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content/article/butler11_posit_contr_lithog_equip.md
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@@ -8,7 +8,7 @@ Tags
: [Multivariable Control]({{< relref "multivariable_control" >}}), [Positioning Stations]({{< relref "positioning_stations" >}})
Reference
: ([Butler 2011](#org79c48f7))
: ([Butler 2011](#org10c4eb8))
Author(s)
: Butler, H.
@@ -17,6 +17,7 @@ Year
: 2011
## Bibliography {#bibliography}
<a id="org79c48f7"></a>Butler, Hans. 2011. “Position Control in Lithographic Equipment.” _IEEE Control Systems_ 31 (5):28–47. <https://doi.org/10.1109/mcs.2011.941882>.
<a id="org10c4eb8"></a>Butler, Hans. 2011. “Position Control in Lithographic Equipment.” _IEEE Control Systems_ 31 (5):28–47. <https://doi.org/10.1109/mcs.2011.941882>.

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content/article/chen00_ident_decoup_contr_flexur_joint_hexap.md
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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference
: ([Chen and McInroy 2000](#orgc009af3))
: ([Chen and McInroy 2000](#orgfcb31bd))
Author(s)
: Chen, Y., & McInroy, J.
@@ -31,7 +31,7 @@ Year
## Introduction {#introduction}
Typical decoupling algorithm impose two constraints:
Typical decoupling algorithm ([Decoupled Control]({{< relref "decoupled_control" >}})) impose two constraints:
- the payload mass/inertia matrix is diagonal
- the geometry of the platform and attachment of the payload must be carefully chosen
@@ -43,9 +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}
The derivation of the dynamic model is done in ([McInroy 1999](#org0e9e807)) ([Notes]({{< relref "mcinroy99_dynam" >}})).
The derivation of the dynamic model is done in ([McInroy 1999](#orgaddeeaf)) ([Notes]({{< relref "mcinroy99_dynam" >}})).
<a id="orge595e9c"></a>
<a id="org3326cce"></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" >}}
@@ -100,8 +100,9 @@ where
## Experimental Results {#experimental-results}
## Bibliography {#bibliography}
<a id="orgc009af3"></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="orgfcb31bd"></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="org0e9e807"></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="orgaddeeaf"></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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content/article/dasgupta00_stewar_platf_manip.md
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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}})
Reference
: ([Dasgupta and Mruthyunjaya 2000](#orgab59d3a))
: ([Dasgupta and Mruthyunjaya 2000](#orgb54a8e7))
Author(s)
: Dasgupta, B., & Mruthyunjaya, T.
@@ -24,16 +24,17 @@ Year
| | **Advantages** | **Disadvantages** |
|--------------|---------------------------|-----------------------|
| **Serial** | Manoeuverability | Poor precision |
| **Serial** | Maneuverability | Poor precision |
| | Large workspace | Bends under high load |
| | | Vibrate at high speed |
| **Parallel** | High stiffness | Small workspace |
| | Good dynamic performances | |
| | Precise positioning | |
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 platform) connected through six extensible legs, each with spherical joints at both ends.
## Bibliography {#bibliography}
<a id="orgab59d3a"></a>Dasgupta, Bhaskar, and T.S. Mruthyunjaya. 2000. “The Stewart Platform Manipulator: A Review.” _Mechanism and Machine Theory_ 35 (1):15–40. <https://doi.org/10.1016/s0094-114x(99)>00006-3.
<a id="orgb54a8e7"></a>Dasgupta, Bhaskar, and T.S. Mruthyunjaya. 2000. “The Stewart Platform Manipulator: A Review.” _Mechanism and Machine Theory_ 35 (1):15–40. <https://doi.org/10.1016/s0094-114x(99)>00006-3.

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content/article/fleming13_review_nanom_resol_posit_sensor.md
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@@ -4,15 +4,11 @@ author = ["Thomas Dehaeze"]
draft = false
+++
Backlinks:
- [Position Sensors]({{< relref "position_sensors" >}})
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
Reference
: ([Fleming 2013](#org35f9cea))
: ([Fleming 2013](#org336a947))
Author(s)
: Fleming, A. J.
@@ -37,7 +33,7 @@ Usually quoted as a percentage of the fill-scale range (FSR):
With \\(e\_m(v)\\) is the mapping error.
<a id="orge06f384"></a>
<a id="org3c27d5a"></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." >}}
@@ -46,7 +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.
<a id="orgc484965"></a>
<a id="org69dcb2d"></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." >}}
@@ -151,9 +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}\\).
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](#org2ee752d)).
There is usually a trade-off between bandwidth and resolution (figure [3](#orge95682f)).
<a id="org2ee752d"></a>
<a id="orge95682f"></a>
{{< figure src="/ox-hugo/fleming13_tradeoff_res_bandwidth.png" caption="Figure 3: The resolution versus banwidth of a position sensor." >}}
@@ -186,6 +182,7 @@ A convenient method for reporting this ratio is in parts-per-million (ppm):
| Encoder | Meters | | 6 nm | >100kHz | 5 ppm FSR |
## Bibliography {#bibliography}
<a id="org35f9cea"></a>Fleming, Andrew J. 2013. “A Review of Nanometer Resolution Position Sensors: Operation and Performance.” _Sensors and Actuators a: Physical_ 190 (nil):106–26. <https://doi.org/10.1016/j.sna.2012.10.016>.
<a id="org336a947"></a>Fleming, Andrew J. 2013. “A Review of Nanometer Resolution Position Sensors: Operation and Performance.” _Sensors and Actuators a: Physical_ 190 (nil):106–26. <https://doi.org/10.1016/j.sna.2012.10.016>.

