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content/article/butler11_posit_contr_lithog_equip.md
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title = "Position control in lithographic equipment"
author = ["Thomas Dehaeze"]
draft = false
draft = true
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Tags
: [Multivariable Control]({{< relref "multivariable_control" >}}), [Positioning Stations]({{< relref "positioning_stations" >}})
: [Multivariable Control]({{<relref "multivariable_control.md#" >}}), [Positioning Stations]({{<relref "positioning_stations.md#" >}})
Reference
: ([Butler 2011](#org338ffef))
: ([Butler 2011](#org9e15931))
Author(s)
: Butler, H.
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## Bibliography {#bibliography}
<a id="org338ffef"></a>Butler, Hans. 2011. “Position Control in Lithographic Equipment.” _IEEE Control Systems_ 31 (5):28–47. <https://doi.org/10.1109/mcs.2011.941882>.
<a id="org9e15931"></a>Butler, Hans. 2011. “Position Control in Lithographic Equipment.” _IEEE Control Systems_ 31 (5):28–47. <https://doi.org/10.1109/mcs.2011.941882>.

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content/article/chen04_decoup_contr_flexur_joint_hexap.md
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title = "Decoupled control of flexure-jointed hexapods using estimated joint-space mass-inertia matrix"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
: [Decoupled Control]({{<relref "decoupled_control.md#" >}})
Reference
: ([Chen and McInroy 2004](#orgbe5d3d7))
: ([Chen and McInroy 2004](#org1a36c5c))
Author(s)
: Chen, Y., & McInroy, J.
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## Bibliography {#bibliography}
<a id="orgbe5d3d7"></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="org1a36c5c"></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>.

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content/article/fleming12_estim.md
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title = "Estimating the resolution of nanopositioning systems from frequency domain data"
author = ["Thomas Dehaeze"]
draft = false
draft = true
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Reference
: ([Fleming 2012](#orgc7d7404))
: ([Fleming 2012](#org26b3187))
Author(s)
: Fleming, A. J.
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## Bibliography {#bibliography}
<a id="orgc7d7404"></a>Fleming, Andrew J. 2012. “Estimating the Resolution of Nanopositioning Systems from Frequency Domain Data.” In _2012 IEEE International Conference on Robotics and Automation_, nil. <https://doi.org/10.1109/icra.2012.6224850>.
<a id="org26b3187"></a>Fleming, Andrew J. 2012. “Estimating the Resolution of Nanopositioning Systems from Frequency Domain Data.” In _2012 IEEE International Conference on Robotics and Automation_, nil. <https://doi.org/10.1109/icra.2012.6224850>.

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content/article/fleming15_low_order_dampin_track_contr.md
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title = "Low-order damping and tracking control for scanning probe systems"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
@ -9,7 +9,7 @@ Tags
Reference
: ([Fleming, Teo, and Leang 2015](#org0b5cc88))
: ([Fleming, Teo, and Leang 2015](#org26aec08))
Author(s)
: Fleming, A. J., Teo, Y. R., & Leang, K. K.
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## Bibliography {#bibliography}
<a id="org0b5cc88"></a>Fleming, Andrew J., Yik Ren Teo, and Kam K. Leang. 2015. “Low-Order Damping and Tracking Control for Scanning Probe Systems.” _Frontiers in Mechanical Engineering_ 1 (nil):nil. <https://doi.org/10.3389/fmech.2015.00014>.
<a id="org26aec08"></a>Fleming, Andrew J., Yik Ren Teo, and Kam K. Leang. 2015. “Low-Order Damping and Tracking Control for Scanning Probe Systems.” _Frontiers in Mechanical Engineering_ 1 (nil):nil. <https://doi.org/10.3389/fmech.2015.00014>.

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content/article/furqan17_studies_stewar_platf_manip.md
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title = "Studies on stewart platform manipulator: a review"
author = ["Thomas Dehaeze"]
draft = false
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Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}})
Reference
: ([Furqan, Suhaib, and Ahmad 2017](#org1144495))
Author(s)
: Furqan, M., Suhaib, M., & Ahmad, N.
Year
: 2017
Lots of references.
## Bibliography {#bibliography}
<a id="org1144495"></a>Furqan, Mohd, Mohd Suhaib, and Nazeer Ahmad. 2017. “Studies on Stewart Platform Manipulator: A Review.” _Journal of Mechanical Science and Technology_ 31 (9):4459–70. <https://doi.org/10.1007/s12206-017-0846-1>.

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content/article/gao15_measur_techn_precis_posit.md
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title = "Measurement technologies for precision positioning"
author = ["Thomas Dehaeze"]
draft = false
draft = true
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Tags
: [Position Sensors]({{< relref "position_sensors" >}})
: [Position Sensors]({{<relref "position_sensors.md#" >}})
Reference
: ([Gao et al. 2015](#org07ae1a8))
: ([Gao et al. 2015](#orgc8ea7ee))
Author(s)
: Gao, W., Kim, S., Bosse, H., Haitjema, H., Chen, Y., Lu, X., Knapp, W., …
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## Bibliography {#bibliography}
<a id="org07ae1a8"></a>Gao, W., S.W. Kim, H. Bosse, H. Haitjema, Y.L. Chen, X.D. Lu, W. Knapp, A. Weckenmann, W.T. Estler, and H. Kunzmann. 2015. “Measurement Technologies for Precision Positioning.” _CIRP Annals_ 64 (2):773–96. <https://doi.org/10.1016/j.cirp.2015.05.009>.
<a id="orgc8ea7ee"></a>Gao, W., S.W. Kim, H. Bosse, H. Haitjema, Y.L. Chen, X.D. Lu, W. Knapp, A. Weckenmann, W.T. Estler, and H. Kunzmann. 2015. “Measurement Technologies for Precision Positioning.” _CIRP Annals_ 64 (2):773–96. <https://doi.org/10.1016/j.cirp.2015.05.009>.

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content/article/jiao18_dynam_model_exper_analy_stewar.md
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title = "Dynamic modeling and experimental analyses of stewart platform with flexible hinges"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
: [Stewart Platforms]({{<relref "stewart_platforms.md#" >}}), [Flexible Joints]({{<relref "flexible_joints.md#" >}})
Reference
: ([Jiao et al. 2018](#org9f472e3))
: ([Jiao et al. 2018](#orgfa41a34))
Author(s)
: Jiao, J., Wu, Y., Yu, K., & Zhao, R.
@ -20,4 +20,4 @@ Year
## Bibliography {#bibliography}
<a id="org9f472e3"></a>Jiao, Jian, Ying Wu, Kaiping Yu, and Rui Zhao. 2018. “Dynamic Modeling and Experimental Analyses of Stewart Platform with Flexible Hinges.” _Journal of Vibration and Control_ 25 (1):151–71. <https://doi.org/10.1177/1077546318772474>.
<a id="orgfa41a34"></a>Jiao, Jian, Ying Wu, Kaiping Yu, and Rui Zhao. 2018. “Dynamic Modeling and Experimental Analyses of Stewart Platform with Flexible Hinges.” _Journal of Vibration and Control_ 25 (1):151–71. <https://doi.org/10.1177/1077546318772474>.

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content/article/kwakernaak93_robus_contr_h_tutor_paper.md
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title = "Robust control and H-Infinity optimization - Tutorial paper"
author = ["Thomas Dehaeze"]
draft = false
draft = true
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Tags
: [H Infinity Control]({{< relref "h_infinity_control" >}}), [Weighting Functions]({{< relref "weighting_functions" >}})
: [H Infinity Control]({{<relref "h_infinity_control.md#" >}}), [Weighting Functions]({{<relref "weighting_functions.md#" >}})
Reference
: ([Kwakernaak 1993](#orge60c373))
: ([Kwakernaak 1993](#orgb190420))
Author(s)
: Kwakernaak, H.
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## Bibliography {#bibliography}
<a id="orge60c373"></a>Kwakernaak, Huibert. 1993. “Robust Control and H$infty$-Optimization - Tutorial Paper.” _Automatica_ 29 (2):255–73. <https://doi.org/10.1016/0005-1098(93)>90122-a.
<a id="orgb190420"></a>Kwakernaak, Huibert. 1993. “Robust Control and H$\Infty$-Optimization - Tutorial Paper.” _Automatica_ 29 (2):255–73. <https://doi.org/10.1016/0005-1098(93)90122-a>.

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content/article/lee03_posit_contr_stewar_platf_using.md
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title = "Position control of a stewart platform using inverse dynamics control with approximate dynamics"
author = ["Thomas Dehaeze"]
draft = false
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content/article/lin06_distur_atten_precis_hexap_point.md
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title = "Disturbance attenuation in precise hexapod pointing using positive force feedback"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
@ -9,7 +9,7 @@ Tags
Reference
: ([Lin and McInroy 2006](#org0bfd86d))
: ([Lin and McInroy 2006](#org5d8be72))
Author(s)
: Lin, H., & McInroy, J. E.
@ -21,4 +21,4 @@ Year
## Bibliography {#bibliography}
<a id="org0bfd86d"></a>Lin, Haomin, and John E. McInroy. 2006. “Disturbance Attenuation in Precise Hexapod Pointing Using Positive Force Feedback.” _Control Engineering Practice_ 14 (11):1377–86. <https://doi.org/10.1016/j.conengprac.2005.10.002>.
<a id="org5d8be72"></a>Lin, Haomin, and John E. McInroy. 2006. “Disturbance Attenuation in Precise Hexapod Pointing Using Positive Force Feedback.” _Control Engineering Practice_ 14 (11):1377–86. <https://doi.org/10.1016/j.conengprac.2005.10.002>.

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content/article/liu19_review_indus_mimo_decoup_contr.md
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title = "A review of industrial mimo decoupling control"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
:
Reference
: ([Liu et al. 2019](#org9f65386))
Author(s)
: Liu, L., Tian, S., Xue, D., Zhang, T., Chen, Y., & Zhang, S.
Year
: 2019
-\* Liu, L. et al. (2019): A review of industrial mimo decoupling control :article:ignore:
## Bibliography {#bibliography}
<a id="org9f65386"></a>Liu, Lu, Siyuan Tian, Dingyu Xue, Tao Zhang, YangQuan Chen, and Shuo Zhang. 2019. “A Review of Industrial Mimo Decoupling Control.” _International Journal of Control, Automation and Systems_ 17 (5):1246–54. <https://doi.org/10.1007/s12555-018-0367-4>.

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content/article/mcinroy00_desig_contr_flexur_joint_hexap.md
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title = "Design and control of flexure jointed hexapods"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
@ -9,7 +9,7 @@ Tags
Reference
: ([McInroy and Hamann 2000](#org04a7c92))
: ([McInroy and Hamann 2000](#orgaf3de6d))
Author(s)
: McInroy, J., & Hamann, J.
@ -21,4 +21,4 @@ Year
## Bibliography {#bibliography}
<a id="org04a7c92"></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="orgaf3de6d"></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>.

