They are always stable.
> - The design methods are generally linear.
> - They can be realized efficiently in hardware.
> - The filter startup transients have finite duration.
>
> 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 <sup id="d875134273304770f6a0334525ecfa27"><a class="reference-link" href="#shaw90_bandw_enhan_posit_measur_using_measur_accel" title="Shaw \&amp; Srinivasan, Bandwidth Enhancement of Position Measurements Using Measured Acceleration, {Mechanical Systems and Signal Processing}, v(1), 23-38 (1990).">(Shaw \& Srinivasan, 1990)</a></sup>
> 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.
> The effective time delay corresponding to the linear phase shift is large and would have a destabilizing effect in closed loop applications.
> IIR filters are computationally less demanding. The fact that their phase shift characteristics do not vary linearly with frequency is not a disadvantage in this application.
> IIR filters are however, more susceptible to signal input and coefficient quantization effects.
From <https://dsp.stackexchange.com/a/30999>
> FIR filters are fairly common in some areas of control theory. As they usually incur a lot of added phase/time-delay, they are not really usable in the feedback path of regular control systems, but they are useful when the added phase/time-delay is not affecting the system in an adverse way, or when the particular phase response and time-delay is desired.
>
> Examples:
>
> - Feed-forward control. FIR filters are useful for producing filters that approximate arbitrary frequency responses, hence they can be used to shape a reference signal. A typical example is to use an FIR filter with the inverse frequency response of the plant -- trying to counteract the dynamics of the plant in order to get a desired output. Phase/time-delay is not interfering with the stability or performance since the computation can be done offline. FIR filters can often produce higher performance than IIR filters, especially where there are non-minimum phase zeros.
# Bibliography
<a class="bibtex-entry" id="shaw90_bandw_enhan_posit_measur_using_measur_accel">Shaw, F., & Srinivasan, K., *Bandwidth enhancement of position measurements using measured acceleration*, Mechanical Systems and Signal Processing, *4(1)*, 23–38 (1990). http://dx.doi.org/10.1016/0888-3270(90)90038-m</a> [↩](#d875134273304770f6a0334525ecfa27)

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title = "Matlab"
author = ["Thomas Dehaeze"]
draft = false
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Tags
:
## Resources on Matlab {#resources-on-matlab}
Books:
- <sup id="88712982e0649b89da706b6abbcbc6c2"><a href="#higham17_matlab" title="Higham, MATLAB guide, Society for Industrial and Applied Mathematics (2017).">(Higham, 2017)</a></sup>
- <sup id="15f4380b6ce8a647387d3ccea25711f1"><a href="#attaway18_matlab" title="Attaway, MATLAB : a practical introduction to programming and problem solving, Butterworth-Heinemann (2018).">(Attaway, 2018)</a></sup>
- <sup id="e770e23b0d222a65eb74f036227b13b2"><a href="#overflow18_matlab_notes_profes" title="Stack OverFlow, MATLAB Notes for Professionals, GoalKicker.com (2018).">(Stack OverFlow, 2018)</a></sup>
- <sup id="87b279fa5b4ec9b1a73abed2d00b313f"><a href="#johnson10_matlab" title="Johnson, The elements of MATLAB style, Cambridge University Press (2010).">(Johnson, 2010)</a></sup>
- <sup id="1b4159c36c5367ee0c92139fb403e7e1"><a href="#hahn16_essen_matlab" title="Hahn \&amp; Valentine, Essential MATLAB for engineers and scientists, Academic Press (2016).">(Hahn \& Valentine, 2016)</a></sup>
## Useful Commands {#useful-commands}
| Command | Description |
|------------------------|-------------------------------------------------------------|
| `desktop` | Open the Matlab Desktop |
| `workspace` | Open the Workspace |
| `who` | List all variables in the workspace |
| `edit <filename>` | Edit the file using Matlab Desktop (usefully for debugging) |
| `help <function>` | |
| `doc <function>` | |
| `checkcode <filename>` | Check Matlab code files for possible problems |
| `preferences` | Open Matlab preferences |
## Tips {#tips}
- Folder that starts with a `+` are automatically added to the path.
