Add all bibliographic notes and zettels

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+title = "Collocated Control"
+author = ["Dehaeze Thomas"]
+draft = false
+++
+
+Tags
+: [Actuators]({{< relref "actuators.md" >}}), [Force Sensors]({{< relref "force_sensors.md" >}}), [Position Sensors]({{< relref "position_sensors.md" >}}), [Inertial Sensors]({{< relref "inertial_sensors.md" >}})
+
+
+## Collocated/Dual actuator and sensor {#collocated-dual-actuator-and-sensor}
+
+According to (<a href="#citeproc_bib_item_1">Preumont 2018</a>):
+
+> 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](#figure--fig:preumont18-nearly-collocated-schematic), 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="figure--fig:preumont18-nearly-collocated-schematic"></a>
+
+{{< figure src="/ox-hugo/preumont18_nearly_collocated_schematic.png" caption="<span class='figure-number'>Figure 1: </span>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]({{< relref "piezoelectric_actuators.md" >}}) 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.
+
+
+## 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. 2018. <i>Vibration Control of Active Structures - Fourth Edition</i>. Solid Mechanics and Its Applications. Springer International Publishing. doi:<a href="https://doi.org/10.1007/978-3-319-72296-2">10.1007/978-3-319-72296-2</a>.</div>
+</div>