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content/article/furqan17_studies_stewar_platf_manip.md
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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}})
Reference
: ([Furqan, Suhaib, and Ahmad 2017](#org7520991))
: ([Furqan, Suhaib, and Ahmad 2017](#orgd310f71))
Author(s)
: Furqan, M., Suhaib, M., & Ahmad, N.
@@ -19,6 +19,7 @@ Year
Lots of references.
## Bibliography {#bibliography}
<a id="org7520991"></a>Furqan, Mohd, Mohd Suhaib, and Nazeer Ahmad. 2017. “Studies on Stewart Platform Manipulator: A Review.” _Journal of Mechanical Science and Technology_ 31 (9):4459–70. <https://doi.org/10.1007/s12206-017-0846-1>.
<a id="orgd310f71"></a>Furqan, Mohd, Mohd Suhaib, and Nazeer Ahmad. 2017. “Studies on Stewart Platform Manipulator: A Review.” _Journal of Mechanical Science and Technology_ 31 (9):4459–70. <https://doi.org/10.1007/s12206-017-0846-1>.

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content/article/furutani04_nanom_cuttin_machin_using_stewar.md
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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference
: ([Furutani, Suzuki, and Kudoh 2004](#orgaf9f119))
: ([Furutani, Suzuki, and Kudoh 2004](#org37254be))
Author(s)
: Furutani, K., Suzuki, M., & Kudoh, R.
@@ -35,6 +35,7 @@ To minimize the errors, a calibration is done between the required leg length an
Then, it is fitted with 4th order polynomial and included in the control architecture.
## Bibliography {#bibliography}
<a id="orgaf9f119"></a>Furutani, Katsushi, Michio Suzuki, and Ryusei Kudoh. 2004. “Nanometre-Cutting Machine Using a Stewart-Platform Parallel Mechanism.” _Measurement Science and Technology_ 15 (2):467–74. <https://doi.org/10.1088/0957-0233/15/2/022>.
<a id="org37254be"></a>Furutani, Katsushi, Michio Suzuki, and Ryusei Kudoh. 2004. “Nanometre-Cutting Machine Using a Stewart-Platform Parallel Mechanism.” _Measurement Science and Technology_ 15 (2):467–74. <https://doi.org/10.1088/0957-0233/15/2/022>.

5
content/article/gao15_measur_techn_precis_posit.md
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@@ -8,7 +8,7 @@ Tags
: [Position Sensors]({{< relref "position_sensors" >}})
Reference
: ([Gao et al. 2015](#org7f49efc))
: ([Gao et al. 2015](#orgb71276a))
Author(s)
: Gao, W., Kim, S., Bosse, H., Haitjema, H., Chen, Y., Lu, X., Knapp, W., …
@@ -17,6 +17,7 @@ Year
: 2015
## Bibliography {#bibliography}
<a id="org7f49efc"></a>Gao, W., S.W. Kim, H. Bosse, H. Haitjema, Y.L. Chen, X.D. Lu, W. Knapp, A. Weckenmann, W.T. Estler, and H. Kunzmann. 2015. “Measurement Technologies for Precision Positioning.” _CIRP Annals_ 64 (2):773–96. <https://doi.org/10.1016/j.cirp.2015.05.009>.
<a id="orgb71276a"></a>Gao, W., S.W. Kim, H. Bosse, H. Haitjema, Y.L. Chen, X.D. Lu, W. Knapp, A. Weckenmann, W.T. Estler, and H. Kunzmann. 2015. “Measurement Technologies for Precision Positioning.” _CIRP Annals_ 64 (2):773–96. <https://doi.org/10.1016/j.cirp.2015.05.009>.

5
content/article/garg07_implem_chall_multiv_contr.md
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@@ -8,7 +8,7 @@ Tags
: [Multivariable Control]({{< relref "multivariable_control" >}})
Reference
: ([Garg 2007](#orga5ede8d))
: ([Garg 2007](#orgae24e63))
Author(s)
: Garg, S.
@@ -35,6 +35,7 @@ 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
## Bibliography {#bibliography}
<a id="orga5ede8d"></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>.
<a id="orgae24e63"></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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content/article/hanieh03_activ_stewar.md
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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Active Damping]({{< relref "active_damping" >}})
Reference
: ([Hanieh 2003](#org5da54db))
: ([Hanieh 2003](#orgd0b61f4))
Author(s)
: Hanieh, A. A.
@@ -17,6 +17,7 @@ Year
: 2003
## Bibliography {#bibliography}
<a id="org5da54db"></a>Hanieh, Ahmed Abu. 2003. “Active Isolation and Damping of Vibrations via Stewart Platform.” Université Libre de Bruxelles, Brussels, Belgium.
<a id="orgd0b61f4"></a>Hanieh, Ahmed Abu. 2003. “Active Isolation and Damping of Vibrations via Stewart Platform.” Université Libre de Bruxelles, Brussels, Belgium.

