Re-export all org mode files

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Thomas Dehaeze 2020-08-17 21:59:26 +02:00
parent bc8c757e21
commit 3816e389e9
37 changed files with 403 additions and 266 deletions

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@ -8,9 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}}) : [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference Reference
: <sup id="ba05ff213f8e5963d91559d95becfbdb"><a class="reference-link" href="#chen00_ident_decoup_contr_flexur_joint_hexap" title="Yixin Chen \&amp; McInroy, Identification and Decoupling Control of Flexure Jointed Hexapods, nil, in in: {Proceedings 2000 ICRA. Millennium Conference. IEEE : ([Chen and McInroy 2000](#orgd504c56))
International Conference on Robotics and Automation. Symposia
Proceedings (Cat. No.00CH37065)}, edited by (2000)">(Yixin Chen \& McInroy, 2000)</a></sup>
Author(s) Author(s)
: Chen, Y., & McInroy, J. : Chen, Y., & McInroy, J.
@ -45,10 +43,9 @@ The algorithm derived herein removes these constraints, thus greatly expanding t
## Dynamic Model of Flexure Jointed Hexapods {#dynamic-model-of-flexure-jointed-hexapods} ## Dynamic Model of Flexure Jointed Hexapods {#dynamic-model-of-flexure-jointed-hexapods}
The derivation of the dynamic model is done in <sup id="5da427f78c552aa92cd64c2a6df961f1"><a class="reference-link" href="#mcinroy99_dynam" title="McInroy, Dynamic modeling of flexure jointed hexapods for control purposes, nil, in in: {Proceedings of the 1999 IEEE International Conference on The derivation of the dynamic model is done in ([McInroy 1999](#orgbf9df90)) ([Notes]({{< relref "mcinroy99_dynam" >}})).
Control Applications (Cat. No.99CH36328)}, edited by (1999)">(McInroy, 1999)</a></sup> ([Notes]({{< relref "mcinroy99_dynam" >}})).
<a id="org81e0a96"></a> <a id="org56416c1"></a>
{{< figure src="/ox-hugo/chen00_flexure_hexapod.png" caption="Figure 1: A flexured joint Hexapod. {P} is a cartesian coordiante frame located at (and rigidly connected to) the payload's center of mass. {B} is a frame attached to the (possibly moving) base, and {U} is a universal inertial frame of reference" >}} {{< figure src="/ox-hugo/chen00_flexure_hexapod.png" caption="Figure 1: A flexured joint Hexapod. {P} is a cartesian coordiante frame located at (and rigidly connected to) the payload's center of mass. {B} is a frame attached to the (possibly moving) base, and {U} is a universal inertial frame of reference" >}}
@ -102,7 +99,9 @@ where
## Experimental Results {#experimental-results} ## Experimental Results {#experimental-results}
# Bibliography
<a class="bibtex-entry" id="chen00_ident_decoup_contr_flexur_joint_hexap">Chen, Y., & McInroy, J., *Identification and decoupling control of flexure jointed hexapods*, In , Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065) (pp. ) (2000). : .</a> [](#ba05ff213f8e5963d91559d95becfbdb)
<a class="bibtex-entry" id="mcinroy99_dynam">McInroy, J., *Dynamic modeling of flexure jointed hexapods for control purposes*, In , Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328) (pp. ) (1999). : .</a> [](#5da427f78c552aa92cd64c2a6df961f1) ## Bibliography {#bibliography}
<a id="orgd504c56"></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="orgbf9df90"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In _Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)_, nil. <https://doi.org/10.1109/cca.1999.806694>.

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@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}) : [Stewart Platforms]({{< relref "stewart_platforms" >}})
Reference Reference
: <sup id="ad17e03f0fbbcc1a070557d7b5a0e1e1"><a class="reference-link" href="#dasgupta00_stewar_platf_manip" title="Bhaskar Dasgupta \&amp; Mruthyunjaya, The Stewart Platform Manipulator: a Review, {Mechanism and Machine Theory}, v(1), 15-40 (2000).">(Bhaskar Dasgupta \& Mruthyunjaya, 2000)</a></sup> : ([Dasgupta and Mruthyunjaya 2000](#orge03a23b))
Author(s) Author(s)
: Dasgupta, B., & Mruthyunjaya, T. : Dasgupta, B., & Mruthyunjaya, T.
@ -33,5 +33,7 @@ Year
The generalized Stewart platforms consists of two rigid bodies (referred to as the base and the platoform) connected through six extensible legs, each with sherical joints at both ends. The generalized Stewart platforms consists of two rigid bodies (referred to as the base and the platoform) connected through six extensible legs, each with sherical joints at both ends.
# Bibliography
<a class="bibtex-entry" id="dasgupta00_stewar_platf_manip">Dasgupta, B., & Mruthyunjaya, T., *The stewart platform manipulator: a review*, Mechanism and Machine Theory, *35(1)*, 1540 (2000). http://dx.doi.org/10.1016/s0094-114x(99)00006-3</a> [](#ad17e03f0fbbcc1a070557d7b5a0e1e1) ## Bibliography {#bibliography}
<a id="orge03a23b"></a>Dasgupta, Bhaskar, and T.S. Mruthyunjaya. 2000. “The Stewart Platform Manipulator: A Review.” _Mechanism and Machine Theory_ 35 (1):1540. <https://doi.org/10.1016/s0094-114x(99)>00006-3.

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@ -8,7 +8,7 @@ Tags
: [Position Sensors]({{< relref "position_sensors" >}}) : [Position Sensors]({{< relref "position_sensors" >}})
Reference Reference
: <sup id="3fb5b61524290e36d639a4fac65703d0"><a class="reference-link" href="#fleming13_review_nanom_resol_posit_sensor" title="Andrew Fleming, A Review of Nanometer Resolution Position Sensors: Operation and Performance, {Sensors and Actuators A: Physical}, v(nil), 106-126 (2013).">(Andrew Fleming, 2013)</a></sup> : ([Fleming 2013](#org66efc4b))
Author(s) Author(s)
: Fleming, A. J. : Fleming, A. J.
@ -33,7 +33,7 @@ Usually quoted as a percentage of the fill-scale range (FSR):
With \\(e\_m(v)\\) is the mapping error. With \\(e\_m(v)\\) is the mapping error.
<a id="org6e00657"></a> <a id="org51fba0c"></a>
{{< figure src="/ox-hugo/fleming13_mapping_error.png" caption="Figure 1: The actual position versus the output voltage of a position sensor. The calibration function \\(f\_{cal}(v)\\) is an approximation of the sensor mapping function \\(f\_a(v)\\) where \\(v\\) is the voltage resulting from a displacement \\(x\\). \\(e\_m(v)\\) is the residual error." >}} {{< figure src="/ox-hugo/fleming13_mapping_error.png" caption="Figure 1: The actual position versus the output voltage of a position sensor. The calibration function \\(f\_{cal}(v)\\) is an approximation of the sensor mapping function \\(f\_a(v)\\) where \\(v\\) is the voltage resulting from a displacement \\(x\\). \\(e\_m(v)\\) is the residual error." >}}
@ -42,7 +42,7 @@ With \\(e\_m(v)\\) is the mapping error.
If the shape of the mapping function actually varies with time, the maximum error due to drift must be evaluated by finding the worst-case mapping error. If the shape of the mapping function actually varies with time, the maximum error due to drift must be evaluated by finding the worst-case mapping error.
<a id="org076fb4b"></a> <a id="org2b35a7e"></a>
{{< figure src="/ox-hugo/fleming13_drift_stability.png" caption="Figure 2: The worst case range of a linear mapping function \\(f\_a(v)\\) for a given error in sensitivity and offset." >}} {{< figure src="/ox-hugo/fleming13_drift_stability.png" caption="Figure 2: The worst case range of a linear mapping function \\(f\_a(v)\\) for a given error in sensitivity and offset." >}}
@ -147,9 +147,9 @@ The empirical rule states that there is a \\(99.7\%\\) probability that a sample
This if we define the resolution as \\(\delta = 6 \sigma\\), we will referred to as the \\(6\sigma\text{-resolution}\\). This if we define the resolution as \\(\delta = 6 \sigma\\), we will referred to as the \\(6\sigma\text{-resolution}\\).
Another important parameter that must be specified when quoting resolution is the sensor bandwidth. Another important parameter that must be specified when quoting resolution is the sensor bandwidth.
There is usually a trade-off between bandwidth and resolution (figure [3](#org92eeb72)). There is usually a trade-off between bandwidth and resolution (figure [3](#org40574f2)).
<a id="org92eeb72"></a> <a id="org40574f2"></a>
{{< figure src="/ox-hugo/fleming13_tradeoff_res_bandwidth.png" caption="Figure 3: The resolution versus banwidth of a position sensor." >}} {{< figure src="/ox-hugo/fleming13_tradeoff_res_bandwidth.png" caption="Figure 3: The resolution versus banwidth of a position sensor." >}}
@ -181,8 +181,10 @@ A convenient method for reporting this ratio is in parts-per-million (ppm):
| Interferometer | Meters | | 0.5 nm | >100kHz | 1 ppm FSR | | Interferometer | Meters | | 0.5 nm | >100kHz | 1 ppm FSR |
| Encoder | Meters | | 6 nm | >100kHz | 5 ppm FSR | | Encoder | Meters | | 6 nm | >100kHz | 5 ppm FSR |
# Bibliography
<a class="bibtex-entry" id="fleming13_review_nanom_resol_posit_sensor">Fleming, A. J., *A review of nanometer resolution position sensors: operation and performance*, Sensors and Actuators A: Physical, *190(nil)*, 106126 (2013). http://dx.doi.org/10.1016/j.sna.2012.10.016</a> [](#3fb5b61524290e36d639a4fac65703d0) ## Bibliography {#bibliography}
<a id="org66efc4b"></a>Fleming, Andrew J. 2013. “A Review of Nanometer Resolution Position Sensors: Operation and Performance.” _Sensors and Actuators a: Physical_ 190 (nil):10626. <https://doi.org/10.1016/j.sna.2012.10.016>.
## Backlinks {#backlinks} ## Backlinks {#backlinks}

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@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}) : [Stewart Platforms]({{< relref "stewart_platforms" >}})
Reference Reference
: <sup id="cc10fe9545c7c381cc2b610e8f91a071"><a class="reference-link" href="#furqan17_studies_stewar_platf_manip" title="Mohd Furqan, Mohd Suhaib \&amp; Nazeer Ahmad, Studies on Stewart Platform Manipulator: a Review, {Journal of Mechanical Science and Technology}, v(9), 4459-4470 (2017).">(Mohd Furqan {\it et al.}, 2017)</a></sup> : ([Furqan, Suhaib, and Ahmad 2017](#org5774b90))
Author(s) Author(s)
: Furqan, M., Suhaib, M., & Ahmad, N. : Furqan, M., Suhaib, M., & Ahmad, N.
@ -18,5 +18,7 @@ Year
Lots of references. Lots of references.
# Bibliography
<a class="bibtex-entry" id="furqan17_studies_stewar_platf_manip">Furqan, M., Suhaib, M., & Ahmad, N., *Studies on stewart platform manipulator: a review*, Journal of Mechanical Science and Technology, *31(9)*, 44594470 (2017). http://dx.doi.org/10.1007/s12206-017-0846-1</a> [](#cc10fe9545c7c381cc2b610e8f91a071) ## Bibliography {#bibliography}
<a id="org5774b90"></a>Furqan, Mohd, Mohd Suhaib, and Nazeer Ahmad. 2017. “Studies on Stewart Platform Manipulator: A Review.” _Journal of Mechanical Science and Technology_ 31 (9):445970. <https://doi.org/10.1007/s12206-017-0846-1>.

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@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}}) : [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference Reference
: <sup id="bedab298599c84f60236313ebaad2714"><a class="reference-link" href="#furutani04_nanom_cuttin_machin_using_stewar" title="Katsushi Furutani, Michio Suzuki \&amp; Ryusei Kudoh, Nanometre-Cutting Machine Using a Stewart-Platform Parallel Mechanism, {Measurement Science and Technology}, v(2), 467-474 (2004).">(Katsushi Furutani {\it et al.}, 2004)</a></sup> : ([Furutani, Suzuki, and Kudoh 2004](#org934975a))
Author(s) Author(s)
: Furutani, K., Suzuki, M., & Kudoh, R. : Furutani, K., Suzuki, M., & Kudoh, R.
@ -34,5 +34,7 @@ Possible sources of error:
To minimize the errors, a calibration is done between the required leg length and the wanted platform pose. To minimize the errors, a calibration is done between the required leg length and the wanted platform pose.
Then, it is fitted with 4th order polynomial and included in the control architecture. Then, it is fitted with 4th order polynomial and included in the control architecture.
# Bibliography
<a class="bibtex-entry" id="furutani04_nanom_cuttin_machin_using_stewar">Furutani, K., Suzuki, M., & Kudoh, R., *Nanometre-cutting machine using a stewart-platform parallel mechanism*, Measurement Science and Technology, *15(2)*, 467474 (2004). http://dx.doi.org/10.1088/0957-0233/15/2/022</a> [](#bedab298599c84f60236313ebaad2714) ## Bibliography {#bibliography}
<a id="org934975a"></a>Furutani, Katsushi, Michio Suzuki, and Ryusei Kudoh. 2004. “Nanometre-Cutting Machine Using a Stewart-Platform Parallel Mechanism.” _Measurement Science and Technology_ 15 (2):46774. <https://doi.org/10.1088/0957-0233/15/2/022>.

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@ -8,7 +8,7 @@ Tags
: [Position Sensors]({{< relref "position_sensors" >}}) : [Position Sensors]({{< relref "position_sensors" >}})
Reference Reference
: <sup id="b820b918ced36901ea0ad4bf653202c6"><a class="reference-link" href="#gao15_measur_techn_precis_posit" title="Gao, Kim, Bosse, Haitjema, , Chen, Lu, Knapp, Weckenmann, , Estler \&amp; Kunzmann, Measurement Technologies for Precision Positioning, {CIRP Annals}, v(2), 773-796 (2015).">(Gao {\it et al.}, 2015)</a></sup> : ([Gao et al. 2015](#org3775d30))
Author(s) Author(s)
: Gao, W., Kim, S., Bosse, H., Haitjema, H., Chen, Y., Lu, X., Knapp, W., … : Gao, W., Kim, S., Bosse, H., Haitjema, H., Chen, Y., Lu, X., Knapp, W., …
@ -16,5 +16,7 @@ Author(s)
Year Year
: 2015 : 2015
# Bibliography
<a class="bibtex-entry" id="gao15_measur_techn_precis_posit">Gao, W., Kim, S., Bosse, H., Haitjema, H., Chen, Y., Lu, X., Knapp, W., …, *Measurement technologies for precision positioning*, CIRP Annals, *64(2)*, 773796 (2015). http://dx.doi.org/10.1016/j.cirp.2015.05.009</a> [](#b820b918ced36901ea0ad4bf653202c6) ## Bibliography {#bibliography}
<a id="org3775d30"></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):77396. <https://doi.org/10.1016/j.cirp.2015.05.009>.

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@ -8,8 +8,7 @@ Tags
: [Multivariable Control]({{< relref "multivariable_control" >}}) : [Multivariable Control]({{< relref "multivariable_control" >}})
Reference Reference
: <sup id="07f63c751c1d9fcfe628178688f7ec24"><a class="reference-link" href="#garg07_implem_chall_multiv_contr" title="Sanjay Garg, Implementation Challenges for Multivariable Control: What you did not learn in school!, nil, in in: {AIAA Guidance, Navigation and Control Conference and : ([Garg 2007](#org2f331c4))
Exhibit}, edited by (2007)">(Sanjay Garg, 2007)</a></sup>
Author(s) Author(s)
: Garg, S. : Garg, S.
@ -35,5 +34,7 @@ The control rate should be weighted appropriately in order to not saturate the s
- importance of scaling the plant prior to synthesis and also replacing pure integrators with slow poles - importance of scaling the plant prior to synthesis and also replacing pure integrators with slow poles
# Bibliography
<a class="bibtex-entry" id="garg07_implem_chall_multiv_contr">Garg, S., *Implementation challenges for multivariable control: what you did not learn in school!*, In , AIAA Guidance, Navigation and Control Conference and Exhibit (pp. ) (2007). : .</a> [](#07f63c751c1d9fcfe628178688f7ec24) ## Bibliography {#bibliography}
<a id="org2f331c4"></a>Garg, Sanjay. 2007. “Implementation Challenges for Multivariable Control: What You Did Not Learn in School!” In _AIAA Guidance, Navigation and Control Conference and Exhibit_, nil. <https://doi.org/10.2514/6.2007-6334>.

