4.6 KiB
+++ title = "A concept of active mount for space applications" author = ["Thomas Dehaeze"] draft = false +++
- Tags
- [Active Damping]({{< relref "active_damping" >}})
- Reference
- (Souleille et al. 2018)
- Author(s)
- Souleille, A., Lampert, T., Lafarga, V., Hellegouarch, S., Rondineau, A., Rodrigues, Gonccalo, & Collette, C.
- Year
- 2018
This article discusses the use of Integral Force Feedback with amplified piezoelectric stack actuators.
In the proposed configuration, it can also be noticed by the softening effect inherent to force control is limited by the metallic suspension.
Single degree-of-freedom isolator
Figure 1 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.
{{< 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" >}}
| Value | Meaning | |
|---|---|---|
| \(m\) | \(1,[kg]\) | Payload mass |
| \(k_e\) | \(4.8,[N/\mu m]\) | Stiffness used to adjust the pole of the isolator |
| \(k_1\) | \(0.96,[N/\mu m]\) | Stiffness of the metallic suspension when the stack is removed |
| \(k_a\) | \(65,[N/\mu m]\) | Stiffness of the actuator |
| \(c_1\) | \(10,[N/(m/s)]\) | Added viscous damping |
The dynamic equation of the system is:
\begin{equation} 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 \end{equation}
The expression of the force measured by the force sensor is:
\begin{equation} 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 \end{equation}
and the control force is given by:
\begin{equation} f = F_s G(s) = F_s \frac{g}{s} \end{equation}
The effect of the controller are shown in Figure 2:
- 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
{{< 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)" >}}
{{< 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
A heavy payload is mounted on a set of three isolators (Figure 4). 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.
{{< 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, both the suspension modes and the flexible modes of the payload can be critically damped.
{{< figure src="/ox-hugo/souleille18_result_damping_transmissibility.png" caption="Figure 5: Transmissibility between the table top \(w\) and \(m_1\)" >}}
Bibliography
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.