7
content/article/holler12_instr_x_ray_nano_imagin.md
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@@ -8,7 +8,7 @@ Tags
: [Nano Active Stabilization System]({{< relref "nano_active_stabilization_system" >}}), [Positioning Stations]({{< relref "positioning_stations" >}})
Reference
: ([Holler et al. 2012](#org289d119))
: ([Holler et al. 2012](#org76dfce6))
Author(s)
: Holler, M., Raabe, J., Diaz, A., Guizar-Sicairos, M., Quitmann, C., Menzel, A., & Bunk, O.
@@ -19,7 +19,7 @@ Year
Instrument similar to the NASS.
Obtain position stability of 10nm (standard deviation).
<a id="orgfed3898"></a>
<a id="orgd10cf36"></a>
{{< figure src="/ox-hugo/holler12_station.png" caption="Figure 1: Schematic of the tomography setup" >}}
@@ -39,6 +39,7 @@ Obtain position stability of 10nm (standard deviation).
- **Feedback Loop**: Using the signals from the 2 interferometers, the loop is closed to compensate low frequency vibrations and thermal drifts.
## Bibliography {#bibliography}
<a id="org289d119"></a>Holler, M., J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk. 2012. “An Instrument for 3d X-Ray Nano-Imaging.” _Review of Scientific Instruments_ 83 (7):073703. <https://doi.org/10.1063/1.4737624>.
<a id="org76dfce6"></a>Holler, M., J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk. 2012. “An Instrument for 3d X-Ray Nano-Imaging.” _Review of Scientific Instruments_ 83 (7):073703. <https://doi.org/10.1063/1.4737624>.

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content/article/holterman05_activ_dampin_based_decoup_colloc_contr.md
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@@ -8,7 +8,7 @@ Tags
: [Active Damping]({{< relref "active_damping" >}})
Reference
: ([Holterman and deVries 2005](#orgfb04a8c))
: ([Holterman and deVries 2005](#org69e08df))
Author(s)
: Holterman, J., & deVries, T.
@@ -17,6 +17,7 @@ Year
: 2005
## Bibliography {#bibliography}
<a id="orgfb04a8c"></a>Holterman, J., and T.J.A. deVries. 2005. “Active Damping Based on Decoupled Collocated Control.” _IEEE/ASME Transactions on Mechatronics_ 10 (2):135–45. <https://doi.org/10.1109/tmech.2005.844702>.
<a id="org69e08df"></a>Holterman, J., and T.J.A. deVries. 2005. “Active Damping Based on Decoupled Collocated Control.” _IEEE/ASME Transactions on Mechatronics_ 10 (2):135–45. <https://doi.org/10.1109/tmech.2005.844702>.

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content/article/jiao18_dynam_model_exper_analy_stewar.md
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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference
: ([Jiao et al. 2018](#orga067c93))
: ([Jiao et al. 2018](#org72b03e6))
Author(s)
: Jiao, J., Wu, Y., Yu, K., & Zhao, R.
@@ -17,6 +17,7 @@ Year
: 2018
## Bibliography {#bibliography}
<a id="orga067c93"></a>Jiao, Jian, Ying Wu, Kaiping Yu, and Rui Zhao. 2018. “Dynamic Modeling and Experimental Analyses of Stewart Platform with Flexible Hinges.” _Journal of Vibration and Control_ 25 (1):151–71. <https://doi.org/10.1177/1077546318772474>.
<a id="org72b03e6"></a>Jiao, Jian, Ying Wu, Kaiping Yu, and Rui Zhao. 2018. “Dynamic Modeling and Experimental Analyses of Stewart Platform with Flexible Hinges.” _Journal of Vibration and Control_ 25 (1):151–71. <https://doi.org/10.1177/1077546318772474>.

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content/article/legnani12_new_isotr_decoup_paral_manip.md
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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}})
Reference
: ([Legnani et al. 2012](#org4d21607))
: ([Legnani et al. 2012](#orga1dea1c))
Author(s)
: Legnani, G., Fassi, I., Giberti, H., Cinquemani, S., & Tosi, D.
@@ -22,15 +22,16 @@ Year
Example of generated isotropic manipulator (not decoupled).
<a id="org584231c"></a>
<a id="org7df2b7f"></a>
{{< figure src="/ox-hugo/legnani12_isotropy_gen.png" caption="Figure 1: Location of the leg axes using an isotropy generator" >}}
<a id="orgfad58c6"></a>
<a id="org4803974"></a>
{{< figure src="/ox-hugo/legnani12_generated_isotropy.png" caption="Figure 2: Isotropic configuration" >}}
## Bibliography {#bibliography}
<a id="org4d21607"></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):64–81. <https://doi.org/10.1016/j.mechmachtheory.2012.07.008>.
<a id="orga1dea1c"></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):64–81. <https://doi.org/10.1016/j.mechmachtheory.2012.07.008>.

