Update Content - 2020-09-21
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title = "Active Isolation Platforms"
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author = ["Thomas Dehaeze"]
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Tags
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: [Vibration Isolation]({{< relref "vibration_isolation" >}})
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| Manufacturers | Links | Country |
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|---------------|------------------------------------------------------------------------|---------|
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| TMC | [link](https://www.techmfg.com/) | USA |
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| Newport | [link](https://www.newport.com/c/optical-tables-%26-isolation-systems) | USA |
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<./biblio/references.bib>
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content/zettels/equipment/active_isolation_platforms.md
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content/zettels/equipment/active_isolation_platforms.md
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title = "Active Isolation Platforms"
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author = ["Thomas Dehaeze"]
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draft = false
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+++
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Tags
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: [Vibration Isolation]({{< relref "vibration_isolation" >}})
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## Manufacturers {#manufacturers}
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| Manufacturers | Links | Country |
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|-------------------|----------------------------------------------------------------------------------|-------------|
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| TMC | [link](https://www.techmfg.com/) | USA |
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| Newport | [link](https://www.newport.com/c/optical-tables-%26-isolation-systems) | USA |
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| Thorlabs | [link](https://www.thorlabs.com/navigation.cfm?guide%5FID=42) | USA |
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| IDE | [link](https://www.ideworld.com/en/active%5Fvibration%5Fisolation.html) | Germany |
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| Harvard Apparatus | [link](https://www.warneronline.com/labmate-vibraplane-workstations-9100-series) | USA |
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| Herzan | [link](https://www.herzan.com/products/active-vibration-control/avi-series.html) | USA |
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| Standa | [link](http://www.standa.lt/products/catalog/optical%5Ftables?item=335) | Lithuania |
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| Table Stable | [link](http://www.tablestable.com/en/products/list/2/) | Switzerland |
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| Accurion | [link](https://www.halcyonics.com/active-vibration-isolation-products) | Germany |
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| Vibiso | [link](https://vibiso.com/?page%5Fid=3433) | USA |
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## Vibration Isolating Pads {#vibration-isolating-pads}
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| Manufacturer | links | Country |
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|--------------|----------------------------------|---------|
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| ACE | [link](https://www.ace-ace.com/) | Germany |
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<./biblio/references.bib>
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@ -10,7 +10,7 @@ Tags
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## SVD of a MIMO system {#svd-of-a-mimo-system}
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This is taken from ([Skogestad and Postlethwaite 2007](#org0179442)).
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This is taken from ([Skogestad and Postlethwaite 2007](#org4953f60)).
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We are interested by the physical interpretation of the SVD when applied to the frequency response of a MIMO system \\(G(s)\\) with \\(m\\) inputs and \\(l\\) outputs.
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@ -18,14 +18,9 @@ We are interested by the physical interpretation of the SVD when applied to the
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G = U \Sigma V^H
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\end{equation}
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\\(\Sigma\\)
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: is an \\(l \times m\\) matrix with \\(k = \min\\{l, m\\}\\) non-negative **singular values** \\(\sigma\_i\\), arranged in descending order along its main diagonal, the other entries are zero.
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\\(U\\)
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: is an \\(l \times l\\) unitary matrix. The columns of \\(U\\), denoted \\(u\_i\\), represent the **output directions** of the plant. They are orthonormal.
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\\(V\\)
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: is an \\(m \times m\\) unitary matrix. The columns of \\(V\\), denoted \\(v\_i\\), represent the **input directions** of the plant. They are orthonormal.
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- \\(\Sigma\\): is an \\(l \times m\\) matrix with \\(k = \min\\{l, m\\}\\) non-negative **singular values** \\(\sigma\_i\\), arranged in descending order along its main diagonal, the other entries are zero.
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- \\(U\\): is an \\(l \times l\\) unitary matrix. The columns of \\(U\\), denoted \\(u\_i\\), represent the **output directions** of the plant. They are orthonormal.
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- \\(V\\): is an \\(m \times m\\) unitary matrix. The columns of \\(V\\), denoted \\(v\_i\\), represent the **input directions** of the plant. They are orthonormal.