It is useful to add function inside such folder.
Then the function is accessible with `folder.function`.
## Snippets {#snippets}
### Do not show legend for one plot {#do-not-show-legend-for-one-plot}
```matlab
figure;
hold on;
plot(x, y1, 'DisplayName, 'lengendname');
plot(x, y2, 'HandleVisibility', 'off');
hold off;
legend('Location', 'northeast');
```
# Bibliography
<a id="higham17_matlab"></a>Higham, D., *Matlab guide* (2017), Philadelphia: Society for Industrial and Applied Mathematics. [↩](#88712982e0649b89da706b6abbcbc6c2)
<a id="attaway18_matlab"></a>Attaway, S., *Matlab : a practical introduction to programming and problem solving* (2018), Amsterdam: Butterworth-Heinemann. [↩](#15f4380b6ce8a647387d3ccea25711f1)
<a id="overflow18_matlab_notes_profes"></a>OverFlow, S., *Matlab notes for professionals* (2018), : GoalKicker.com. [↩](#e770e23b0d222a65eb74f036227b13b2)
<a id="johnson10_matlab"></a>Johnson, R. K., *The elements of matlab style* (2010), : Cambridge University Press. [↩](#87b279fa5b4ec9b1a73abed2d00b313f)
<a id="hahn16_essen_matlab"></a>Hahn, B., & Valentine, D. T., *Essential matlab for engineers and scientists* (2016), : Academic Press. [↩](#1b4159c36c5367ee0c92139fb403e7e1)

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Tags
:
: [Norms]({{< relref "norms" >}})
<./biblio/references.bib>
## Backlinks {#backlinks}
- [Multivariable control systems: an engineering approach]({{< relref "albertos04_multiv_contr_system" >}})
- [Position control in lithographic equipment]({{< relref "butler11_posit_contr_lithog_equip" >}})
- [Implementation challenges for multivariable control: what you did not learn in school!]({{< relref "garg07_implem_chall_multiv_contr" >}})
- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
- [Multivariable control systems: an engineering approach]({{< relref "albertos04_multiv_contr_system" >}})
- [Multivariable feedback control: analysis and design]({{< relref "skogestad07_multiv_feedb_contr" >}})

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## Backlinks {#backlinks}
- [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" >}})
- [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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title = "Systems and Signals Norms"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
:
Resources:
- <sup id="ad6f62e369b7a8d31c21671886adec1f"><a href="#skogestad07_multiv_feedb_contr" title="Skogestad \&amp; Postlethwaite, Multivariable Feedback Control: Analysis and Design, John Wiley (2007).">(Skogestad \& Postlethwaite, 2007)</a></sup>
- <sup id="90e96a2c8cdb40b7bdf895cf013c0946"><a href="#toivonen02_robus_contr_method" title="@misc{toivonen02_robus_contr_method,
author = {Hannu T. Toivonen},
institution = {Abo Akademi University},
title = {Robust Control Methods},
year = 2002,
}">(Hannu Toivonen, 2002)</a></sup>
- <sup id="8db224194542fbd4c7f4fbe56fdd4e73"><a href="#zhang11_quant_proces_contr_theor" title="Zhang, Quantitative Process Control Theory, CRC Press (2011).">(Zhang, 2011)</a></sup>
## \\(\mathcal{H}\_\infty\\) Norm {#mathcal-h-infty--norm}
SISO Systems => absolute value => bode plot
MIMO Systems => singular value
Signal
## \\(\mathcal{H}\_2\\) Norm {#mathcal-h-2--norm}
RMS value
The \\(\mathcal{H}\_2\\) is very useful when combined to [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}}).
