Add notes about sensors/actuators

content/zettels/collocated_control.md

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+title = "Collocated Control"
+author = ["Thomas Dehaeze"]
+draft = false
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+
+Tags
+: [Actuators]({{< relref "actuators" >}}), [Force Sensors]({{< relref "force_sensors" >}}), [Position Sensors]({{< relref "position_sensors" >}}), [Inertial Sensors]({{< relref "inertial_sensors" >}})
+
+
+## Collocated/Dual actuator and sensor {#collocated-dual-actuator-and-sensor}
+
+According to <sup id="454500a3af67ef66a7a754d1f2e1bd4a"><a class="reference-link" href="#preumont18_vibrat_contr_activ_struc_fourt_edition" title="Andre Preumont, Vibration Control of Active Structures - Fourth Edition, Springer International Publishing (2018).">(Andre Preumont, 2018)</a></sup>:
+
+> A **collocated** control system is a control system where the actuator and the sensor are attached to the same degree of freedom.
+>
+> It is not sufficient to be attached to the same location, but they must also be **dual**, that is a force actuator must be associated with a translation sensor (measuring displacement, velocity, or acceleration), in such a way that the product of the actuator signal and the sensor signal represents the energy (power) exchange between the structure and the control system.
+
+
+## Nearly Collocated Actuator Sensor Pair {#nearly-collocated-actuator-sensor-pair}
+
+From Figure [1](#org00adcca), it is clear that at some frequency / for some mode, the actuator and the sensor will not be collocated anymore (here starting with mode 3).
+
+<a id="org00adcca"></a>
+
+{{< figure src="/ox-hugo/preumont18_nearly_collocated_schematic.png" caption="Figure 1: Mode shapes for a uniform beam. \\(u\\) and \\(y\\) are not collocated actuator and sensor" >}}
+
+
+## Piezoelectric Stack as a sensor/actuator pair {#piezoelectric-stack-as-a-sensor-actuator-pair}
+
+One can use on part of a piezoelectric stack as an actuator and the other part as a sensor.
+
+At some frequency, the sensor/actuator pair will not be collocated anymore.
+
+If we want to be collocated up to the highest possible frequency, the sensor part should be made small.
+Of course, this will reduce the sensibility.
+
+-   [ ] What happens is small pieces of actuators are mixed with small pieces of sensors?
+
+# Bibliography
+<a class="bibtex-entry" id="preumont18_vibrat_contr_activ_struc_fourt_edition">Preumont, A., *Vibration control of active structures - fourth edition* (2018), : Springer International Publishing.</a> [↩](#454500a3af67ef66a7a754d1f2e1bd4a)