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content/article/oomen18_advan_motion_contr_precis_mechat.md
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title = "Advanced motion control for precision mechatronics: control, identification, and learning of complex systems"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
: [Motion Control](motion_control.md)
: [Motion Control]({{<relref "motion_control.md#" >}})
Reference
: ([Oomen 2018](#orge2156f8))
: ([Oomen 2018](#org5ed8cf0))
Author(s)
: Oomen, T.
@ -16,7 +16,7 @@ Author(s)
Year
: 2018
<a id="org6d729fe"></a>
<a id="orgd73938c"></a>
{{< figure src="/ox-hugo/oomen18_next_gen_loop_gain.png" caption="Figure 1: Envisaged developments in motion systems. In traditional motion systems, the control bandwidth takes place in the rigid-body region. In the next generation systemes, flexible dynamics are foreseen to occur within the control bandwidth." >}}
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## Bibliography {#bibliography}
<a id="orge2156f8"></a>Oomen, Tom. 2018. “Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems.” _IEEJ Journal of Industry Applications_ 7 (2):127–40. <https://doi.org/10.1541/ieejjia.7.127>.
<a id="org5ed8cf0"></a>Oomen, Tom. 2018. “Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems.” _IEEJ Journal of Industry Applications_ 7 (2):127–40. <https://doi.org/10.1541/ieejjia.7.127>.

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content/article/schellekens98_desig_precis.md
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title = "Design for precision: current status and trends"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
: [Precision Engineering]({{< relref "precision_engineering" >}})
: [Precision Engineering]({{<relref "precision_engineering.md#" >}})
Reference
: ([Schellekens et al. 1998](#org035ecc6))
: ([Schellekens et al. 1998](#orgc8457bd))
Author(s)
: Schellekens, P., Rosielle, N., Vermeulen, H., Vermeulen, M., Wetzels, S., & Pril, W.
@ -20,4 +20,4 @@ Year
## Bibliography {#bibliography}
<a id="org035ecc6"></a>Schellekens, P., N. Rosielle, H. Vermeulen, M. Vermeulen, S. Wetzels, and W. Pril. 1998. “Design for Precision: Current Status and Trends.” _Cirp Annals_, no. 2:557–86. <https://doi.org/10.1016/s0007-8506(07)>63243-0.
<a id="orgc8457bd"></a>Schellekens, P., N. Rosielle, H. Vermeulen, M. Vermeulen, S. Wetzels, and W. Pril. 1998. “Design for Precision: Current Status and Trends.” _Cirp Annals_, no. 2:557–86. <https://doi.org/10.1016/s0007-8506(07)63243-0>.

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content/article/schroeck01_compen_desig_linear_time_invar.md
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title = "On compensator design for linear time-invariant dual-input single-output systems"
author = ["Thomas Dehaeze"]
draft = false
draft = true
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@ -9,7 +9,7 @@ Tags
Reference
: ([Schroeck, Messner, and McNab 2001](#orga580bdc))
: ([Schroeck, Messner, and McNab 2001](#org722a59f))
Author(s)
: Schroeck, S., Messner, W., & McNab, R.
@ -21,4 +21,4 @@ Year
## Bibliography {#bibliography}
<a id="orga580bdc"></a>Schroeck, S.J., W.C. Messner, and R.J. McNab. 2001. “On Compensator Design for Linear Time-Invariant Dual-Input Single-Output Systems.” _IEEE/ASME Transactions on Mechatronics_ 6 (1):50–57. <https://doi.org/10.1109/3516.914391>.
<a id="org722a59f"></a>Schroeck, S.J., W.C. Messner, and R.J. McNab. 2001. “On Compensator Design for Linear Time-Invariant Dual-Input Single-Output Systems.” _IEEE/ASME Transactions on Mechatronics_ 6 (1):50–57. <https://doi.org/10.1109/3516.914391>.

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content/article/sebastian12_nanop_with_multip_sensor.md
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title = "Nanopositioning with multiple sensors: a case study in data storage"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
: [Sensor Fusion]({{< relref "sensor_fusion" >}})
: [Sensor Fusion]({{<relref "sensor_fusion.md#" >}})
Reference
: ([Sebastian and Pantazi 2012](#orge399d74))
: ([Sebastian and Pantazi 2012](#org22b1de0))
Author(s)
: Sebastian, A., & Pantazi, A.
@ -20,4 +20,4 @@ Year
## Bibliography {#bibliography}
<a id="orge399d74"></a>Sebastian, Abu, and Angeliki Pantazi. 2012. “Nanopositioning with Multiple Sensors: A Case Study in Data Storage.” _IEEE Transactions on Control Systems Technology_ 20 (2):382–94. <https://doi.org/10.1109/tcst.2011.2177982>.
<a id="org22b1de0"></a>Sebastian, Abu, and Angeliki Pantazi. 2012. “Nanopositioning with Multiple Sensors: A Case Study in Data Storage.” _IEEE Transactions on Control Systems Technology_ 20 (2):382–94. <https://doi.org/10.1109/tcst.2011.2177982>.

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content/article/sun16_pract_multiv_contr_approac_based.md
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title = "A practical multivariable control approach based on inverted decoupling and decentralized active disturbance rejection control"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Decoupled Control](decoupled_control.md)
Reference
: ([Sun et al. 2016](#org2268976))
Author(s)
: Sun, L., Dong, J., Li, D., & Lee, K. Y.
Year
: 2016
## Bibliography {#bibliography}
<a id="org2268976"></a>Sun, Li, Junyi Dong, Donghai Li, and Kwang Y. Lee. 2016. “A Practical Multivariable Control Approach Based on Inverted Decoupling and Decentralized Active Disturbance Rejection Control.” _Industrial & Engineering Chemistry Research_ 55 (7):2008–19. <https://doi.org/10.1021/acs.iecr.5b03738>.

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content/article/tang18_decen_vibrat_contr_voice_coil.md
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title = "Decentralized vibration control of a voice coil motor-based stewart parallel mechanism: simulation and experiments"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}})
: [Stewart Platforms]({{<relref "stewart_platforms.md#" >}})
Reference
: ([Tang, Cao, and Yu 2018](#orgb3d3aa7))
: ([Tang, Cao, and Yu 2018](#org2c23b98))
Author(s)
: Tang, J., Cao, D., & Yu, T.
@ -20,4 +20,4 @@ Year
## Bibliography {#bibliography}
<a id="orgb3d3aa7"></a>Tang, Jie, Dengqing Cao, and Tianhu Yu. 2018. “Decentralized Vibration Control of a Voice Coil Motor-Based Stewart Parallel Mechanism: Simulation and Experiments.” _Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science_ 233 (1):132–45. <https://doi.org/10.1177/0954406218756941>.
<a id="org2c23b98"></a>Tang, Jie, Dengqing Cao, and Tianhu Yu. 2018. “Decentralized Vibration Control of a Voice Coil Motor-Based Stewart Parallel Mechanism: Simulation and Experiments.” _Proceedings of the Institution of Mechanical Engineers, Part c: Journal of Mechanical Engineering Science_ 233 (1):132–45. <https://doi.org/10.1177/0954406218756941>.

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content/article/thayer02_six_axis_vibrat_isolat_system.md
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Reference
: ([Thayer et al. 2002](#org7584b4b))
: ([Thayer et al. 2002](#org3291862))
Author(s)
: Thayer, D., Campbell, M., Vagners, J., & Flotow, A. v.
@ -20,4 +20,4 @@ Year
## Bibliography {#bibliography}
<a id="org7584b4b"></a>Thayer, Doug, Mark Campbell, Juris Vagners, and Andrew von Flotow. 2002. “Six-Axis Vibration Isolation System Using Soft Actuators and Multiple Sensors.” _Journal of Spacecraft and Rockets_ 39 (2):206–12. <https://doi.org/10.2514/2.3821>.
<a id="org3291862"></a>Thayer, Doug, Mark Campbell, Juris Vagners, and Andrew von Flotow. 2002. “Six-Axis Vibration Isolation System Using Soft Actuators and Multiple Sensors.” _Journal of Spacecraft and Rockets_ 39 (2):206–12. <https://doi.org/10.2514/2.3821>.

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content/article/thurner15_fiber_based_distan_sensin_inter.md
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title = "Fiber-Based Distance Sensing Interferometry"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
: [Interferometers]({{< relref "interferometers" >}})
: [Interferometers]({{<relref "interferometers.md#" >}})
Reference
: ([Thurner et al. 2015](#org6f5a8f6))
: ([Thurner et al. 2015](#org7174c7b))
Author(s)
: Thurner, K., Quacquarelli, F. P., Braun, Pierre-Francois, Dal Savio, C., & Karrai, K.
@ -17,6 +17,7 @@ Year
: 2015
## Bibliography {#bibliography}
<a id="org6f5a8f6"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” _Applied Optics_ 54 (10). Optical Society of America:3051–63.
<a id="org7174c7b"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” _Applied Optics_ 54 (10). Optical Society of America:3051–63.

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content/article/voorhoeve15_ident_high_tech_motion_system.md
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title = "Identification of high-tech motion systems: an active vibration isolation benchmark"
author = ["Thomas Dehaeze"]
draft = false
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content/article/yun20_inves_two_stage_vibrat_suppr.md
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title = "Investigation on two-stage vibration suppression and precision pointing for space optical payloads"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
@ -9,7 +9,7 @@ Tags
Reference
: ([Yun et al. 2020](#org70fb5c6))
: ([Yun et al. 2020](#org7bb249c))
Author(s)
: Yun, H., Liu, L., Li, Q., & Yang, H.
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## Bibliography {#bibliography}
<a id="org70fb5c6"></a>Yun, Hai, Lei Liu, Qing Li, and Hongjie Yang. 2020. “Investigation on Two-Stage Vibration Suppression and Precision Pointing for Space Optical Payloads.” _Aerospace Science and Technology_ 96 (nil):105543. <https://doi.org/10.1016/j.ast.2019.105543>.
<a id="org7bb249c"></a>Yun, Hai, Lei Liu, Qing Li, and Hongjie Yang. 2020. “Investigation on Two-Stage Vibration Suppression and Precision Pointing for Space Optical Payloads.” _Aerospace Science and Technology_ 96 (nil):105543. <https://doi.org/10.1016/j.ast.2019.105543>.

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content/book/fleming14_desig_model_contr_nanop_system.md
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content/book/leach14_fundam_princ_engin_nanom.md
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title = "Fundamental principles of engineering nanometrology"
author = ["Thomas Dehaeze"]
keywords = ["Metrology"]
draft = true
draft = false
+++
Tags
: [Metrology]({{< relref "metrology" >}})
: [Metrology]({{<relref "metrology.md#" >}})
Reference
: ([Leach 2014](#org284df16))
: ([Leach 2014](#org27b4df3))
Author(s)
: Leach, R.
@ -91,4 +91,4 @@ This type of angular interferometer is used to measure small angles (less than \
## Bibliography {#bibliography}
<a id="org284df16"></a>Leach, Richard. 2014. _Fundamental Principles of Engineering Nanometrology_. Elsevier. <https://doi.org/10.1016/c2012-0-06010-3>.
<a id="org27b4df3"></a>Leach, Richard. 2014. _Fundamental Principles of Engineering Nanometrology_. Elsevier. <https://doi.org/10.1016/c2012-0-06010-3>.

