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content/article/fleming10_nanop_system_with_force_feedb.md
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### Backlinks {#backlinks} Backlinks:
- [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}}) - [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
- [Force Sensors]({{< relref "force_sensors" >}}) - [Force Sensors]({{< relref "force_sensors" >}})
@ -13,7 +13,7 @@ Tags
: [Sensor Fusion]({{< relref "sensor_fusion" >}}), [Force Sensors]({{< relref "force_sensors" >}}) : [Sensor Fusion]({{< relref "sensor_fusion" >}}), [Force Sensors]({{< relref "force_sensors" >}})
Reference Reference
: ([Fleming 2010](#org6fe1b59)) : ([Fleming 2010](#org5c1a566))
Author(s) Author(s)
: Fleming, A. : Fleming, A.
@ -36,7 +36,7 @@ Year
## Model of a multi-layer monolithic piezoelectric stack actuator {#model-of-a-multi-layer-monolithic-piezoelectric-stack-actuator} ## Model of a multi-layer monolithic piezoelectric stack actuator {#model-of-a-multi-layer-monolithic-piezoelectric-stack-actuator}
<a id="orgb6bab68"></a> <a id="org8318193"></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="Figure 1: Schematic of a multi-layer monolithic piezoelectric stack actuator model" >}}
@ -119,6 +119,13 @@ The current noise density of a general purpose LM833 FET-input op-amp is \\(0.5\
The capacitance of a piezoelectric stack is typically between \\(1 \mu F\\) and \\(100 \mu F\\). The capacitance of a piezoelectric stack is typically between \\(1 \mu F\\) and \\(100 \mu F\\).
## Tested feedback control strategies {#tested-feedback-control-strategies}
<a id="orgab9a9d3"></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" >}}
## Bibliography {#bibliography} ## Bibliography {#bibliography}
<a id="org6fe1b59"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>. <a id="org5c1a566"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.

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| Cedrat | [link](http://www.cedrat-technologies.com/) | France | | Cedrat | [link](http://www.cedrat-technologies.com/) | France |
| PI | [link](https://www.physikinstrumente.com/en/) | USA | | PI | [link](https://www.physikinstrumente.com/en/) | USA |
| Piezo System | [link](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/) | Germany | | Piezo System | [link](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/) | Germany |
| Noliac | [link](http://www.noliac.com/) | Denmark | | Noliac | [link](http://www.noliac.com/products/actuators/plate-stacks/) | Denmark |
| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA | | Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA |
| PiezoDrive | [link](https://www.piezodrive.com/actuators/) | Australia | | PiezoDrive | [link](https://www.piezodrive.com/actuators/) | Australia |
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/10.html) | Japan | | Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/10.html) | Japan |
@ -35,7 +35,7 @@ Tags
### Model {#model} ### Model {#model}
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgf8860c8)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})). A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#org2c80449)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel. Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel.
@ -48,16 +48,25 @@ with:
- \\(k\_a\\) is the actuator stiffness [N/m] - \\(k\_a\\) is the actuator stiffness [N/m]
## Piezoelectric Plate Actuators {#piezoelectric-plate-actuators}
Some manufacturers propose "raw" plate actuators that can be used as actuator / sensors.
| Manufacturers | Links | Country |
|---------------|-------------------------------------------------------------------|---------|
| Noliac | [link](http://www.noliac.com/products/actuators/plate-actuators/) | Denmak |
## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators} ## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#org98162bd)): The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#org95701f0)):
> The displacement amplification effect is related in a first approximation to the ratio of the shell long axis length to the short axis height. > The displacement amplification effect is related in a first approximation to the ratio of the shell long axis length to the short axis height.
> The flatter is the actuator, the higher is the amplification. > The flatter is the actuator, the higher is the amplification.
A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org47bb392)). A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#orgb10ad87)).
<a id="orgeb77af2"></a> <a id="org98b8df0"></a>
{{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="Figure 1: Topology of several types of compliant mechanisms <sup id=\"d9e8b33774f1e65d16bd79114db8ac64\"><a href=\"#ling16_enhan_mathem_model_displ_amplif\" title=\"Mingxiang Ling, Junyi Cao, Minghua Zeng, Jing Lin, \&amp; Daniel J Inman, Enhanced Mathematical Modeling of the Displacement Amplification Ratio for Piezoelectric Compliant Mechanisms, {Smart Materials and Structures}, v(7), 075022 (2016).\">ling16_enhan_mathem_model_displ_amplif</a></sup>" >}} {{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="Figure 1: Topology of several types of compliant mechanisms <sup id=\"d9e8b33774f1e65d16bd79114db8ac64\"><a href=\"#ling16_enhan_mathem_model_displ_amplif\" title=\"Mingxiang Ling, Junyi Cao, Minghua Zeng, Jing Lin, \&amp; Daniel J Inman, Enhanced Mathematical Modeling of the Displacement Amplification Ratio for Piezoelectric Compliant Mechanisms, {Smart Materials and Structures}, v(7), 075022 (2016).\">ling16_enhan_mathem_model_displ_amplif</a></sup>" >}}
@ -149,51 +158,51 @@ For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolut
### Electrical Capacitance {#electrical-capacitance} ### Electrical Capacitance {#electrical-capacitance}
The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#org297ca75)). The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#org6712594)).