As explained in <sup id="651e626e040250ee71a0847aec41b60c"><a href="#monkhorst04_dynam_error_budget" title="@phdthesis{monkhorst04_dynam_error_budget,
author = {Wouter Monkhorst},
school = {Delft University},
title = {Dynamic Error Budgeting, a design approach},
year = 2004,
}">@phdthesis{monkhorst04_dynam_error_budget,
author = {Wouter Monkhorst},
school = {Delft University},
title = {Dynamic Error Budgeting, a design approach},
year = 2004,
}</a></sup>, 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.
## Link between signal and system norms {#link-between-signal-and-system-norms}
# Bibliography
<a id="skogestad07_multiv_feedb_contr"></a>Skogestad, S., & Postlethwaite, I., *Multivariable feedback control: analysis and design* (2007), : John Wiley. [↩](#ad6f62e369b7a8d31c21671886adec1f)
<a id="toivonen02_robus_contr_method"></a>Toivonen, H. T. (2002). *Robust Control Methods*. Retrieved from [](). . [↩](#90e96a2c8cdb40b7bdf895cf013c0946)
<a id="zhang11_quant_proces_contr_theor"></a>Zhang, W., *Quantitative Process Control Theory* (2011), : CRC Press. [↩](#8db224194542fbd4c7f4fbe56fdd4e73)
<a id="monkhorst04_dynam_error_budget"></a>Monkhorst, W., *Dynamic error budgeting, a design approach* (Doctoral dissertation) (2004). Delft University, . [↩](#651e626e040250ee71a0847aec41b60c)
## Backlinks {#backlinks}
- [Multivariable Control]({{< relref "multivariable_control" >}})

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Tags
: [Inertial Sensors]({{< relref "inertial_sensors" >}})
: [Inertial Sensors]({{< relref "inertial_sensors" >}}), [Force Sensors]({{< relref "force_sensors" >}}), [Sensor Fusion]({{< relref "sensor_fusion" >}})
## Reviews of position sensors {#reviews-of-position-sensors}
## Absolute Position Sensors {#absolute-position-sensors}
- <sup id="0b0b67de6dddc4d28031ab2d3b28cd3d"><a href="#collette12_compar" title="Collette, Janssens, Mokrani, Fueyo-Roza, L, Artoos, Esposito, Fernandez-Carmona, , Guinchard \&amp; Leuxe, Comparison of new absolute displacement sensors, in in: {International Conference on Noise and Vibration Engineering
- Collette, C. et al., Review: inertial sensors for low-frequency seismic vibration measurement <sup id="dd5109075933cf543c7eba0979c0ba50"><a href="#collette12_review" title="Collette, Janssens, Fernandez-Carmona, , Artoos, Guinchard, Hauviller \&amp; Preumont, Review: Inertial Sensors for Low-Frequency Seismic Vibration Measurement, {Bulletin of the Seismological Society of America}, v(4), 1289-1300 (2012).">(Collette {\it et al.}, 2012)</a></sup>
- Collette, C. et al., Comparison of new absolute displacement sensors <sup id="0b0b67de6dddc4d28031ab2d3b28cd3d"><a href="#collette12_compar" title="Collette, Janssens, Mokrani, Fueyo-Roza, L, Artoos, Esposito, Fernandez-Carmona, , Guinchard \&amp; Leuxe, Comparison of new absolute displacement sensors, in in: {International Conference on Noise and Vibration Engineering
(ISMA)}, edited by (2012)">(Collette {\it et al.}, 2012)</a></sup>
- Fleming, A. J., A review of nanometer resolution position sensors: operation and performance <sup id="3fb5b61524290e36d639a4fac65703d0"><a href="#fleming13_review_nanom_resol_posit_sensor" title="Andrew Fleming, A Review of Nanometer Resolution Position Sensors: Operation and Performance, {Sensors and Actuators A: Physical}, v(nil), 106-126 (2013).">(Andrew Fleming, 2013)</a></sup> ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