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@ -1,7 +1,7 @@
+++
title = "Control of wafer scanners: methods and developments"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
@ -9,7 +9,7 @@ Tags
Reference
: ([Heertjes et al. 2020](#org38a977c))
: ([Heertjes et al. 2020](#org3f3475f))
Author(s)
: Heertjes, Marcel Fran\ccois, Butler, H., Dirkx, N., van der Meulen, S., Ahlawat, R., O'Brien, K., Simonelli, J., …
@ -20,4 +20,4 @@ Year
## Bibliography {#bibliography}
<a id="org38a977c"></a>Heertjes, Marcel François, Hans Butler, NJ Dirkx, SH van der Meulen, R Ahlawat, K O’Brien, J Simonelli, KT Teng, and Y Zhao. 2020. “Control of Wafer Scanners: Methods and Developments.” In _2020 American Control Conference (ACC)_, 3686–3703. IEEE.
<a id="org3f3475f"></a>Heertjes, Marcel François, Hans Butler, NJ Dirkx, SH van der Meulen, R Ahlawat, K O’Brien, J Simonelli, KT Teng, and Y Zhao. 2020. “Control of Wafer Scanners: Methods and Developments.” In _2020 American Control Conference (ACC)_, 3686–3703. IEEE.

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@ -1,14 +1,14 @@
+++
title = "Vibrations and dynamic isotropy in hexapods-analytical studies"
author = ["Thomas Dehaeze"]
draft = true
draft = false
+++
Tags
: [Stewart Platforms]({{<relref "stewart_platforms.md#" >}}), [Isotropy of Parallel Manipulator]({{<relref "isotropy_of_parallel_manipulator.md#" >}})
Reference
: ([Afzali-Far 2016](#orga93b30a))
: ([Afzali-Far 2016](#orge2f1c73))
Author(s)
: Afzali-Far, B.
@ -95,7 +95,7 @@ Dynamic isotropy for the Stewart platform leads to a series of restrictive condi
When considering inertia of the struts, conditions are becoming more complex.
<a id="org64466c7"></a>
<a id="org51c1dc1"></a>
{{< figure src="/ox-hugo/afzali-far16_isotropic_hexapod_example.png" caption="Figure 1: Architecture of the obtained dynamically isotropic hexapod" >}}
@ -115,25 +115,28 @@ where \\(\sigma I\\) is a scaled identity matrix.
The isotropic constrain of the standard hexapod imposes special inertia of the top platform which may not be wanted in practice (\\(I\_{zz} = 4 I\_{yy} = 4 I\_{xx}\\)).
A class of generalized Gough-Stewart platforms are proposed to eliminate the above constrains.
Figure [2](#orgfab85fb) shows a schematic of proposed generalized hexapod.
Figure [2](#org14fbbb3) shows a schematic of proposed generalized hexapod.
<a id="orgfab85fb"></a>
<a id="org14fbbb3"></a>
{{< figure src="/ox-hugo/afzali-far16_proposed_generalized_hexapod.png" caption="Figure 2: Parametrization of the proposed generalized hexapod" >}}
## Conclusions {#conclusions}
<summary>
<div class="sum">
<div></div>
The main findings of this dissertation are:
- Comprehensive and fully parametric model of the hexapod for symmetric configurations are established both in the Cartesian and joint space.
- Inertia of the struts are taken into account to refine the model.
- A novel approach in order to obtain dynamically isotropic hexapods is proposed.
- A novel architecture of hexapod is introduced (Figure [2](#orgfab85fb)) which is dynamically isotropic for a wide range of inertia properties.
</summary>
- A novel architecture of hexapod is introduced (Figure [2](#org14fbbb3)) which is dynamically isotropic for a wide range of inertia properties.
</div>
## Bibliography {#bibliography}
<a id="orga93b30a"></a>Afzali-Far, Behrouz. 2016. “Vibrations and Dynamic Isotropy in Hexapods-Analytical Studies.” Lund University.
<a id="orge2f1c73"></a>Afzali-Far, Behrouz. 2016. “Vibrations and Dynamic Isotropy in Hexapods-Analytical Studies.” Lund University.

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@ -0,0 +1,23 @@
+++
title = "Development of precision pointing controllers with and without vibration suppression for the NPS precision pointing hexapod"
author = ["Thomas Dehaeze"]
draft = true
+++
Tags
:
Reference
: ([Bishop Jr 2002](#org6e5ba62))
Author(s)
: Bishop Jr, R. M.
Year
: 2002
## Bibliography {#bibliography}
<a id="org6e5ba62"></a>Bishop Jr, Ronald M. 2002. “Development of Precision Pointing Controllers with and without Vibration Suppression for the NPS Precision Pointing Hexapod.” Naval Postgraduate School, Monterey, California.

8
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@ -1,14 +1,14 @@
+++
title = "Active isolation and damping of vibrations via stewart platform"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Active Damping]({{< relref "active_damping" >}})
: [Stewart Platforms]({{<relref "stewart_platforms.md#" >}}), [Vibration Isolation]({{<relref "vibration_isolation.md#" >}}), [Active Damping]({{<relref "active_damping.md#" >}})
Reference
: ([Hanieh 2003](#org2d21f87))
: ([Hanieh 2003](#org68b0cb0))
Author(s)
: Hanieh, A. A.
@ -20,4 +20,4 @@ Year
## Bibliography {#bibliography}
<a id="org2d21f87"></a>Hanieh, Ahmed Abu. 2003. “Active Isolation and Damping of Vibrations via Stewart Platform.” Université Libre de Bruxelles, Brussels, Belgium.
<a id="org68b0cb0"></a>Hanieh, Ahmed Abu. 2003. “Active Isolation and Damping of Vibrations via Stewart Platform.” Université Libre de Bruxelles, Brussels, Belgium.