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content/article/li01_simul_fault_vibrat_isolat_point.md
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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Cubic Architecture]({{< relref "cubic_architecture" >}}), [Flexible Joints]({{< relref "flexible_joints" >}}), [Multivariable Control]({{< relref "multivariable_control" >}})
Reference
: ([Li 2001](#org9c3830b))
: ([Li 2001](#org7799941))
Author(s)
: Li, X.
@@ -24,7 +24,7 @@ Year
- Cubic (mutually orthogonal)
- Flexure Joints => eliminate friction and backlash but add complexity to the dynamics
<a id="org0b311b0"></a>
<a id="org6847e54"></a>
{{< figure src="/ox-hugo/li01_stewart_platform.png" caption="Figure 1: Flexure jointed Stewart platform used for analysis and control" >}}
@@ -38,18 +38,18 @@ Year
The origin of \\(\\{P\\}\\) is taken as the center of mass of the payload.
**Decoupling**:
If we refine the (force) inputs and (displacement) outputs as shown in Figure [2](#orgdda87ef) or in Figure [3](#orga45a9ca), we obtain a decoupled plant provided that:
If we refine the (force) inputs and (displacement) outputs as shown in Figure [2](#org7d1b81f) or in Figure [3](#orgc8972f9), we obtain a decoupled plant provided that:
1. the payload mass/inertia matrix must be diagonal (the CoM is coincident with the origin of frame \\(\\{P\\}\\))
2. the geometry of the hexapod and the attachment of the payload to the hexapod must be carefully chosen
> For instance, if the hexapod has a mutually orthogonal geometry (cubic configuration), the payload's center of mass must coincide with the center of the cube formed by the orthogonal struts.
<a id="orgdda87ef"></a>
<a id="org7d1b81f"></a>
{{< figure src="/ox-hugo/li01_decoupling_conf.png" caption="Figure 2: Decoupling the dynamics of the Stewart Platform using the Jacobians" >}}
<a id="orga45a9ca"></a>
<a id="orgc8972f9"></a>
{{< figure src="/ox-hugo/li01_decoupling_conf_bis.png" caption="Figure 3: Decoupling the dynamics of the Stewart Platform using the Jacobians" >}}
@@ -75,15 +75,15 @@ The control bandwidth is divided as follows:
### Vibration Isolation {#vibration-isolation}
The system is decoupled into six independent SISO subsystems using the architecture shown in Figure [4](#org2bd4cf2).
The system is decoupled into six independent SISO subsystems using the architecture shown in Figure [4](#orgabd1d61).
<a id="org2bd4cf2"></a>
<a id="orgabd1d61"></a>
{{< figure src="/ox-hugo/li01_vibration_isolation_control.png" caption="Figure 4: Figure caption" >}}
One of the subsystem plant transfer function is shown in Figure [4](#org2bd4cf2)
One of the subsystem plant transfer function is shown in Figure [4](#orgabd1d61)
<a id="org16f5e77"></a>
<a id="org5a1c162"></a>
{{< figure src="/ox-hugo/li01_vibration_control_plant.png" caption="Figure 5: Plant transfer function of one of the SISO subsystem for Vibration Control" >}}
@@ -97,9 +97,9 @@ The unity control bandwidth of the isolation loop is designed to be from **5Hz t
### Pointing Control {#pointing-control}
A block diagram of the pointing control system is shown in Figure [6](#orge508ebf).
A block diagram of the pointing control system is shown in Figure [6](#orga9c8d31).
<a id="orge508ebf"></a>
<a id="orga9c8d31"></a>
{{< figure src="/ox-hugo/li01_pointing_control.png" caption="Figure 6: Figure caption" >}}
@@ -108,9 +108,9 @@ The compensators are design with inverse-dynamics methods.
The unity control bandwidth of the pointing loop is designed to be from **0Hz to 20Hz**.
A feedforward control is added as shown in Figure [7](#org68e9af0).
A feedforward control is added as shown in Figure [7](#org78d2b0e).
<a id="org68e9af0"></a>
<a id="org78d2b0e"></a>
{{< figure src="/ox-hugo/li01_feedforward_control.png" caption="Figure 7: Feedforward control" >}}
@@ -122,17 +122,17 @@ The simultaneous vibration isolation and pointing control is approached in two w
1. design and implement the vibration isolation control first, identify the pointing plant when the isolation loops are closed, then implement the pointing compensators
2. the reverse design order
Figure [8](#orgdb53c99) shows a parallel control structure where \\(G\_1(s)\\) is the dynamics from input force to output strut length.
Figure [8](#org94ed578) shows a parallel control structure where \\(G\_1(s)\\) is the dynamics from input force to output strut length.
<a id="orgdb53c99"></a>
<a id="org94ed578"></a>
{{< figure src="/ox-hugo/li01_parallel_control.png" caption="Figure 8: A parallel scheme" >}}