<a id="org436fa72"></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" >}}
## Relative Position Sensors {#relative-position-sensors}
- Fleming, A. J., A review of nanometer resolution position sensors: operation and performance <sup id="3fb5b61524290e36d639a4fac65703d0"><a href="#fleming13_review_nanom_resol_posit_sensor" title="Andrew Fleming, A Review of Nanometer Resolution Position Sensors: Operation and Performance, {Sensors and Actuators A: Physical}, v(nil), 106-126 (2013).">(Andrew Fleming, 2013)</a></sup> ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
<a id="table--tab:characteristics-relative-sensor"></a>
<div class="table-caption">
<span class="table-number"><a href="#table--tab:characteristics-relative-sensor">Table 1</a></span>:
@@ -111,9 +117,9 @@ Description:
<sup id="7658b1219a4458a62ae8c6f51b767542"><a href="#jang17_compen_refrac_index_air_laser" title="Yoon-Soo Jang \&amp; Seung-Woo Kim, Compensation of the Refractive Index of Air in Laser Interferometer for Distance Measurement: a Review, {International Journal of Precision Engineering and
Manufacturing}, v(12), 1881-1890 (2017).">(Yoon-Soo Jang \& Seung-Woo Kim, 2017)</a></sup>
<a id="orge1e204f"></a>
<a id="orgb68b41e"></a>
{{< figure src="/ox-hugo/position_sensor_interferometer_precision.png" caption="Figure 1: Expected precision of interferometer as a function of measured distance" >}}
{{< figure src="/ox-hugo/position_sensor_interferometer_precision.png" caption="Figure 2: Expected precision of interferometer as a function of measured distance" >}}
### Fiber Optic Displacement Sensor {#fiber-optic-displacement-sensor}
@@ -123,6 +129,8 @@ Description:
| Unipulse | [link](https://www.unipulse.com/product/atw200-2/) |
# Bibliography
<a id="collette12_review"></a>Collette, C., Janssens, S., Fernandez-Carmona, P., Artoos, K., Guinchard, M., Hauviller, C., & Preumont, A., *Review: inertial sensors for low-frequency seismic vibration measurement*, Bulletin of the Seismological Society of America, *102(4)*, 1289–1300 (2012). http://dx.doi.org/10.1785/0120110223 [↩](#dd5109075933cf543c7eba0979c0ba50)
<a id="collette12_compar"></a>Collette, C., Janssens, S., Mokrani, B., Fueyo-Roza, L., Artoos, K., Esposito, M., Fernandez-Carmona, P., …, *Comparison of new absolute displacement sensors*, In , International Conference on Noise and Vibration Engineering (ISMA) (pp. ) (2012). : . [↩](#0b0b67de6dddc4d28031ab2d3b28cd3d)
<a id="fleming13_review_nanom_resol_posit_sensor"></a>Fleming, A. J., *A review of nanometer resolution position sensors: operation and performance*, Sensors and Actuators A: Physical, *190(nil)*, 106–126 (2013). http://dx.doi.org/10.1016/j.sna.2012.10.016 [↩](#3fb5b61524290e36d639a4fac65703d0)
@@ -134,5 +142,6 @@ Description:
## Backlinks {#backlinks}
- [Measurement technologies for precision positioning]({{< relref "gao15_measur_techn_precis_posit" >}})
- [A review of nanometer resolution position sensors: operation and performance]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}})
- [Measurement technologies for precision positioning]({{< relref "gao15_measur_techn_precis_posit" >}})
- [Inertial Sensors]({{< relref "inertial_sensors" >}})

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## Backlinks {#backlinks}
- [Interferometric characterization of rotation stages for x-ray nanotomography]({{< relref "stankevic17_inter_charac_rotat_stages_x_ray_nanot" >}})