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@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{<relref "stewart_platforms.md#" >}}), [Vibration Isolation]({{<relref "vibration_isolation.md#" >}}), [Cubic Architecture]({{<relref "cubic_architecture.md#" >}}), [Flexible Joints]({{<relref "flexible_joints.md#" >}}), [Multivariable Control]({{<relref "multivariable_control.md#" >}})
Reference
: ([Li 2001](#org7277b25))
: ([Li 2001](#orgc147fe0))
Author(s)
: Li, X.
@ -22,15 +22,15 @@ Year
### Flexure Jointed Hexapods {#flexure-jointed-hexapods}
A general flexible jointed hexapod is shown in Figure [1](#org858f898).
A general flexible jointed hexapod is shown in Figure [1](#orge84e431).
<a id="org858f898"></a>
<a id="orge84e431"></a>
{{< figure src="/ox-hugo/li01_flexure_hexapod_model.png" caption="Figure 1: A flexure jointed hexapod. {P} is a cartesian coordinate frame located at, and rigidly attached to the payload's center of mass. {B} is the frame attached to the base, and {U} is a universal inertial frame of reference" >}}
Flexure jointed hexapods have been developed to meet two needs illustrated in Figure [2](#orgda07839).
Flexure jointed hexapods have been developed to meet two needs illustrated in Figure [2](#orga3eb26a).
<a id="orgda07839"></a>
<a id="orga3eb26a"></a>
{{< figure src="/ox-hugo/li01_quet_dirty_box.png" caption="Figure 2: (left) Vibration machinery must be isolated from a precision bus. (right) A precision paylaod must be manipulated in the presence of base vibrations and/or exogenous forces." >}}
@ -41,12 +41,12 @@ On the other hand, the flexures add some complexity to the hexapod dynamics.
Although the flexure joints do eliminate friction and backlash, they add spring dynamics and severely limit the workspace.
Moreover, base and/or payload vibrations become significant contributors to the motion.
The University of Wyoming hexapods (example in Figure [3](#orgccc775c)) are:
The University of Wyoming hexapods (example in Figure [3](#org051e360)) are:
- Cubic (mutually orthogonal)
- Flexure Jointed
<a id="orgccc775c"></a>
<a id="org051e360"></a>
{{< figure src="/ox-hugo/li01_stewart_platform.png" caption="Figure 3: Flexure jointed Stewart platform used for analysis and control" >}}
@ -85,7 +85,7 @@ J = \begin{bmatrix}
\end{bmatrix}
\end{equation}
where (see Figure [1](#org858f898)) \\(p\_i\\) denotes the payload attachment point of strut \\(i\\), the prescripts denote the frame of reference, and \\(\hat{u}\_i\\) denotes a unit vector along strut \\(i\\).
where (see Figure [1](#orge84e431)) \\(p\_i\\) denotes the payload attachment point of strut \\(i\\), the prescripts denote the frame of reference, and \\(\hat{u}\_i\\) denotes a unit vector along strut \\(i\\).
To make the dynamic model as simple as possible, the origin of {P} is located at the payload's center of mass.
Thus all \\({}^Pp\_i\\) are found with respect to the center of mass.
@ -94,43 +94,96 @@ Thus all \\({}^Pp\_i\\) are found with respect to the center of mass.
The dynamics of a flexure jointed hexapod can be written in joint space:
\begin{equation}
\begin{equation} \label{eq:hexapod\_eq\_motion}
\begin{split}
& \left( J^{-T} {}^B\_PR^P M\_x {}^B\_PR^T J^{-1} + M\_s \right) \ddot{l} + B \dot{l} + K (l - l\_r) = \\\\\\
&\quad f\_m - \left( M\_s + J^{-T} {}^B\_PR^P M\_x {}^U\_PR^T J\_c J\_b^{-1} \right) \ddot{q}\_u + J^{-T} {}^U\_BR\_T(\mathcal{F}\_e + \mathcal{G} + \mathcal{C})
& \left( J^{-T} \cdot {}^B\_PR \cdot {}^PM\_x \cdot {}^B\_PR^T \cdot J^{-1} + M\_s \right) \ddot{l} + B \dot{l} + K (l - l\_r) = \\\\\\
&\quad f\_m - \left( M\_s + J^{-T} \cdot {}^B\_PR \cdot {}^PM\_x \cdot {}^U\_PR^T \cdot J\_c \cdot J\_b^{-1} \right) \ddot{q}\_u + J^{-T} \cdot {}^U\_BR^T(\mathcal{F}\_e + \mathcal{G} + \mathcal{C})
\end{split}
\end{equation}
where:
### Test {#test}
- \\({}^PM\_x\\) is the 6x6 mass/inertia matrix of the payload, found with respect to the payload frame {P}, whose origin is at the hexapod payload's center of mass
- \\({}^U\_BR\\) is the 6x6 rotation matrix from the base frame {B} to the inertial frame of reference {U} (it consists of two identical 3x3 rotation matrices forming a block diagonal 6x6 matrix).
Similarly, \\({}^B\_PR\\) is the rotation matrix from the payload frame to the base frame, and \\({}^U\_PR = {}^U\_BR {}^B\_PR\\)
- \\(J\\) is the 6x6 Jacobian matrix relating payload cartesian movements to strut length changes
- \\(M\_s\\) is a diagonal 6x6 matrix containing the moving mass of each strut
- \\(l\\) is the 6x1 vector of strut lengths
- \\(B\\) and \\(K\\) are 6x6 diagonal matrices containing the damping and stiffness, respectively, of each strut
- \\(l\_r\\) is the constant vector of relaxed strut lengths
- \\(f\_m\\) is the vector of strut motor force
- \\(J\_c\\) and \\(J\_b\\) are 6x6 Jacobian matrices capturing base motion
- \\(\ddot{q}\_u\\) is a 6x1 vector of base acceleration along each strut
- \\(\mathcal{F}\_r\\) is a vector of payload exogenous generalized forces
- \\(\mathcal{C}\\) is a vector containing all the Coriolis and centripetal terms
- \\(\mathcal{G}\\) is a vector containing all gravity terms
**Jacobian Analysis**:
\\[ \delta \mathcal{L} = J \delta \mathcal{X} \\]
The origin of \\(\\{P\\}\\) is taken as the center of mass of the payload.
**Decoupling**:
If we refine the (force) inputs and (displacement) outputs as shown in Figure [4](#org7721136) or in Figure [5](#orgdc42940), we obtain a decoupled plant provided that:
#### Decoupling {#decoupling}
Two decoupling algorithms are proposed by combining static input-output transformations with hexapod geometric design.
Define a new input and a new output:
\begin{equation}
u\_1 = J^T f\_m, \quad y = J^{-1} (l - l\_r)
\end{equation}
Equation \eqref{eq:hexapod_eq_motion} can be rewritten as:
\begin{equation} \label{eq:hexapod\_eq\_motion\_decoup\_1}
\begin{split}
& \left( {}^B\_PR \cdot {}^PM\_x \cdot {}^B\_PR^T + J^T \cdot M\_s \cdot J \right) \cdot \ddot{y} + J^T \cdot B J \dot{y} + J^T \cdot K \cdot J y = \\\\\\
&\quad u\_1 - \left( J^T \cdot M\_s + {}^B\_PR \cdot {}^PM\_x \cdot {}^U\_PR^T \cdot J\_c \cdot J\_b^{-1} \right) \ddot{q}\_u + {}^U\_BR^T\mathcal{F}\_e
\end{split}
\end{equation}
If the hexapod is designed such that the payload mass/inertia matrix written in the base frame (\\(^BM\_x = {}^B\_PR \cdot {}^PM\_x \cdot {}^B\_PR\_T\\)) and \\(J^T J\\) are diagonal, the dynamics from \\(u\_1\\) to \\(y\\) are decoupled (Figure [4](#org8deb4db)).
<a id="org8deb4db"></a>
{{< figure src="/ox-hugo/li01_decoupling_conf.png" caption="Figure 4: Decoupling the dynamics of the Stewart Platform using the Jacobians" >}}
Alternatively, a new set of inputs and outputs can be defined:
\begin{equation}
u\_2 = J^{-1} f\_m, \quad y = J^{-1} (l - l\_r)
\end{equation}
And another decoupled plant is found (Figure [5](#org7a23a21)):
\begin{equation} \label{eq:hexapod\_eq\_motion\_decoup\_2}
\begin{split}
& \left( J^{-1} \cdot J^{-T} \cdot {}^BM\_x + M\_s \right) \cdot \ddot{y} + B \dot{y} + K y = \\\\\\
&\quad u\_2 - J^{-1} \cdot J^{-T} \left( J^T \cdot M\_s + {}^B\_PR \cdot {}^PM\_x \cdot {}^U\_PR^T \cdot J\_c \cdot J\_b^{-1} \right) \ddot{q}\_u + {}^U\_BR^T\mathcal{F}\_e
\end{split}
\end{equation}
<a id="org7a23a21"></a>
{{< figure src="/ox-hugo/li01_decoupling_conf_bis.png" caption="Figure 5: Decoupling the dynamics of the Stewart Platform using the Jacobians" >}}
<div class="important">
<div></div>
These decoupling algorithms have two constraints:
1. the payload mass/inertia matrix must be diagonal (the CoM is coincident with the origin of frame \\(\\{P\\}\\))
2. the geometry of the hexapod and the attachment of the payload to the hexapod must be carefully chosen
> For instance, if the hexapod has a mutually orthogonal geometry (cubic configuration), the payload's center of mass must coincide with the center of the cube formed by the orthogonal struts.
For instance, if the hexapod has a mutually orthogonal geometry (cubic configuration), the payload's center of mass must coincide with the center of the cube formed by the orthogonal struts.
<a id="org7721136"></a>
{{< figure src="/ox-hugo/li01_decoupling_conf.png" caption="Figure 4: Decoupling the dynamics of the Stewart Platform using the Jacobians" >}}
<a id="orgdc42940"></a>
{{< figure src="/ox-hugo/li01_decoupling_conf_bis.png" caption="Figure 5: Decoupling the dynamics of the Stewart Platform using the Jacobians" >}}
</div>
## Simultaneous Vibration Isolation and Pointing Control {#simultaneous-vibration-isolation-and-pointing-control}
Basic idea:
Many applications require simultaneous vibration isolation and precision pointing.
- acceleration feedback is used to provide high-frequency vibration isolation
- cartesian pointing feedback can be used to provide low-frequency pointing
The basic idea to achieve such objective is to use:
- acceleration feedback to provide high-frequency vibration isolation
- cartesian pointing feedback to provide low-frequency pointing
The compensation is divided in frequency because:
@ -139,115 +192,158 @@ The compensation is divided in frequency because:
The control bandwidth is divided as follows:
- low-frequency disturbances as attenuated and tracking is accomplished by feedback from low bandwidth pointing sensors
- low-frequency disturbances are attenuated and tracking is accomplished by feedback from low bandwidth pointing sensors
- mid-frequency disturbances are attenuated by feedback from band-pass sensors like accelerometer or load cells
- high-frequency disturbances are attenuated by passive isolation techniques
### Vibration Isolation {#vibration-isolation}
The system is decoupled into six independent SISO subsystems using the architecture shown in Figure [6](#org0dd19dc).
The system is decoupled into six independent SISO subsystems using the architecture shown in Figure [6](#org0dc1d11).
<a id="org0dd19dc"></a>
<a id="org0dc1d11"></a>
{{< figure src="/ox-hugo/li01_vibration_isolation_control.png" caption="Figure 6: Figure caption" >}}
{{< figure src="/ox-hugo/li01_vibration_isolation_control.png" caption="Figure 6: Vibration isolation control strategy" >}}
One of the subsystem plant transfer function is shown in Figure [6](#org0dd19dc)
One of the subsystem plant transfer function is shown in Figure [6](#org0dc1d11)
<a id="org6a21353"></a>
<a id="orgcd4b06b"></a>
{{< figure src="/ox-hugo/li01_vibration_control_plant.png" caption="Figure 7: Plant transfer function of one of the SISO subsystem for Vibration Control" >}}
Each compensator is designed using simple loop-shaping techniques.
A typical compensator consists of the following elements:
The unity control bandwidth of the isolation loop is designed to be from **5Hz to 50Hz**.
- first order lag-lead filter to provide adequate phase margin a the low frequency crossover
- a second order lag-lead filter to increase the gain between crossovers and provide adequate phase margin at the high frequency crossover
- a second order notch filter to cancel the mode at 150Hz
- a second order low pass filter to provide steep roll-off and gain stabilize the plant at high frequency
- a first order high pass filter to eliminate DC signals
> Despite a reasonably good match between the modeled and the measured transfer functions, the model based decoupling algorithm does not produce the expected decoupling.
> Only about 20 dB separation is achieve between the diagonal and off-diagonal responses.
The unity control bandwidth of the isolation loop is designed to be from **5Hz to 50Hz**, so the vibration isolation loop works as a band-pass filter.
<div class="important">
<div></div>
Despite a reasonably good match between the modeled and the measured transfer functions, the model based decoupling algorithm does not produce the expected decoupling.
Only about 20 dB separation is achieve between the diagonal and off-diagonal responses.
</div>
<div class="note">
<div></div>
Severe phase delay exists in the actual transfer function.
This is due to the limited sample frequency and sensor bandwidth limitation.
The zero at around 130Hz is non-minimum phase which limits the control bandwidth.
The reason is not explained.
</div>
### Pointing Control {#pointing-control}
### Pointing Control Techniques {#pointing-control-techniques}
A block diagram of the pointing control system is shown in Figure [8](#orgb338488).
A block diagram of the pointing control system is shown in Figure [8](#orgec13571).
<a id="orgb338488"></a>
<a id="orgec13571"></a>
{{< figure src="/ox-hugo/li01_pointing_control.png" caption="Figure 8: Figure caption" >}}
The plant is decoupled into two independent SISO subsystems.
The compensators are design with inverse-dynamics methods.
The decoupling matrix consists of the columns of \\(J\\) corresponding to the pointing DoFs.
Figure [9](#org23ec3f5) shows the measured transfer function of the \\(\theta\_x\\) axis.
<a id="org23ec3f5"></a>
{{< figure src="/ox-hugo/li01_transfer_function_angle.png" caption="Figure 9: Experimentally measured plant transfer function of \\(\theta\_x/\theta\_{x\_d}\\)" >}}
A typical compensator consists of the following elements:
- a first order low pass filter to increase the low frequency loop gain and provide a slope of -20dB/decade for the magnitude curve at the crossover
- two complex zeros with high \\(Q\\) to provide adequate phase margin at the crossover
- a pole after the zeros to decrease the excess gain caused by these zeros
- a second order notch filter to cancel the mode at 150Hz
- a second order low pass filter to provide steep roll off and gain stabilize the plant at high frequency
The unity control bandwidth of the pointing loop is designed to be from **0Hz to 20Hz**.
A feedforward control is added as shown in Figure [9](#orgb372596).
A feedforward control is added as shown in Figure [10](#org68adfa5).
\\(C\_f\\) is the feedforward compensator which is a 2x2 diagonal matrix.
Ideally, the feedforward compensator is an invert of the plant dynamics.
<a id="orgb372596"></a>
<a id="org68adfa5"></a>
{{< figure src="/ox-hugo/li01_feedforward_control.png" caption="Figure 9: Feedforward control" >}}
{{< figure src="/ox-hugo/li01_feedforward_control.png" caption="Figure 10: Feedforward control" >}}
### Simultaneous Control {#simultaneous-control}
The simultaneous vibration isolation and pointing control is approached in two ways:
1. design and implement the vibration isolation control first, identify the pointing plant when the isolation loops are closed, then implement the pointing compensators
2. the reverse design order
1. **Closing the vibration isolation loop first**: Design and implement the vibration isolation control first, identify the pointing plant when the isolation loops are closed, then implement the pointing compensators.
2. **Closing the pointing loop first**: Reverse order.
Figure [10](#orgbafcf4b) shows a parallel control structure where \\(G\_1(s)\\) is the dynamics from input force to output strut length.
Figure [11](#orgedfc92b) shows a parallel control structure where \\(G\_1(s)\\) is the dynamics from input force to output strut length.
<a id="orgbafcf4b"></a>
<a id="orgedfc92b"></a>
{{< figure src="/ox-hugo/li01_parallel_control.png" caption="Figure 10: A parallel scheme" >}}
{{< figure src="/ox-hugo/li01_parallel_control.png" caption="Figure 11: A parallel scheme" >}}
The transfer function matrix for the pointing loop after the vibration isolation is closed is still decoupled. The same happens when closing the pointing loop first and looking at the transfer function matrix of the vibration isolation.
<div class="important">
<div></div>
The effect of the isolation loop on the pointing loop is large around the natural frequency of the plant as shown in Figure [11](#org2a20ab8).
The transfer function matrix for the pointing loop after the vibration isolation is closed is still decoupled.
The same happens when closing the pointing loop first and looking at the transfer function matrix of the vibration isolation.
<a id="org2a20ab8"></a>
However, the interaction between loops may affect the transfer functions of the **first** closed loop, and thus affect its relative stability.
{{< figure src="/ox-hugo/li01_effect_isolation_loop_closed.png" caption="Figure 11: \\(\theta\_x/\theta\_{x\_d}\\) transfer function with the isolation loop closed (simulation)" >}}
The effect of pointing control on the isolation plant has not much effect.
> The interaction between loops may affect the transfer functions of the **first** closed loop, and thus affect its relative stability.
</div>
The dynamic interaction effect:
- only happens in the unity bandwidth of the loop transmission of the first closed loop.
- affect the closed loop transmission of the loop first closed (see Figures [12](#orgc137ea3) and [13](#orgc06274a))
- Only happens in the unity bandwidth of the loop transmission of the first closed loop.
- Affect the closed loop transmission of the loop first closed (see Figures [12](#orgfc5ad76) and [13](#org8dcf497))
As shown in Figure [12](#orgc137ea3), the peak resonance of the pointing loop increase after the isolation loop is closed.
As shown in Figure [12](#orgfc5ad76), the peak resonance of the pointing loop increase after the isolation loop is closed.
The resonances happen at both crossovers of the isolation loop (15Hz and 50Hz) and they may show of loss of robustness.
<a id="orgc137ea3"></a>
<a id="orgfc5ad76"></a>
{{< figure src="/ox-hugo/li01_closed_loop_pointing.png" caption="Figure 12: Closed-loop transfer functions \\(\theta\_y/\theta\_{y\_d}\\) of the pointing loop before and after the vibration isolation loop is closed" >}}
The same happens when first closing the vibration isolation loop and after the pointing loop (Figure [13](#orgc06274a)).
The same happens when first closing the vibration isolation loop and after the pointing loop (Figure [13](#org8dcf497)).
The first peak resonance of the vibration isolation loop at 15Hz is increased when closing the pointing loop.
<a id="orgc06274a"></a>
<a id="org8dcf497"></a>
{{< figure src="/ox-hugo/li01_closed_loop_vibration.png" caption="Figure 13: Closed-loop transfer functions of the vibration isolation loop before and after the pointing control loop is closed" >}}
> The isolation loop adds a second resonance peak at its high-frequency crossover in the pointing closed-loop transfer function, which may cause instability.
> Thus, it is recommended to design and implement the isolation control system first, and then identify the pointing plant with the isolation loop closed.
<div class="important">
<div></div>
From the analysis above, it is hard to say which loop has more significant affect on the other loop, but the isolation loop adds a second resonance peak at its high frequency crossover in the pointing closed loop transfer function, which may cause instability.
Thus, it is recommended to design and implement the isolation control system first, and then identify the pointing plant with the isolation loop closed.
</div>
### Experimental results {#experimental-results}
Two hexapods are stacked (Figure [14](#org2a11277)):
Two hexapods are stacked (Figure [14](#org66cdd5c)):
- the bottom hexapod is used to generate disturbances matching candidate applications
- the top hexapod provide simultaneous vibration isolation and pointing control
<a id="org2a11277"></a>
<a id="org66cdd5c"></a>
{{< figure src="/ox-hugo/li01_test_bench.png" caption="Figure 14: Stacked Hexapods" >}}
Using the vibration isolation control alone, no attenuation is achieved below 1Hz as shown in figure [15](#org5933a45).
First, the vibration isolation and pointing controls were implemented separately.
Using the vibration isolation control alone, no attenuation is achieved below 1Hz as shown in figure [15](#org3b66ca1).
<a id="org5933a45"></a>
<a id="org3b66ca1"></a>
{{< figure src="/ox-hugo/li01_vibration_isolation_control_results.png" caption="Figure 15: Vibration isolation control: open-loop (solid) vs. closed-loop (dashed)" >}}
@ -256,15 +352,34 @@ The simultaneous control is of dual use:
- it provide simultaneous pointing and isolation control
- it can also be used to expand the bandwidth of the isolation control to low frequencies because the pointing loops suppress pointing errors due to both base vibrations and tracking
The results of simultaneous control is shown in Figure [16](#org996a848) where the bandwidth of the isolation control is expanded to very low frequency.
The results of simultaneous control is shown in Figure [16](#orgb25318f) where the bandwidth of the isolation control is expanded to very low frequency.
<a id="org996a848"></a>
<a id="orgb25318f"></a>
{{< figure src="/ox-hugo/li01_simultaneous_control_results.png" caption="Figure 16: Simultaneous control: open-loop (solid) vs. closed-loop (dashed)" >}}
### Summary and Conclusion {#summary-and-conclusion}
<div class="sum">
<div></div>
A parallel control scheme is proposed in this chapters.
This scheme is suitable for simultaneous vibration isolation and pointing control.
Part of this scheme involves closing one loop first, then re-identifying and designing the new control before closed the other loop.
An investigation into the interaction between loops shows that the order of closing loops is not important.
However, only two channels need to be re-designed or adjusted for the pointing loop if the isolation loop is closed first.
Experiments show that this scheme takes advantage of the bandwidths of both pointing and vibration sensors, and provides vibration isolation and pointing controls over a broad band.
</div>
## Future research areas {#future-research-areas}
<div class="sum">
<div></div>
Proposed future research areas include:
- **Include base dynamics in the control**:
@ -286,8 +401,10 @@ Proposed future research areas include:
- **LVDT** to provide differential position of the hexapod payload with respect to the base
- **Geophones** to provide payload and base velocity information
</div>
## Bibliography {#bibliography}
<a id="org7277b25"></a>Li, Xiaochun. 2001. “Simultaneous, Fault-Tolerant Vibration Isolation and Pointing Control of Flexure Jointed Hexapods.” University of Wyoming.
<a id="orgc147fe0"></a>Li, Xiaochun. 2001. “Simultaneous, Fault-Tolerant Vibration Isolation and Pointing Control of Flexure Jointed Hexapods.” University of Wyoming.