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@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Active Damping]({{< relref "active_damping" >}}) : [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Active Damping]({{< relref "active_damping" >}})
Reference Reference
: <sup id="10e535e895bdcd6b921bff33ef68cd81"><a class="reference-link" href="#hanieh03_activ_stewar" title="Hanieh, Active isolation and damping of vibrations via Stewart platform (2003).">(Hanieh, 2003)</a></sup> : ([Hanieh 2003](#org16a7ca0))
Author(s) Author(s)
: Hanieh, A. A. : Hanieh, A. A.
@ -16,5 +16,7 @@ Author(s)
Year Year
: 2003 : 2003
# Bibliography
<a class="bibtex-entry" id="hanieh03_activ_stewar">Hanieh, A. A., *Active isolation and damping of vibrations via stewart platform* (2003). Universit{\'e} Libre de Bruxelles, Brussels, Belgium.</a> [](#10e535e895bdcd6b921bff33ef68cd81) ## Bibliography {#bibliography}
<a id="org16a7ca0"></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" >}}), [Flexible Joints]({{< relref "flexible_joints" >}}) : [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference Reference
: <sup id="ee917739f88877d6c2758c1c36565deb"><a class="reference-link" href="#jiao18_dynam_model_exper_analy_stewar" title="Jian Jiao, Ying Wu, Kaiping Yu \&amp; Rui Zhao, Dynamic Modeling and Experimental Analyses of Stewart Platform With Flexible Hinges, {Journal of Vibration and Control}, v(1), 151-171 (2018).">(Jian Jiao {\it et al.}, 2018)</a></sup> : ([Jiao et al. 2018](#orga81be47))
Author(s) Author(s)
: Jiao, J., Wu, Y., Yu, K., & Zhao, R. : Jiao, J., Wu, Y., Yu, K., & Zhao, R.
@ -16,5 +16,7 @@ Author(s)
Year Year
: 2018 : 2018
# Bibliography
<a class="bibtex-entry" id="jiao18_dynam_model_exper_analy_stewar">Jiao, J., Wu, Y., Yu, K., & Zhao, R., *Dynamic modeling and experimental analyses of stewart platform with flexible hinges*, Journal of Vibration and Control, *25(1)*, 151171 (2018). http://dx.doi.org/10.1177/1077546318772474</a> [](#ee917739f88877d6c2758c1c36565deb) ## Bibliography {#bibliography}
<a id="orga81be47"></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):15171. <https://doi.org/10.1177/1077546318772474>.

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@ -2,14 +2,13 @@
title = "A new isotropic and decoupled 6-dof parallel manipulator" title = "A new isotropic and decoupled 6-dof parallel manipulator"
author = ["Thomas Dehaeze"] author = ["Thomas Dehaeze"]
draft = false draft = false
GHissueID = 1
+++ +++
Tags Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}) : [Stewart Platforms]({{< relref "stewart_platforms" >}})
Reference Reference
: <sup id="17295cbc2858c65ecc60d51b450233e3"><a class="reference-link" href="#legnani12_new_isotr_decoup_paral_manip" title="Legnani, Fassi, Giberti, Cinquemani, \&amp; Tosi, A New Isotropic and Decoupled 6-dof Parallel Manipulator, {Mechanism and Machine Theory}, v(nil), 64-81 (2012).">(Legnani {\it et al.}, 2012)</a></sup> : ([Legnani et al. 2012](#orgfeceab9))
Author(s) Author(s)
: Legnani, G., Fassi, I., Giberti, H., Cinquemani, S., & Tosi, D. : Legnani, G., Fassi, I., Giberti, H., Cinquemani, S., & Tosi, D.
@ -23,13 +22,15 @@ Year
Example of generated isotropic manipulator (not decoupled). Example of generated isotropic manipulator (not decoupled).
<a id="org9b13cfd"></a> <a id="orgcc7f670"></a>
{{< figure src="/ox-hugo/legnani12_isotropy_gen.png" caption="Figure 1: Location of the leg axes using an isotropy generator" >}} {{< figure src="/ox-hugo/legnani12_isotropy_gen.png" caption="Figure 1: Location of the leg axes using an isotropy generator" >}}
<a id="org958618e"></a> <a id="orgb85ffa0"></a>
{{< figure src="/ox-hugo/legnani12_generated_isotropy.png" caption="Figure 2: Isotropic configuration" >}} {{< figure src="/ox-hugo/legnani12_generated_isotropy.png" caption="Figure 2: Isotropic configuration" >}}
# Bibliography
<a class="bibtex-entry" id="legnani12_new_isotr_decoup_paral_manip">Legnani, G., Fassi, I., Giberti, H., Cinquemani, S., & Tosi, D., *A new isotropic and decoupled 6-dof parallel manipulator*, Mechanism and Machine Theory, *58(nil)*, 6481 (2012). http://dx.doi.org/10.1016/j.mechmachtheory.2012.07.008</a> [](#17295cbc2858c65ecc60d51b450233e3) ## Bibliography {#bibliography}
<a id="orgfeceab9"></a>Legnani, G., I. Fassi, H. Giberti, S. Cinquemani, and D. Tosi. 2012. “A New Isotropic and Decoupled 6-Dof Parallel Manipulator.” _Mechanism and Machine Theory_ 58 (nil):6481. <https://doi.org/10.1016/j.mechmachtheory.2012.07.008>.

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@ -9,7 +9,7 @@ Tags
Reference Reference
: <sup id="f6d310236552ee92579cf0673a2ca695"><a href="#mcinroy00_desig_contr_flexur_joint_hexap" title="McInroy \&amp; Hamann, Design and Control of Flexure Jointed Hexapods, {IEEE Transactions on Robotics and Automation}, v(4), 372-381 (2000).">(McInroy \& Hamann, 2000)</a></sup> : ([McInroy and Hamann 2000](#orgc9838dc))
Author(s) Author(s)
: McInroy, J., & Hamann, J. : McInroy, J., & Hamann, J.
@ -17,5 +17,7 @@ Author(s)
Year Year
: 2000 : 2000
# Bibliography
<a id="mcinroy00_desig_contr_flexur_joint_hexap"></a>McInroy, J., & Hamann, J., *Design and control of flexure jointed hexapods*, IEEE Transactions on Robotics and Automation, *16(4)*, 372381 (2000). http://dx.doi.org/10.1109/70.864229 [](#f6d310236552ee92579cf0673a2ca695) ## Bibliography {#bibliography}
<a id="orgc9838dc"></a>McInroy, J.E., and J.C. Hamann. 2000. “Design and Control of Flexure Jointed Hexapods.” _IEEE Transactions on Robotics and Automation_ 16 (4):37281. <https://doi.org/10.1109/70.864229>.

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@ -8,7 +8,7 @@ Tags
: [Motion Control]({{< relref "motion_control" >}}) : [Motion Control]({{< relref "motion_control" >}})
Reference Reference
: <sup id="73fd325bd20a6ef8972145e535f38198"><a class="reference-link" href="#oomen18_advan_motion_contr_precis_mechat" title="Tom Oomen, Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems, {IEEJ Journal of Industry Applications}, v(2), 127-140 (2018).">(Tom Oomen, 2018)</a></sup> : ([Oomen 2018](#orga6f6c0b))
Author(s) Author(s)
: Oomen, T. : Oomen, T.
@ -16,9 +16,11 @@ Author(s)
Year Year
: 2018 : 2018
<a id="org5cf2052"></a> <a id="org2caf38a"></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." >}} {{< 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." >}}
# Bibliography
<a class="bibtex-entry" id="oomen18_advan_motion_contr_precis_mechat">Oomen, T., *Advanced motion control for precision mechatronics: control, identification, and learning of complex systems*, IEEJ Journal of Industry Applications, *7(2)*, 127140 (2018). http://dx.doi.org/10.1541/ieejjia.7.127</a> [](#73fd325bd20a6ef8972145e535f38198) ## Bibliography {#bibliography}
<a id="orga6f6c0b"></a>Oomen, Tom. 2018. “Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems.” _IEEJ Journal of Industry Applications_ 7 (2):12740. <https://doi.org/10.1541/ieejjia.7.127>.

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@ -8,7 +8,7 @@ Tags
: [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}}) : [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference Reference
: <sup id="8096d5b2df73551d836ef96b7ca7efa4"><a class="reference-link" href="#preumont07_six_axis_singl_stage_activ" title="Preumont, Horodinca, Romanescu, de, Marneffe, Avraam, Deraemaeker, Bossens, \&amp; Abu Hanieh, A Six-Axis Single-Stage Active Vibration Isolator Based on Stewart Platform, {Journal of Sound and Vibration}, v(3-5), 644-661 (2007).">(Preumont {\it et al.}, 2007)</a></sup> : ([Preumont et al. 2007](#org89d2c27))
Author(s) Author(s)
: Preumont, A., Horodinca, M., Romanescu, I., Marneffe, B. d., Avraam, M., Deraemaeker, A., Bossens, F., … : Preumont, A., Horodinca, M., Romanescu, I., Marneffe, B. d., Avraam, M., Deraemaeker, A., Bossens, F., …
@ -18,32 +18,34 @@ Year
Summary: Summary:
- **Cubic** Stewart platform (Figure [3](#org2d41889)) - **Cubic** Stewart platform (Figure [3](#orgfb89e2d))
- Provides uniform control capability - Provides uniform control capability
- Uniform stiffness in all directions - Uniform stiffness in all directions
- minimizes the cross-coupling among actuators and sensors of different legs - minimizes the cross-coupling among actuators and sensors of different legs
- Flexible joints (Figure [2](#orgf58a4b4)) - Flexible joints (Figure [2](#org2dfd058))
- Piezoelectric force sensors - Piezoelectric force sensors
- Voice coil actuators - Voice coil actuators
- Decentralized feedback control approach for vibration isolation - Decentralized feedback control approach for vibration isolation
- Effect of parasitic stiffness of the flexible joints on the IFF performance (Figure [1](#org6835865)) - Effect of parasitic stiffness of the flexible joints on the IFF performance (Figure [1](#org7e6bce7))
- The Stewart platform has 6 suspension modes at different frequencies. - The Stewart platform has 6 suspension modes at different frequencies.
Thus the gain of the IFF controller cannot be optimal for all the modes. Thus the gain of the IFF controller cannot be optimal for all the modes.
It is better if all the modes of the platform are near to each other. It is better if all the modes of the platform are near to each other.
- Discusses the design of the legs in order to maximize the natural frequency of the local modes. - Discusses the design of the legs in order to maximize the natural frequency of the local modes.
- To estimate the isolation performance of the Stewart platform, a scalar indicator is defined as the Frobenius norm of the transmissibility matrix - To estimate the isolation performance of the Stewart platform, a scalar indicator is defined as the Frobenius norm of the transmissibility matrix
<a id="org6835865"></a> <a id="org7e6bce7"></a>
{{< figure src="/ox-hugo/preumont07_iff_effect_stiffness.png" caption="Figure 1: Root locus with IFF with no parasitic stiffness and with parasitic stiffness" >}} {{< figure src="/ox-hugo/preumont07_iff_effect_stiffness.png" caption="Figure 1: Root locus with IFF with no parasitic stiffness and with parasitic stiffness" >}}
<a id="orgf58a4b4"></a> <a id="org2dfd058"></a>
{{< figure src="/ox-hugo/preumont07_flexible_joints.png" caption="Figure 2: Flexible joints used for the Stewart platform" >}} {{< figure src="/ox-hugo/preumont07_flexible_joints.png" caption="Figure 2: Flexible joints used for the Stewart platform" >}}
<a id="org2d41889"></a> <a id="orgfb89e2d"></a>
{{< figure src="/ox-hugo/preumont07_stewart_platform.png" caption="Figure 3: Stewart platform" >}} {{< figure src="/ox-hugo/preumont07_stewart_platform.png" caption="Figure 3: Stewart platform" >}}
# Bibliography
<a class="bibtex-entry" id="preumont07_six_axis_singl_stage_activ">Preumont, A., Horodinca, M., Romanescu, I., Marneffe, B. d., Avraam, M., Deraemaeker, A., Bossens, F., …, *A six-axis single-stage active vibration isolator based on stewart platform*, Journal of Sound and Vibration, *300(3-5)*, 644661 (2007). http://dx.doi.org/10.1016/j.jsv.2006.07.050</a> [](#8096d5b2df73551d836ef96b7ca7efa4) ## Bibliography {#bibliography}
<a id="org89d2c27"></a>Preumont, A., M. Horodinca, I. Romanescu, B. de Marneffe, M. Avraam, A. Deraemaeker, F. Bossens, and A. Abu Hanieh. 2007. “A Six-Axis Single-Stage Active Vibration Isolator Based on Stewart Platform.” _Journal of Sound and Vibration_ 300 (3-5):64461. <https://doi.org/10.1016/j.jsv.2006.07.050>.

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@ -9,7 +9,7 @@ Tags
Reference Reference
: <sup id="e71cc5e3ec879813f2344a6dce1ac11f"><a href="#sayed01_survey_spect_factor_method" title="Sayed \&amp; Kailath, A Survey of Spectral Factorization Methods, {Numerical Linear Algebra with Applications}, v(6-7), 467-496 (2001).">(Sayed \& Kailath, 2001)</a></sup> : ([Sayed and Kailath 2001](#org0cb985f))
Author(s) Author(s)
: Sayed, A. H., & Kailath, T. : Sayed, A. H., & Kailath, T.
@ -17,5 +17,7 @@ Author(s)
Year Year
: 2001 : 2001
# Bibliography
<a id="sayed01_survey_spect_factor_method"></a>Sayed, A. H., & Kailath, T., *A survey of spectral factorization methods*, Numerical Linear Algebra with Applications, *8(6-7)*, 467496 (2001). http://dx.doi.org/10.1002/nla.250 [](#e71cc5e3ec879813f2344a6dce1ac11f) ## Bibliography {#bibliography}
<a id="org0cb985f"></a>Sayed, A. H., and T. Kailath. 2001. “A Survey of Spectral Factorization Methods.” _Numerical Linear Algebra with Applications_ 8 (6-7):46796. <https://doi.org/10.1002/nla.250>.

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@ -9,7 +9,7 @@ Tags
Reference Reference
: <sup id="ee9f1b2ad5707e86bf7c26e8c325b324"><a class="reference-link" href="#schroeck01_compen_desig_linear_time_invar" title="Schroeck, Messner \&amp; McNab, On Compensator Design for Linear Time-Invariant Dual-Input Single-Output Systems, {IEEE/ASME Transactions on Mechatronics}, v(1), 50-57 (2001).">(Schroeck {\it et al.}, 2001)</a></sup> : ([Schroeck, Messner, and McNab 2001](#orga714386))
Author(s) Author(s)
: Schroeck, S., Messner, W., & McNab, R. : Schroeck, S., Messner, W., & McNab, R.
@ -17,5 +17,7 @@ Author(s)
Year Year
: 2001 : 2001
# Bibliography
<a class="bibtex-entry" id="schroeck01_compen_desig_linear_time_invar">Schroeck, S., Messner, W., & McNab, R., *On compensator design for linear time-invariant dual-input single-output systems*, IEEE/ASME Transactions on Mechatronics, *6(1)*, 5057 (2001). http://dx.doi.org/10.1109/3516.914391</a> [](#ee9f1b2ad5707e86bf7c26e8c325b324) ## Bibliography {#bibliography}
<a id="orga714386"></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):5057. <https://doi.org/10.1109/3516.914391>.

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@ -8,7 +8,7 @@ Tags
: [Active Damping]({{< relref "active_damping" >}}) : [Active Damping]({{< relref "active_damping" >}})
Reference Reference
: <sup id="d5c1263eebe6caa1e91b078b620d72f1"><a class="reference-link" href="#souleille18_concep_activ_mount_space_applic" title="Souleille, Lampert, Lafarga, , Hellegouarch, Rondineau, Rodrigues, Gon\ccalo \&amp; Collette, A Concept of Active Mount for Space Applications, {CEAS Space Journal}, v(2), 157--165 (2018).">(Souleille {\it et al.}, 2018)</a></sup> : ([Souleille et al. 2018](#org91c3531))
Author(s) Author(s)
: Souleille, A., Lampert, T., Lafarga, V., Hellegouarch, S., Rondineau, A., Rodrigues, Gonccalo, & Collette, C. : Souleille, A., Lampert, T., Lafarga, V., Hellegouarch, S., Rondineau, A., Rodrigues, Gonccalo, & Collette, C.
@ -23,10 +23,10 @@ This article discusses the use of Integral Force Feedback with amplified piezoel
## Single degree-of-freedom isolator {#single-degree-of-freedom-isolator} ## Single degree-of-freedom isolator {#single-degree-of-freedom-isolator}
Figure [1](#orgec40a2d) shows a picture of the amplified piezoelectric stack. Figure [1](#org4fea547) shows a picture of the amplified piezoelectric stack.
The piezoelectric actuator is divided into two parts: one is used as an actuator, and the other one is used as a force sensor. The piezoelectric actuator is divided into two parts: one is used as an actuator, and the other one is used as a force sensor.
<a id="orgec40a2d"></a> <a id="org4fea547"></a>
{{< figure src="/ox-hugo/souleille18_model_piezo.png" caption="Figure 1: Picture of an APA100M from Cedrat Technologies. Simplified model of a one DoF payload mounted on such isolator" >}} {{< figure src="/ox-hugo/souleille18_model_piezo.png" caption="Figure 1: Picture of an APA100M from Cedrat Technologies. Simplified model of a one DoF payload mounted on such isolator" >}}
@ -61,36 +61,38 @@ and the control force is given by:
f = F\_s G(s) = F\_s \frac{g}{s} f = F\_s G(s) = F\_s \frac{g}{s}
\end{equation} \end{equation}
The effect of the controller are shown in Figure [2](#org656442f): The effect of the controller are shown in Figure [2](#orgfc78016):
- the resonance peak is almost critically damped - the resonance peak is almost critically damped
- the passive isolation \\(\frac{x\_1}{w}\\) is not degraded at high frequencies - the passive isolation \\(\frac{x\_1}{w}\\) is not degraded at high frequencies
- the degradation of the compliance \\(\frac{x\_1}{F}\\) induced by feedback is limited at \\(\frac{1}{k\_1}\\) - the degradation of the compliance \\(\frac{x\_1}{F}\\) induced by feedback is limited at \\(\frac{1}{k\_1}\\)
- the fraction of the force transmitted to the payload that is measured by the force sensor is reduced at low frequencies - the fraction of the force transmitted to the payload that is measured by the force sensor is reduced at low frequencies
<a id="org656442f"></a> <a id="orgfc78016"></a>
{{< figure src="/ox-hugo/souleille18_tf_iff_result.png" caption="Figure 2: Matrix of transfer functions from input (w, f, F) to output (Fs, x1) in open loop (blue curves) and closed loop (dashed red curves)" >}} {{< figure src="/ox-hugo/souleille18_tf_iff_result.png" caption="Figure 2: Matrix of transfer functions from input (w, f, F) to output (Fs, x1) in open loop (blue curves) and closed loop (dashed red curves)" >}}
<a id="orgd1fa41a"></a> <a id="org86440e0"></a>
{{< figure src="/ox-hugo/souleille18_root_locus.png" caption="Figure 3: Single DoF system. Comparison between the theoretical (solid curve) and the experimental (crosses) root-locus" >}} {{< figure src="/ox-hugo/souleille18_root_locus.png" caption="Figure 3: Single DoF system. Comparison between the theoretical (solid curve) and the experimental (crosses) root-locus" >}}
## Flexible payload mounted on three isolators {#flexible-payload-mounted-on-three-isolators} ## Flexible payload mounted on three isolators {#flexible-payload-mounted-on-three-isolators}
A heavy payload is mounted on a set of three isolators (Figure [4](#org59a9fbf)). A heavy payload is mounted on a set of three isolators (Figure [4](#org2b1d225)).
The payload consists of two masses, connected through flexible blades such that the flexible resonance of the payload in the vertical direction is around 65Hz. The payload consists of two masses, connected through flexible blades such that the flexible resonance of the payload in the vertical direction is around 65Hz.
<a id="org59a9fbf"></a> <a id="org2b1d225"></a>
{{< figure src="/ox-hugo/souleille18_setup_flexible_payload.png" caption="Figure 4: Right: picture of the experimental setup. It consists of a flexible payload mounted on a set of three isolators. Left: simplified sketch of the setup, showing only the vertical direction" >}} {{< figure src="/ox-hugo/souleille18_setup_flexible_payload.png" caption="Figure 4: Right: picture of the experimental setup. It consists of a flexible payload mounted on a set of three isolators. Left: simplified sketch of the setup, showing only the vertical direction" >}}
As shown in Figure [5](#orgb30c1f0), both the suspension modes and the flexible modes of the payload can be critically damped. As shown in Figure [5](#orge25f187), both the suspension modes and the flexible modes of the payload can be critically damped.
<a id="orgb30c1f0"></a> <a id="orge25f187"></a>
{{< figure src="/ox-hugo/souleille18_result_damping_transmissibility.png" caption="Figure 5: Transmissibility between the table top \\(w\\) and \\(m\_1\\)" >}} {{< figure src="/ox-hugo/souleille18_result_damping_transmissibility.png" caption="Figure 5: Transmissibility between the table top \\(w\\) and \\(m\_1\\)" >}}
# Bibliography
<a class="bibtex-entry" id="souleille18_concep_activ_mount_space_applic">Souleille, A., Lampert, T., Lafarga, V., Hellegouarch, S., Rondineau, A., Rodrigues, Gon\ccalo, & Collette, C., *A concept of active mount for space applications*, CEAS Space Journal, *10(2)*, 157165 (2018). </a> [](#d5c1263eebe6caa1e91b078b620d72f1) ## Bibliography {#bibliography}
<a id="org91c3531"></a>Souleille, Adrien, Thibault Lampert, V Lafarga, Sylvain Hellegouarch, Alan Rondineau, Gonçalo Rodrigues, and Christophe Collette. 2018. “A Concept of Active Mount for Space Applications.” _CEAS Space Journal_ 10 (2). Springer:15765.

