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title = "Sensors and control of a space-based six-axis vibration isolation system"
author = ["Thomas Dehaeze"]
author = ["Dehaeze Thomas"]
draft = false
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Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Cubic Architecture]({{< relref "cubic_architecture" >}})
: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}}), [Cubic Architecture]({{< relref "cubic_architecture.md" >}})
Reference
: ([Hauge and Campbell 2004](#org186272b))
: (<a href="#citeproc_bib_item_1">Hauge and Campbell 2004</a>)
Author(s)
: Hauge, G., & Campbell, M.
: Hauge, G., &amp; Campbell, M.
Year
: 2004
@@ -24,22 +24,22 @@ Year
- Vibration isolation using a Stewart platform
- Experimental comparison of Force sensor and Inertial Sensor and associated control architecture for vibration isolation
<a id="org37bf22a"></a>
<a id="figure--fig:hauge04-stewart-platform"></a>
{{< figure src="/ox-hugo/hauge04_stewart_platform.png" caption="Figure 1: Hexapod for active vibration isolation" >}}
{{< figure src="/ox-hugo/hauge04_stewart_platform.png" caption="<span class=\"figure-number\">Figure 1: </span>Hexapod for active vibration isolation" >}}
**Stewart platform** (Figure [1](#org37bf22a)):
**Stewart platform** (Figure [1](#figure--fig:hauge04-stewart-platform)):
- Low corner frequency
- Large actuator stroke (\\(\pm5mm\\))
- Sensors in each strut (Figure [2](#org8b97871)):
- Sensors in each strut (Figure [2](#figure--fig:hauge05-struts)):
- three-axis load cell
- base and payload geophone in parallel with the struts
- LVDT
<a id="org8b97871"></a>
<a id="figure--fig:hauge05-struts"></a>
{{< figure src="/ox-hugo/hauge05_struts.png" caption="Figure 2: Strut" >}}
{{< figure src="/ox-hugo/hauge05_struts.png" caption="<span class=\"figure-number\">Figure 2: </span>Strut" >}}
> Force sensors typically work well because they are not as sensitive to payload and base dynamics, but are limited in performance by a low-frequency zero pair resulting from the cross-axial stiffness.
@@ -64,9 +64,9 @@ With \\(|T(\omega)|\\) is the Frobenius norm of the transmissibility matrix and
- single strut axis as the cubic Stewart platform can be decomposed into 6 single-axis systems
<a id="org1bec2a6"></a>
<a id="figure--fig:hauge05-strut-model"></a>
{{< figure src="/ox-hugo/hauge04_strut_model.png" caption="Figure 3: Strut model" >}}
{{< figure src="/ox-hugo/hauge04_strut_model.png" caption="<span class=\"figure-number\">Figure 3: </span>Strut model" >}}
**Zero Pair when using a Force Sensor**:
@@ -76,8 +76,8 @@ With \\(|T(\omega)|\\) is the Frobenius norm of the transmissibility matrix and
**Control**:
- Single-axis controllers => combine them into a full six-axis controller => evaluate the full controller in terms of stability and robustness
- Sensitivity weighted LQG controller (SWLQG) => address robustness in flexible dynamic systems
- Single-axis controllers =&gt; combine them into a full six-axis controller =&gt; evaluate the full controller in terms of stability and robustness
- Sensitivity weighted LQG controller (SWLQG) =&gt; address robustness in flexible dynamic systems
- Three type of controller:
- Force feedback (cell-based)
- Inertial feedback (geophone-based)
@@ -126,7 +126,7 @@ And we find that for \\(u\\) and \\(y\\) to be an acceptable pair for high gain
**Inertial feedback**:
- Non-Collocated => multiple phase drops that limit the bandwidth of the controller
- Non-Collocated =&gt; multiple phase drops that limit the bandwidth of the controller
- Good performance, but the transmissibility "pops" due to low phase margin and thus this indicates robustness problems
**Combined force/velocity feedback**:
@@ -136,12 +136,13 @@ And we find that for \\(u\\) and \\(y\\) to be an acceptable pair for high gain
- The performance requirements are met
- Good robustness
<a id="org0a496f7"></a>
{{< figure src="/ox-hugo/hauge04_obtained_transmissibility.png" caption="Figure 4: Experimental open loop (solid) and closed loop six-axis transmissibility using the geophone only controller (dotted), and combined geophone/load cell controller (dashed)" >}}
<a id="figure--fig:hauge04-obtained-transmissibility"></a>
{{< figure src="/ox-hugo/hauge04_obtained_transmissibility.png" caption="<span class=\"figure-number\">Figure 4: </span>Experimental open loop (solid) and closed loop six-axis transmissibility using the geophone only controller (dotted), and combined geophone/load cell controller (dashed)" >}}
## Bibliography {#bibliography}
<a id="org186272b"></a>Hauge, G.S., and M.E. Campbell. 2004. “Sensors and Control of a Space-Based Six-Axis Vibration Isolation System.” _Journal of Sound and Vibration_ 269 (3-5):91331. <https://doi.org/10.1016/s0022-460x(03)>00206-2.
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Hauge, G.S., and M.E. Campbell. 2004. “Sensors and Control of a Space-Based Six-Axis Vibration Isolation System.” <i>Journal of Sound and Vibration</i> 269 (3-5): 91331. doi:<a href="https://doi.org/10.1016/s0022-460x(03)00206-2">10.1016/s0022-460x(03)00206-2</a>.</div>
</div>