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+++
title = "Modeling and robust adaptive tracking control of a planar precision positioning system"
author = ["Thomas Dehaeze"]
draft = true
+++
Tags
:
Reference
: ([Treichel 2017](#org1662bdf))
Author(s)
: Treichel, K.
Year
: 2017
## Bibliography {#bibliography}
<a id="org1662bdf"></a>Treichel, Kai. 2017. “Modeling and Robust Adaptive Tracking Control of a Planar Precision Positioning System.” Ilmenau University of Technology.

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+++
title = "Dynamic modeling, experimental identification, and active vibration control design of a smart parallel manipulator."
author = ["Thomas Dehaeze"]
draft = true
+++
Tags
:
Reference
: ([Wang 2007](#org006aaaa))
Author(s)
: Wang, X.
Year
: 2007
## Bibliography {#bibliography}
<a id="org006aaaa"></a>Wang, Xiaoyun. 2007. “Dynamic Modeling, Experimental Identification, and Active Vibration Control Design of a Smart Parallel Manipulator.” University of Toronto.

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@ -5,10 +5,10 @@ draft = false
+++
Tags
: [Vibration Isolation]({{< relref "vibration_isolation" >}})
: [Vibration Isolation]({{<relref "vibration_isolation.md#" >}})
Reference
: ([Zuo 2004](#orgf5a4502))
: ([Zuo 2004](#org700ab89))
Author(s)
: Zuo, L.
@ -40,19 +40,19 @@ Year
> They found that coupling from flexible modes is much smaller than in soft active mounts in the load (force) feedback.
> Note that reaction force actuators can also work with soft mounts or hard mounts.
<a id="org9c33e29"></a>
<a id="org44c9181"></a>
{{< figure src="/ox-hugo/zuo04_piezo_spring_series.png" caption="Figure 1: PZT actuator and spring in series" >}}
<a id="org141cdb3"></a>
<a id="org631f004"></a>
{{< figure src="/ox-hugo/zuo04_voice_coil_spring_parallel.png" caption="Figure 2: Voice coil actuator and spring in parallel" >}}
<a id="org2ed63ef"></a>
<a id="orgc4102de"></a>
{{< figure src="/ox-hugo/zuo04_piezo_plant.png" caption="Figure 3: Transmission from PZT voltage to geophone output" >}}
<a id="orgc14af87"></a>
<a id="org063d6bb"></a>
{{< figure src="/ox-hugo/zuo04_voice_coil_plant.png" caption="Figure 4: Transmission from voice coil voltage to geophone output" >}}
@ -60,4 +60,4 @@ Year
## Bibliography {#bibliography}
<a id="orgf5a4502"></a>Zuo, Lei. 2004. “Element and System Design for Active and Passive Vibration Isolation.” Massachusetts Institute of Technology.
<a id="org700ab89"></a>Zuo, Lei. 2004. “Element and System Design for Active and Passive Vibration Isolation.” Massachusetts Institute of Technology.

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+++
title = "Parallel manipulators. part i: theory design, kinematics, dynamics and control"
author = ["Thomas Dehaeze"]
draft = false
draft = true
+++
Tags
: [Stewart Platforms](stewart_platforms.md)
: [Stewart Platforms]({{<relref "stewart_platforms.md#" >}})
Reference
: ([Merlet 1987](#org6a131ba))
: ([Merlet 1987](#org0892e4b))
Author(s)
: Merlet, J.
@ -20,4 +20,4 @@ Year
## Bibliography {#bibliography}
<a id="org6a131ba"></a>Merlet, Jean-Pierre. 1987. “Parallel Manipulators. Part I: Theory Design, Kinematics, Dynamics and Control.” INRIA.
<a id="org0892e4b"></a>Merlet, Jean-Pierre. 1987. “Parallel Manipulators. Part I: Theory Design, Kinematics, Dynamics and Control.” INRIA.