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@ -8,8 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}) : [Stewart Platforms]({{< relref "stewart_platforms" >}})
Reference Reference
: <sup id="85f81ff678aabc195636437548e4234a"><a class="reference-link" href="#tang18_decen_vibrat_contr_voice_coil" title="Jie Tang, Dengqing Cao \&amp; Tianhu Yu, Decentralized Vibration Control of a Voice Coil Motor-Based Stewart Parallel Mechanism: Simulation and Experiments, {Proceedings of the Institution of Mechanical Engineers, : ([Tang, Cao, and Yu 2018](#org6d9be33))
Part C: Journal of Mechanical Engineering Science}, v(1), 132-145 (2018).">(Jie Tang {\it et al.}, 2018)</a></sup>
Author(s) Author(s)
: Tang, J., Cao, D., & Yu, T. : Tang, J., Cao, D., & Yu, T.
@ -17,5 +16,7 @@ Author(s)
Year Year
: 2018 : 2018
# Bibliography
<a class="bibtex-entry" id="tang18_decen_vibrat_contr_voice_coil">Tang, J., Cao, D., & Yu, T., *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)*, 132145 (2018). http://dx.doi.org/10.1177/0954406218756941</a> [](#85f81ff678aabc195636437548e4234a) ## Bibliography {#bibliography}
<a id="org6d9be33"></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):13245. <https://doi.org/10.1177/0954406218756941>.

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@ -8,7 +8,7 @@ Tags
: [Nano Active Stabilization System]({{< relref "nano_active_stabilization_system" >}}) : [Nano Active Stabilization System]({{< relref "nano_active_stabilization_system" >}})
Reference Reference
: <sup id="1bccbe15e35ed02229afbc6528c5057e"><a class="reference-link" href="#wang12_autom_marker_full_field_hard" title="Jun Wang, Yu-chen Karen Chen, Qingxi Yuan, Andrei, Tkachuk, Can Erdonmez, Benjamin Hornberger, Michael \&amp; Feser, Automated Markerless Full Field Hard X-Ray Microscopic Tomography At Sub-50 Nm 3-dimension Spatial Resolution, {Applied Physics Letters}, v(14), 143107 (2012).">(Jun Wang {\it et al.}, 2012)</a></sup> : ([Wang et al. 2012](#org72cf603))
Author(s) Author(s)
: Wang, J., Chen, Y. K., Yuan, Q., Tkachuk, A., Erdonmez, C., Hornberger, B., & Feser, M. : Wang, J., Chen, Y. K., Yuan, Q., Tkachuk, A., Erdonmez, C., Hornberger, B., & Feser, M.
@ -25,5 +25,7 @@ There is a need for markerless nano-tomography
**Passive rotational run-out error system**: **Passive rotational run-out error system**:
It uses calibrated metrology disc and capacitive sensors It uses calibrated metrology disc and capacitive sensors
# Bibliography
<a class="bibtex-entry" id="wang12_autom_marker_full_field_hard">Wang, J., Chen, Y. K., Yuan, Q., Tkachuk, A., Erdonmez, C., Hornberger, B., & Feser, M., *Automated markerless full field hard x-ray microscopic tomography at sub-50 nm 3-dimension spatial resolution*, Applied Physics Letters, *100(14)*, 143107 (2012). http://dx.doi.org/10.1063/1.3701579</a> [](#1bccbe15e35ed02229afbc6528c5057e) ## Bibliography {#bibliography}
<a id="org72cf603"></a>Wang, Jun, Yu-chen Karen Chen, Qingxi Yuan, Andrei Tkachuk, Can Erdonmez, Benjamin Hornberger, and Michael Feser. 2012. “Automated Markerless Full Field Hard X-Ray Microscopic Tomography at Sub-50 Nm 3-Dimension Spatial Resolution.” _Applied Physics Letters_ 100 (14):143107. <https://doi.org/10.1063/1.3701579>.

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@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Flexible Joints]({{< relref "flexible_joints" >}}) : [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference Reference
: <sup id="db95fac7cd46c14e2b4f38e8ca4158fe"><a class="reference-link" href="#wang16_inves_activ_vibrat_isolat_stewar" title="Wang, Xie, Chen, Zhang \&amp; Zhiyi, Investigation on Active Vibration Isolation of a Stewart Platform With Piezoelectric Actuators, {Journal of Sound and Vibration}, v(), 1-19 (2016).">(Wang {\it et al.}, 2016)</a></sup> : ([Wang et al. 2016](#org22df838))
Author(s) Author(s)
: Wang, C., Xie, X., Chen, Y., & Zhang, Z. : Wang, C., Xie, X., Chen, Y., & Zhang, Z.
@ -25,7 +25,7 @@ Year
The model is compared with a Finite Element model and is shown to give the same results. The model is compared with a Finite Element model and is shown to give the same results.
The proposed model is thus effective. The proposed model is thus effective.
<a id="orgd3fa417"></a> <a id="org0dd5327"></a>
{{< figure src="/ox-hugo/wang16_stewart_platform.png" caption="Figure 1: Stewart Platform" >}} {{< figure src="/ox-hugo/wang16_stewart_platform.png" caption="Figure 1: Stewart Platform" >}}
@ -35,11 +35,11 @@ Combines:
- the FxLMS-based adaptive inverse control => suppress transmission of periodic vibrations - the FxLMS-based adaptive inverse control => suppress transmission of periodic vibrations
- direct feedback of integrated forces => dampen vibration of inherent modes and thus reduce random vibrations - direct feedback of integrated forces => dampen vibration of inherent modes and thus reduce random vibrations
Force Feedback (Figure [2](#org55d173d)). Force Feedback (Figure [2](#org0b0c9ed)).
- the force sensor is mounted **between the base and the strut** - the force sensor is mounted **between the base and the strut**
<a id="org55d173d"></a> <a id="org0b0c9ed"></a>
{{< figure src="/ox-hugo/wang16_force_feedback.png" caption="Figure 2: Feedback of integrated forces in the platform" >}} {{< figure src="/ox-hugo/wang16_force_feedback.png" caption="Figure 2: Feedback of integrated forces in the platform" >}}
@ -53,5 +53,7 @@ Sorts of HAC-LAC control:
- All 6 transfer function from actuator force to force sensors are almost the same (gain offset) - All 6 transfer function from actuator force to force sensors are almost the same (gain offset)
- Effectiveness of control methods are shown - Effectiveness of control methods are shown
# Bibliography
<a class="bibtex-entry" id="wang16_inves_activ_vibrat_isolat_stewar">Wang, C., Xie, X., Chen, Y., & Zhang, Z., *Investigation on active vibration isolation of a stewart platform with piezoelectric actuators*, Journal of Sound and Vibration, *383()*, 119 (2016). http://dx.doi.org/10.1016/j.jsv.2016.07.021</a> [](#db95fac7cd46c14e2b4f38e8ca4158fe) ## Bibliography {#bibliography}
<a id="org22df838"></a>Wang, Chaoxin, Xiling Xie, Yanhao Chen, and Zhiyi Zhang. 2016. “Investigation on Active Vibration Isolation of a Stewart Platform with Piezoelectric Actuators.” _Journal of Sound and Vibration_ 383 (November). Elsevier BV:119. <https://doi.org/10.1016/j.jsv.2016.07.021>.

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@ -9,7 +9,7 @@ Tags
Reference Reference
: <sup id="44caf201a37b1b3af63de65257785085"><a class="reference-link" href="#yun20_inves_two_stage_vibrat_suppr" title="Hai Yun, Lei Liu, Qing Li \&amp; Hongjie Yang, Investigation on Two-Stage Vibration Suppression and Precision Pointing for Space Optical Payloads, {Aerospace Science and Technology}, v(nil), 105543 (2020).">(Hai Yun {\it et al.}, 2020)</a></sup> : ([Yun et al. 2020](#org63dfd15))
Author(s) Author(s)
: Yun, H., Liu, L., Li, Q., & Yang, H. : Yun, H., Liu, L., Li, Q., & Yang, H.
@ -17,5 +17,7 @@ Author(s)
Year Year
: 2020 : 2020
# Bibliography
<a class="bibtex-entry" id="yun20_inves_two_stage_vibrat_suppr">Yun, H., Liu, L., Li, Q., & Yang, H., *Investigation on two-stage vibration suppression and precision pointing for space optical payloads*, Aerospace Science and Technology, *96(nil)*, 105543 (2020). http://dx.doi.org/10.1016/j.ast.2019.105543</a> [](#44caf201a37b1b3af63de65257785085) ## Bibliography {#bibliography}
<a id="org63dfd15"></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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@ -8,7 +8,7 @@ Tags
: [Vibration Isolation]({{< relref "vibration_isolation" >}}) : [Vibration Isolation]({{< relref "vibration_isolation" >}})
Reference Reference
: <sup id="e9037e3bf20089c45ab77215406558ca"><a class="reference-link" href="#zuo04_elemen_system_desig_activ_passiv_vibrat_isolat" title="Zuo, Element and System Design for Active and Passive Vibration Isolation (2004).">(Zuo, 2004)</a></sup> : ([Zuo 2004](#org21a244a))
Author(s) Author(s)
: Zuo, L. : Zuo, L.
@ -26,21 +26,23 @@ Year
> They found that coupling from flexible modes is much smaller than in soft active mounts in the load (force) feedback. > 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. > Note that reaction force actuators can also work with soft mounts or hard mounts.
<a id="org0286cf1"></a> <a id="org813c7b5"></a>
{{< figure src="/ox-hugo/zuo04_piezo_spring_series.png" caption="Figure 1: PZT actuator and spring in series" >}} {{< figure src="/ox-hugo/zuo04_piezo_spring_series.png" caption="Figure 1: PZT actuator and spring in series" >}}
<a id="org679f77c"></a> <a id="orgb0453c3"></a>
{{< figure src="/ox-hugo/zuo04_voice_coil_spring_parallel.png" caption="Figure 2: Voice coil actuator and spring in parallel" >}} {{< figure src="/ox-hugo/zuo04_voice_coil_spring_parallel.png" caption="Figure 2: Voice coil actuator and spring in parallel" >}}
<a id="orged24ee6"></a> <a id="orgc0f3c0e"></a>
{{< figure src="/ox-hugo/zuo04_piezo_plant.png" caption="Figure 3: Transmission from PZT voltage to geophone output" >}} {{< figure src="/ox-hugo/zuo04_piezo_plant.png" caption="Figure 3: Transmission from PZT voltage to geophone output" >}}
<a id="org9b75d10"></a> <a id="org0739a0f"></a>
{{< figure src="/ox-hugo/zuo04_voice_coil_plant.png" caption="Figure 4: Transmission from voice coil voltage to geophone output" >}} {{< figure src="/ox-hugo/zuo04_voice_coil_plant.png" caption="Figure 4: Transmission from voice coil voltage to geophone output" >}}
# Bibliography
<a class="bibtex-entry" id="zuo04_elemen_system_desig_activ_passiv_vibrat_isolat">Zuo, L., *Element and system design for active and passive vibration isolation* (2004). Massachusetts Institute of Technology.</a> [](#e9037e3bf20089c45ab77215406558ca) ## Bibliography {#bibliography}
<a id="org21a244a"></a>Zuo, Lei. 2004. “Element and System Design for Active and Passive Vibration Isolation.” Massachusetts Institute of Technology.

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@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}) : [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}})
Reference Reference
: <sup id="1d38bd128d92142dd456ab4e9bb4eb84"><a href="#du10_model_contr_vibrat_mechan_system" title="Chunling Du \&amp; Lihua Xie, Modeling and Control of Vibration in Mechanical Systems, CRC Press (2010).">(Chunling Du \& Lihua Xie, 2010)</a></sup> : ([Du and Xie 2010](#org31ab1b9))
Author(s) Author(s)
: Du, C., & Xie, L. : Du, C., & Xie, L.
@ -18,5 +18,7 @@ Year
Read Chapter 1 and 3. Read Chapter 1 and 3.
# Bibliography
<a id="du10_model_contr_vibrat_mechan_system"></a>Du, C., & Xie, L., *Modeling and control of vibration in mechanical systems* (2010), : CRC Press. [](#1d38bd128d92142dd456ab4e9bb4eb84) ## Bibliography {#bibliography}
<a id="org31ab1b9"></a>Du, Chunling, and Lihua Xie. 2010. _Modeling and Control of Vibration in Mechanical Systems_. Automation and Control Engineering. CRC Press. <https://doi.org/10.1201/9781439817995>.