This is due to the fact that voltage amplifier has a limitation on the deliverable current. This is due to the fact that voltage amplifier has a limitation on the deliverable current.
[Voltage Amplifier]({{< relref "voltage_amplifier" >}}) with high maximum output current should be used if either high bandwidth is wanted or piezoelectric stacks with high capacitance are to be used. [Voltage Amplifier]({{< relref "voltage_amplifier" >}}) with high maximum output current should be used if either high bandwidth is wanted or piezoelectric stacks with high capacitance are to be used.
<a id="org297ca75"></a> <a id="org6712594"></a>
{{< figure src="/ox-hugo/piezoelectric_capacitance_voltage_max.png" caption="Figure 2: Maximum sin-wave amplitude as a function of frequency for several piezoelectric capacitance" >}} {{< figure src="/ox-hugo/piezoelectric_capacitance_voltage_max.png" caption="Figure 2: Maximum sin-wave amplitude as a function of frequency for several piezoelectric capacitance" >}}
## Piezoelectric actuator experiencing a mass load {#piezoelectric-actuator-experiencing-a-mass-load} ## Piezoelectric actuator experiencing a mass load {#piezoelectric-actuator-experiencing-a-mass-load}
When the piezoelectric actuator is supporting a payload, it will experience a static deflection due to its finite stiffness \\(\Delta l\_n = \frac{mg}{k\_p}\\), but its stroke will remain unchanged (Figure [3](#org481d529)). When the piezoelectric actuator is supporting a payload, it will experience a static deflection due to its finite stiffness \\(\Delta l\_n = \frac{mg}{k\_p}\\), but its stroke will remain unchanged (Figure [3](#orgaf653d1)).
<a id="org481d529"></a> <a id="orgaf653d1"></a>
{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="Figure 3: Motion of a piezoelectric stack actuator under external constant force" >}} {{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="Figure 3: Motion of a piezoelectric stack actuator under external constant force" >}}
## Piezoelectric actuator in contact with a spring load {#piezoelectric-actuator-in-contact-with-a-spring-load} ## Piezoelectric actuator in contact with a spring load {#piezoelectric-actuator-in-contact-with-a-spring-load}
Then the piezoelectric actuator is in contact with a spring load \\(k\_e\\), its maximum stroke \\(\Delta L\\) is less than its free stroke \\(\Delta L\_f\\) (Figure [4](#orgf063765)): Then the piezoelectric actuator is in contact with a spring load \\(k\_e\\), its maximum stroke \\(\Delta L\\) is less than its free stroke \\(\Delta L\_f\\) (Figure [4](#org796d9a3)):
\begin{equation} \begin{equation}
\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e} \Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
\end{equation} \end{equation}
<a id="orgf063765"></a> <a id="org796d9a3"></a>
{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="Figure 4: Motion of a piezoelectric stack actuator in contact with a stiff environment" >}} {{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="Figure 4: Motion of a piezoelectric stack actuator in contact with a stiff environment" >}}
For piezo actuators, force and displacement are inversely related (Figure [5](#org82b8a4e)). For piezo actuators, force and displacement are inversely related (Figure [5](#org05901df)).
Maximum, or blocked, force (\\(F\_b\\)) occurs when there is no displacement. Maximum, or blocked, force (\\(F\_b\\)) occurs when there is no displacement.
Likewise, at maximum displacement, or free stroke, (\\(\Delta L\_f\\)) no force is generated. Likewise, at maximum displacement, or free stroke, (\\(\Delta L\_f\\)) no force is generated.
When an external load is applied, the stiffness of the load (\\(k\_e\\)) determines the displacement (\\(\Delta L\_A\\)) and force (\\(\Delta F\_A\\)) that can be produced. When an external load is applied, the stiffness of the load (\\(k\_e\\)) determines the displacement (\\(\Delta L\_A\\)) and force (\\(\Delta F\_A\\)) that can be produced.
<a id="org82b8a4e"></a> <a id="org05901df"></a>
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}} {{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
## Bibliography {#bibliography} ## Bibliography {#bibliography}
<a id="org98162bd"></a>Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” _Ferroelectrics_ 351 (1):3–14. <https://doi.org/10.1080/00150190701351865>. <a id="org95701f0"></a>Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” _Ferroelectrics_ 351 (1):3–14. <https://doi.org/10.1080/00150190701351865>.
<a id="orgf8860c8"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>. <a id="org2c80449"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.
<a id="org47bb392"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.” <a id="orgb10ad87"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”

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