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content/article/preumont02_force_feedb_versus_accel_feedb.md

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+title = "Force feedback versus acceleration feedback in active vibration isolation"
+author = ["Dehaeze Thomas"]
+draft = false
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+
+Tags
+: [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
+
+Reference
+: (<a href="#citeproc_bib_item_1">Preumont et al. 2002</a>)
+
+Author(s)
+: Preumont, A., A. Francois, Bossens, F., &amp; Abu-Hanieh, A.
+
+Year
+: 2002
+
+Summary:
+
+-   Compares the force feedback and acceleration feedback for active damping
+-   The use of a force sensor always give alternating poles and zeros in the open-loop transfer function between for force actuator and the force sensor which **guarantees the stability of the closed loop**
+-   Acceleration feedback produces alternating poles and zeros only when the flexible structure is stiff compared to the isolation system
+
+The force applied to a **rigid body** is proportional to its acceleration, thus sensing the total interface force gives a measured of the absolute acceleration of the solid body.
+Thus force feedback and acceleration feedback are equivalent for solid bodies.
+When there is a flexible payload, the two sensing options are not longer equivalent.
+
+-   For light payload ([Figure 1](#figure--fig:preumont02-force-acc-fb-light)), the acceleration feedback gives larger damping on the higher mode.
+-   For heavy payload ([Figure 2](#figure--fig:preumont02-force-acc-fb-heavy)), the acceleration feedback do not give alternating poles and zeros and thus for high control gains, the system becomes unstable
+
+<a id="figure--fig:preumont02-force-acc-fb-light"></a>
+
+{{< figure src="/ox-hugo/preumont02_force_acc_fb_light.png" caption="<span class='figure-number'>Figure 1: </span>Root locus for **light** flexible payload, (a) Force feedback, (b) acceleration feedback" >}}
+
+<a id="figure--fig:preumont02-force-acc-fb-heavy"></a>
+
+{{< figure src="/ox-hugo/preumont02_force_acc_fb_heavy.png" caption="<span class='figure-number'>Figure 2: </span>Root locus for **heavy** flexible payload, (a) Force feedback, (b) acceleration feedback" >}}
+
+Guaranteed stability of the force feedback:
+
+> If two arbitrary flexible, undamped structures are connected with a single-axis soft isolator with force feedback, the poles and zeros of the open-loop transfer function from the force actuator to the force sensor alternate on the imaginary axis.
+
+The same is true for the transfer function from the force actuator to the relative displacement of the actuator.
+
+> According to physical interpretation of the zeros, they represent the resonances of the subsystem  constrained by the sensor and the actuator.
+
+
+## Bibliography {#bibliography}
+
+<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>Preumont, A., A. François, F. Bossens, and A. Abu-Hanieh. 2002. “Force Feedback versus Acceleration Feedback in Active Vibration Isolation.” <i>Journal of Sound and Vibration</i> 257 (4): 605–13. doi:<a href="https://doi.org/10.1006/jsvi.2002.5047">10.1006/jsvi.2002.5047</a>.</div>
+</div>