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@ -5,10 +5,10 @@ draft = false
+++ +++
Tags Tags
: [System Identification]({{< relref "system_identification" >}}), [Reference Books]({{< relref "reference_books" >}}) : [System Identification]({{< relref "system_identification" >}}), [Reference Books]({{< relref "reference_books" >}}), [Modal Analysis]({{< relref "modal_analysis" >}})
Reference Reference
: ([Ewins 2000](#org84d73f8)) : ([Ewins 2000](#org57f8bf9))
Author(s) Author(s)
: Ewins, D. : Ewins, D.
@ -141,7 +141,7 @@ The main measurement technique studied are those which will permit to make **dir
The type of test best suited to FRF measurement is shown in figure [fig:modal_analysis_schematic](#fig:modal_analysis_schematic). The type of test best suited to FRF measurement is shown in figure [fig:modal_analysis_schematic](#fig:modal_analysis_schematic).
<a id="orga193754"></a> <a id="org0b82329"></a>
{{< figure src="/ox-hugo/ewins00_modal_analysis_schematic.png" caption="Figure 1: Basic components of FRF measurement system" >}} {{< figure src="/ox-hugo/ewins00_modal_analysis_schematic.png" caption="Figure 1: Basic components of FRF measurement system" >}}
@ -215,7 +215,7 @@ This assumption allows us to use the circular nature of a modulus/phase polar pl
This process can be **repeated** for each resonance individually until the whole curve has been analyzed. This process can be **repeated** for each resonance individually until the whole curve has been analyzed.
At this stage, a theoretical regeneration of the FRF is possible using the set of coefficients extracted. At this stage, a theoretical regeneration of the FRF is possible using the set of coefficients extracted.
<a id="org37e66c2"></a> <a id="org8ff4e51"></a>
{{< figure src="/ox-hugo/ewins00_sdof_modulus_phase.png" caption="Figure 2: Curve fit to resonant FRF data" >}} {{< figure src="/ox-hugo/ewins00_sdof_modulus_phase.png" caption="Figure 2: Curve fit to resonant FRF data" >}}
@ -253,7 +253,7 @@ Theoretical foundations of modal testing are of paramount importance to its succ
The three phases through a typical theoretical vibration analysis progresses are shown on figure [fig:vibration_analysis_procedure](#fig:vibration_analysis_procedure). The three phases through a typical theoretical vibration analysis progresses are shown on figure [fig:vibration_analysis_procedure](#fig:vibration_analysis_procedure).
Generally, we start with a description of the structure's physical characteristics (mass, stiffness and damping properties), this is referred to as the **Spatial model**. Generally, we start with a description of the structure's physical characteristics (mass, stiffness and damping properties), this is referred to as the **Spatial model**.
<a id="org00d3f58"></a> <a id="org4cdbdfc"></a>
{{< figure src="/ox-hugo/ewins00_vibration_analysis_procedure.png" caption="Figure 3: Theoretical route to vibration analysis" >}} {{< figure src="/ox-hugo/ewins00_vibration_analysis_procedure.png" caption="Figure 3: Theoretical route to vibration analysis" >}}
@ -298,7 +298,7 @@ Three classes of system model will be described:
The basic model for the SDOF system is shown in figure [fig:sdof_model](#fig:sdof_model) where \\(f(t)\\) and \\(x(t)\\) are general time-varying force and displacement response quantities. The basic model for the SDOF system is shown in figure [fig:sdof_model](#fig:sdof_model) where \\(f(t)\\) and \\(x(t)\\) are general time-varying force and displacement response quantities.
The spatial model consists of a **mass** \\(m\\), a **spring** \\(k\\) and (when damped) either a **viscous dashpot** \\(c\\) or **hysteretic damper** \\(d\\). The spatial model consists of a **mass** \\(m\\), a **spring** \\(k\\) and (when damped) either a **viscous dashpot** \\(c\\) or **hysteretic damper** \\(d\\).
<a id="org470c5bf"></a> <a id="orga199d06"></a>
{{< figure src="/ox-hugo/ewins00_sdof_model.png" caption="Figure 4: Single degree-of-freedom system" >}} {{< figure src="/ox-hugo/ewins00_sdof_model.png" caption="Figure 4: Single degree-of-freedom system" >}}
@ -374,7 +374,7 @@ which is a single mode of vibration with a complex natural frequency having two
The physical significance of these two parts is illustrated in the typical free response plot shown in figure [fig:sdof_response](#fig:sdof_response) The physical significance of these two parts is illustrated in the typical free response plot shown in figure [fig:sdof_response](#fig:sdof_response)
<a id="org169b90c"></a> <a id="org8c327c7"></a>
{{< figure src="/ox-hugo/ewins00_sdof_response.png" caption="Figure 5: Oscillatory and decay part" >}} {{< figure src="/ox-hugo/ewins00_sdof_response.png" caption="Figure 5: Oscillatory and decay part" >}}
@ -418,7 +418,7 @@ The damping effect of such a component can conveniently be defined by the ratio
| ![](/ox-hugo/ewins00_material_histeresis.png) | ![](/ox-hugo/ewins00_dry_friction.png) | ![](/ox-hugo/ewins00_viscous_damper.png) | | ![](/ox-hugo/ewins00_material_histeresis.png) | ![](/ox-hugo/ewins00_dry_friction.png) | ![](/ox-hugo/ewins00_viscous_damper.png) |
|-----------------------------------------------|----------------------------------------|------------------------------------------| |-----------------------------------------------|----------------------------------------|------------------------------------------|
| <a id="orgb3a7b8e"></a> Material hysteresis | <a id="org68fe7c2"></a> Dry friction | <a id="org03c75ad"></a> Viscous damper | | <a id="org30686c0"></a> Material hysteresis | <a id="org151c775"></a> Dry friction | <a id="org45c6c45"></a> Viscous damper |
| height=2cm | height=2cm | height=2cm | | height=2cm | height=2cm | height=2cm |
Another common source of energy dissipation in practical structures, is the **friction** which exist in joints between components of the structure. Another common source of energy dissipation in practical structures, is the **friction** which exist in joints between components of the structure.
@ -537,7 +537,7 @@ Bode plot are usually displayed using logarithmic scales as shown on figure [fig
| ![](/ox-hugo/ewins00_bode_receptance.png) | ![](/ox-hugo/ewins00_bode_mobility.png) | ![](/ox-hugo/ewins00_bode_accelerance.png) | | ![](/ox-hugo/ewins00_bode_receptance.png) | ![](/ox-hugo/ewins00_bode_mobility.png) | ![](/ox-hugo/ewins00_bode_accelerance.png) |
|-------------------------------------------|-----------------------------------------|--------------------------------------------| |-------------------------------------------|-----------------------------------------|--------------------------------------------|
| <a id="org4673396"></a> Receptance FRF | <a id="org9f41af5"></a> Mobility FRF | <a id="org6696bcf"></a> Accelerance FRF | | <a id="org17728b2"></a> Receptance FRF | <a id="org90cee96"></a> Mobility FRF | <a id="orge43a020"></a> Accelerance FRF |
| width=\linewidth | width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth | width=\linewidth |
Each plot can be divided into three regimes: Each plot can be divided into three regimes:
@ -560,7 +560,7 @@ This type of display is not widely used as we cannot use logarithmic axes (as we
| ![](/ox-hugo/ewins00_plot_receptance_real.png) | ![](/ox-hugo/ewins00_plot_receptance_imag.png) | | ![](/ox-hugo/ewins00_plot_receptance_real.png) | ![](/ox-hugo/ewins00_plot_receptance_imag.png) |
|------------------------------------------------|------------------------------------------------| |------------------------------------------------|------------------------------------------------|
| <a id="org66926ef"></a> Real part | <a id="orgaf2afdd"></a> Imaginary part | | <a id="org3aaddc5"></a> Real part | <a id="orgfd7fd7d"></a> Imaginary part |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
@ -578,7 +578,7 @@ Figure [fig:inverse_frf_mixed](#fig:inverse_frf_mixed) shows an example of a plo
| ![](/ox-hugo/ewins00_inverse_frf_mixed.png) | ![](/ox-hugo/ewins00_inverse_frf_viscous.png) | | ![](/ox-hugo/ewins00_inverse_frf_mixed.png) | ![](/ox-hugo/ewins00_inverse_frf_viscous.png) |
|---------------------------------------------|-----------------------------------------------| |---------------------------------------------|-----------------------------------------------|
| <a id="org84ad953"></a> Mixed | <a id="orgc18e658"></a> Viscous | | <a id="orgeb3ce3c"></a> Mixed | <a id="org8418622"></a> Viscous |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
@ -595,7 +595,7 @@ The missing information (in this case, the frequency) must be added by identifyi
| ![](/ox-hugo/ewins00_nyquist_receptance_viscous.png) | ![](/ox-hugo/ewins00_nyquist_receptance_structural.png) | | ![](/ox-hugo/ewins00_nyquist_receptance_viscous.png) | ![](/ox-hugo/ewins00_nyquist_receptance_structural.png) |
|------------------------------------------------------|---------------------------------------------------------| |------------------------------------------------------|---------------------------------------------------------|
| <a id="orgfee48c0"></a> Viscous damping | <a id="org41c7d29"></a> Structural damping | | <a id="orgef2e4cd"></a> Viscous damping | <a id="orgd4187e9"></a> Structural damping |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
The Nyquist plot has the particularity of distorting the plot so as to focus on the resonance area. The Nyquist plot has the particularity of distorting the plot so as to focus on the resonance area.
@ -1103,7 +1103,7 @@ Equally, in a real mode, all parts of the structure pass through their **zero de
While the real mode has the appearance of a **standing wave**, the complex mode is better described as exhibiting **traveling waves** (illustrated on figure [fig:real_complex_modes](#fig:real_complex_modes)). While the real mode has the appearance of a **standing wave**, the complex mode is better described as exhibiting **traveling waves** (illustrated on figure [fig:real_complex_modes](#fig:real_complex_modes)).
<a id="org05c0f39"></a> <a id="org0991bf9"></a>
{{< figure src="/ox-hugo/ewins00_real_complex_modes.png" caption="Figure 6: Real and complex mode shapes displays" >}} {{< figure src="/ox-hugo/ewins00_real_complex_modes.png" caption="Figure 6: Real and complex mode shapes displays" >}}
@ -1118,7 +1118,7 @@ Note that the almost-real mode shape does not necessarily have vector elements w
| ![](/ox-hugo/ewins00_argand_diagram_a.png) | ![](/ox-hugo/ewins00_argand_diagram_b.png) | ![](/ox-hugo/ewins00_argand_diagram_c.png) | | ![](/ox-hugo/ewins00_argand_diagram_a.png) | ![](/ox-hugo/ewins00_argand_diagram_b.png) | ![](/ox-hugo/ewins00_argand_diagram_c.png) |
|--------------------------------------------|--------------------------------------------|-----------------------------------------------| |--------------------------------------------|--------------------------------------------|-----------------------------------------------|
| <a id="orgc7a8526"></a> Almost-real mode | <a id="orgcd8be0a"></a> Complex Mode | <a id="orgf34a135"></a> Measure of complexity | | <a id="org193debd"></a> Almost-real mode | <a id="org69bb630"></a> Complex Mode | <a id="org3bb718c"></a> Measure of complexity |
| width=\linewidth | width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth | width=\linewidth |
@ -1235,7 +1235,7 @@ On a logarithmic plot, this produces the antiresonance characteristic which refl
| ![](/ox-hugo/ewins00_mobility_frf_mdof_point.png) | ![](/ox-hugo/ewins00_mobility_frf_mdof_transfer.png) | | ![](/ox-hugo/ewins00_mobility_frf_mdof_point.png) | ![](/ox-hugo/ewins00_mobility_frf_mdof_transfer.png) |
|---------------------------------------------------|------------------------------------------------------| |---------------------------------------------------|------------------------------------------------------|
| <a id="org04908dc"></a> Point FRF | <a id="orgc9e36d0"></a> Transfer FRF | | <a id="org06f37e2"></a> Point FRF | <a id="orgdc266be"></a> Transfer FRF |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
For the plot in figure [fig:mobility_frf_mdof_transfer](#fig:mobility_frf_mdof_transfer), between the two resonances, the two components have the same sign and they add up, no antiresonance is present. For the plot in figure [fig:mobility_frf_mdof_transfer](#fig:mobility_frf_mdof_transfer), between the two resonances, the two components have the same sign and they add up, no antiresonance is present.
@ -1260,7 +1260,7 @@ Most mobility plots have this general form as long as the modes are relatively w
This condition is satisfied unless the separation between adjacent natural frequencies is of the same order as, or less than, the modal damping factors, in which case it becomes difficult to distinguish the individual modes. This condition is satisfied unless the separation between adjacent natural frequencies is of the same order as, or less than, the modal damping factors, in which case it becomes difficult to distinguish the individual modes.
<a id="org3342d4f"></a> <a id="orgd2ab4ee"></a>
{{< figure src="/ox-hugo/ewins00_frf_damped_system.png" caption="Figure 7: Mobility plot of a damped system" >}} {{< figure src="/ox-hugo/ewins00_frf_damped_system.png" caption="Figure 7: Mobility plot of a damped system" >}}
@ -1281,7 +1281,7 @@ The plot for the transfer receptance \\(\alpha\_{21}\\) is presented in figure [
| ![](/ox-hugo/ewins00_nyquist_point.png) | ![](/ox-hugo/ewins00_nyquist_transfer.png) | | ![](/ox-hugo/ewins00_nyquist_point.png) | ![](/ox-hugo/ewins00_nyquist_transfer.png) |
|------------------------------------------|---------------------------------------------| |------------------------------------------|---------------------------------------------|
| <a id="org51d6859"></a> Point receptance | <a id="org49ad44a"></a> Transfer receptance | | <a id="org2814a00"></a> Point receptance | <a id="org000b88d"></a> Transfer receptance |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
In the two figures [fig:nyquist_nonpropdamp_point](#fig:nyquist_nonpropdamp_point) and [fig:nyquist_nonpropdamp_transfer](#fig:nyquist_nonpropdamp_transfer), we show corresponding data for **non-proportional** damping. In the two figures [fig:nyquist_nonpropdamp_point](#fig:nyquist_nonpropdamp_point) and [fig:nyquist_nonpropdamp_transfer](#fig:nyquist_nonpropdamp_transfer), we show corresponding data for **non-proportional** damping.
@ -1296,7 +1296,7 @@ Now we find that the individual modal circles are no longer "upright" but are **
| ![](/ox-hugo/ewins00_nyquist_nonpropdamp_point.png) | ![](/ox-hugo/ewins00_nyquist_nonpropdamp_transfer.png) | | ![](/ox-hugo/ewins00_nyquist_nonpropdamp_point.png) | ![](/ox-hugo/ewins00_nyquist_nonpropdamp_transfer.png) |
|-----------------------------------------------------|--------------------------------------------------------| |-----------------------------------------------------|--------------------------------------------------------|
| <a id="orgbc84787"></a> Point receptance | <a id="org1fde70c"></a> Transfer receptance | | <a id="orge62d92d"></a> Point receptance | <a id="orgaaeb314"></a> Transfer receptance |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
@ -1450,7 +1450,7 @@ Examples of random signals, autocorrelation function and power spectral density
| ![](/ox-hugo/ewins00_random_time.png) | ![](/ox-hugo/ewins00_random_autocorrelation.png) | ![](/ox-hugo/ewins00_random_psd.png) | | ![](/ox-hugo/ewins00_random_time.png) | ![](/ox-hugo/ewins00_random_autocorrelation.png) | ![](/ox-hugo/ewins00_random_psd.png) |
|---------------------------------------|--------------------------------------------------|------------------------------------------------| |---------------------------------------|--------------------------------------------------|------------------------------------------------|
| <a id="org9b223d2"></a> Time history | <a id="orgf89ee65"></a> Autocorrelation Function | <a id="org839a4fd"></a> Power Spectral Density | | <a id="org73b51a5"></a> Time history | <a id="org29b2840"></a> Autocorrelation Function | <a id="orgb8db3ea"></a> Power Spectral Density |
| width=\linewidth | width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth | width=\linewidth |
A similar concept can be applied to a pair of functions such as \\(f(t)\\) and \\(x(t)\\) to produce **cross correlation** and **cross spectral density** functions. A similar concept can be applied to a pair of functions such as \\(f(t)\\) and \\(x(t)\\) to produce **cross correlation** and **cross spectral density** functions.
@ -1547,7 +1547,7 @@ Then in [fig:frf_feedback_model](#fig:frf_feedback_model) is given a more detail
| ![](/ox-hugo/ewins00_frf_siso_model.png) | ![](/ox-hugo/ewins00_frf_feedback_model.png) | | ![](/ox-hugo/ewins00_frf_siso_model.png) | ![](/ox-hugo/ewins00_frf_feedback_model.png) |
|------------------------------------------|--------------------------------------------------| |------------------------------------------|--------------------------------------------------|
| <a id="orgf9a7bf7"></a> Basic SISO model | <a id="org258a6e2"></a> SISO model with feedback | | <a id="orgf32d3c7"></a> Basic SISO model | <a id="org56469a4"></a> SISO model with feedback |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
In this configuration, it can be seen that there are two feedback mechanisms which apply. In this configuration, it can be seen that there are two feedback mechanisms which apply.
@ -1580,7 +1580,7 @@ We obtain two alternative formulas:
In practical application of both of these formulae, care must be taken to ensure the non-singularity of the spectral density matrix which is to be inverted, and it is in this respect that the former version may be found to be more reliable. In practical application of both of these formulae, care must be taken to ensure the non-singularity of the spectral density matrix which is to be inverted, and it is in this respect that the former version may be found to be more reliable.
<a id="org00c19fd"></a> <a id="orgf429f5f"></a>
{{< figure src="/ox-hugo/ewins00_frf_mimo.png" caption="Figure 8: System for FRF determination via MIMO model" >}} {{< figure src="/ox-hugo/ewins00_frf_mimo.png" caption="Figure 8: System for FRF determination via MIMO model" >}}
@ -1852,7 +1852,7 @@ The experimental setup used for mobility measurement contains three major items:
A typical layout for the measurement system is shown on figure [fig:general_frf_measurement_setup](#fig:general_frf_measurement_setup). A typical layout for the measurement system is shown on figure [fig:general_frf_measurement_setup](#fig:general_frf_measurement_setup).
<a id="org76e9cb0"></a> <a id="orga0fe90a"></a>
{{< figure src="/ox-hugo/ewins00_general_frf_measurement_setup.png" caption="Figure 9: General layout of FRF measurement system" >}} {{< figure src="/ox-hugo/ewins00_general_frf_measurement_setup.png" caption="Figure 9: General layout of FRF measurement system" >}}
@ -1909,7 +1909,7 @@ This can modify the response of the system in those directions.
In order to avoid that, a drive rod which is stiff in one direction and flexible in the other five directions is attached between the shaker and the structure as shown on figure [fig:shaker_rod](#fig:shaker_rod). In order to avoid that, a drive rod which is stiff in one direction and flexible in the other five directions is attached between the shaker and the structure as shown on figure [fig:shaker_rod](#fig:shaker_rod).
Typical size for the rod are \\(5\\) to \\(\SI{10}{mm}\\) long and \\(\SI{1}{mm}\\) in diameter, if the rod is longer, it may introduce the effect of its own resonances. Typical size for the rod are \\(5\\) to \\(\SI{10}{mm}\\) long and \\(\SI{1}{mm}\\) in diameter, if the rod is longer, it may introduce the effect of its own resonances.
<a id="orga841e57"></a> <a id="org1ae0c38"></a>
{{< figure src="/ox-hugo/ewins00_shaker_rod.png" caption="Figure 10: Exciter attachment and drive rod assembly" >}} {{< figure src="/ox-hugo/ewins00_shaker_rod.png" caption="Figure 10: Exciter attachment and drive rod assembly" >}}
@ -1930,7 +1930,7 @@ Figure [fig:shaker_mount_3](#fig:shaker_mount_3) shows an unsatisfactory setup.
| ![](/ox-hugo/ewins00_shaker_mount_1.png) | ![](/ox-hugo/ewins00_shaker_mount_2.png) | ![](/ox-hugo/ewins00_shaker_mount_3.png) | | ![](/ox-hugo/ewins00_shaker_mount_1.png) | ![](/ox-hugo/ewins00_shaker_mount_2.png) | ![](/ox-hugo/ewins00_shaker_mount_3.png) |
|---------------------------------------------|-------------------------------------------------|------------------------------------------| |---------------------------------------------|-------------------------------------------------|------------------------------------------|
| <a id="org5ad1e59"></a> Ideal Configuration | <a id="orge10385d"></a> Suspended Configuration | <a id="orgf027a3a"></a> Unsatisfactory | | <a id="orgda674d1"></a> Ideal Configuration | <a id="orgc2ebc7e"></a> Suspended Configuration | <a id="org91922e6"></a> Unsatisfactory |
| width=\linewidth | width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth | width=\linewidth |
@ -1948,7 +1948,7 @@ The frequency range which is effectively excited is controlled by the stiffness
When the hammer tip impacts the test structure, this will experience a force pulse as shown on figure [fig:hammer_impulse](#fig:hammer_impulse). When the hammer tip impacts the test structure, this will experience a force pulse as shown on figure [fig:hammer_impulse](#fig:hammer_impulse).
A pulse of this type (half-sine shape) has a frequency content of the form illustrated on figure [fig:hammer_impulse](#fig:hammer_impulse). A pulse of this type (half-sine shape) has a frequency content of the form illustrated on figure [fig:hammer_impulse](#fig:hammer_impulse).
<a id="org1e8111f"></a> <a id="orgfae6204"></a>
{{< figure src="/ox-hugo/ewins00_hammer_impulse.png" caption="Figure 11: Typical impact force pulse and spectrum" >}} {{< figure src="/ox-hugo/ewins00_hammer_impulse.png" caption="Figure 11: Typical impact force pulse and spectrum" >}}
@ -1979,7 +1979,7 @@ By suitable design, such a material may be incorporated into a device which **in
The force transducer is the simplest type of piezoelectric transducer. The force transducer is the simplest type of piezoelectric transducer.
The transmitter force \\(F\\) is applied directly across the crystal, which thus generates a corresponding charge \\(q\\), proportional to \\(F\\) (figure [fig:piezo_force_transducer](#fig:piezo_force_transducer)). The transmitter force \\(F\\) is applied directly across the crystal, which thus generates a corresponding charge \\(q\\), proportional to \\(F\\) (figure [fig:piezo_force_transducer](#fig:piezo_force_transducer)).
<a id="orge942cb7"></a> <a id="org63f47b9"></a>
{{< figure src="/ox-hugo/ewins00_piezo_force_transducer.png" caption="Figure 12: Force transducer" >}} {{< figure src="/ox-hugo/ewins00_piezo_force_transducer.png" caption="Figure 12: Force transducer" >}}
@ -1992,7 +1992,7 @@ In an accelerometer, transduction is indirect and is achieved using a seismic ma
In this configuration, the force exerted on the crystals is the inertia force of the seismic mass (\\(m\ddot{z}\\)). In this configuration, the force exerted on the crystals is the inertia force of the seismic mass (\\(m\ddot{z}\\)).
Thus, so long as the body and the seismic mass move together, the output of the transducer will be proportional to the acceleration of its body \\(x\\). Thus, so long as the body and the seismic mass move together, the output of the transducer will be proportional to the acceleration of its body \\(x\\).
<a id="orged1c285"></a> <a id="org34a2291"></a>
{{< figure src="/ox-hugo/ewins00_piezo_accelerometer.png" caption="Figure 13: Compression-type of piezoelectric accelerometer" >}} {{< figure src="/ox-hugo/ewins00_piezo_accelerometer.png" caption="Figure 13: Compression-type of piezoelectric accelerometer" >}}
@ -2040,7 +2040,7 @@ Shown on figure [fig:transducer_mounting_response](#fig:transducer_mounting_resp
| ![](/ox-hugo/ewins00_transducer_mounting_types.png) | ![](/ox-hugo/ewins00_transducer_mounting_response.png) | | ![](/ox-hugo/ewins00_transducer_mounting_types.png) | ![](/ox-hugo/ewins00_transducer_mounting_response.png) |
|-----------------------------------------------------|------------------------------------------------------------| |-----------------------------------------------------|------------------------------------------------------------|
| <a id="org7c446c6"></a> Attachment methods | <a id="org9920b7a"></a> Frequency response characteristics | | <a id="org4f8e7e0"></a> Attachment methods | <a id="orga55d5b4"></a> Frequency response characteristics |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
@ -2127,7 +2127,7 @@ Aliasing originates from the discretisation of the originally continuous time hi
With this discretisation process, the **existence of very high frequencies in the original signal may well be misinterpreted if the sampling rate is too slow**. With this discretisation process, the **existence of very high frequencies in the original signal may well be misinterpreted if the sampling rate is too slow**.
These high frequencies will be **indistinguishable** from genuine low frequency components as shown on figure [fig:aliasing](#fig:aliasing). These high frequencies will be **indistinguishable** from genuine low frequency components as shown on figure [fig:aliasing](#fig:aliasing).
<a id="orgd434c7d"></a> <a id="orgffd8935"></a>
{{< figure src="/ox-hugo/ewins00_aliasing.png" caption="Figure 14: The phenomenon of aliasing. On top: Low-frequency signal, On the bottom: High frequency signal" >}} {{< figure src="/ox-hugo/ewins00_aliasing.png" caption="Figure 14: The phenomenon of aliasing. On top: Low-frequency signal, On the bottom: High frequency signal" >}}
@ -2144,7 +2144,7 @@ This is illustrated on figure [fig:effect_aliasing](#fig:effect_aliasing).
| ![](/ox-hugo/ewins00_aliasing_no_distortion.png) | ![](/ox-hugo/ewins00_aliasing_distortion.png) | | ![](/ox-hugo/ewins00_aliasing_no_distortion.png) | ![](/ox-hugo/ewins00_aliasing_distortion.png) |
|--------------------------------------------------|-----------------------------------------------------| |--------------------------------------------------|-----------------------------------------------------|
| <a id="org6412686"></a> True spectrum of signal | <a id="orgd099bc4"></a> Indicated spectrum from DFT | | <a id="orga51438f"></a> True spectrum of signal | <a id="org2e9d2ef"></a> Indicated spectrum from DFT |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