The transfer function matrix for the pointing loop after the vibration isolation is closed is still decoupled. The same happens when closing the pointing loop first and looking at the transfer function matrix of the vibration isolation.
The effect of the isolation loop on the pointing loop is large around the natural frequency of the plant as shown in Figure [9](#org3ec32bc).
The effect of the isolation loop on the pointing loop is large around the natural frequency of the plant as shown in Figure [9](#orgae8c117).
<a id="org3ec32bc"></a>
<a id="orgae8c117"></a>
{{< figure src="/ox-hugo/li01_effect_isolation_loop_closed.png" caption="Figure 9: \\(\theta\_x/\theta\_{x\_d}\\) transfer function with the isolation loop closed (simulation)" >}}
@@ -143,19 +143,19 @@ The effect of pointing control on the isolation plant has not much effect.
The dynamic interaction effect:
- only happens in the unity bandwidth of the loop transmission of the first closed loop.
- affect the closed loop transmission of the loop first closed (see Figures [10](#org4a1beff) and [11](#org945793e))
- affect the closed loop transmission of the loop first closed (see Figures [10](#org00362f7) and [11](#org77c322d))
As shown in Figure [10](#org4a1beff), the peak resonance of the pointing loop increase after the isolation loop is closed.
As shown in Figure [10](#org00362f7), the peak resonance of the pointing loop increase after the isolation loop is closed.
The resonances happen at both crossovers of the isolation loop (15Hz and 50Hz) and they may show of loss of robustness.
<a id="org4a1beff"></a>
<a id="org00362f7"></a>
{{< figure src="/ox-hugo/li01_closed_loop_pointing.png" caption="Figure 10: Closed-loop transfer functions \\(\theta\_y/\theta\_{y\_d}\\) of the pointing loop before and after the vibration isolation loop is closed" >}}
The same happens when first closing the vibration isolation loop and after the pointing loop (Figure [11](#org945793e)).
The same happens when first closing the vibration isolation loop and after the pointing loop (Figure [11](#org77c322d)).
The first peak resonance of the vibration isolation loop at 15Hz is increased when closing the pointing loop.
<a id="org945793e"></a>
<a id="org77c322d"></a>
{{< figure src="/ox-hugo/li01_closed_loop_vibration.png" caption="Figure 11: Closed-loop transfer functions of the vibration isolation loop before and after the pointing control loop is closed" >}}
@@ -165,18 +165,18 @@ The first peak resonance of the vibration isolation loop at 15Hz is increased wh
### Experimental results {#experimental-results}
Two hexapods are stacked (Figure [12](#orgbdc7900)):
Two hexapods are stacked (Figure [12](#org5977cb3)):
- the bottom hexapod is used to generate disturbances matching candidate applications
- the top hexapod provide simultaneous vibration isolation and pointing control
<a id="orgbdc7900"></a>
<a id="org5977cb3"></a>
{{< figure src="/ox-hugo/li01_test_bench.png" caption="Figure 12: Stacked Hexapods" >}}
Using the vibration isolation control alone, no attenuation is achieved below 1Hz as shown in figure [13](#org7a6d899).
Using the vibration isolation control alone, no attenuation is achieved below 1Hz as shown in figure [13](#org4707691).
<a id="org7a6d899"></a>
<a id="org4707691"></a>
{{< figure src="/ox-hugo/li01_vibration_isolation_control_results.png" caption="Figure 13: Vibration isolation control: open-loop (solid) vs. closed-loop (dashed)" >}}
@@ -185,9 +185,9 @@ The simultaneous control is of dual use:
- it provide simultaneous pointing and isolation control
- it can also be used to expand the bandwidth of the isolation control to low frequencies because the pointing loops suppress pointing errors due to both base vibrations and tracking
The results of simultaneous control is shown in Figure [14](#org15d93e5) where the bandwidth of the isolation control is expanded to very low frequency.
The results of simultaneous control is shown in Figure [14](#orge4b1f73) where the bandwidth of the isolation control is expanded to very low frequency.
<a id="org15d93e5"></a>
<a id="orge4b1f73"></a>
{{< figure src="/ox-hugo/li01_simultaneous_control_results.png" caption="Figure 14: Simultaneous control: open-loop (solid) vs. closed-loop (dashed)" >}}
@@ -216,6 +216,7 @@ Proposed future research areas include:
- **Geophones** to provide payload and base velocity information
## Bibliography {#bibliography}
<a id="org9c3830b"></a>Li, Xiaochun. 2001. “Simultaneous, Fault-Tolerant Vibration Isolation and Pointing Control of Flexure Jointed Hexapods.” University of Wyoming.
<a id="org7799941"></a>Li, Xiaochun. 2001. “Simultaneous, Fault-Tolerant Vibration Isolation and Pointing Control of Flexure Jointed Hexapods.” University of Wyoming.