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The input and output directions are related through the singular values:
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@ -48,7 +43,7 @@ Then is follows that:
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## SVD to pseudo inverse rectangular matrices {#svd-to-pseudo-inverse-rectangular-matrices}
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This is taken from ([Preumont 2018](#org37ddb8b)).
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This is taken from ([Preumont 2018](#org6558f35)).
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The **Singular Value Decomposition** (SVD) is a generalization of the eigenvalue decomposition of a rectangular matrix:
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\\[ J = U \Sigma V^T = \sum\_{i=1}^r \sigma\_i u\_i v\_i^T \\]
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@ -70,6 +65,6 @@ This will have usually little impact of the fitting error while reducing conside
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## Bibliography {#bibliography}
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<a id="org37ddb8b"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.
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<a id="org6558f35"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.
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<a id="org0179442"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
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<a id="org4953f60"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
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@ -11,7 +11,6 @@ Backlinks:
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- [Investigation on active vibration isolation of a stewart platform with piezoelectric actuators]({{< relref "wang16_inves_activ_vibrat_isolat_stewar" >}})
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- [Active isolation and damping of vibrations via stewart platform]({{< relref "hanieh03_activ_stewar" >}})
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- [Modeling and control of vibration in mechanical systems]({{< relref "du10_model_contr_vibrat_mechan_system" >}})
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- [Vibration Control of Active Structures - Fourth Edition]({{< relref "preumont18_vibrat_contr_activ_struc_fourt_edition" >}})
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- [Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods]({{< relref "li01_simul_fault_vibrat_isolat_point" >}})
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- [Sensor fusion for active vibration isolation in precision equipment]({{< relref "tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip" >}})
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- [An intelligent control system for multiple degree-of-freedom vibration isolation]({{< relref "geng95_intel_contr_system_multip_degree" >}})
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@ -27,31 +26,9 @@ Backlinks:
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- [Sensors and control of a space-based six-axis vibration isolation system]({{< relref "hauge04_sensor_contr_space_based_six" >}})
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- [An exploration of active hard mount vibration isolation for precision equipment]({{< relref "poel10_explor_activ_hard_mount_vibrat" >}})
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- [Sensor fusion methods for high performance active vibration isolation systems]({{< relref "collette15_sensor_fusion_method_high_perfor" >}})
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- [Vibration Control of Active Structures - Fourth Edition]({{< relref "preumont18_vibrat_contr_activ_struc_fourt_edition" >}})
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Tags
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:
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## Vibration Isolating Pads {#vibration-isolating-pads}
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| Manufacturer | links | Country |
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|--------------|----------------------------------|---------|
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| ACE | [link](https://www.ace-ace.com/) | Germany |
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## Vibration Isolation Tables {#vibration-isolation-tables}
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| Manufacturer | links | Country |
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|-------------------|----------------------------------------------------------------------------------|-------------|
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| TMC | [link](https://www.techmfg.com/products/stacis/stacisiii) | USA |
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| Newport | [link](https://www.newport.com/f/guardian-active-isolation-workstations) | USA |
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| Thorlabs | [link](https://www.thorlabs.com/navigation.cfm?guide%5FID=42) | USA |
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| IDE | [link](https://www.ideworld.com/en/active%5Fvibration%5Fisolation.html) | Germany |
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| Harvard Apparatus | [link](https://www.warneronline.com/labmate-vibraplane-workstations-9100-series) | USA |
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| Herzan | [link](https://www.herzan.com/products/active-vibration-control/avi-series.html) | USA |
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| Standa | [link](http://www.standa.lt/products/catalog/optical%5Ftables?item=335) | Lithuania |
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| Table Stable | [link](http://www.tablestable.com/en/products/list/2/) | Switzerland |
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| Accurion | [link](https://www.halcyonics.com/active-vibration-isolation-products) | Germany |
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| Vibiso | [link](https://vibiso.com/?page%5Fid=3433) | USA |
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<./biblio/references.bib>
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