The solution of the problem is to use an **anti-aliasing filter** which subjects the original time signal to a low-pass, sharp cut-off filter. The solution of the problem is to use an **anti-aliasing filter** which subjects the original time signal to a low-pass, sharp cut-off filter.
@ -2165,7 +2165,7 @@ Leakage is a problem which is a direct **consequence of the need to take only a
| ![](/ox-hugo/ewins00_leakage_ok.png) | ![](/ox-hugo/ewins00_leakage_nok.png) | | ![](/ox-hugo/ewins00_leakage_ok.png) | ![](/ox-hugo/ewins00_leakage_nok.png) |
|--------------------------------------|----------------------------------------| |--------------------------------------|----------------------------------------|
| <a id="org18c664c"></a> Ideal signal | <a id="org71abe57"></a> Awkward signal | | <a id="org86baf6e"></a> Ideal signal | <a id="orge49931c"></a> Awkward signal |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
The problem is illustrated on figure [fig:leakage](#fig:leakage). The problem is illustrated on figure [fig:leakage](#fig:leakage).
@ -2190,7 +2190,7 @@ Windowing involves the imposition of a prescribed profile on the time signal pri
The profiles, or "windows" are generally depicted as a time function \\(w(t)\\) as shown in figure [fig:windowing_examples](#fig:windowing_examples). The profiles, or "windows" are generally depicted as a time function \\(w(t)\\) as shown in figure [fig:windowing_examples](#fig:windowing_examples).
<a id="org4e17829"></a> <a id="org4354099"></a>
{{< figure src="/ox-hugo/ewins00_windowing_examples.png" caption="Figure 15: Different types of window. (a) Boxcar, (b) Hanning, (c) Cosine-taper, (d) Exponential" >}} {{< figure src="/ox-hugo/ewins00_windowing_examples.png" caption="Figure 15: Different types of window. (a) Boxcar, (b) Hanning, (c) Cosine-taper, (d) Exponential" >}}
@ -2211,7 +2211,7 @@ Common filters are: low-pass, high-pass, band-limited, narrow-band, notch.
#### Improving Resolution {#improving-resolution} #### Improving Resolution {#improving-resolution}
<a id="orgc547d0b"></a> <a id="orgde35ed6"></a>
##### Increasing transform size {#increasing-transform-size} ##### Increasing transform size {#increasing-transform-size}
@ -2247,10 +2247,10 @@ If we apply a band-pass filter to the signal, as shown on figure [fig:zoom_bandp
| ![](/ox-hugo/ewins00_zoom_range.png) | ![](/ox-hugo/ewins00_zoom_bandpass.png) | | ![](/ox-hugo/ewins00_zoom_range.png) | ![](/ox-hugo/ewins00_zoom_bandpass.png) |
|------------------------------------------------|------------------------------------------| |------------------------------------------------|------------------------------------------|
| <a id="org78b0c83"></a> Spectrum of the signal | <a id="orge62379a"></a> Band-pass filter | | <a id="org7059865"></a> Spectrum of the signal | <a id="org833d09d"></a> Band-pass filter |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
<a id="org9584b09"></a> <a id="org3216002"></a>
{{< figure src="/ox-hugo/ewins00_zoom_result.png" caption="Figure 16: Effective frequency translation for zoom" >}} {{< figure src="/ox-hugo/ewins00_zoom_result.png" caption="Figure 16: Effective frequency translation for zoom" >}}
@ -2322,7 +2322,7 @@ This is the traditional method of FRF measurement and involves the use of a swee
It is necessary to check that progress through the frequency range is sufficiently slow to check that steady-state response conditions are attained. It is necessary to check that progress through the frequency range is sufficiently slow to check that steady-state response conditions are attained.
If excessive sweep rate is used, then distortions of the FRF plot are introduced as shown on figure [fig:sweep_distortions](#fig:sweep_distortions). If excessive sweep rate is used, then distortions of the FRF plot are introduced as shown on figure [fig:sweep_distortions](#fig:sweep_distortions).
<a id="orgbf547e6"></a> <a id="orga631403"></a>
{{< figure src="/ox-hugo/ewins00_sweep_distortions.png" caption="Figure 17: FRF measurements by sine sweep test" >}} {{< figure src="/ox-hugo/ewins00_sweep_distortions.png" caption="Figure 17: FRF measurements by sine sweep test" >}}
@ -2440,7 +2440,7 @@ It is known that a low coherence can arise in a measurement where the frequency
This is known as a **bias** error and leakage is often the most likely source of low coherence on lightly-damped structures as shown on figure [fig:coherence_resonance](#fig:coherence_resonance). This is known as a **bias** error and leakage is often the most likely source of low coherence on lightly-damped structures as shown on figure [fig:coherence_resonance](#fig:coherence_resonance).
<a id="orgb273bd2"></a> <a id="orge1dbfba"></a>
{{< figure src="/ox-hugo/ewins00_coherence_resonance.png" caption="Figure 18: Coherence \\(\gamma^2\\) and FRF estimate \\(H\_1(\omega)\\) for a lightly damped structure" >}} {{< figure src="/ox-hugo/ewins00_coherence_resonance.png" caption="Figure 18: Coherence \\(\gamma^2\\) and FRF estimate \\(H\_1(\omega)\\) for a lightly damped structure" >}}
@ -2483,7 +2483,7 @@ For the chirp and impulse excitations, each individual sample is collected and p
Burst excitation signals consist of short sections of an underlying continuous signal (which may be a sine wave, a sine sweep or a random signal), followed by a period of zero output, resulting in a response which shows a transient build-up followed by a decay (see figure [fig:burst_excitation](#fig:burst_excitation)). Burst excitation signals consist of short sections of an underlying continuous signal (which may be a sine wave, a sine sweep or a random signal), followed by a period of zero output, resulting in a response which shows a transient build-up followed by a decay (see figure [fig:burst_excitation](#fig:burst_excitation)).
<a id="org4a271bc"></a> <a id="org728a5e0"></a>
{{< figure src="/ox-hugo/ewins00_burst_excitation.png" caption="Figure 19: Example of burst excitation and response signals" >}} {{< figure src="/ox-hugo/ewins00_burst_excitation.png" caption="Figure 19: Example of burst excitation and response signals" >}}
@ -2502,7 +2502,7 @@ The chirp consist of a short duration signal which has the form shown in figure
The frequency content of the chirp can be precisely chosen by the starting and finishing frequencies of the sweep. The frequency content of the chirp can be precisely chosen by the starting and finishing frequencies of the sweep.
<a id="org9c55941"></a> <a id="org85fd1c4"></a>
{{< figure src="/ox-hugo/ewins00_chirp_excitation.png" caption="Figure 20: Example of chirp excitation and response signals" >}} {{< figure src="/ox-hugo/ewins00_chirp_excitation.png" caption="Figure 20: Example of chirp excitation and response signals" >}}
@ -2513,7 +2513,7 @@ The hammer blow produces an input and response as shown in the figure [fig:impul
This and the chirp excitation are very similar in the analysis point of view, the main difference is that the chirp offers the possibility of greater control of both amplitude and frequency content of the input and also permits the input of a greater amount of vibration energy. This and the chirp excitation are very similar in the analysis point of view, the main difference is that the chirp offers the possibility of greater control of both amplitude and frequency content of the input and also permits the input of a greater amount of vibration energy.
<a id="org0ed8171"></a> <a id="orgb13d46a"></a>
{{< figure src="/ox-hugo/ewins00_impulsive_excitation.png" caption="Figure 21: Example of impulsive excitation and response signals" >}} {{< figure src="/ox-hugo/ewins00_impulsive_excitation.png" caption="Figure 21: Example of impulsive excitation and response signals" >}}
@ -2523,7 +2523,7 @@ However, it should be recorded that in the region below the first cut-off freque
On some structures, the movement of the structure in response to the hammer blow can be such that it returns and **rebounds** on the hammer tip before the user has had time to move that out of the way. On some structures, the movement of the structure in response to the hammer blow can be such that it returns and **rebounds** on the hammer tip before the user has had time to move that out of the way.
In such cases, the spectrum of the excitation is seen to have "holes" in it at certain frequencies (figure [fig:double_hits](#fig:double_hits)). In such cases, the spectrum of the excitation is seen to have "holes" in it at certain frequencies (figure [fig:double_hits](#fig:double_hits)).
<a id="org6bd77b6"></a> <a id="orgce8e98e"></a>
{{< figure src="/ox-hugo/ewins00_double_hits.png" caption="Figure 22: Double hits time domain and frequency content" >}} {{< figure src="/ox-hugo/ewins00_double_hits.png" caption="Figure 22: Double hits time domain and frequency content" >}}
@ -2598,7 +2598,7 @@ Suppose the response parameter is acceleration, then the FRF obtained is inertan
Figure [fig:calibration_setup](#fig:calibration_setup) shows a typical calibration setup. Figure [fig:calibration_setup](#fig:calibration_setup) shows a typical calibration setup.
<a id="org5e0d830"></a> <a id="org93751d7"></a>
{{< figure src="/ox-hugo/ewins00_calibration_setup.png" caption="Figure 23: Mass calibration procedure, measurement setup" >}} {{< figure src="/ox-hugo/ewins00_calibration_setup.png" caption="Figure 23: Mass calibration procedure, measurement setup" >}}
@ -2613,7 +2613,7 @@ This is because near resonance, the actual applied force becomes very small and
This same argument applies on a lesser scale as we examine the detail around the attachment to the structure, as shown in figure [fig:mass_cancellation](#fig:mass_cancellation). This same argument applies on a lesser scale as we examine the detail around the attachment to the structure, as shown in figure [fig:mass_cancellation](#fig:mass_cancellation).
<a id="org3d2d464"></a> <a id="orgb4f3160"></a>
{{< figure src="/ox-hugo/ewins00_mass_cancellation.png" caption="Figure 24: Added mass to be cancelled (crossed area)" >}} {{< figure src="/ox-hugo/ewins00_mass_cancellation.png" caption="Figure 24: Added mass to be cancelled (crossed area)" >}}
@ -2670,7 +2670,7 @@ There are two problems to be tackled:
The first of these is less difficult and techniques usually use a pair a matched conventional accelerometers placed at a short distance apart on the structure to be measured as shown on figure [fig:rotational_measurement](#fig:rotational_measurement). The first of these is less difficult and techniques usually use a pair a matched conventional accelerometers placed at a short distance apart on the structure to be measured as shown on figure [fig:rotational_measurement](#fig:rotational_measurement).
<a id="org8a3adca"></a> <a id="org70ba613"></a>
{{< figure src="/ox-hugo/ewins00_rotational_measurement.png" caption="Figure 25: Measurement of rotational response" >}} {{< figure src="/ox-hugo/ewins00_rotational_measurement.png" caption="Figure 25: Measurement of rotational response" >}}
@ -2691,7 +2691,7 @@ First, a single applied excitation force \\(F\_1\\) corresponds to a simultaneou
Then, the same excitation force is applied at the second position that gives a force \\(F\_0 = F\_2\\) and moment \\(M\_0 = F\_2 l\_2\\). Then, the same excitation force is applied at the second position that gives a force \\(F\_0 = F\_2\\) and moment \\(M\_0 = F\_2 l\_2\\).
By adding and subtracting the responses produced by these two separate excitations conditions, we can deduce the translational and rotational responses to the translational force and the rotational moment separately, thus enabling the measurement of all four types of FRF: \\(X/F\\), \\(\Theta/F\\), \\(X/M\\) and \\(\Theta/M\\). By adding and subtracting the responses produced by these two separate excitations conditions, we can deduce the translational and rotational responses to the translational force and the rotational moment separately, thus enabling the measurement of all four types of FRF: \\(X/F\\), \\(\Theta/F\\), \\(X/M\\) and \\(\Theta/M\\).
<a id="orgd9d3238"></a> <a id="org3d91028"></a>
{{< figure src="/ox-hugo/ewins00_rotational_excitation.png" caption="Figure 26: Application of moment excitation" >}} {{< figure src="/ox-hugo/ewins00_rotational_excitation.png" caption="Figure 26: Application of moment excitation" >}}
@ -3031,7 +3031,7 @@ The two groups are usually separated by a clear gap (depending of the noise pres
| ![](/ox-hugo/ewins00_PRF_numerical_FRF.png) | ![](/ox-hugo/ewins00_PRF_numerical_svd.png) | ![](/ox-hugo/ewins00_PRF_numerical_PRF.png) | | ![](/ox-hugo/ewins00_PRF_numerical_FRF.png) | ![](/ox-hugo/ewins00_PRF_numerical_svd.png) | ![](/ox-hugo/ewins00_PRF_numerical_PRF.png) |
|---------------------------------------------|---------------------------------------------|---------------------------------------------| |---------------------------------------------|---------------------------------------------|---------------------------------------------|
| <a id="org27a7bd2"></a> FRF | <a id="org0725348"></a> Singular Values | <a id="orgcc8943d"></a> PRF | | <a id="org729f249"></a> FRF | <a id="org5ffbfd5"></a> Singular Values | <a id="org61f8f16"></a> PRF |
| width=\linewidth | width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth | width=\linewidth |
<a id="table--fig:PRF-measured"></a> <a id="table--fig:PRF-measured"></a>
@ -3042,7 +3042,7 @@ The two groups are usually separated by a clear gap (depending of the noise pres
| ![](/ox-hugo/ewins00_PRF_measured_FRF.png) | ![](/ox-hugo/ewins00_PRF_measured_svd.png) | ![](/ox-hugo/ewins00_PRF_measured_PRF.png) | | ![](/ox-hugo/ewins00_PRF_measured_FRF.png) | ![](/ox-hugo/ewins00_PRF_measured_svd.png) | ![](/ox-hugo/ewins00_PRF_measured_PRF.png) |
|--------------------------------------------|--------------------------------------------|--------------------------------------------| |--------------------------------------------|--------------------------------------------|--------------------------------------------|
| <a id="orgad6d59c"></a> FRF | <a id="orged00ce0"></a> Singular Values | <a id="orga025551"></a> PRF | | <a id="org830b4d0"></a> FRF | <a id="orgac004ea"></a> Singular Values | <a id="org4f86091"></a> PRF |
| width=\linewidth | width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth | width=\linewidth |
@ -3084,7 +3084,7 @@ Associated with the CMIF values at each natural frequency \\(\omega\_r\\) are tw
- the left singular vector \\(\\{U(\omega\_r)\\}\_1\\) which approximates the **mode shape** of that mode - the left singular vector \\(\\{U(\omega\_r)\\}\_1\\) which approximates the **mode shape** of that mode
- the right singular vector \\(\\{V(\omega\_r)\\}\_1\\) which represents the approximate **force pattern necessary to generate a response on that mode only** - the right singular vector \\(\\{V(\omega\_r)\\}\_1\\) which represents the approximate **force pattern necessary to generate a response on that mode only**
<a id="org80fd4e8"></a> <a id="org54c1d8d"></a>
{{< figure src="/ox-hugo/ewins00_mifs.png" caption="Figure 27: Complex Mode Indicator Function (CMIF)" >}} {{< figure src="/ox-hugo/ewins00_mifs.png" caption="Figure 27: Complex Mode Indicator Function (CMIF)" >}}
@ -3179,7 +3179,7 @@ The peak-picking method is applied as follows (illustrated on figure [fig:peak_a
It must be noted that the estimates of both damping and modal constant depend heavily on the accuracy of the maximum FRF level \\(|\hat{H}|\\) which is difficult to measure with great accuracy, especially for lightly damped systems. It must be noted that the estimates of both damping and modal constant depend heavily on the accuracy of the maximum FRF level \\(|\hat{H}|\\) which is difficult to measure with great accuracy, especially for lightly damped systems.
Only real modal constants and thus real modes can be deduced by this method. Only real modal constants and thus real modes can be deduced by this method.
<a id="org7d69374"></a> <a id="orgc953f95"></a>
{{< figure src="/ox-hugo/ewins00_peak_amplitude.png" caption="Figure 28: Peak Amplitude method of modal analysis" >}} {{< figure src="/ox-hugo/ewins00_peak_amplitude.png" caption="Figure 28: Peak Amplitude method of modal analysis" >}}
@ -3214,7 +3214,7 @@ A plot of the quantity \\(\alpha(\omega)\\) is given in figure [fig:modal_circle
| ![](/ox-hugo/ewins00_modal_circle.png) | ![](/ox-hugo/ewins00_modal_circle_bis.png) | | ![](/ox-hugo/ewins00_modal_circle.png) | ![](/ox-hugo/ewins00_modal_circle_bis.png) |
|----------------------------------------|--------------------------------------------------------------------| |----------------------------------------|--------------------------------------------------------------------|
| <a id="org290c571"></a> Properties | <a id="orgc059e31"></a> \\(\omega\_b\\) and \\(\omega\_a\\) points | | <a id="org1b60ce7"></a> Properties | <a id="orgb28d972"></a> \\(\omega\_b\\) and \\(\omega\_a\\) points |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
For any frequency \\(\omega\\), we have the following relationship: For any frequency \\(\omega\\), we have the following relationship:
@ -3328,7 +3328,7 @@ The sequence is:
5. **Determine modal constant modulus and argument**. 5. **Determine modal constant modulus and argument**.
The magnitude and argument of the modal constant is determined from the diameter of the circle and from its orientation relative to the Real and Imaginary axis. The magnitude and argument of the modal constant is determined from the diameter of the circle and from its orientation relative to the Real and Imaginary axis.
<a id="orga4f6a8d"></a> <a id="org0244ba6"></a>
{{< figure src="/ox-hugo/ewins00_circle_fit_natural_frequency.png" caption="Figure 29: Location of natural frequency for a Circle-fit modal analysis" >}} {{< figure src="/ox-hugo/ewins00_circle_fit_natural_frequency.png" caption="Figure 29: Location of natural frequency for a Circle-fit modal analysis" >}}
@ -3453,7 +3453,7 @@ However, by the inclusion of two simple extra terms (the "**residuals**"), the m
| ![](/ox-hugo/ewins00_residual_without.png) | ![](/ox-hugo/ewins00_residual_with.png) | | ![](/ox-hugo/ewins00_residual_without.png) | ![](/ox-hugo/ewins00_residual_with.png) |
|--------------------------------------------|-----------------------------------------| |--------------------------------------------|-----------------------------------------|
| <a id="orgb0a10e7"></a> without residual | <a id="org7168563"></a> with residuals | | <a id="org441a50e"></a> without residual | <a id="org8c87686"></a> with residuals |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
If we regenerate an FRF curve from the modal parameters we have extracted from the measured data, we shall use a formula of the type If we regenerate an FRF curve from the modal parameters we have extracted from the measured data, we shall use a formula of the type
@ -3484,7 +3484,7 @@ The three terms corresponds to:
These three terms are illustrated on figure [fig:low_medium_high_modes](#fig:low_medium_high_modes). These three terms are illustrated on figure [fig:low_medium_high_modes](#fig:low_medium_high_modes).
<a id="org3ba03ab"></a> <a id="org4214379"></a>
{{< figure src="/ox-hugo/ewins00_low_medium_high_modes.png" caption="Figure 30: Numerical simulation of contribution of low, medium and high frequency modes" >}} {{< figure src="/ox-hugo/ewins00_low_medium_high_modes.png" caption="Figure 30: Numerical simulation of contribution of low, medium and high frequency modes" >}}
@ -3785,7 +3785,7 @@ As an example, a set of mobilities measured are shown individually in figure [fi
| ![](/ox-hugo/ewins00_composite_raw.png) | ![](/ox-hugo/ewins00_composite_sum.png) | | ![](/ox-hugo/ewins00_composite_raw.png) | ![](/ox-hugo/ewins00_composite_sum.png) |
|-------------------------------------------|-----------------------------------------| |-------------------------------------------|-----------------------------------------|
| <a id="orgf1eae63"></a> Individual curves | <a id="org156012b"></a> Composite curve | | <a id="org3564b55"></a> Individual curves | <a id="org7736a33"></a> Composite curve |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
The global analysis methods have the disadvantages first, that the computation power required is high and second that there may be valid reasons why the various FRF curves exhibit slight differences in their characteristics and it may not always be appropriate to average them. The global analysis methods have the disadvantages first, that the computation power required is high and second that there may be valid reasons why the various FRF curves exhibit slight differences in their characteristics and it may not always be appropriate to average them.
@ -4332,7 +4332,7 @@ Measured coordinates of the test structure are first linked as shown on figure [
Then, the grid of measured coordinate points is redrawn on the same plot but this time displaced by an amount proportional to the corresponding element in the mode shape vector as shown on figure [fig:static_display](#fig:static_display) (b). Then, the grid of measured coordinate points is redrawn on the same plot but this time displaced by an amount proportional to the corresponding element in the mode shape vector as shown on figure [fig:static_display](#fig:static_display) (b).
The elements in the vector are scaled according the normalization process used (usually mass-normalized), and their absolute magnitudes have no particular significance. The elements in the vector are scaled according the normalization process used (usually mass-normalized), and their absolute magnitudes have no particular significance.
<a id="orgaffacf3"></a> <a id="org4a1c4d1"></a>
{{< figure src="/ox-hugo/ewins00_static_display.png" caption="Figure 31: Static display of modes shapes. (a) basic grid (b) single-frame deflection pattern (c) multiple-frame deflection pattern (d) complex mode (e) Argand diagram - quasi-real mode (f) Argand diagram - complex mode" >}} {{< figure src="/ox-hugo/ewins00_static_display.png" caption="Figure 31: Static display of modes shapes. (a) basic grid (b) single-frame deflection pattern (c) multiple-frame deflection pattern (d) complex mode (e) Argand diagram - quasi-real mode (f) Argand diagram - complex mode" >}}
@ -4377,7 +4377,7 @@ If we consider the first six modes of the beam, whose mode shapes are sketched i
All the higher modes will be indistinguishable from these first few. All the higher modes will be indistinguishable from these first few.
This is a well known problem of **spatial aliasing**. This is a well known problem of **spatial aliasing**.
<a id="org1952587"></a> <a id="orgc20b9b6"></a>
{{< figure src="/ox-hugo/ewins00_beam_modes.png" caption="Figure 32: Misinterpretation of mode shapes by spatial aliasing" >}} {{< figure src="/ox-hugo/ewins00_beam_modes.png" caption="Figure 32: Misinterpretation of mode shapes by spatial aliasing" >}}
@ -4440,7 +4440,7 @@ The inclusion of these two additional terms (obtained here only after measuring
| ![](/ox-hugo/ewins00_H22_without_residual.png) | ![](/ox-hugo/ewins00_H22_with_residual.png) | | ![](/ox-hugo/ewins00_H22_without_residual.png) | ![](/ox-hugo/ewins00_H22_with_residual.png) |
|--------------------------------------------------------|-----------------------------------------------------------| |--------------------------------------------------------|-----------------------------------------------------------|
| <a id="org7d9a13a"></a> Using measured modal data only | <a id="orgae3b985"></a> After inclusion of residual terms | | <a id="org376d498"></a> Using measured modal data only | <a id="orgb025b02"></a> After inclusion of residual terms |
| width=\linewidth | width=\linewidth | | width=\linewidth | width=\linewidth |
The appropriate expression for a "correct" response model, derived via a set of modal properties is thus The appropriate expression for a "correct" response model, derived via a set of modal properties is thus
@ -4495,7 +4495,7 @@ If the transmissibility is measured during a modal test which has a single excit
In general, the transmissibility **depends significantly on the excitation point** (\\({}\_iT\_{jk}(\omega) \neq {}\_qT\_{jk}(\omega)\\) where \\(q\\) is a different DOF than \\(i\\)) and it is shown on figure [fig:transmissibility_plots](#fig:transmissibility_plots). In general, the transmissibility **depends significantly on the excitation point** (\\({}\_iT\_{jk}(\omega) \neq {}\_qT\_{jk}(\omega)\\) where \\(q\\) is a different DOF than \\(i\\)) and it is shown on figure [fig:transmissibility_plots](#fig:transmissibility_plots).
This may explain why transmissibilities are not widely used in modal analysis. This may explain why transmissibilities are not widely used in modal analysis.
<a id="orgd4fb092"></a> <a id="org5d97d3b"></a>
{{< figure src="/ox-hugo/ewins00_transmissibility_plots.png" caption="Figure 33: Transmissibility plots" >}} {{< figure src="/ox-hugo/ewins00_transmissibility_plots.png" caption="Figure 33: Transmissibility plots" >}}
@ -4516,7 +4516,7 @@ The fact that the excitation force is not measured is responsible for the lack o
| ![](/ox-hugo/ewins00_conventional_modal_test_setup.png) | ![](/ox-hugo/ewins00_base_excitation_modal_setup.png) | | ![](/ox-hugo/ewins00_conventional_modal_test_setup.png) | ![](/ox-hugo/ewins00_base_excitation_modal_setup.png) |
|---------------------------------------------------------|-------------------------------------------------------| |---------------------------------------------------------|-------------------------------------------------------|
| <a id="org1dc5bf9"></a> Conventional modal test setup | <a id="orge8f2893"></a> Base excitation setup | | <a id="org5b39165"></a> Conventional modal test setup | <a id="org6815dc0"></a> Base excitation setup |
| height=4cm | height=4cm | | height=4cm | height=4cm |
@ -4559,4 +4559,4 @@ Because the rank of each pseudo matrix is less than its order, it cannot be inve
## Bibliography {#bibliography} ## Bibliography {#bibliography}
<a id="org84d73f8"></a>Ewins, DJ. 2000. _Modal Testing: Theory, Practice and Application_. _Research Studies Pre, 2nd Ed., ISBN-13_. Baldock, Hertfordshire, England Philadelphia, PA: Wiley-Blackwell. <a id="org57f8bf9"></a>Ewins, DJ. 2000. _Modal Testing: Theory, Practice and Application_. _Research Studies Pre, 2nd Ed., ISBN-13_. Baldock, Hertfordshire, England Philadelphia, PA: Wiley-Blackwell.