- [Position control in lithographic equipment]({{< relref "butler11_posit_contr_lithog_equip" >}})
- [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" >}})

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## Backlinks {#backlinks}
- [Design for precision: current status and trends]({{< relref "schellekens98_desig_precis" >}})
- [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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- [Modal testing: theory, practice and application]({{< relref "ewins00_modal" >}})
- [The art of electronics - third edition]({{< relref "horowitz15_art_of_elect_third_edition" >}})
- [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" >}})
- [Parallel robots : mechanics and control]({{< relref "taghirad13_paral" >}})
- [The design of high performance mechatronics - 2nd revised edition]({{< relref "schmidt14_desig_high_perfor_mechat_revis_edition" >}})
- [Multivariable feedback control: analysis and design]({{< relref "skogestad07_multiv_feedb_contr" >}})

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Tags
:
: [Actuator Fusion]({{< relref "actuator_fusion" >}}), [Complementary Filters]({{< relref "complementary_filters" >}})
<./biblio/references.bib>
## Backlinks {#backlinks}
- [Sensor fusion for active vibration isolation in precision equipment]({{< relref "tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip" >}})
- [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" >}})
- [Nanopositioning system with force feedback for high-performance tracking and vibration control]({{< relref "fleming10_nanop_system_with_force_feedb" >}})
- [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" >}})
- [Position Sensors]({{< relref "position_sensors" >}})

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title = "Signal to Noise Ratio"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Electronics]({{< relref "electronics" >}}), [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}})
From <sup id="3b7899e183dba866e6a6419cf820467f"><a href="#jabben07_mechat" title="@phdthesis{jabben07_mechat,
author = {Jabben, Leon},
school = {Delft University},
title = {Mechatronic design of a magnetically suspended rotating
platform},
year = 2007,
}">@phdthesis{jabben07_mechat,
author = {Jabben, Leon},
school = {Delft University},
title = {Mechatronic design of a magnetically suspended rotating
platform},
year = 2007,
}</a></sup> (Section 3.3.2):
> Electronic equipment does most often not come with detailed electric schemes, in which case the PSD should be determined from measurements.
> In the design phase however, one has to rely on information provided by specification sheets from the manufacturer.
> The noise performance of components like sensors, amplifiers, converters, etc., is often specified in terms of a **Signal to Noise Ratio** (SNR).
> The SNR gives the ratio of the RMS value of a sine that covers the full range of the channel through which the signal is propagating over the RMS value of the electrical noise.
>
> Usually, the SNR is specified up to a certain cut-off frequency.
> If no information on the colouring of the noise is available, then the corresponding **PSD can be assumed to be white up to the cut-off frequency** \\(f\_c\\):
> \\[ S\_{snr} = \frac{x\_{fr}^2}{8 f\_c C\_{snr}^2} \\]
> with \\(x\_{fr}\\) the full range of \\(x\\), and \\(C\_{snr}\\) the SNR.