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@@ -9,7 +9,7 @@ Tags
Reference
: ([McInroy and Hamann 2000](#orgb4fc604))
: ([McInroy and Hamann 2000](#org6ce0f37))
Author(s)
: McInroy, J., & Hamann, J.
@@ -18,6 +18,7 @@ Year
: 2000
## Bibliography {#bibliography}
<a id="orgb4fc604"></a>McInroy, J.E., and J.C. Hamann. 2000. “Design and Control of Flexure Jointed Hexapods.” _IEEE Transactions on Robotics and Automation_ 16 (4):372–81. <https://doi.org/10.1109/70.864229>.
<a id="org6ce0f37"></a>McInroy, J.E., and J.C. Hamann. 2000. “Design and Control of Flexure Jointed Hexapods.” _IEEE Transactions on Robotics and Automation_ 16 (4):372–81. <https://doi.org/10.1109/70.864229>.

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@@ -4,15 +4,11 @@ author = ["Thomas Dehaeze"]
draft = false
+++
Backlinks:
- [Identification and decoupling control of flexure jointed hexapods]({{< relref "chen00_ident_decoup_contr_flexur_joint_hexap" >}})
Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference
: ([McInroy 1999](#orgfc7fa52))
: ([McInroy 1999](#org788f3dd))
Author(s)
: McInroy, J.
@@ -20,7 +16,7 @@ Author(s)
Year
: 1999
This conference paper has been further published in a journal as a short note ([McInroy 2002](#org7752c60)).
This conference paper has been further published in a journal as a short note ([McInroy 2002](#org6bd1808)).
## Abstract {#abstract}
@@ -42,22 +38,22 @@ The actuators for FJHs can be divided into two categories:
1. soft (voice coil), which employs a spring flexure mount
2. hard (piezoceramic or magnetostrictive), which employs a compressive load spring.
<a id="orgd835559"></a>
<a id="orge71c3a4"></a>
{{< figure src="/ox-hugo/mcinroy99_general_hexapod.png" caption="Figure 1: A general Stewart Platform" >}}
Since both actuator types employ force production in parallel with a spring, they can both be modeled as shown in Figure [2](#org26f1840).
Since both actuator types employ force production in parallel with a spring, they can both be modeled as shown in Figure [2](#orgc6987ef).
In order to provide low frequency passive vibration isolation, the hard actuators are sometimes placed in series with additional passive springs.
<a id="org26f1840"></a>
<a id="orgc6987ef"></a>
{{< figure src="/ox-hugo/mcinroy99_strut_model.png" caption="Figure 2: The dynamics of the i'th strut. A parallel spring, damper and actuator drives the moving mass of the strut and a payload" >}}
<a id="table--tab:mcinroy99-strut-model"></a>
<div class="table-caption">
<span class="table-number"><a href="#table--tab:mcinroy99-strut-model">Table 1</a></span>:
Definition of quantities on Figure <a href="#org26f1840">2</a>
Definition of quantities on Figure <a href="#orgc6987ef">2</a>
</div>
| **Symbol** | **Meaning** |
@@ -74,11 +70,11 @@ In order to provide low frequency passive vibration isolation, the hard actuator
| \\(v\_i = p\_i - q\_i\\) | vector pointing from the bottom to the top |
| \\(\hat{u}\_i = v\_i/l\_i\\) | unit direction of the strut |
It is here supposed that \\(f\_{p\_i}\\) is predominantly in the strut direction (explained in ([McInroy 2002](#org7752c60))).
It is here supposed that \\(f\_{p\_i}\\) is predominantly in the strut direction (explained in ([McInroy 2002](#org6bd1808))).
This is a good approximation unless the spherical joints and extremely stiff or massive, of high inertia struts are used.
This allows to reduce considerably the complexity of the model.
From Figure [2](#org26f1840) (b), forces along the strut direction are summed to yield (projected along the strut direction, hence the \\(\hat{u}\_i^T\\) term):
From Figure [2](#orgc6987ef) (b), forces along the strut direction are summed to yield (projected along the strut direction, hence the \\(\hat{u}\_i^T\\) term):
\begin{equation}
m\_i \hat{u}\_i^T \ddot{p}\_i = f\_{m\_i} - f\_{p\_i} - m\_i \hat{u}\_i^Tg - k\_i(l\_i - l\_{r\_i}) - b\_i \dot{l}\_i
@@ -166,8 +162,9 @@ In the next section, a connection between the two will be found to complete the
## Control Example {#control-example}
## Bibliography {#bibliography}
<a id="orgfc7fa52"></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="org788f3dd"></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="org7752c60"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” _IEEE/ASME Transactions on Mechatronics_ 7 (1):95–99. <https://doi.org/10.1109/3516.990892>.
<a id="org6bd1808"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” _IEEE/ASME Transactions on Mechatronics_ 7 (1):95–99. <https://doi.org/10.1109/3516.990892>.

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@@ -8,7 +8,7 @@ Tags
: [Motion Control]({{< relref "motion_control" >}})
Reference
: ([Oomen 2018](#org18923fa))
: ([Oomen 2018](#org93151b9))
Author(s)
: Oomen, T.
@@ -16,11 +16,12 @@ Author(s)
Year
: 2018
<a id="orgf64e727"></a>
<a id="orgcc3437a"></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." >}}
## Bibliography {#bibliography}
<a id="org18923fa"></a>Oomen, Tom. 2018. “Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems.” _IEEJ Journal of Industry Applications_ 7 (2):127–40. <https://doi.org/10.1541/ieejjia.7.127>.
<a id="org93151b9"></a>Oomen, Tom. 2018. “Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems.” _IEEJ Journal of Industry Applications_ 7 (2):127–40. <https://doi.org/10.1541/ieejjia.7.127>.

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@@ -8,7 +8,7 @@ Tags
: [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
Reference
: ([Preumont et al. 2007](#org3b370bf))
: ([Preumont et al. 2007](#org66383b9))
Author(s)
: Preumont, A., Horodinca, M., Romanescu, I., Marneffe, B. d., Avraam, M., Deraemaeker, A., Bossens, F., …
@@ -18,34 +18,35 @@ Year
Summary:
- **Cubic** Stewart platform (Figure [3](#org0274a43))
- **Cubic** Stewart platform (Figure [3](#orga6bbb17))
- Provides uniform control capability
- Uniform stiffness in all directions
- minimizes the cross-coupling among actuators and sensors of different legs
- Flexible joints (Figure [2](#orge9ceb91))
- Flexible joints (Figure [2](#orga37017c))
- Piezoelectric force sensors
- Voice coil actuators
- Decentralized feedback control approach for vibration isolation
- Effect of parasitic stiffness of the flexible joints on the IFF performance (Figure [1](#orgb3c0578))
- Effect of parasitic stiffness of the flexible joints on the IFF performance (Figure [1](#orgec64e08))
- The Stewart platform has 6 suspension modes at different frequencies.
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.
- 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
<a id="orgb3c0578"></a>
<a id="orgec64e08"></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" >}}
<a id="orge9ceb91"></a>
<a id="orga37017c"></a>
{{< figure src="/ox-hugo/preumont07_flexible_joints.png" caption="Figure 2: Flexible joints used for the Stewart platform" >}}
<a id="org0274a43"></a>
<a id="orga6bbb17"></a>
{{< figure src="/ox-hugo/preumont07_stewart_platform.png" caption="Figure 3: Stewart platform" >}}
## Bibliography {#bibliography}
<a id="org3b370bf"></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):644–61. <https://doi.org/10.1016/j.jsv.2006.07.050>.
<a id="org66383b9"></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):644–61. <https://doi.org/10.1016/j.jsv.2006.07.050>.