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@ -8,7 +8,7 @@ Tags
: [Metrology]({{< relref "metrology" >}}) : [Metrology]({{< relref "metrology" >}})
Reference Reference
: <sup id="58bd6e601168ed1397ab2ec3cc3bab2d"><a href="#leach14_fundam_princ_engin_nanom" title="Richard Leach, Fundamental Principles of Engineering Nanometrology, Elsevier (2014).">(Richard Leach, 2014)</a></sup> : ([Leach 2014](#orgc5df692))
Author(s) Author(s)
: Leach, R. : Leach, R.
@ -86,5 +86,7 @@ The measurement of angles is then relative.
This type of angular interferometer is used to measure small angles (less than \\(10deg\\)). This type of angular interferometer is used to measure small angles (less than \\(10deg\\)).
# Bibliography
<a id="leach14_fundam_princ_engin_nanom"></a>Leach, R., *Fundamental principles of engineering nanometrology* (2014), : Elsevier. [](#58bd6e601168ed1397ab2ec3cc3bab2d) ## Bibliography {#bibliography}
<a id="orgc5df692"></a>Leach, Richard. 2014. _Fundamental Principles of Engineering Nanometrology_. Elsevier. <https://doi.org/10.1016/c2012-0-06010-3>.

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@ -8,7 +8,7 @@ Tags
: [Precision Engineering]({{< relref "precision_engineering" >}}) : [Precision Engineering]({{< relref "precision_engineering" >}})
Reference Reference
: <sup id="cc6e42420309d21c1aa596152d84cf8b"><a href="#leach18_basic_precis_engin_edition" title="Richard Leach \&amp; Stuart Smith, Basics of Precision Engineering - 1st Edition, CRC Press (2018).">(Richard Leach \& Stuart Smith, 2018)</a></sup> : ([Leach and Smith 2018](#org285ffd0))
Author(s) Author(s)
: Leach, R., & Smith, S. T. : Leach, R., & Smith, S. T.
@ -16,5 +16,7 @@ Author(s)
Year Year
: 2018 : 2018
# Bibliography
<a id="leach18_basic_precis_engin_edition"></a>Leach, R., & Smith, S. T., *Basics of precision engineering - 1st edition* (2018), : CRC Press. [](#cc6e42420309d21c1aa596152d84cf8b) ## Bibliography {#bibliography}
<a id="org285ffd0"></a>Leach, Richard, and Stuart T. Smith. 2018. _Basics of Precision Engineering - 1st Edition_. CRC Press.