# Bibliography
<a id="jabben07_mechat"></a>Jabben, L., *Mechatronic design of a magnetically suspended rotating platform* (Doctoral dissertation) (2007). Delft University, . [↩](#3b7899e183dba866e6a6419cf820467f)

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Tags
:
<./biblio/references.bib>
## Flexure Jointed Stewart Platforms {#flexure-jointed-stewart-platforms}
Papers by J.E. McInroy:
- <sup id="89a9631ad2f0fb051d6fb8a91dc96cb2"><a href="#obrien98_lesson" title="O'Brien, McInroy, Bodtke, Bruch, \&amp; Hamann, Lessons learned in nonlinear systems and flexible robots through experiments on a 6 legged platform, nil, in in: {Proceedings of the 1998 American Control Conference. ACC
(IEEE Cat. No.98CH36207)}, edited by (1998)">(O'Brien {\it et al.}, 1998)</a></sup>
- <sup id="fecc3b6c835f5247abb57a170e2f5364"><a href="#mcinroy99_precis_fault_toler_point_using_stewar_platf" title="McInroy, O'Brien \&amp; Neat, Precise, Fault-Tolerant Pointing Using a Stewart Platform, {IEEE/ASME Transactions on Mechatronics}, v(1), 91-95 (1999).">(McInroy {\it et al.}, 1999)</a></sup>
- <sup id="5da427f78c552aa92cd64c2a6df961f1"><a href="#mcinroy99_dynam" title="McInroy, Dynamic modeling of flexure jointed hexapods for control purposes, nil, in in: {Proceedings of the 1999 IEEE International Conference on
Control Applications (Cat. No.99CH36328)}, edited by (1999)">(McInroy, 1999)</a></sup>
- <sup id="f6d310236552ee92579cf0673a2ca695"><a href="#mcinroy00_desig_contr_flexur_joint_hexap" title="McInroy \&amp; Hamann, Design and Control of Flexure Jointed Hexapods, {IEEE Transactions on Robotics and Automation}, v(4), 372-381 (2000).">(McInroy \& Hamann, 2000)</a></sup>
- <sup id="ba05ff213f8e5963d91559d95becfbdb"><a href="#chen00_ident_decoup_contr_flexur_joint_hexap" title="Yixin Chen \&amp; McInroy, Identification and Decoupling Control of Flexure Jointed Hexapods, nil, in in: {Proceedings 2000 ICRA. Millennium Conference. IEEE
International Conference on Robotics and Automation. Symposia
Proceedings (Cat. No.00CH37065)}, edited by (2000)">(Yixin Chen \& McInroy, 2000)</a></sup>
- <sup id="8bfe2d2dce902a584fa016e86a899044"><a href="#mcinroy02_model_desig_flexur_joint_stewar" title="McInroy, Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes, {IEEE/ASME Transactions on Mechatronics}, v(1), 95-99 (2002).">(McInroy, 2002)</a></sup>
- <sup id="e3df2691f750617c3995644d056d553a"><a href="#li01_simul_vibrat_isolat_point_contr" title="Xiaochun Li, Jerry Hamann \&amp; John McInroy, Simultaneous Vibration Isolation and Pointing Control of Flexure Jointed Hexapods, nil, in in: {Smart Structures and Materials 2001: Smart Structures and
Integrated Systems}, edited by (2001)">(Xiaochun Li {\it et al.}, 2001)</a></sup>
- <sup id="7c236658343683951ee18f3f771a68db"><a href="#lin03_adapt_sinus_distur_cancel_precis" title="Haomin Lin \&amp; McInroy, Adaptive Sinusoidal Disturbance Cancellation for Precise Pointing of Stewart Platforms, {IEEE Transactions on Control Systems Technology}, v(2), 267-272 (2003).">(Haomin Lin \& McInroy, 2003)</a></sup>
- <sup id="5cc6cbf419f21bb039148a3c012723d0"><a href="#jafari03_orthog_gough_stewar_platf_microm" title="Jafari \&amp; McInroy, Orthogonal Gough-Stewart Platforms for Micromanipulation, {IEEE Transactions on Robotics and Automation}, v(4), 595-603 (2003).">(Jafari \& McInroy, 2003)</a></sup>
- <sup id="7683f004697e712d8aebd697ab7c7bf7"><a href="#chen04_decoup_contr_flexur_joint_hexap" title="Chen \&amp; McInroy, Decoupled Control of Flexure-Jointed Hexapods Using Estimated Joint-Space Mass-Inertia Matrix, {IEEE Transactions on Control Systems Technology}, v(3), 413-421 (2004).">(Chen \& McInroy, 2004)</a></sup>