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title = "Acquisition Systems"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Analog to Digital Converters]({{< relref "analog_to_digital_converters" >}})
: [Analog to Digital Converters]({{<relref "analog_to_digital_converters.md#" >}})
## Manufacturers {#manufacturers}

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title = "Active Isolation Platforms"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Vibration Isolation]({{< relref "vibration_isolation" >}})
: [Vibration Isolation]({{<relref "vibration_isolation.md#" >}})
## Manufacturers {#manufacturers}

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@ -9,20 +9,20 @@ Tags
Links to specific actuators:
- [Voice Coil Actuators]({{< relref "voice_coil_actuators" >}})
- [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
- [Voice Coil Actuators]({{<relref "voice_coil_actuators.md#" >}})
- [Piezoelectric Actuators]({{<relref "piezoelectric_actuators.md#" >}})
## How to choose the correct actuator for my application? {#how-to-choose-the-correct-actuator-for-my-application}
For vibration isolation:
- In ([Ito and Schitter 2016](#orga71edd4)), the effect of the actuator stiffness on the attainable vibration isolation is studied ([Notes]({{< relref "ito16_compar_class_high_precis_actuat" >}}))
- In ([Ito and Schitter 2016](#orge96c061)), the effect of the actuator stiffness on the attainable vibration isolation is studied ([Notes]({{<relref "ito16_compar_class_high_precis_actuat.md#" >}}))
## Brush-less DC Motor {#brush-less-dc-motor}
- ([Yedamale 2003](#org0ac1a74))
- ([Yedamale 2003](#org9fa946a))
<https://www.electricaltechnology.org/2016/05/bldc-brushless-dc-motor-construction-working-principle.html>
@ -30,6 +30,6 @@ For vibration isolation:
## Bibliography {#bibliography}
<a id="orga71edd4"></a>Ito, Shingo, and Georg Schitter. 2016. “Comparison and Classification of High-Precision Actuators Based on Stiffness Influencing Vibration Isolation.” _IEEE/ASME Transactions on Mechatronics_ 21 (2):1169–78. <https://doi.org/10.1109/tmech.2015.2478658>.
<a id="orge96c061"></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="org0ac1a74"></a>Yedamale, Padmaraja. 2003. “Brushless Dc (BLDC) Motor Fundamentals.” _Microchip Technology Inc_ 20:3–15.
<a id="org9fa946a"></a>Yedamale, Padmaraja. 2003. “Brushless Dc (BLDC) Motor Fundamentals.” _Microchip Technology Inc_ 20:3–15.

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author = ["Thomas Dehaeze"]
keywords = ["electronics"]
draft = false
category = "equipment"
+++
Tags
: [Electronics]({{< relref "electronics" >}})
: [Electronics]({{<relref "electronics.md#" >}})
## Types of Analog to Digital Converters {#types-of-analog-to-digital-converters}
<https://dewesoft.com/daq/types-of-adc-converters>
- Delta Sigma ([Baker 2011](#org60f0e22))
- Delta Sigma ([Baker 2011](#orgbdb61af))
- Successive Approximation
@ -32,9 +33,9 @@ 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](#orgee08810)).
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](#org4bd731c)).
<a id="orgee08810"></a>
<a id="org4bd731c"></a>
{{< figure src="/ox-hugo/probability_density_function_adc.png" caption="Figure 1: Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}}
@ -89,4 +90,4 @@ The quantization is:
## Bibliography {#bibliography}
<a id="org60f0e22"></a>Baker, Bonnie. 2011. “How Delta-Sigma Adcs Work, Part.” _Analog Applications_ 7.
<a id="orgbdb61af"></a>Baker, Bonnie. 2011. “How Delta-Sigma Adcs Work, Part.” _Analog Applications_ 7.

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title = "Cables"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Connectors]({{< relref "connectors" >}})
: [Connectors]({{<relref "connectors.md#" >}})
## Typical Cables {#typical-cables}

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title = "Capacitive Sensors"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
: [Position Sensors]({{<relref "position_sensors.md#" >}})
## Description of Capacitive Sensors {#description-of-capacitive-sensors}

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title = "Charge Amplifiers"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Electronics]({{< relref "electronics" >}})
: [Electronics]({{<relref "electronics.md#" >}})
## Description {#description}
@ -17,19 +18,19 @@ This can be typically used to interface with piezoelectric sensors.
## Basic Circuit {#basic-circuit}
Two basic circuits of charge amplifiers are shown in Figure [1](#org7d016e2) (taken from ([Fleming 2010](#org467f88f))) and Figure [2](#orgb83f736) (taken from ([Schmidt, Schitter, and Rankers 2014](#org80f2485)))
Two basic circuits of charge amplifiers are shown in Figure [1](#org0d411fa) (taken from ([Fleming 2010](#org7834496))) and Figure [2](#org1c3e25d) (taken from ([Schmidt, Schitter, and Rankers 2014](#orgd26dd11)))
<a id="org7d016e2"></a>
<a id="org0d411fa"></a>
{{< figure src="/ox-hugo/charge_amplifier_circuit.png" caption="Figure 1: Electrical model of a piezoelectric force sensor is shown in gray. The op-amp charge amplifier is shown on the right. The output voltage \\(V\_s\\) equal to \\(-q/C\_s\\)" >}}
<a id="orgb83f736"></a>
<a id="org1c3e25d"></a>
{{< figure src="/ox-hugo/charge_amplifier_circuit_bis.png" caption="Figure 2: A piezoelectric accelerometer with a charge amplifier as signal conditioning element" >}}
The input impedance of the charge amplifier is very small (unlike when using a voltage amplifier).
The gain of the charge amplified (Figure [1](#org7d016e2)) is equal to:
The gain of the charge amplified (Figure [1](#org0d411fa)) is equal to:
\\[ \frac{V\_s}{q} = \frac{-1}{C\_s} \\]
@ -50,6 +51,6 @@ The gain of the charge amplified (Figure [1](#org7d016e2)) is equal to:
## Bibliography {#bibliography}
<a id="org467f88f"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.
<a id="org7834496"></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="org80f2485"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.
<a id="orgd26dd11"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.

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title = "Connectors"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Cables]({{< relref "cables" >}})
: [Cables]({{<relref "cables.md#" >}})
## Manufacturers {#manufacturers}
@ -19,8 +20,8 @@ Tags
## BNC {#bnc}
BNC connectors can have an impedance of 50Ohms or 75Ohms as shown in Figure [1](#orgd1b23d3).
BNC connectors can have an impedance of 50Ohms or 75Ohms as shown in Figure [1](#orgf757f74).
<a id="orgd1b23d3"></a>
<a id="orgf757f74"></a>
{{< figure src="/ox-hugo/bnc_50_75_ohms.jpg" caption="Figure 1: 75Ohms and 50Ohms BNC connectors" >}}

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title = "Digital to Analog Converters"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Electronics]({{< relref "electronics" >}})
: [Electronics]({{<relref "electronics.md#" >}})

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title = "Eddy Current Sensors"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
: [Position Sensors]({{<relref "position_sensors.md#" >}})
## Manufacturers {#manufacturers}

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title = "Encoders"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
: [Position Sensors]({{<relref "position_sensors.md#" >}})
There are two main types of encoders: optical encoders, and magnetic encoders.

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@ -12,33 +12,43 @@ Tags
Books:
- ([Lobontiu 2002](#org0e711a7))
- ([Henein 2003](#org4fb65e1))
- ([Smith 2005](#orgbf46163))
- ([Soemers 2011](#orgf482067))
- ([Cosandier 2017](#orgf099485))
- ([Lobontiu 2002](#orgb45af18))
- ([Henein 2003](#org8ce4916))
- ([Smith 2005](#orgccbed32))
- ([Soemers 2011](#org772b663))
- ([Cosandier 2017](#org7ebf41f))
## Flexure Joints for Stewart Platforms: {#flexure-joints-for-stewart-platforms}
From ([Chen and McInroy 2000](#org14378b5)):
From ([Chen and McInroy 2000](#org64f8175)):
> 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.
## Materials {#materials}
- ([Smith 2000](#org299921c))
- ([Lobontiu 2002](#orgb45af18))
- ([Henein 2003](#org8ce4916))
- ([Cosandier 2017](#org7ebf41f))
## Bibliography {#bibliography}
<a id="org14378b5"></a>Chen, Yixin, and J.E. McInroy. 2000. “Identification and Decoupling Control of Flexure Jointed Hexapods.” In _Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)_, nil. <https://doi.org/10.1109/robot.2000.844878>.
<a id="org64f8175"></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="orgf099485"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="org7ebf41f"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="org4fb65e1"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="org8ce4916"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="org0e711a7"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="orgb45af18"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="orgbf46163"></a>Smith, Stuart T. 2005. _Foundations of Ultra-Precision Mechanism Design_. Vol. 2. CRC Press.
<a id="org299921c"></a>Smith, Stuart T. 2000. _Flexures: Elements of Elastic Mechanisms_. Crc Press.
<a id="orgf482067"></a>Soemers, Herman. 2011. _Design Principles for Precision Mechanisms_. T-Pointprint.
<a id="orgccbed32"></a>———. 2005. _Foundations of Ultra-Precision Mechanism Design_. Vol. 2. CRC Press.
<a id="org772b663"></a>Soemers, Herman. 2011. _Design Principles for Precision Mechanisms_. T-Pointprint.

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+++
title = "Flexures"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Flexible Joints]({{< relref "flexible_joints" >}})
## Material Used {#material-used}
## Materials {#materials}
- ([Smith 2000](#org903194d))
- ([Lobontiu 2002](#org353b748))
- ([Henein 2003](#org26cb408))
- ([Cosandier 2017](#org684f025))
## Bibliography {#bibliography}
<a id="org684f025"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="org26cb408"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="org353b748"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="org903194d"></a>Smith, Stuart T. 2000. _Flexures: Elements of Elastic Mechanisms_. Crc Press.

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title = "Force Sensors"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Signal Conditioner]({{< relref "signal_conditioner" >}}), [Modal Analysis]({{< relref "modal_analysis" >}})
: [Signal Conditioner]({{<relref "signal_conditioner.md#" >}}), [Modal Analysis]({{<relref "modal_analysis.md#" >}})
## Technologies {#technologies}
@ -17,9 +18,9 @@ There are two main technique for force sensors:
The choice between the two is usually based on whether the measurement is static (strain gauge) or dynamics (piezoelectric).
Main differences between the two are shown in Figure [1](#orgd4cde6e).
Main differences between the two are shown in Figure [1](#orgc9e9a88).
<a id="orgd4cde6e"></a>
<a id="orgc9e9a88"></a>
{{< figure src="/ox-hugo/force_sensor_piezo_vs_strain_gauge.png" caption="Figure 1: Piezoelectric Force sensor VS Strain Gauge Force sensor" >}}
@ -29,7 +30,7 @@ Main differences between the two are shown in Figure [1](#orgd4cde6e).
### 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](#org6f75dec)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
An analysis the dynamics and noise of a piezoelectric force sensor is done in ([Fleming 2010](#org024e377)) ([Notes]({{<relref "fleming10_nanop_system_with_force_feedb.md#" >}})).
### Manufacturers {#manufacturers}
@ -45,7 +46,7 @@ An analysis the dynamics and noise of a piezoelectric force sensor is done in ([
### Signal Conditioner {#signal-conditioner}
The voltage generated by the piezoelectric material generally needs to be amplified using a [Signal Conditioner]({{< relref "signal_conditioner" >}}).
The voltage generated by the piezoelectric material generally needs to be amplified using a [Signal Conditioner]({{<relref "signal_conditioner.md#" >}}).
Either **charge** amplifiers or **voltage** amplifiers can be used.
@ -78,4 +79,4 @@ However, if a charge conditioner is used, the signal will be doubled.
## Bibliography {#bibliography}
<a id="org6f75dec"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.
<a id="org024e377"></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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title = "Granite"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags