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@ -12,5 +12,6 @@ Tags
## Backlinks {#backlinks} ## Backlinks {#backlinks}
- [A concept of active mount for space applications]({{< relref "souleille18_concep_activ_mount_space_applic" >}})
- [Active isolation and damping of vibrations via stewart platform]({{< relref "hanieh03_activ_stewar" >}}) - [Active isolation and damping of vibrations via stewart platform]({{< relref "hanieh03_activ_stewar" >}})
- [Active damping based on decoupled collocated control]({{< relref "holterman05_activ_dampin_based_decoup_colloc_contr" >}}) - [Active damping based on decoupled collocated control]({{< relref "holterman05_activ_dampin_based_decoup_colloc_contr" >}})

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@ -12,6 +12,6 @@ Tags
## Backlinks {#backlinks} ## Backlinks {#backlinks}
- [Advances in internal model control technique: a review and future prospects]({{< relref "saxena12_advan_inter_model_contr_techn" >}})
- [Actuator Fusion]({{< relref "actuator_fusion" >}}) - [Actuator Fusion]({{< relref "actuator_fusion" >}})
- [Sensor Fusion]({{< relref "sensor_fusion" >}}) - [Sensor Fusion]({{< relref "sensor_fusion" >}})
- [Advances in internal model control technique: a review and future prospects]({{< relref "saxena12_advan_inter_model_contr_techn" >}})

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@ -13,19 +13,19 @@ Tags
## Special Properties {#special-properties} ## Special Properties {#special-properties}
Cubic Stewart Platforms can be decoupled provided that (from <sup id="ba05ff213f8e5963d91559d95becfbdb"><a href="#chen00_ident_decoup_contr_flexur_joint_hexap" title="Yixin Chen \&amp; McInroy, Identification and Decoupling Control of Flexure Jointed Hexapods, nil, in in: {Proceedings 2000 ICRA. Millennium Conference. IEEE Cubic Stewart Platforms can be decoupled provided that (from ([Chen and McInroy 2000](#orgf50ffa1)))
International Conference on Robotics and Automation. Symposia
Proceedings (Cat. No.00CH37065)}, edited by (2000)">(Yixin Chen \& McInroy, 2000)</a></sup>)
> 1. The payload mass-inertia matrix is diagonal > 1. The payload mass-inertia matrix is diagonal
> 2. If a mutually orthogonal geometry has been selected, the payload's center of mass must coincide with the center of the cube formed by the orthogonal struts. > 2. If a mutually orthogonal geometry has been selected, the payload's center of mass must coincide with the center of the cube formed by the orthogonal struts.
# Bibliography
<a id="chen00_ident_decoup_contr_flexur_joint_hexap"></a>Chen, Y., & McInroy, J., *Identification and decoupling control of flexure jointed hexapods*, In , Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065) (pp. ) (2000). : . [](#ba05ff213f8e5963d91559d95becfbdb) ## Bibliography {#bibliography}
<a id="orgf50ffa1"></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>.
## Backlinks {#backlinks} ## Backlinks {#backlinks}
- [Sensors and control of a space-based six-axis vibration isolation system]({{< relref "hauge04_sensor_contr_space_based_six" >}})
- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}}) - [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
- [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}}) - [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}})
- [Sensors and control of a space-based six-axis vibration isolation system]({{< relref "hauge04_sensor_contr_space_based_six" >}})

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@ -12,44 +12,44 @@ Tags
Books: Books:
- <sup id="7d07367ac4d34d56738dbfe0eb53371f"><a href="#lobontiu02_compl" title="Lobontiu, Compliant mechanisms: design of flexure hinges, CRC press (2002).">(Lobontiu, 2002)</a></sup> - ([Lobontiu 2002](#orgb3f874f))
- <sup id="53d819004fa64ee1fe2e715469c5991f"><a href="#henein03_concep_guidag_flexib" title="Henein, Conception des Guidages Flexibles, Presses polytechniques et universitaires romandes (2003).">(Henein, 2003)</a></sup> - ([Henein 2003](#orgad0500e))
- <sup id="ccc31a1054040cbdbbb28ba9e590af72"><a href="#smith05_found" title="Smith, Foundations of ultra-precision mechanism design, CRC Press (2005).">(Smith, 2005)</a></sup> - ([Smith 2005](#org48acd08))
- <sup id="13540f4d4ba6bb415fdc21c85dde63cc"><a href="#soemers11_desig_princ" title="Soemers, Design Principles for precision mechanisms, T-Pointprint (2011).">(Soemers, 2011)</a></sup> - ([Soemers 2011](#org03d0c96))
- <sup id="880641d23cd52fb47b40104731883e32"><a href="#cosandier17_flexur_mechan_desig" title="Cosandier, Flexure Mechanism Design, Distributed by CRC Press, 2017EOFL Press (2017).">(Cosandier, 2017)</a></sup> - ([Cosandier 2017](#org6494792))
## Flexure Joints for Stewart Platforms: {#flexure-joints-for-stewart-platforms} ## Flexure Joints for Stewart Platforms: {#flexure-joints-for-stewart-platforms}
From <sup id="ba05ff213f8e5963d91559d95becfbdb"><a href="#chen00_ident_decoup_contr_flexur_joint_hexap" title="Yixin Chen \&amp; McInroy, Identification and Decoupling Control of Flexure Jointed Hexapods, nil, in in: {Proceedings 2000 ICRA. Millennium Conference. IEEE From ([Chen and McInroy 2000](#org2cba46e)):
International Conference on Robotics and Automation. Symposia
Proceedings (Cat. No.00CH37065)}, edited by (2000)">(Yixin Chen \& McInroy, 2000)</a></sup>:
> To avoid the extremely non-linear micro-dynamics of joint friction and backlash, these hexapods employ flexure joints. > 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. > 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. > This does eliminate friction and backlash, but adds spring dynamics and limits the workspace.
# Bibliography
<a id="lobontiu02_compl"></a>Lobontiu, N., *Compliant mechanisms: design of flexure hinges* (2002), : CRC press. [](#7d07367ac4d34d56738dbfe0eb53371f)
<a id="henein03_concep_guidag_flexib"></a>Henein, S., *Conception des guidages flexibles* (2003), Lausanne, Suisse: Presses polytechniques et universitaires romandes. [](#53d819004fa64ee1fe2e715469c5991f) ## Bibliography {#bibliography}
<a id="smith05_found"></a>Smith, S. T., *Foundations of ultra-precision mechanism design* (2005), : CRC Press. [](#ccc31a1054040cbdbbb28ba9e590af72) <a id="org2cba46e"></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="soemers11_desig_princ"></a>Soemers, H., *Design principles for precision mechanisms* (2011), : T-Pointprint. [](#13540f4d4ba6bb415fdc21c85dde63cc) <a id="org6494792"></a>Cosandier, Florent. 2017. _Flexure Mechanism Design_. Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press.
<a id="cosandier17_flexur_mechan_desig"></a>Cosandier, F., *Flexure Mechanism Design* (2017), Boca Raton, FL Lausanne, Switzerland: Distributed by CRC Press, 2017EOFL Press. [](#880641d23cd52fb47b40104731883e32) <a id="orgad0500e"></a>Henein, Simon. 2003. _Conception Des Guidages Flexibles_. Lausanne, Suisse: Presses polytechniques et universitaires romandes.
<a id="chen00_ident_decoup_contr_flexur_joint_hexap"></a>Chen, Y., & McInroy, J., *Identification and decoupling control of flexure jointed hexapods*, In , Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065) (pp. ) (2000). : . [](#ba05ff213f8e5963d91559d95becfbdb) <a id="orgb3f874f"></a>Lobontiu, Nicolae. 2002. _Compliant Mechanisms: Design of Flexure Hinges_. CRC press.
<a id="org48acd08"></a>Smith, Stuart T. 2005. _Foundations of Ultra-Precision Mechanism Design_. Vol. 2. CRC Press.
<a id="org03d0c96"></a>Soemers, Herman. 2011. _Design Principles for Precision Mechanisms_. T-Pointprint.
## Backlinks {#backlinks} ## Backlinks {#backlinks}
- [Nanometre-cutting machine using a stewart-platform parallel mechanism]({{< relref "furutani04_nanom_cuttin_machin_using_stewar" >}}) - [Identification and decoupling control of flexure jointed hexapods]({{< relref "chen00_ident_decoup_contr_flexur_joint_hexap" >}})
- [Dynamic modeling and experimental analyses of stewart platform with flexible hinges]({{< relref "jiao18_dynam_model_exper_analy_stewar" >}}) - [Dynamic modeling and experimental analyses of stewart platform with flexible hinges]({{< relref "jiao18_dynam_model_exper_analy_stewar" >}})
- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
- [A six-axis single-stage active vibration isolator based on stewart platform]({{< relref "preumont07_six_axis_singl_stage_activ" >}}) - [A six-axis single-stage active vibration isolator based on stewart platform]({{< relref "preumont07_six_axis_singl_stage_activ" >}})
- [Investigation on active vibration isolation of a stewart platform with piezoelectric actuators]({{< relref "wang16_inves_activ_vibrat_isolat_stewar" >}}) - [Investigation on active vibration isolation of a stewart platform with piezoelectric actuators]({{< relref "wang16_inves_activ_vibrat_isolat_stewar" >}})
- [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}}) - [Nanometre-cutting machine using a stewart-platform parallel mechanism]({{< relref "furutani04_nanom_cuttin_machin_using_stewar" >}})
- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
- [Dynamic modeling of flexure jointed hexapods for control purposes]({{< relref "mcinroy99_dynam" >}}) - [Dynamic modeling of flexure jointed hexapods for control purposes]({{< relref "mcinroy99_dynam" >}})
- [Identification and decoupling control of flexure jointed hexapods]({{< relref "chen00_ident_decoup_contr_flexur_joint_hexap" >}}) - [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}})

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@ -0,0 +1,18 @@
+++
title = "Instrumented Hammer"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Modal Analysis]({{< relref "modal_analysis" >}})
## Manufacturers {#manufacturers}
| Manufacturers | Links |
|---------------|---------------------------------------------------------------------------------------------------------------|
| PCB | [link](https://www.pcb.com/sensors-for-test-measurement/impact-hammers-electrodynamic-shakers/impact-hammers) |
| DJB | [link](https://www.djbinstruments.com/products/instrumentation/impact-hammers) |
<./biblio/references.bib>

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@ -32,7 +32,7 @@ Tags
> >
> The primary disadvantage of FIR filters is that they often require a much higher filter order than IIR filters to achieve a given level of performance. Correspondingly, the delay of these filters is often much greater than for an equal performance IIR filter. > The primary disadvantage of FIR filters is that they often require a much higher filter order than IIR filters to achieve a given level of performance. Correspondingly, the delay of these filters is often much greater than for an equal performance IIR filter.
From <sup id="d875134273304770f6a0334525ecfa27"><a class="reference-link" href="#shaw90_bandw_enhan_posit_measur_using_measur_accel" title="Shaw \&amp; Srinivasan, Bandwidth Enhancement of Position Measurements Using Measured Acceleration, {Mechanical Systems and Signal Processing}, v(1), 23-38 (1990).">(Shaw \& Srinivasan, 1990)</a></sup> From ([Shaw and Srinivasan 1990](#org7a68e45))
> The FIR are capable of realizing filters with linear phase shift characteristics and furthermore are less susceptible to signal input and filter coefficient quantization effects. > The FIR are capable of realizing filters with linear phase shift characteristics and furthermore are less susceptible to signal input and filter coefficient quantization effects.
> However, their computational demands are excessively large because of the large number of multiplications and additions to be performed at each sampling interval. > However, their computational demands are excessively large because of the large number of multiplications and additions to be performed at each sampling interval.
@ -48,5 +48,7 @@ From <https://dsp.stackexchange.com/a/30999>
> >
> - Feed-forward control. FIR filters are useful for producing filters that approximate arbitrary frequency responses, hence they can be used to shape a reference signal. A typical example is to use an FIR filter with the inverse frequency response of the plant -- trying to counteract the dynamics of the plant in order to get a desired output. Phase/time-delay is not interfering with the stability or performance since the computation can be done offline. FIR filters can often produce higher performance than IIR filters, especially where there are non-minimum phase zeros. > - Feed-forward control. FIR filters are useful for producing filters that approximate arbitrary frequency responses, hence they can be used to shape a reference signal. A typical example is to use an FIR filter with the inverse frequency response of the plant -- trying to counteract the dynamics of the plant in order to get a desired output. Phase/time-delay is not interfering with the stability or performance since the computation can be done offline. FIR filters can often produce higher performance than IIR filters, especially where there are non-minimum phase zeros.
# Bibliography
<a class="bibtex-entry" id="shaw90_bandw_enhan_posit_measur_using_measur_accel">Shaw, F., & Srinivasan, K., *Bandwidth enhancement of position measurements using measured acceleration*, Mechanical Systems and Signal Processing, *4(1)*, 2338 (1990). http://dx.doi.org/10.1016/0888-3270(90)90038-m</a> [](#d875134273304770f6a0334525ecfa27) ## Bibliography {#bibliography}
<a id="org7a68e45"></a>Shaw, F.R., and K. Srinivasan. 1990. “Bandwidth Enhancement of Position Measurements Using Measured Acceleration.” _Mechanical Systems and Signal Processing_ 4 (1):2338. <https://doi.org/10.1016/0888-3270(90)>90038-m.

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@ -5,18 +5,18 @@ draft = false
+++ +++
Tags Tags
: : [Simulink]({{< relref "simulink" >}})
## Resources on Matlab {#resources-on-matlab} ## Resources on Matlab {#resources-on-matlab}
Books: Books:
- ([Higham 2017](#org311950e)) - ([Higham 2017](#org8ba8e47))
- ([Attaway 2018](#org2d4cbee)) - ([Attaway 2018](#org4c6aa3b))
- ([OverFlow 2018](#org84f4050)) - ([OverFlow 2018](#orgad9dce4))
- ([Johnson 2010](#orgd1edf93)) - ([Johnson 2010](#org1aa5652))
- ([Hahn and Valentine 2016](#org07606c6)) - ([Hahn and Valentine 2016](#orgc9b02db))
## Useful Commands {#useful-commands} ## Useful Commands {#useful-commands}
@ -70,17 +70,43 @@ To install Toolboxes, the best is to Download the Matlab installer from mathwork
## Used Toolboxes {#used-toolboxes} ## Used Toolboxes {#used-toolboxes}
Nice functions:
- <https://github.com/jmrplens/SetFigPaper>
- <https://github.com/altmany/export%5Ffig>
- Matlab's `exportgraphics`
- `vfit3` ([link](https://www.sintef.no/projectweb/vectorfitting/)): used to identify transfer functions - `vfit3` ([link](https://www.sintef.no/projectweb/vectorfitting/)): used to identify transfer functions
## Debug Scripts {#debug-scripts}
<https://fr.mathworks.com/help/matlab/debugging-code.html>
<https://stackoverflow.com/questions/22853116/how-to-debug-matlab-code-without-gui>
| Command | Effect |
|------------|--------------------------------------------------------------|
| `dbclear` | Remove breakpoints |
| `dbcont` | Resume execution |
| `dbdown` | Reverse dbup workspace shift |
| `dbquit` | Quit debug mode |
| `dbstack` | Function call stack |
| `dbstatus` | List all breakpoints |
| `dbstep` | Execute next executable line from current breakpoint |
| `dbstop` | Set breakpoints for debugging |
| `dbtype` | Display file with line numbers |
| `dbup` | Shift current workspace to workspace of caller in debug mode |
| `keyboard` | Give control to keyboard |
| `echo` | Display statements during function execution |
## Bibliography {#bibliography} ## Bibliography {#bibliography}
<a id="org2d4cbee"></a>Attaway, Stormy. 2018. _MATLAB : a Practical Introduction to Programming and Problem Solving_. Amsterdam: Butterworth-Heinemann. <a id="org4c6aa3b"></a>Attaway, Stormy. 2018. _MATLAB : a Practical Introduction to Programming and Problem Solving_. Amsterdam: Butterworth-Heinemann.
<a id="org07606c6"></a>Hahn, Brian, and Daniel T Valentine. 2016. _Essential MATLAB for Engineers and Scientists_. Academic Press. <a id="orgc9b02db"></a>Hahn, Brian, and Daniel T Valentine. 2016. _Essential MATLAB for Engineers and Scientists_. Academic Press.
<a id="org311950e"></a>Higham, Desmond. 2017. _MATLAB Guide_. Philadelphia: Society for Industrial and Applied Mathematics. <a id="org8ba8e47"></a>Higham, Desmond. 2017. _MATLAB Guide_. Philadelphia: Society for Industrial and Applied Mathematics.
<a id="orgd1edf93"></a>Johnson, Richard K. 2010. _The Elements of MATLAB Style_. Cambridge University Press. <a id="org1aa5652"></a>Johnson, Richard K. 2010. _The Elements of MATLAB Style_. Cambridge University Press.
<a id="org84f4050"></a>OverFlow, Stack. 2018. _MATLAB Notes for Professionals_. GoalKicker.com. <a id="orgad9dce4"></a>OverFlow, Stack. 2018. _MATLAB Notes for Professionals_. GoalKicker.com.

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@ -0,0 +1,16 @@
+++
title = "Modal Analysis"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
: [Inertial Sensors]({{< relref "inertial_sensors" >}}), [Shaker]({{< relref "shaker" >}})
<./biblio/references.bib>
## Backlinks {#backlinks}
- [Modal testing: theory, practice and application]({{< relref "ewins00_modal" >}})
- [Instrumented Hammer]({{< relref "instrumented_hammer" >}})

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@ -12,8 +12,8 @@ Tags
## Backlinks {#backlinks} ## Backlinks {#backlinks}
- [Multivariable control systems: an engineering approach]({{< relref "albertos04_multiv_contr_system" >}})
- [Position control in lithographic equipment]({{< relref "butler11_posit_contr_lithog_equip" >}})
- [Implementation challenges for multivariable control: what you did not learn in school!]({{< relref "garg07_implem_chall_multiv_contr" >}}) - [Implementation challenges for multivariable control: what you did not learn in school!]({{< relref "garg07_implem_chall_multiv_contr" >}})
- [Multivariable control systems: an engineering approach]({{< relref "albertos04_multiv_contr_system" >}})
- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}}) - [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
- [Multivariable feedback control: analysis and design]({{< relref "skogestad07_multiv_feedb_contr" >}}) - [Multivariable feedback control: analysis and design]({{< relref "skogestad07_multiv_feedb_contr" >}})
- [Position control in lithographic equipment]({{< relref "butler11_posit_contr_lithog_equip" >}})

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@ -9,9 +9,9 @@ Tags
Tutorial about Power Spectral Density is accessible [here](https://tdehaeze.github.io/spectral-analysis/). Tutorial about Power Spectral Density is accessible [here](https://tdehaeze.github.io/spectral-analysis/).
A good article about how to use the `pwelch` function with Matlab ([Schmid 2012](#org8fdb443)). A good article about how to use the `pwelch` function with Matlab ([Schmid 2012](#org206dff2)).
## Bibliography {#bibliography} ## Bibliography {#bibliography}
<a id="org8fdb443"></a>Schmid, Hanspeter. 2012. “How to Use the FFT and Matlabs Pwelch Function for Signal and Noise Simulations and Measurements.” _Institute of Microelectronics_. <a id="org206dff2"></a>Schmid, Hanspeter. 2012. “How to Use the FFT and Matlabs Pwelch Function for Signal and Noise Simulations and Measurements.” _Institute of Microelectronics_.

