97 lines
4.9 KiB
Markdown
97 lines
4.9 KiB
Markdown
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title = "A concept of active mount for space applications"
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author = ["Thomas Dehaeze"]
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: [Active Damping]({{< relref "active_damping" >}})
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Reference
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: <sup id="d5c1263eebe6caa1e91b078b620d72f1"><a class="reference-link" href="#souleille18_concep_activ_mount_space_applic" title="Souleille, Lampert, Lafarga, , Hellegouarch, Rondineau, Rodrigues, Gon\ccalo \& Collette, A Concept of Active Mount for Space Applications, {CEAS Space Journal}, v(2), 157--165 (2018).">(Souleille {\it et al.}, 2018)</a></sup>
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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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Year
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: 2018
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This article discusses the use of Integral Force Feedback with amplified piezoelectric stack actuators.
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> In the proposed configuration, it can also be noticed by the softening effect inherent to force control is limited by the metallic suspension.
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## Single degree-of-freedom isolator {#single-degree-of-freedom-isolator}
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Figure [1](#orgec40a2d) 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="orgec40a2d"></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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<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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The dynamic equation of the system is:
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\begin{equation}
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m \ddot{x}\_1 = \left( k\_1 + \frac{k\_ek\_a}{k\_e + k\_a} \right) ( w - x\_1) + c\_1 (\dot{w} - \dot{x}\_1) + F + \left( \frac{k\_e}{k\_e + k\_a} \right)f
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\end{equation}
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The expression of the force measured by the force sensor is:
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\begin{equation}
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F\_s = \left( -\frac{k\_e k\_a}{k\_e + k\_a} \right) x\_1 + \left( \frac{k\_e k\_a}{k\_e + k\_a} \right) w + \left( \frac{k\_e}{k\_e + k\_a} \right) f
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\end{equation}
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and the control force is given by:
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\begin{equation}
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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](#org656442f):
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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="org656442f"></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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<a id="orgd1fa41a"></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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## 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](#org59a9fbf)).
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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="org59a9fbf"></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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As shown in Figure [5](#orgb30c1f0), both the suspension modes and the flexible modes of the payload can be critically damped.
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<a id="orgb30c1f0"></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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# Bibliography
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<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)*, 157–165 (2018). </a> [↩](#d5c1263eebe6caa1e91b078b620d72f1)
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