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title = "Inertial Sensors"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
: [Position Sensors]({{<relref "position_sensors.md#" >}})
## 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](#orga092f9a))
- Collette, C. et al., Comparison of new absolute displacement sensors ([Collette, Janssens, Mokrani, et al. 2012](#orgef1075b))
- Collette, C. et al., Review: inertial sensors for low-frequency seismic vibration measurement ([Collette, Janssens, Fernandez-Carmona, et al. 2012](#orgc1383e0))
- Collette, C. et al., Comparison of new absolute displacement sensors ([Collette, Janssens, Mokrani, et al. 2012](#org7b301f5))
<a id="org9a5fa73"></a>
<a id="orgf969bc3"></a>
{{< figure src="/ox-hugo/collette12_absolute_disp_sensors.png" caption="Figure 1: Dynamic range of several types of inertial sensors; Price versus resolution for several types of inertial sensors" >}}
@ -35,7 +36,7 @@ Wireless Accelerometers
- <https://micromega-dynamics.com/products/recovib/miniature-vibration-recorder/>
<a id="org1693047"></a>
<a id="orga2a662e"></a>
{{< figure src="/ox-hugo/inertial_sensors_characteristics_accelerometers.png" caption="Figure 2: Characteristics of commercially available accelerometers <sup id=\"642a18d86de4e062c6afb0f5f20501c4\"><a href=\"#collette11_review\" title=\"Collette, Artoos, Guinchard, Janssens, , Carmona Fernandez \&amp; Hauviller, Review of sensors for low frequency seismic vibration measurement, CERN, (2011).\">collette11_review</a></sup>" >}}
@ -52,7 +53,7 @@ Wireless Accelerometers
| [Guralp](https://www.guralp.com/products/surface) | UK |
| [Nanometric](https://www.nanometrics.ca/products/seismometers) | Canada |
<a id="org6d70737"></a>
<a id="org431a804"></a>
{{< figure src="/ox-hugo/inertial_sensors_characteristics_geophone.png" caption="Figure 3: Characteristics of commercially available geophones <sup id=\"642a18d86de4e062c6afb0f5f20501c4\"><a href=\"#collette11_review\" title=\"Collette, Artoos, Guinchard, Janssens, , Carmona Fernandez \&amp; Hauviller, Review of sensors for low frequency seismic vibration measurement, CERN, (2011).\">collette11_review</a></sup>" >}}
@ -60,6 +61,6 @@ Wireless Accelerometers
## Bibliography {#bibliography}
<a id="orga092f9a"></a>Collette, C., S. Janssens, P. Fernandez-Carmona, K. Artoos, M. Guinchard, C. Hauviller, and A. Preumont. 2012. “Review: Inertial Sensors for Low-Frequency Seismic Vibration Measurement.” _Bulletin of the Seismological Society of America_ 102 (4):1289–1300. <https://doi.org/10.1785/0120110223>.
<a id="orgc1383e0"></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="orgef1075b"></a>Collette, C, S Janssens, B Mokrani, L Fueyo-Roza, K Artoos, M Esposito, P Fernandez-Carmona, M Guinchard, and R Leuxe. 2012. “Comparison of New Absolute Displacement Sensors.” In _International Conference on Noise and Vibration Engineering (ISMA)_.
<a id="org7b301f5"></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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title = "Instrumented Hammer"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Modal Analysis]({{< relref "modal_analysis" >}}), [Force Sensors]({{< relref "force_sensors" >}})
: [Modal Analysis]({{<relref "modal_analysis.md#" >}}), [Force Sensors]({{<relref "force_sensors.md#" >}})
And instrumented hammer consist of a regular hammer with a force sensor fixed at its tip.

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title = "Interferometers"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
@ -24,12 +25,12 @@ Tags
## Reviews {#reviews}
([Ducourtieux 2018](#orgba5debb), [2018](#orgba5debb); [Bobroff 1993](#org9cfc0be), [1993](#org9cfc0be); [Thurner et al. 2015](#org9f4a3ed), [2015](#org9f4a3ed); [Loughridge and Abramovitch 2013](#org2c02ae6))
([Ducourtieux 2018](#org538e4dc), [2018](#org538e4dc); [Bobroff 1993](#org9f4652e), [1993](#org9f4652e); [Thurner et al. 2015](#orgdcf4929), [2015](#orgdcf4929); [Loughridge and Abramovitch 2013](#orgd91ce9e))
## Effect of Refractive Index - Environmental Units {#effect-of-refractive-index-environmental-units}
The measured distance is proportional to the refractive index of the air that depends on several quantities as shown in Table [1](#table--tab:index-air) (Taken from ([Thurner et al. 2015](#org9f4a3ed))).
The measured distance is proportional to the refractive index of the air that depends on several quantities as shown in Table [1](#table--tab:index-air) (Taken from ([Thurner et al. 2015](#orgdcf4929))).
<a id="table--tab:index-air"></a>
<div class="table-caption">
@ -64,16 +65,16 @@ Typical characteristics of commercial environmental units are shown in Table [2]
## Interferometer Precision {#interferometer-precision}
Figure [1](#org1406d51) shows the expected precision as a function of the measured distance due to change of refractive index of the air (taken from ([Jang and Kim 2017](#orgcfb1fbe))).
Figure [1](#org24527f3) shows the expected precision as a function of the measured distance due to change of refractive index of the air (taken from ([Jang and Kim 2017](#org0cf5512))).
<a id="org1406d51"></a>
<a id="org24527f3"></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](#orgba5debb)).
Sources of error in laser interferometry are well described in ([Ducourtieux 2018](#org538e4dc)).
It includes:
@ -83,10 +84,10 @@ It includes:
- Pressure: \\(K\_P \approx 0.27 ppm hPa^{-1}\\)
- Humidity: \\(K\_{HR} \approx 0.01 ppm \% RH^{-1}\\)
- These errors can partially be compensated using an environmental unit.
- Air turbulence (Figure [2](#org690599c))
- Air turbulence (Figure [2](#org1d0f37d))
- Non linearity
<a id="org690599c"></a>
<a id="org1d0f37d"></a>
{{< figure src="/ox-hugo/interferometers_air_turbulence.png" caption="Figure 2: Effect of air turbulences on measurement stability" >}}
@ -94,12 +95,12 @@ It includes:
## Bibliography {#bibliography}
<a id="org9cfc0be"></a>Bobroff, N. 1993. “Recent Advances in Displacement Measuring Interferometry.” _Measurement Science and Technology_ 4 (9):907–26. <https://doi.org/10.1088/0957-0233/4/9/001>.
<a id="org9f4652e"></a>Bobroff, N. 1993. “Recent Advances in Displacement Measuring Interferometry.” _Measurement Science and Technology_ 4 (9):907–26. <https://doi.org/10.1088/0957-0233/4/9/001>.
<a id="orgba5debb"></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="org538e4dc"></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="orgcfb1fbe"></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="org0cf5512"></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="org2c02ae6"></a>Loughridge, Russell, and Daniel Y. Abramovitch. 2013. “A Tutorial on Laser Interferometry for Precision Measurements.” In _2013 American Control Conference_, nil. <https://doi.org/10.1109/acc.2013.6580402>.
<a id="orgd91ce9e"></a>Loughridge, Russell, and Daniel Y. Abramovitch. 2013. “A Tutorial on Laser Interferometry for Precision Measurements.” In _2013 American Control Conference_, nil. <https://doi.org/10.1109/acc.2013.6580402>.
<a id="org9f4a3ed"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” _Applied Optics_ 54 (10). Optical Society of America:3051–63.
<a id="orgdcf4929"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” _Applied Optics_ 54 (10). Optical Society of America:3051–63.

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title = "Linear Guides"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
@ -14,5 +15,3 @@ Tags
|----------------------------------------------------------------------------------------------------------------------------|---------|
| [Bosch Rexroth](https://www.boschrexroth.com/en/xc/products/product-groups/linear-motion-technology/topics/linear-guides/) | Germany |
| [THK](https://www.thk.com/?q=eng/node/231) | Japan |
<./biblio/references.bib>

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title = "Linear variable differential transformers"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
: [Position Sensors]({{<relref "position_sensors.md#" >}})
## Manufacturers {#manufacturers}

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title = "Parallel Manipulators"
author = ["Thomas Dehaeze"]
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:

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title = "Piezoelectric Actuators"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Actuators](actuators.md), [Voltage Amplifier](voltage_amplifier.md)
: [Actuators]({{<relref "actuators.md#" >}}), [Voltage Amplifier]({{<relref "voltage_amplifier.md#" >}})
## Piezoelectric Stack Actuators {#piezoelectric-stack-actuators}
@ -32,7 +33,7 @@ Tags
### Model {#model}
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgc916f93)) ([Notes](fleming10_nanop_system_with_force_feedb.md)).
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgd563065)) ([Notes]({{<relref "fleming10_nanop_system_with_force_feedb.md#" >}})).
Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel.
@ -56,14 +57,14 @@ 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](#orgaaabf8d)):
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#orgb463c4c)):
> 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](#org8ca201e)).
A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org2bf81f0)).
<a id="org5d92181"></a>
<a id="org77a46eb"></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>" >}}
@ -141,9 +142,9 @@ with:
### Resolution {#resolution}
The resolution is limited by the noise in the [Voltage Amplifier](voltage_amplifier.md).
The resolution is limited by the noise in the [Voltage Amplifier]({{<relref "voltage_amplifier.md#" >}}).
Typical [Signal to Noise Ratio](signal_to_noise_ratio.md) of voltage amplifiers is \\(100dB = 10^{5}\\).
Typical [Signal to Noise Ratio]({{<relref "signal_to_noise_ratio.md#" >}}) of voltage amplifiers is \\(100dB = 10^{5}\\).
Thus, for a piezoelectric stack with a displacement \\(L\\), the resolution will be
\begin{equation}
@ -155,58 +156,58 @@ 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](#org2c60a2d)).
The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#orgca6870e)).
This is due to the fact that voltage amplifier has a limitation on the deliverable current.
[Voltage Amplifier](voltage_amplifier.md) with high maximum output current should be used if either high bandwidth is wanted or piezoelectric stacks with high capacitance are to be used.
[Voltage Amplifier]({{<relref "voltage_amplifier.md#" >}}) 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="org2c60a2d"></a>
<a id="orgca6870e"></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](#org7af4476)).
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](#orge05f5e6)).
<a id="org7af4476"></a>
<a id="orge05f5e6"></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](#org97370ea)):
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](#orgfcd374f)):
\begin{equation}
\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
\end{equation}
<a id="org97370ea"></a>
<a id="orgfcd374f"></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](#org8c01425)).
For piezo actuators, force and displacement are inversely related (Figure [5](#orgada6c4c)).
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="org8c01425"></a>
<a id="orgada6c4c"></a>
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
## Driving Electronics {#driving-electronics}
Piezoelectric actuators can be driven either using a voltage to charge converter or a [Voltage Amplifier](voltage_amplifier.md).
Limitations of the electronics is discussed in [Design, modeling and control of nanopositioning systems](fleming14_desig_model_contr_nanop_system.md).
Piezoelectric actuators can be driven either using a voltage to charge converter or a [Voltage Amplifier]({{<relref "voltage_amplifier.md#" >}}).
Limitations of the electronics is discussed in [Design, modeling and control of nanopositioning systems]({{<relref "fleming14_desig_model_contr_nanop_system.md#" >}}).
## Bibliography {#bibliography}
<a id="orgaaabf8d"></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="orgb463c4c"></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="orgc916f93"></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="orgd563065"></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="org8ca201e"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
<a id="org2bf81f0"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”