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@@ -8,7 +8,7 @@ Tags
: [Complementary Filters]({{< relref "complementary_filters" >}}), [Virtual Sensor Fusion]({{< relref "virtual_sensor_fusion" >}})
Reference
: ([Saxena and Hote 2012](#org0284b71))
: ([Saxena and Hote 2012](#org6d87fa3))
Author(s)
: Saxena, S., & Hote, Y.
@@ -85,6 +85,7 @@ Issues:
The interesting feature regarding IMC is that the design scheme is identical to the open-loop control design procedure and the implementation of IMC results in a feedback system, thereby copying the disturbances and parameter uncertainties, while open-loop control is not.
## Bibliography {#bibliography}
<a id="org0284b71"></a>Saxena, Sahaj, and YogeshV Hote. 2012. “Advances in Internal Model Control Technique: A Review and Future Prospects.” _IETE Technical Review_ 29 (6):461. <https://doi.org/10.4103/0256-4602.105001>.
<a id="org6d87fa3"></a>Saxena, Sahaj, and YogeshV Hote. 2012. “Advances in Internal Model Control Technique: A Review and Future Prospects.” _IETE Technical Review_ 29 (6):461. <https://doi.org/10.4103/0256-4602.105001>.

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@@ -9,7 +9,7 @@ Tags
Reference
: ([Sayed and Kailath 2001](#orgaf03ac4))
: ([Sayed and Kailath 2001](#org9b5be86))
Author(s)
: Sayed, A. H., & Kailath, T.
@@ -18,6 +18,7 @@ Year
: 2001
## Bibliography {#bibliography}
<a id="orgaf03ac4"></a>Sayed, A. H., and T. Kailath. 2001. “A Survey of Spectral Factorization Methods.” _Numerical Linear Algebra with Applications_ 8 (6-7):467–96. <https://doi.org/10.1002/nla.250>.
<a id="org9b5be86"></a>Sayed, A. H., and T. Kailath. 2001. “A Survey of Spectral Factorization Methods.” _Numerical Linear Algebra with Applications_ 8 (6-7):467–96. <https://doi.org/10.1002/nla.250>.

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@@ -9,7 +9,7 @@ Tags
Reference
: ([Schroeck, Messner, and McNab 2001](#orgf8182bc))
: ([Schroeck, Messner, and McNab 2001](#org5e2e067))
Author(s)
: Schroeck, S., Messner, W., & McNab, R.
@@ -18,6 +18,7 @@ Year
: 2001
## Bibliography {#bibliography}
<a id="orgf8182bc"></a>Schroeck, S.J., W.C. Messner, and R.J. McNab. 2001. “On Compensator Design for Linear Time-Invariant Dual-Input Single-Output Systems.” _IEEE/ASME Transactions on Mechatronics_ 6 (1):50–57. <https://doi.org/10.1109/3516.914391>.
<a id="org5e2e067"></a>Schroeck, S.J., W.C. Messner, and R.J. McNab. 2001. “On Compensator Design for Linear Time-Invariant Dual-Input Single-Output Systems.” _IEEE/ASME Transactions on Mechatronics_ 6 (1):50–57. <https://doi.org/10.1109/3516.914391>.

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@@ -8,7 +8,7 @@ Tags
: [Sensor Fusion]({{< relref "sensor_fusion" >}})
Reference
: ([Sebastian and Pantazi 2012](#org03bb39f))
: ([Sebastian and Pantazi 2012](#orgacf93b4))
Author(s)
: Sebastian, A., & Pantazi, A.
@@ -17,6 +17,7 @@ Year
: 2012
## Bibliography {#bibliography}
<a id="org03bb39f"></a>Sebastian, Abu, and Angeliki Pantazi. 2012. “Nanopositioning with Multiple Sensors: A Case Study in Data Storage.” _IEEE Transactions on Control Systems Technology_ 20 (2):382–94. <https://doi.org/10.1109/tcst.2011.2177982>.
<a id="orgacf93b4"></a>Sebastian, Abu, and Angeliki Pantazi. 2012. “Nanopositioning with Multiple Sensors: A Case Study in Data Storage.” _IEEE Transactions on Control Systems Technology_ 20 (2):382–94. <https://doi.org/10.1109/tcst.2011.2177982>.

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@@ -8,7 +8,7 @@ Tags
: [Active Damping]({{< relref "active_damping" >}})
Reference
: ([Souleille et al. 2018](#org5546d0c))
: ([Souleille et al. 2018](#org5548942))
Author(s)
: 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}
Figure [1](#org8634178) shows a picture of the amplified piezoelectric stack.
Figure [1](#org0952ca2) 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.
<a id="org8634178"></a>
<a id="org0952ca2"></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" >}}
@@ -61,38 +61,39 @@ and the control force is given by:
f = F\_s G(s) = F\_s \frac{g}{s}
\end{equation}
The effect of the controller are shown in Figure [2](#orgcb733df):
The effect of the controller are shown in Figure [2](#orgb36ba37):
- the resonance peak is almost critically damped
- 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 fraction of the force transmitted to the payload that is measured by the force sensor is reduced at low frequencies
<a id="orgcb733df"></a>
<a id="orgb36ba37"></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)" >}}
<a id="orga434456"></a>
<a id="org5119227"></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" >}}
## 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](#org09ac00a)).
A heavy payload is mounted on a set of three isolators (Figure [4](#orgbe1030b)).
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="org09ac00a"></a>
<a id="orgbe1030b"></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" >}}
As shown in Figure [5](#org2dcbc51), both the suspension modes and the flexible modes of the payload can be critically damped.
As shown in Figure [5](#orgbb573b8), both the suspension modes and the flexible modes of the payload can be critically damped.
<a id="org2dcbc51"></a>
<a id="orgbb573b8"></a>
{{< figure src="/ox-hugo/souleille18_result_damping_transmissibility.png" caption="Figure 5: Transmissibility between the table top \\(w\\) and \\(m\_1\\)" >}}
## Bibliography {#bibliography}
<a id="org5546d0c"></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:157–65.
<a id="org5548942"></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:157–65.

