44 lines
2.4 KiB
Markdown
44 lines
2.4 KiB
Markdown
+++
|
|
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, Andre. 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>
|