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@ -0,0 +1,35 @@
+++
title = "Simulink"
author = ["Thomas Dehaeze"]
draft = false
+++
Tags
:
## Useful Key Bindings {#useful-key-bindings}
| Key Binding | Action |
|----------------|-----------------------------|
| `spc` | Fit to view |
| `ctrl-shift-A` | Rearrange all the blocks |
| `ctrl-shift-I` | Open the Property Inspector |
| `ctrl-G` | Create a subsystem |
| `ctrl-J` | Show the Sampling Time |
| `ctrl-T` | Run Model |
| `ctrl-shit-T` | Stop Model |
| `ctrl-D` | Update Model |
| `ctrl-B` | Build Model |
| `ctrl-H` | Open Model Explorer |
Tips:
- It is possible to share configuration between files with **referenced configuration**
## Linearize portion of Simulink file {#linearize-portion-of-simulink-file}
<https://in.mathworks.com/help/slcontrol/ug/specify-model-portion-to-linearize.html>
<./biblio/references.bib>

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@ -12,64 +12,61 @@ Tags
Papers by J.E. McInroy: Papers by J.E. McInroy:
- <sup id="89a9631ad2f0fb051d6fb8a91dc96cb2"><a href="#obrien98_lesson" title="O'Brien, McInroy, Bodtke, Bruch, \&amp; Hamann, Lessons learned in nonlinear systems and flexible robots through experiments on a 6 legged platform, nil, in in: {Proceedings of the 1998 American Control Conference. ACC - ([OBrien et al. 1998](#orgd3ca372))
(IEEE Cat. No.98CH36207)}, edited by (1998)">(O'Brien {\it et al.}, 1998)</a></sup> - ([McInroy, OBrien, and Neat 1999](#orgf721e37))
- <sup id="fecc3b6c835f5247abb57a170e2f5364"><a href="#mcinroy99_precis_fault_toler_point_using_stewar_platf" title="McInroy, O'Brien \&amp; Neat, Precise, Fault-Tolerant Pointing Using a Stewart Platform, {IEEE/ASME Transactions on Mechatronics}, v(1), 91-95 (1999).">(McInroy {\it et al.}, 1999)</a></sup> - ([McInroy 1999](#org3433881))
- <sup id="5da427f78c552aa92cd64c2a6df961f1"><a href="#mcinroy99_dynam" title="McInroy, Dynamic modeling of flexure jointed hexapods for control purposes, nil, in in: {Proceedings of the 1999 IEEE International Conference on - ([McInroy and Hamann 2000](#org637713e))
Control Applications (Cat. No.99CH36328)}, edited by (1999)">(McInroy, 1999)</a></sup> - ([Chen and McInroy 2000](#org36c0c78))
- <sup id="f6d310236552ee92579cf0673a2ca695"><a href="#mcinroy00_desig_contr_flexur_joint_hexap" title="McInroy \&amp; Hamann, Design and Control of Flexure Jointed Hexapods, {IEEE Transactions on Robotics and Automation}, v(4), 372-381 (2000).">(McInroy \& Hamann, 2000)</a></sup> - ([McInroy 2002](#org9e4db5a))
- <sup id="ba05ff213f8e5963d91559d95becfbdb"><a href="#chen00_ident_decoup_contr_flexur_joint_hexap" title="Yixin Chen \&amp; McInroy, Identification and Decoupling Control of Flexure Jointed Hexapods, nil, in in: {Proceedings 2000 ICRA. Millennium Conference. IEEE - ([Li, Hamann, and McInroy 2001](#orgeede940))
International Conference on Robotics and Automation. Symposia - ([Lin and McInroy 2003](#orgdc4ea44))
Proceedings (Cat. No.00CH37065)}, edited by (2000)">(Yixin Chen \& McInroy, 2000)</a></sup> - ([Jafari and McInroy 2003](#org567288a))
- <sup id="8bfe2d2dce902a584fa016e86a899044"><a href="#mcinroy02_model_desig_flexur_joint_stewar" title="McInroy, Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes, {IEEE/ASME Transactions on Mechatronics}, v(1), 95-99 (2002).">(McInroy, 2002)</a></sup> - ([Chen and McInroy 2004](#org9cf3624))
- <sup id="e3df2691f750617c3995644d056d553a"><a href="#li01_simul_vibrat_isolat_point_contr" title="Xiaochun Li, Jerry Hamann \&amp; John McInroy, Simultaneous Vibration Isolation and Pointing Control of Flexure Jointed Hexapods, nil, in in: {Smart Structures and Materials 2001: Smart Structures and
Integrated Systems}, edited by (2001)">(Xiaochun Li {\it et al.}, 2001)</a></sup>
- <sup id="7c236658343683951ee18f3f771a68db"><a href="#lin03_adapt_sinus_distur_cancel_precis" title="Haomin Lin \&amp; McInroy, Adaptive Sinusoidal Disturbance Cancellation for Precise Pointing of Stewart Platforms, {IEEE Transactions on Control Systems Technology}, v(2), 267-272 (2003).">(Haomin Lin \& McInroy, 2003)</a></sup>
- <sup id="5cc6cbf419f21bb039148a3c012723d0"><a href="#jafari03_orthog_gough_stewar_platf_microm" title="Jafari \&amp; McInroy, Orthogonal Gough-Stewart Platforms for Micromanipulation, {IEEE Transactions on Robotics and Automation}, v(4), 595-603 (2003).">(Jafari \& McInroy, 2003)</a></sup>
- <sup id="7683f004697e712d8aebd697ab7c7bf7"><a href="#chen04_decoup_contr_flexur_joint_hexap" title="Chen \&amp; McInroy, Decoupled Control of Flexure-Jointed Hexapods Using Estimated Joint-Space Mass-Inertia Matrix, {IEEE Transactions on Control Systems Technology}, v(3), 413-421 (2004).">(Chen \& McInroy, 2004)</a></sup>
# Bibliography
<a id="obrien98_lesson"></a>O'Brien, J., McInroy, J., Bodtke, D., Bruch, M., & Hamann, J., *Lessons learned in nonlinear systems and flexible robots through experiments on a 6 legged platform*, In , Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207) (pp. ) (1998). : . [](#89a9631ad2f0fb051d6fb8a91dc96cb2)
<a id="mcinroy99_precis_fault_toler_point_using_stewar_platf"></a>McInroy, J., O'Brien, J., & Neat, G., *Precise, fault-tolerant pointing using a stewart platform*, IEEE/ASME Transactions on Mechatronics, *4(1)*, 9195 (1999). http://dx.doi.org/10.1109/3516.752089 [](#fecc3b6c835f5247abb57a170e2f5364) ## Bibliography {#bibliography}
<a id="mcinroy99_dynam"></a>McInroy, J., *Dynamic modeling of flexure jointed hexapods for control purposes*, In , Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328) (pp. ) (1999). : . [](#5da427f78c552aa92cd64c2a6df961f1) <a id="org9cf3624"></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):41321. <https://doi.org/10.1109/tcst.2004.824339>.
<a id="mcinroy00_desig_contr_flexur_joint_hexap"></a>McInroy, J., & Hamann, J., *Design and control of flexure jointed hexapods*, IEEE Transactions on Robotics and Automation, *16(4)*, 372381 (2000). http://dx.doi.org/10.1109/70.864229 [](#f6d310236552ee92579cf0673a2ca695) <a id="org36c0c78"></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="chen00_ident_decoup_contr_flexur_joint_hexap"></a>Chen, Y., & McInroy, J., *Identification and decoupling control of flexure jointed hexapods*, In , Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065) (pp. ) (2000). : . [](#ba05ff213f8e5963d91559d95becfbdb) <a id="org567288a"></a>Jafari, F., and J.E. McInroy. 2003. “Orthogonal Gough-Stewart Platforms for Micromanipulation.” _IEEE Transactions on Robotics and Automation_ 19 (4). Institute of Electrical and Electronics Engineers (IEEE):595603. <https://doi.org/10.1109/tra.2003.814506>.
<a id="mcinroy02_model_desig_flexur_joint_stewar"></a>McInroy, J., *Modeling and design of flexure jointed stewart platforms for control purposes*, IEEE/ASME Transactions on Mechatronics, *7(1)*, 9599 (2002). http://dx.doi.org/10.1109/3516.990892 [](#8bfe2d2dce902a584fa016e86a899044) <a id="orgdc4ea44"></a>Lin, Haomin, and J.E. McInroy. 2003. “Adaptive Sinusoidal Disturbance Cancellation for Precise Pointing of Stewart Platforms.” _IEEE Transactions on Control Systems Technology_ 11 (2):26772. <https://doi.org/10.1109/tcst.2003.809248>.
<a id="li01_simul_vibrat_isolat_point_contr"></a>Li, X., Hamann, J. C., & McInroy, J. E., *Simultaneous vibration isolation and pointing control of flexure jointed hexapods*, In , Smart Structures and Materials 2001: Smart Structures and Integrated Systems (pp. ) (2001). : . [](#e3df2691f750617c3995644d056d553a) <a id="orgeede940"></a>Li, Xiaochun, Jerry C. Hamann, and John E. McInroy. 2001. “Simultaneous Vibration Isolation and Pointing Control of Flexure Jointed Hexapods.” In _Smart Structures and Materials 2001: Smart Structures and Integrated Systems_, nil. <https://doi.org/10.1117/12.436521>.
<a id="lin03_adapt_sinus_distur_cancel_precis"></a>Lin, H., & McInroy, J., *Adaptive sinusoidal disturbance cancellation for precise pointing of stewart platforms*, IEEE Transactions on Control Systems Technology, *11(2)*, 267272 (2003). http://dx.doi.org/10.1109/tcst.2003.809248 [](#7c236658343683951ee18f3f771a68db) <a id="org3433881"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In _Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)_, nil. <https://doi.org/10.1109/cca.1999.806694>.
<a id="jafari03_orthog_gough_stewar_platf_microm"></a>Jafari, F., & McInroy, J., *Orthogonal gough-stewart platforms for micromanipulation*, IEEE Transactions on Robotics and Automation, *19(4)*, 595603 (2003). http://dx.doi.org/10.1109/tra.2003.814506 [](#5cc6cbf419f21bb039148a3c012723d0) <a id="org9e4db5a"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” _IEEE/ASME Transactions on Mechatronics_ 7 (1):9599. <https://doi.org/10.1109/3516.990892>.
<a id="chen04_decoup_contr_flexur_joint_hexap"></a>Chen, Y., & McInroy, J., *Decoupled control of flexure-jointed hexapods using estimated joint-space mass-inertia matrix*, IEEE Transactions on Control Systems Technology, *12(3)*, 413421 (2004). http://dx.doi.org/10.1109/tcst.2004.824339 [](#7683f004697e712d8aebd697ab7c7bf7) <a id="org637713e"></a>McInroy, J.E., and J.C. Hamann. 2000. “Design and Control of Flexure Jointed Hexapods.” _IEEE Transactions on Robotics and Automation_ 16 (4):37281. <https://doi.org/10.1109/70.864229>.
<a id="orgf721e37"></a>McInroy, J.E., J.F. OBrien, and G.W. Neat. 1999. “Precise, Fault-Tolerant Pointing Using a Stewart Platform.” _IEEE/ASME Transactions on Mechatronics_ 4 (1):9195. <https://doi.org/10.1109/3516.752089>.
<a id="orgd3ca372"></a>OBrien, J.F., J.E. McInroy, D. Bodtke, M. Bruch, and J.C. Hamann. 1998. “Lessons Learned in Nonlinear Systems and Flexible Robots Through Experiments on a 6 Legged Platform.” In _Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)_, nil. <https://doi.org/10.1109/acc.1998.703532>.
## Backlinks {#backlinks} ## Backlinks {#backlinks}
- [The stewart platform manipulator: a review]({{< relref "dasgupta00_stewar_platf_manip" >}})
- [Modeling and control of vibration in mechanical systems]({{< relref "du10_model_contr_vibrat_mechan_system" >}})
- [Studies on stewart platform manipulator: a review]({{< relref "furqan17_studies_stewar_platf_manip" >}})
- [Nanometre-cutting machine using a stewart-platform parallel mechanism]({{< relref "furutani04_nanom_cuttin_machin_using_stewar" >}})
- [An intelligent control system for multiple degree-of-freedom vibration isolation]({{< relref "geng95_intel_contr_system_multip_degree" >}})
- [Active isolation and damping of vibrations via stewart platform]({{< relref "hanieh03_activ_stewar" >}})
- [Sensors and control of a space-based six-axis vibration isolation system]({{< relref "hauge04_sensor_contr_space_based_six" >}})
- [Dynamic modeling and experimental analyses of stewart platform with flexible hinges]({{< relref "jiao18_dynam_model_exper_analy_stewar" >}})
- [A new isotropic and decoupled 6-dof parallel manipulator]({{< relref "legnani12_new_isotr_decoup_paral_manip" >}})
- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
- [Simultaneous vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_vibrat_isolat_point_contr" >}})
- [A six-axis single-stage active vibration isolator based on stewart platform]({{< relref "preumont07_six_axis_singl_stage_activ" >}})
- [Vibration Control of Active Structures - Fourth Edition]({{< relref "preumont18_vibrat_contr_activ_struc_fourt_edition" >}})
- [A soft 6-axis active vibration isolator]({{< relref "spanos95_soft_activ_vibrat_isolat" >}})
- [Parallel robots : mechanics and control]({{< relref "taghirad13_paral" >}})
- [Decentralized vibration control of a voice coil motor-based stewart parallel mechanism: simulation and experiments]({{< relref "tang18_decen_vibrat_contr_voice_coil" >}}) - [Decentralized vibration control of a voice coil motor-based stewart parallel mechanism: simulation and experiments]({{< relref "tang18_decen_vibrat_contr_voice_coil" >}})
- [Investigation on active vibration isolation of a stewart platform with piezoelectric actuators]({{< relref "wang16_inves_activ_vibrat_isolat_stewar" >}})
- [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}})
- [Six dof active vibration control using stewart platform with non-cubic configuration]({{< relref "zhang11_six_dof" >}})
- [Dynamic modeling of flexure jointed hexapods for control purposes]({{< relref "mcinroy99_dynam" >}})
- [Identification and decoupling control of flexure jointed hexapods]({{< relref "chen00_ident_decoup_contr_flexur_joint_hexap" >}}) - [Identification and decoupling control of flexure jointed hexapods]({{< relref "chen00_ident_decoup_contr_flexur_joint_hexap" >}})
- [Dynamic modeling and experimental analyses of stewart platform with flexible hinges]({{< relref "jiao18_dynam_model_exper_analy_stewar" >}})
- [A six-axis single-stage active vibration isolator based on stewart platform]({{< relref "preumont07_six_axis_singl_stage_activ" >}})
- [Investigation on active vibration isolation of a stewart platform with piezoelectric actuators]({{< relref "wang16_inves_activ_vibrat_isolat_stewar" >}})
- [Nanometre-cutting machine using a stewart-platform parallel mechanism]({{< relref "furutani04_nanom_cuttin_machin_using_stewar" >}})
- [Active isolation and damping of vibrations via stewart platform]({{< relref "hanieh03_activ_stewar" >}})
- [Studies on stewart platform manipulator: a review]({{< relref "furqan17_studies_stewar_platf_manip" >}})
- [Modeling and control of vibration in mechanical systems]({{< relref "du10_model_contr_vibrat_mechan_system" >}})
- [A new isotropic and decoupled 6-dof parallel manipulator]({{< relref "legnani12_new_isotr_decoup_paral_manip" >}})
- [The stewart platform manipulator: a review]({{< relref "dasgupta00_stewar_platf_manip" >}})
- [Vibration Control of Active Structures - Fourth Edition]({{< relref "preumont18_vibrat_contr_activ_struc_fourt_edition" >}})
- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
- [Dynamic modeling of flexure jointed hexapods for control purposes]({{< relref "mcinroy99_dynam" >}})
- [An intelligent control system for multiple degree-of-freedom vibration isolation]({{< relref "geng95_intel_contr_system_multip_degree" >}})
- [A soft 6-axis active vibration isolator]({{< relref "spanos95_soft_activ_vibrat_isolat" >}})
- [Six dof active vibration control using stewart platform with non-cubic configuration]({{< relref "zhang11_six_dof" >}})
- [Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation]({{< relref "yang19_dynam_model_decoup_contr_flexib" >}})
- [Parallel robots : mechanics and control]({{< relref "taghirad13_paral" >}})
- [Simultaneous vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_vibrat_isolat_point_contr" >}})
- [Sensors and control of a space-based six-axis vibration isolation system]({{< relref "hauge04_sensor_contr_space_based_six" >}})