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+++
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" >}})
: [Inertial Sensors]({{<relref "inertial_sensors.md#" >}}), [Force Sensors]({{<relref "force_sensors.md#" >}}), [Sensor Fusion]({{<relref "sensor_fusion.md#" >}}), [Signal Conditioner]({{<relref "signal_conditioner.md#" >}}), [Signal to Noise Ratio]({{<relref "signal_to_noise_ratio.md#" >}})
## Types of Positioning sensors {#types-of-positioning-sensors}
High precision positioning sensors include:
- [Interferometers]({{< relref "interferometers" >}})
- [Capacitive Sensors]({{< relref "capacitive_sensors" >}})
- [LVDT]({{< relref "linear_variable_differential_transformers" >}})
- [Eddy Current Sensors]({{< relref "eddy_current_sensors" >}})
- [Encoders]({{< relref "encoders" >}})
- [Interferometers]({{<relref "interferometers.md#" >}})
- [Capacitive Sensors]({{<relref "capacitive_sensors.md#" >}})
- [LVDT]({{<relref "linear_variable_differential_transformers.md#" >}})
- [Eddy Current Sensors]({{<relref "eddy_current_sensors.md#" >}})
- [Encoders]({{<relref "encoders.md#" >}})
## 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](#orgbadb097)) ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
- Fleming, A. J., A review of nanometer resolution position sensors: operation and performance ([Fleming 2013](#org654bd0b)) ([Notes]({{<relref "fleming13_review_nanom_resol_posit_sensor.md#" >}}))
<a id="table--tab:characteristics-relative-sensor"></a>
<div class="table-caption">
@ -57,7 +57,7 @@ High precision positioning sensors include:
Capacitive Sensors and Eddy-Current sensors are compare [here](https://www.lionprecision.com/comparing-capacitive-and-eddy-current-sensors/).
<a id="org2b23cef"></a>
<a id="orgff7dc3a"></a>
{{< figure src="/ox-hugo/position_sensors_thurner15.png" caption="Figure 1: Overview of range and precision of different position displacement sensors. Taken from <sup id=\"53230532ada812541a7cd984b3aa2662\"><a href=\"#thurner15_fiber_based_distan_sensin_inter\" title=\"Thurner, Quacquarelli, Braun, Pierre-Fran\ccois, Dal Savio, Karrai \&amp; Khaled, Fiber-Based Distance Sensing Interferometry, {Applied optics}, v(10), 3051--3063 (2015).\">thurner15_fiber_based_distan_sensin_inter</a></sup>" >}}
@ -65,4 +65,4 @@ Capacitive Sensors and Eddy-Current sensors are compare [here](https://www.lionp
## Bibliography {#bibliography}
<a id="orgbadb097"></a>Fleming, Andrew J. 2013. “A Review of Nanometer Resolution Position Sensors: Operation and Performance.” _Sensors and Actuators a: Physical_ 190 (nil):106–26. <https://doi.org/10.1016/j.sna.2012.10.016>.
<a id="org654bd0b"></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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title = "Rotation Stage"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Slip Rings]({{< relref "slip_rings" >}})
: [Slip Rings]({{<relref "slip_rings.md#" >}})
## Manufacturers {#manufacturers}

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title = "Shaker"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Voice Coil Actuators]({{< relref "voice_coil_actuators" >}})
: [Voice Coil Actuators]({{<relref "voice_coil_actuators.md#" >}})
## Manufacturers {#manufacturers}

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title = "Signal Conditioner"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Sensors]({{< relref "sensors" >}}), [Electronics]({{< relref "electronics" >}})
: [Sensors]({{<relref "sensors.md#" >}}), [Electronics]({{<relref "electronics.md#" >}})
Most sensors needs some signal conditioner electronics before digitize the signal.
Few examples are:
@ -25,6 +26,6 @@ The signal conditioning electronics can have different functions:
Depending on the electrical quantity that is meaningful for the measurement, different types of amplifiers are used:
- Current to Voltage ([Transimpedance Amplifiers]({{< relref "transimpedance_amplifiers" >}}))
- Charge to Voltage ([Charge Amplifiers]({{< relref "charge_amplifiers" >}}))
- Voltage to Voltage ([Voltage Amplifier]({{< relref "voltage_amplifier" >}}))
- Current to Voltage ([Transimpedance Amplifiers]({{<relref "transimpedance_amplifiers.md#" >}}))
- Charge to Voltage ([Charge Amplifiers]({{<relref "charge_amplifiers.md#" >}}))
- Voltage to Voltage ([Voltage Amplifier]({{<relref "voltage_amplifier.md#" >}}))

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title = "Simulink Real Time Target Machines"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags

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title = "Slip Rings"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Rotation Stage]({{< relref "rotation_stage" >}})
: [Rotation Stage]({{<relref "rotation_stage.md#" >}})
## Manufacturers {#manufacturers}

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title = "Springs"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
@ -18,5 +19,3 @@ Tags
| [Paulstra](https://www.paulstra-industry.com/en/ranges/metal-mountings/v1210) | France |
| [Norelem](https://www.norelem.com/us/en/Products/Product-overview/Systems-and-components-for-machine-and-plant-construction/26000-Compression-springs-Elastomer-springs-Rubber-buffers-Shock-absorbers-Gas-springs.html) | France |
| [VibraSystems](https://vibrasystems.com/elastomer-and-spring-hangers.html) | USA |
<./biblio/references.bib>

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title = "Tip-Tilt Mirrors"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
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Tags

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title = "Transconductance Amplifiers"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Electronics]({{< relref "electronics" >}}), [Voice Coil Actuators]({{< relref "voice_coil_actuators" >}})
: [Electronics]({{<relref "electronics.md#" >}}), [Voice Coil Actuators]({{<relref "voice_coil_actuators.md#" >}})
## Description {#description}

3
content/zettels/transimpedance_amplifiers.md
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@ -2,10 +2,11 @@
title = "Transimpedance Amplifiers"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Electronics]({{< relref "electronics" >}})
: [Electronics]({{<relref "electronics.md#" >}})
## Description {#description}

9
content/zettels/voice_coil_actuators.md
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@ -2,10 +2,11 @@
title = "Voice Coil Actuators"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Actuators]({{< relref "actuators" >}})
: [Actuators]({{<relref "actuators.md#" >}})
## Working Principle {#working-principle}
@ -16,12 +17,12 @@ Tags
## Model of a Voice Coil Actuator {#model-of-a-voice-coil-actuator}
([Schmidt, Schitter, and Rankers 2014](#orgc4c6d58))
([Schmidt, Schitter, and Rankers 2014](#org173764e))
## Driving Electronics {#driving-electronics}
As the force is proportional to the current, a [Transconductance Amplifiers]({{< relref "transconductance_amplifiers" >}}) (voltage-controller current source) is generally used as the driving electronics.
As the force is proportional to the current, a [Transconductance Amplifiers]({{<relref "transconductance_amplifiers.md#" >}}) (voltage-controller current source) is generally used as the driving electronics.
## Manufacturers {#manufacturers}
@ -43,4 +44,4 @@ As the force is proportional to the current, a [Transconductance Amplifiers]({{<
## Bibliography {#bibliography}
<a id="orgc4c6d58"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.
<a id="org173764e"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2014. _The Design of High Performance Mechatronics - 2nd Revised Edition_. Ios Press.

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@ -2,10 +2,11 @@
title = "Voltage Amplifier"
author = ["Thomas Dehaeze"]
draft = false
category = "equipment"
+++
Tags
: [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}}), [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}}), [Electronics]({{< relref "electronics" >}})
: [Signal to Noise Ratio]({{<relref "signal_to_noise_ratio.md#" >}}), [Piezoelectric Actuators]({{<relref "piezoelectric_actuators.md#" >}}), [Electronics]({{<relref "electronics.md#" >}})
## Voltage Amplifiers to drive Capacitive Loads {#voltage-amplifiers-to-drive-capacitive-loads}
@ -33,9 +34,9 @@ Tags
The piezoelectric stack can be represented as a capacitance.
Let's take a capacitance driven by a voltage amplifier (Figure [1](#org14569de)).
Let's take a capacitance driven by a voltage amplifier (Figure [1](#org63f8350)).
<a id="org14569de"></a>
<a id="org63f8350"></a>
{{< figure src="/ox-hugo/voltage_amplifier_capacitance.png" caption="Figure 1: Piezoelectric actuator model with a voltage source" >}}
@ -55,7 +56,7 @@ 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](#orga5b5a57).
The maximum voltage as a function of frequency is shown in Figure [2](#orgfbd4a45).
```matlab
Vpkp = 170; % [V]
@ -69,7 +70,7 @@ The maximum voltage as a function of frequency is shown in Figure [2](#orga5b5a5
56.172
```
<a id="orga5b5a57"></a>
<a id="orgfbd4a45"></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\\)" >}}
@ -89,7 +90,7 @@ Specifications are usually:
- Maximum Current
- DC Gain (usually around 10)
- Output Noise or [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})
- Output Noise or [Signal to Noise Ratio]({{<relref "signal_to_noise_ratio.md#" >}})
The bandwidth can be estimated from the Maximum Current and the Capacitance of the Piezoelectric Actuator.
@ -105,7 +106,7 @@ 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](#org8deb271)).
Sources of noise in a system comprising a voltage amplifier and a capactive load are discussed in ([Spengen 2020](#org2170119)).
Proper enclosures and cabling are necessary to protect the system from capacitive and inductive interferance.
@ -117,14 +118,14 @@ The **input** impedance of voltage amplifiers are generally set to \\(50 \Omega\
The **output** (or internal) impedance of voltage amplifier is generally wanted small in order to have a small voltage drop when large current are drawn.
However, for stability reasons and to avoid overshoot (due to the internal negative feedback loop), this impedance can be chosen quite large.
This is discussed in ([Spengen 2017](#org22b2168)).
This is discussed in ([Spengen 2017](#org55e5dcc)).
## Bibliography {#bibliography}
<a id="org6dde1c6"></a>Fleming, Andrew J., and Kam K. Leang. 2014. _Design, Modeling and Control of Nanopositioning Systems_. Advances in Industrial Control. Springer International Publishing. <https://doi.org/10.1007/978-3-319-06617-2>.
<a id="org200fc06"></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="org22b2168"></a>Spengen, W. Merlijn van. 2017. “High Voltage Amplifiers and the Ubiquitous 50 Ohms: Caveats and Benefits.” Falco Systems.
<a id="org55e5dcc"></a>Spengen, W. Merlijn van. 2017. “High Voltage Amplifiers and the Ubiquitous 50 Ohms: Caveats and Benefits.” Falco Systems.
<a id="org8deb271"></a>———. 2020. “High Voltage Amplifiers: So You Think You Have Noise!” Falco Systems.
<a id="org2170119"></a>———. 2020. “High Voltage Amplifiers: So You Think You Have Noise!” Falco Systems.

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