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title = "A concept of active mount for space applications"
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author = ["Thomas Dehaeze"]
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author = ["Dehaeze Thomas"]
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draft = false
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Tags
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: [Active Damping](active_damping.md)
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: [Active Damping]({{< relref "active_damping.md" >}})
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Reference
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: ([Souleille et al. 2018](#orgdd47abc))
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: (<a href="#citeproc_bib_item_1">Souleille et al. 2018</a>)
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Author(s)
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: Souleille, A., Lampert, T., Lafarga, V., Hellegouarch, S., Rondineau, A., Rodrigues, Gonccalo, & Collette, C.
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: Souleille, A., Lampert, T., Lafarga, V., Hellegouarch, S., Rondineau, A., Rodrigues, Gonccalo, & Collette, C.
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Year
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: 2018
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@@ -23,25 +23,25 @@ This article discusses the use of Integral Force Feedback with amplified piezoel
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## Single degree-of-freedom isolator {#single-degree-of-freedom-isolator}
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Figure [1](#org4d65c6e) shows a picture of the amplified piezoelectric stack.
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Figure [1](#figure--fig:souleille18-model-piezo) shows a picture of the amplified piezoelectric stack.
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The piezoelectric actuator is divided into two parts: one is used as an actuator, and the other one is used as a force sensor.
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<a id="org4d65c6e"></a>
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<a id="figure--fig:souleille18-model-piezo"></a>
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{{< 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" >}}
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{{< figure src="/ox-hugo/souleille18_model_piezo.png" caption="<span class=\"figure-number\">Figure 1: </span>Picture of an APA100M from Cedrat Technologies. Simplified model of a one DoF payload mounted on such isolator" >}}
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<div class="table-caption">
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<span class="table-number">Table 1</span>:
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Parameters used for the model of the APA 100M
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</div>
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| | Value | Meaning |
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|------------|-----------------------|----------------------------------------------------------------|
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| \\(m\\) | \\(1\,[kg]\\) | Payload mass |
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| \\(k\_e\\) | \\(4.8\,[N/\mu m]\\) | Stiffness used to adjust the pole of the isolator |
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| \\(k\_1\\) | \\(0.96\,[N/\mu m]\\) | Stiffness of the metallic suspension when the stack is removed |
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| \\(k\_a\\) | \\(65\,[N/\mu m]\\) | Stiffness of the actuator |
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| \\(c\_1\\) | \\(10\,[N/(m/s)]\\) | Added viscous damping |
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| | Value | Meaning |
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|------------|------------------------|----------------------------------------------------------------|
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| \\(m\\) | \\(1\\,[kg]\\) | Payload mass |
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| \\(k\_e\\) | \\(4.8\\,[N/\mu m]\\) | Stiffness used to adjust the pole of the isolator |
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| \\(k\_1\\) | \\(0.96\\,[N/\mu m]\\) | Stiffness of the metallic suspension when the stack is removed |
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| \\(k\_a\\) | \\(65\\,[N/\mu m]\\) | Stiffness of the actuator |
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| \\(c\_1\\) | \\(10\\,[N/(m/s)]\\) | Added viscous damping |
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The dynamic equation of the system is:
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@@ -61,39 +61,40 @@ and the control force is given by:
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f = F\_s G(s) = F\_s \frac{g}{s}
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\end{equation}
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The effect of the controller are shown in Figure [2](#org3336e8f):
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The effect of the controller are shown in Figure [2](#figure--fig:souleille18-tf-iff-result):
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- the resonance peak is almost critically damped
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- the passive isolation \\(\frac{x\_1}{w}\\) is not degraded at high frequencies
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- the degradation of the compliance \\(\frac{x\_1}{F}\\) induced by feedback is limited at \\(\frac{1}{k\_1}\\)
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- the fraction of the force transmitted to the payload that is measured by the force sensor is reduced at low frequencies
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<a id="org3336e8f"></a>
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<a id="figure--fig:souleille18-tf-iff-result"></a>
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{{< 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)" >}}
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{{< figure src="/ox-hugo/souleille18_tf_iff_result.png" caption="<span class=\"figure-number\">Figure 2: </span>Matrix of transfer functions from input (w, f, F) to output (Fs, x1) in open loop (blue curves) and closed loop (dashed red curves)" >}}
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<a id="org20a69be"></a>
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<a id="figure--fig:souleille18-root-locus"></a>
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{{< 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" >}}
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{{< figure src="/ox-hugo/souleille18_root_locus.png" caption="<span class=\"figure-number\">Figure 3: </span>Single DoF system. Comparison between the theoretical (solid curve) and the experimental (crosses) root-locus" >}}
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## Flexible payload mounted on three isolators {#flexible-payload-mounted-on-three-isolators}
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A heavy payload is mounted on a set of three isolators (Figure [4](#orga310d92)).
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A heavy payload is mounted on a set of three isolators (Figure [4](#figure--fig:souleille18-setup-flexible-payload)).
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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.
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<a id="orga310d92"></a>
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<a id="figure--fig:souleille18-setup-flexible-payload"></a>
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{{< 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" >}}
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{{< figure src="/ox-hugo/souleille18_setup_flexible_payload.png" caption="<span class=\"figure-number\">Figure 4: </span>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" >}}
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As shown in Figure [5](#org3c2e029), both the suspension modes and the flexible modes of the payload can be critically damped.
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As shown in Figure [5](#figure--fig:souleille18-result-damping-transmissibility), both the suspension modes and the flexible modes of the payload can be critically damped.
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<a id="org3c2e029"></a>
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{{< figure src="/ox-hugo/souleille18_result_damping_transmissibility.png" caption="Figure 5: Transmissibility between the table top \\(w\\) and \\(m\_1\\)" >}}
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<a id="figure--fig:souleille18-result-damping-transmissibility"></a>
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{{< figure src="/ox-hugo/souleille18_result_damping_transmissibility.png" caption="<span class=\"figure-number\">Figure 5: </span>Transmissibility between the table top \\(w\\) and \\(m\_1\\)" >}}
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## Bibliography {#bibliography}
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<a id="orgdd47abc"></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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<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
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<div class="csl-entry"><a id="citeproc_bib_item_1"></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.” <i>Ceas Space Journal</i> 10 (2). Springer: 157–65.</div>
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</div>
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