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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}})
Reference
: ([Tang, Cao, and Yu 2018](#org45ebb6f))
: ([Tang, Cao, and Yu 2018](#org44aa05e))
Author(s)
: Tang, J., Cao, D., & Yu, T.
@@ -17,6 +17,7 @@ Year
: 2018
## Bibliography {#bibliography}
<a id="org45ebb6f"></a>Tang, Jie, Dengqing Cao, and Tianhu Yu. 2018. “Decentralized Vibration Control of a Voice Coil Motor-Based Stewart Parallel Mechanism: Simulation and Experiments.” _Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science_ 233 (1):132–45. <https://doi.org/10.1177/0954406218756941>.
<a id="org44aa05e"></a>Tang, Jie, Dengqing Cao, and Tianhu Yu. 2018. “Decentralized Vibration Control of a Voice Coil Motor-Based Stewart Parallel Mechanism: Simulation and Experiments.” _Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science_ 233 (1):132–45. <https://doi.org/10.1177/0954406218756941>.

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@@ -8,7 +8,7 @@ Tags
: [Nano Active Stabilization System]({{< relref "nano_active_stabilization_system" >}})
Reference
: ([Wang et al. 2012](#org187cf70))
: ([Wang et al. 2012](#org172c2d6))
Author(s)
: Wang, J., Chen, Y. K., Yuan, Q., Tkachuk, A., Erdonmez, C., Hornberger, B., & Feser, M.
@@ -26,6 +26,7 @@ There is a need for markerless nano-tomography
It uses calibrated metrology disc and capacitive sensors
## Bibliography {#bibliography}
<a id="org187cf70"></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>.
<a id="org172c2d6"></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" >}})
Reference
: ([Wang et al. 2016](#orgda82aa7))
: ([Wang et al. 2016](#org6a7c8f9))
Author(s)
: 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 proposed model is thus effective.
<a id="orgc0b4cf5"></a>
<a id="org5acb23c"></a>
{{< 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
- direct feedback of integrated forces => dampen vibration of inherent modes and thus reduce random vibrations
Force Feedback (Figure [2](#orgaf56f94)).
Force Feedback (Figure [2](#org25780ff)).
- the force sensor is mounted **between the base and the strut**
<a id="orgaf56f94"></a>
<a id="org25780ff"></a>
{{< figure src="/ox-hugo/wang16_force_feedback.png" caption="Figure 2: Feedback of integrated forces in the platform" >}}
@@ -54,6 +54,7 @@ Sorts of HAC-LAC control:
- Effectiveness of control methods are shown
## Bibliography {#bibliography}
<a id="orgda82aa7"></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:1–19. <https://doi.org/10.1016/j.jsv.2016.07.021>.
<a id="org6a7c8f9"></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:1–19. <https://doi.org/10.1016/j.jsv.2016.07.021>.

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Reference
: ([Yun et al. 2020](#orgd3a0930))
: ([Yun et al. 2020](#org2a2f02a))
Author(s)
: Yun, H., Liu, L., Li, Q., & Yang, H.
@@ -18,6 +18,7 @@ Year
: 2020
## Bibliography {#bibliography}
<a id="orgd3a0930"></a>Yun, Hai, Lei Liu, Qing Li, and Hongjie Yang. 2020. “Investigation on Two-Stage Vibration Suppression and Precision Pointing for Space Optical Payloads.” _Aerospace Science and Technology_ 96 (nil):105543. <https://doi.org/10.1016/j.ast.2019.105543>.
<a id="org2a2f02a"></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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: [Vibration Isolation]({{< relref "vibration_isolation" >}})
Reference
: ([Zuo 2004](#orgb4186fb))
: ([Zuo 2004](#orgd9c4f73))
Author(s)
: Zuo, L.
@@ -40,23 +40,24 @@ Year
> They found that coupling from flexible modes is much smaller than in soft active mounts in the load (force) feedback.
> Note that reaction force actuators can also work with soft mounts or hard mounts.
<a id="orgd66c057"></a>
<a id="orgc88908d"></a>
{{< figure src="/ox-hugo/zuo04_piezo_spring_series.png" caption="Figure 1: PZT actuator and spring in series" >}}
<a id="org1008b43"></a>
<a id="orgb14b6c0"></a>
{{< figure src="/ox-hugo/zuo04_voice_coil_spring_parallel.png" caption="Figure 2: Voice coil actuator and spring in parallel" >}}
<a id="orgab03e30"></a>
<a id="org96eaaed"></a>
{{< figure src="/ox-hugo/zuo04_piezo_plant.png" caption="Figure 3: Transmission from PZT voltage to geophone output" >}}
<a id="orgc03f8c8"></a>
<a id="orgaf13ec6"></a>
{{< figure src="/ox-hugo/zuo04_voice_coil_plant.png" caption="Figure 4: Transmission from voice coil voltage to geophone output" >}}
## Bibliography {#bibliography}
<a id="orgb4186fb"></a>Zuo, Lei. 2004. “Element and System Design for Active and Passive Vibration Isolation.” Massachusetts Institute of Technology.
<a id="orgd9c4f73"></a>Zuo, Lei. 2004. “Element and System Design for Active and Passive Vibration Isolation.” Massachusetts Institute of Technology.