# Bibliography
<a id="obrien98_lesson"></a>O'Brien, J., McInroy, J., Bodtke, D., Bruch, M., & Hamann, J., *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) (pp. ) (1998). : . [↩](#89a9631ad2f0fb051d6fb8a91dc96cb2)
<a id="mcinroy99_precis_fault_toler_point_using_stewar_platf"></a>McInroy, J., O'Brien, J., & Neat, G., *Precise, fault-tolerant pointing using a stewart platform*, IEEE/ASME Transactions on Mechatronics, *4(1)*, 91–95 (1999). http://dx.doi.org/10.1109/3516.752089 [↩](#fecc3b6c835f5247abb57a170e2f5364)
<a id="mcinroy99_dynam"></a>McInroy, J., *Dynamic modeling of flexure jointed hexapods for control purposes*, In , Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328) (pp. ) (1999). : . [↩](#5da427f78c552aa92cd64c2a6df961f1)
<a id="mcinroy00_desig_contr_flexur_joint_hexap"></a>McInroy, J., & Hamann, J., *Design and control of flexure jointed hexapods*, IEEE Transactions on Robotics and Automation, *16(4)*, 372–381 (2000). http://dx.doi.org/10.1109/70.864229 [↩](#f6d310236552ee92579cf0673a2ca695)
<a id="chen00_ident_decoup_contr_flexur_joint_hexap"></a>Chen, Y., & McInroy, J., *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) (pp. ) (2000). : . [↩](#ba05ff213f8e5963d91559d95becfbdb)
<a id="mcinroy02_model_desig_flexur_joint_stewar"></a>McInroy, J., *Modeling and design of flexure jointed stewart platforms for control purposes*, IEEE/ASME Transactions on Mechatronics, *7(1)*, 95–99 (2002). http://dx.doi.org/10.1109/3516.990892 [↩](#8bfe2d2dce902a584fa016e86a899044)
<a id="li01_simul_vibrat_isolat_point_contr"></a>Li, X., Hamann, J. C., & McInroy, J. E., *Simultaneous vibration isolation and pointing control of flexure jointed hexapods*, In , Smart Structures and Materials 2001: Smart Structures and Integrated Systems (pp. ) (2001). : . [↩](#e3df2691f750617c3995644d056d553a)
<a id="lin03_adapt_sinus_distur_cancel_precis"></a>Lin, H., & McInroy, J., *Adaptive sinusoidal disturbance cancellation for precise pointing of stewart platforms*, IEEE Transactions on Control Systems Technology, *11(2)*, 267–272 (2003). http://dx.doi.org/10.1109/tcst.2003.809248 [↩](#7c236658343683951ee18f3f771a68db)
<a id="jafari03_orthog_gough_stewar_platf_microm"></a>Jafari, F., & McInroy, J., *Orthogonal gough-stewart platforms for micromanipulation*, IEEE Transactions on Robotics and Automation, *19(4)*, 595–603 (2003). http://dx.doi.org/10.1109/tra.2003.814506 [↩](#5cc6cbf419f21bb039148a3c012723d0)
<a id="chen04_decoup_contr_flexur_joint_hexap"></a>Chen, Y., & McInroy, J., *Decoupled control of flexure-jointed hexapods using estimated joint-space mass-inertia matrix*, IEEE Transactions on Control Systems Technology, *12(3)*, 413–421 (2004). http://dx.doi.org/10.1109/tcst.2004.824339 [↩](#7683f004697e712d8aebd697ab7c7bf7)
## Backlinks {#backlinks}
- [Six dof active vibration control using stewart platform with non-cubic configuration]({{< relref "zhang11_six_dof" >}})
- [Decentralized vibration control of a voice coil motor-based stewart parallel mechanism: simulation and experiments]({{< relref "tang18_decen_vibrat_contr_voice_coil" >}})
- [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}})
- [Parallel robots : mechanics and control]({{< relref "taghirad13_paral" >}})
- [Investigation on active vibration isolation of a stewart platform with piezoelectric actuators]({{< relref "wang16_inves_activ_vibrat_isolat_stewar" >}})
- [Identification and decoupling control of flexure jointed hexapods]({{< relref "chen00_ident_decoup_contr_flexur_joint_hexap" >}})
- [The stewart platform manipulator: a review]({{< relref "dasgupta00_stewar_platf_manip" >}})
- [Modeling and control of vibration in mechanical systems]({{< relref "du10_model_contr_vibrat_mechan_system" >}})
