Update Content - 2022-03-15

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title = "Nanopositioning system with force feedback for high-performance tracking and vibration control"
author = ["Thomas Dehaeze"]
author = ["Dehaeze Thomas"]
draft = false
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Tags
: [Sensor Fusion]({{< relref "sensor_fusion" >}}), [Force Sensors]({{< relref "force_sensors" >}})
: [Sensor Fusion]({{< relref "sensor_fusion.md" >}}), [Force Sensors]({{< relref "force_sensors.md" >}})
Reference
: ([Fleming 2010](#org21788cf))
: (<a href="#citeproc_bib_item_1">Fleming 2010</a>)
Author(s)
: Fleming, A.
@@ -31,9 +31,9 @@ Year
## Model of a multi-layer monolithic piezoelectric stack actuator {#model-of-a-multi-layer-monolithic-piezoelectric-stack-actuator}
<a id="org699947b"></a>
<a id="figure--fig:fleming10-piezo-model"></a>
{{< figure src="/ox-hugo/fleming10_piezo_model.png" caption="Figure 1: Schematic of a multi-layer monolithic piezoelectric stack actuator model" >}}
{{< figure src="/ox-hugo/fleming10_piezo_model.png" caption="<span class=\"figure-number\">Figure 1: </span>Schematic of a multi-layer monolithic piezoelectric stack actuator model" >}}
The actuator experiences an internal stress in response to an applied voltage.
This stress is represented by the voltage dependent force \\(F\_a\\) and is related to free displacement by
@@ -78,7 +78,7 @@ If an **n-layer** piezoelectric transducer is used as a force sensor, the genera
We can use a **charge amplifier** to measure the force \\(F\_s\\).
{{< figure src="/ox-hugo/fleming10_charge_ampl_piezo.png" caption="Figure 2: Electrical model of a piezoelectric force sensor is shown in gray. Developed charge \\(q\\) is proportional to the strain and hence the force experienced by the sensor. Op-amp charge amplifier produces an output voltage \\(V\_s\\) equal to \\(-q/C\_s\\)" >}}
{{< figure src="/ox-hugo/fleming10_charge_ampl_piezo.png" caption="<span class=\"figure-number\">Figure 2: </span>Electrical model of a piezoelectric force sensor is shown in gray. Developed charge \\(q\\) is proportional to the strain and hence the force experienced by the sensor. Op-amp charge amplifier produces an output voltage \\(V\_s\\) equal to \\(-q/C\_s\\)" >}}
The output voltage \\(V\_s\\) is equal to
\\[ V\_s = -\frac{q}{C\_s} = -\frac{n d\_{33}F\_s}{C\_s} \\]
@@ -116,12 +116,13 @@ The capacitance of a piezoelectric stack is typically between \\(1 \mu F\\) and
## Tested feedback control strategies {#tested-feedback-control-strategies}
<a id="orgc6b14a0"></a>
{{< figure src="/ox-hugo/fleming10_fb_control_strats.png" caption="Figure 3: Comparison of: (a) basic integral control. (b) direct tracking control. (c) dual-sensor feedback. (d) low frequency bypass" >}}
<a id="figure--fig:fleming10-fb-control-strats"></a>
{{< figure src="/ox-hugo/fleming10_fb_control_strats.png" caption="<span class=\"figure-number\">Figure 3: </span>Comparison of: (a) basic integral control. (b) direct tracking control. (c) dual-sensor feedback. (d) low frequency bypass" >}}
## Bibliography {#bibliography}
<a id="org21788cf"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):43347. <https://doi.org/10.1109/tmech.2009.2028422>.
<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>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” <i>Ieee/Asme Transactions on Mechatronics</i> 15 (3): 43347. doi:<a href="https://doi.org/10.1109/tmech.2009.2028422">10.1109/tmech.2009.2028422</a>.</div>
</div>