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@ -4,7 +4,7 @@ author = ["Thomas Dehaeze"]
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### Backlinks {#backlinks}
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Backlinks:
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- [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
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- [Force Sensors]({{< relref "force_sensors" >}})
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@ -13,7 +13,7 @@ Tags
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: [Sensor Fusion]({{< relref "sensor_fusion" >}}), [Force Sensors]({{< relref "force_sensors" >}})
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Reference
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: ([Fleming 2010](#org6fe1b59))
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: ([Fleming 2010](#org5c1a566))
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Author(s)
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: Fleming, A.
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@ -36,7 +36,7 @@ Year
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## Model of a multi-layer monolithic piezoelectric stack actuator {#model-of-a-multi-layer-monolithic-piezoelectric-stack-actuator}
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<a id="orgb6bab68"></a>
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<a id="org8318193"></a>
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{{< figure src="/ox-hugo/fleming10_piezo_model.png" caption="Figure 1: Schematic of a multi-layer monolithic piezoelectric stack actuator model" >}}
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@ -119,6 +119,13 @@ The current noise density of a general purpose LM833 FET-input op-amp is \\(0.5\
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The capacitance of a piezoelectric stack is typically between \\(1 \mu F\\) and \\(100 \mu F\\).
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## Tested feedback control strategies {#tested-feedback-control-strategies}
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<a id="orgab9a9d3"></a>
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{{< 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" >}}
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## Bibliography {#bibliography}
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<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>.
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<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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@ -23,7 +23,7 @@ Tags
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| Cedrat | [link](http://www.cedrat-technologies.com/) | France |
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| PI | [link](https://www.physikinstrumente.com/en/) | USA |
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| Piezo System | [link](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/) | Germany |
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| Noliac | [link](http://www.noliac.com/) | Denmark |
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| Noliac | [link](http://www.noliac.com/products/actuators/plate-stacks/) | Denmark |
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| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA |
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| PiezoDrive | [link](https://www.piezodrive.com/actuators/) | Australia |
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| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/10.html) | Japan |
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@ -35,7 +35,7 @@ Tags
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### Model {#model}
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A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgf8860c8)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
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A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#org2c80449)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
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Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel.
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@ -48,16 +48,25 @@ with:
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- \\(k\_a\\) is the actuator stiffness [N/m]
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## Piezoelectric Plate Actuators {#piezoelectric-plate-actuators}
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Some manufacturers propose "raw" plate actuators that can be used as actuator / sensors.
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| Manufacturers | Links | Country |
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|---------------|-------------------------------------------------------------------|---------|
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| Noliac | [link](http://www.noliac.com/products/actuators/plate-actuators/) | Denmak |
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## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}
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The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#org98162bd)):
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The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#org95701f0)):
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> The displacement amplification effect is related in a first approximation to the ratio of the shell long axis length to the short axis height.
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> The flatter is the actuator, the higher is the amplification.
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A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org47bb392)).
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A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#orgb10ad87)).
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<a id="orgeb77af2"></a>
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<a id="org98b8df0"></a>
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{{< 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, \& 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>" >}}
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@ -149,51 +158,51 @@ For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolut
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### Electrical Capacitance {#electrical-capacitance}
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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)).
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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)).
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This is due to the fact that voltage amplifier has a limitation on the deliverable current.
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[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.
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<a id="org297ca75"></a>
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<a id="org6712594"></a>
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{{< 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" >}}
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## Piezoelectric actuator experiencing a mass load {#piezoelectric-actuator-experiencing-a-mass-load}
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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)).
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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)).
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<a id="org481d529"></a>
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<a id="orgaf653d1"></a>
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{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="Figure 3: Motion of a piezoelectric stack actuator under external constant force" >}}
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## Piezoelectric actuator in contact with a spring load {#piezoelectric-actuator-in-contact-with-a-spring-load}
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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)):
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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)):
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\begin{equation}
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\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
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\end{equation}
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<a id="orgf063765"></a>
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<a id="org796d9a3"></a>
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{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="Figure 4: Motion of a piezoelectric stack actuator in contact with a stiff environment" >}}
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For piezo actuators, force and displacement are inversely related (Figure [5](#org82b8a4e)).
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For piezo actuators, force and displacement are inversely related (Figure [5](#org05901df)).
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Maximum, or blocked, force (\\(F\_b\\)) occurs when there is no displacement.
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Likewise, at maximum displacement, or free stroke, (\\(\Delta L\_f\\)) no force is generated.
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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.
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<a id="org82b8a4e"></a>
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<a id="org05901df"></a>
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{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
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## Bibliography {#bibliography}
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<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>.
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<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>.
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<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>.
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<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>.
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<a id="org47bb392"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
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<a id="orgb10ad87"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
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