- [Studies on stewart platform manipulator: a review]({{< relref "furqan17_studies_stewar_platf_manip" >}})
@@ -26,9 +60,16 @@ Tags
- [Active isolation and damping of vibrations via stewart platform]({{< relref "hanieh03_activ_stewar" >}})
- [Sensors and control of a space-based six-axis vibration isolation system]({{< relref "hauge04_sensor_contr_space_based_six" >}})
- [Dynamic modeling and experimental analyses of stewart platform with flexible hinges]({{< relref "jiao18_dynam_model_exper_analy_stewar" >}})
- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
- [A new isotropic and decoupled 6-dof parallel manipulator]({{< relref "legnani12_new_isotr_decoup_paral_manip" >}})
- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
- [Simultaneous vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_vibrat_isolat_point_contr" >}})
- [A six-axis single-stage active vibration isolator based on stewart platform]({{< relref "preumont07_six_axis_singl_stage_activ" >}})
- [Vibration Control of Active Structures - Fourth Edition]({{< relref "preumont18_vibrat_contr_activ_struc_fourt_edition" >}})
- [A soft 6-axis active vibration isolator]({{< relref "spanos95_soft_activ_vibrat_isolat" >}})
- [Parallel robots : mechanics and control]({{< relref "taghirad13_paral" >}})
- [Decentralized vibration control of a voice coil motor-based stewart parallel mechanism: simulation and experiments]({{< relref "tang18_decen_vibrat_contr_voice_coil" >}})
- [Investigation on active vibration isolation of a stewart platform with piezoelectric actuators]({{< relref "wang16_inves_activ_vibrat_isolat_stewar" >}})
- [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}})
- [Six dof active vibration control using stewart platform with non-cubic configuration]({{< relref "zhang11_six_dof" >}})
- [Dynamic modeling of flexure jointed hexapods for control purposes]({{< relref "mcinroy99_dynam" >}})
- [Identification and decoupling control of flexure jointed hexapods]({{< relref "chen00_ident_decoup_contr_flexur_joint_hexap" >}})

7
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@@ -12,9 +12,6 @@ Tags
## Backlinks {#backlinks}
- [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" >}})
- [Investigation on active vibration isolation of a stewart platform with piezoelectric actuators]({{< relref "wang16_inves_activ_vibrat_isolat_stewar" >}})
- [Review of active vibration isolation strategies]({{< relref "collette11_review_activ_vibrat_isolat_strat" >}})
- [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" >}})
@@ -31,3 +28,7 @@ Tags
- [Vibration Control of Active Structures - Fourth Edition]({{< relref "preumont18_vibrat_contr_activ_struc_fourt_edition" >}})
- [A soft 6-axis active vibration isolator]({{< relref "spanos95_soft_activ_vibrat_isolat" >}})
- [Sensor fusion for active vibration isolation in precision equipment]({{< relref "tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip" >}})
- [Investigation on active vibration isolation of a stewart platform with piezoelectric actuators]({{< relref "wang16_inves_activ_vibrat_isolat_stewar" >}})
- [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}})
- [Six dof active vibration control using stewart platform with non-cubic configuration]({{< relref "zhang11_six_dof" >}})
- [Element and system design for active and passive vibration isolation]({{< relref "zuo04_elemen_system_desig_activ_passiv_vibrat_isolat" >}})

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+++
title = "Virtual Sensor Fusion"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
:
<./biblio/references.bib>
## Backlinks {#backlinks}
- [Advances in internal model control technique: a review and future prospects]({{< relref "saxena12_advan_inter_model_contr_techn" >}})