diff --git a/content/book/fleming14_desig_model_contr_nanop_system.md b/content/book/fleming14_desig_model_contr_nanop_system.md index 8cebfb6..049abb5 100644 --- a/content/book/fleming14_desig_model_contr_nanop_system.md +++ b/content/book/fleming14_desig_model_contr_nanop_system.md @@ -10,7 +10,7 @@ Tags : [Piezoelectric Actuators](piezoelectric_actuators.md), [Flexible Joints](flexible_joints.md) Reference -: ([Fleming and Leang 2014](#orgc8028e0)) +: ([Fleming and Leang 2014](#org3a2500f)) Author(s) : Fleming, A. J., & Leang, K. K. @@ -783,11 +783,11 @@ Year ### Amplifier and Piezo electrical models {#amplifier-and-piezo-electrical-models} - + {{< figure src="/ox-hugo/fleming14_amplifier_model.png" caption="Figure 1: A voltage source \\(V\_s\\) driving a piezoelectric load. The actuator is modeled by a capacitance \\(C\_p\\) and strain-dependent voltage source \\(V\_p\\). The resistance \\(R\_s\\) is the output impedance and \\(L\\) the cable inductance." >}} -Consider the electrical circuit shown in Figure [1](#orgded1d91) where a voltage source is connected to a piezoelectric actuator. +Consider the electrical circuit shown in Figure [1](#org1b7a832) where a voltage source is connected to a piezoelectric actuator. The actuator is modeled as a capacitance \\(C\_p\\) in series with a strain-dependent voltage source \\(V\_p\\). The resistance \\(R\_s\\) and inductance \\(L\\) are the source impedance and the cable inductance respectively. @@ -911,4 +911,4 @@ The bandwidth limitations of standard piezoelectric drives were identified as: ## Bibliography {#bibliography} -Fleming, Andrew J., and Kam K. Leang. 2014. _Design, Modeling and Control of Nanopositioning Systems_. Advances in Industrial Control. Springer International Publishing. . +Fleming, Andrew J., and Kam K. Leang. 2014. _Design, Modeling and Control of Nanopositioning Systems_. Advances in Industrial Control. Springer International Publishing. . diff --git a/content/zettels/piezoelectric_actuators.md b/content/zettels/piezoelectric_actuators.md index f62d078..26a61c6 100644 --- a/content/zettels/piezoelectric_actuators.md +++ b/content/zettels/piezoelectric_actuators.md @@ -5,7 +5,7 @@ draft = false +++ Tags -: [Actuators]({{< relref "actuators" >}}), [Voltage Amplifier]({{< relref "voltage_amplifier" >}}) +: [Actuators](actuators.md), [Voltage Amplifier](voltage_amplifier.md) ## Piezoelectric Stack Actuators {#piezoelectric-stack-actuators} @@ -32,7 +32,7 @@ Tags ### Model {#model} -A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#org4089875)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})). +A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgc916f93)) ([Notes](fleming10_nanop_system_with_force_feedb.md)). Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel. @@ -56,14 +56,14 @@ Some manufacturers propose "raw" plate actuators that can be used as actuator / ## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators} -The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#orge4dbf99)): +The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#orgaaabf8d)): > 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. -A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#orga7e7177)). +A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org8ca201e)). - + {{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="Figure 1: Topology of several types of compliant mechanisms ling16_enhan_mathem_model_displ_amplif" >}} @@ -141,9 +141,9 @@ with: ### Resolution {#resolution} -The resolution is limited by the noise in the [Voltage Amplifier]({{< relref "voltage_amplifier" >}}). +The resolution is limited by the noise in the [Voltage Amplifier](voltage_amplifier.md). -Typical [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}}) of voltage amplifiers is \\(100dB = 10^{5}\\). +Typical [Signal to Noise Ratio](signal_to_noise_ratio.md) of voltage amplifiers is \\(100dB = 10^{5}\\). Thus, for a piezoelectric stack with a displacement \\(L\\), the resolution will be \begin{equation} @@ -155,58 +155,58 @@ For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolut ### 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](#org38927da)). +The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#org2c60a2d)). 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](voltage_amplifier.md) with high maximum output current should be used if either high bandwidth is wanted or piezoelectric stacks with high capacitance are to be used. - + {{< 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} -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](#org35604e1)). +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](#org7af4476)). - + {{< 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} -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](#org2f55c26)): +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](#org97370ea)): \begin{equation} \Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e} \end{equation} - + {{< 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](#orgf384614)). +For piezo actuators, force and displacement are inversely related (Figure [5](#org8c01425)). 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. 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. - + {{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}} ## Driving Electronics {#driving-electronics} -Piezoelectric actuators can be driven either using a voltage to charge converter or a [Voltage Amplifier]({{< relref "voltage_amplifier" >}}). -Limitations of the electronics is discussed in the book [Design, modeling and control of nanopositioning systems]({{< relref "fleming14_desig_model_contr_nanop_system#electrical-considerations" >}}). +Piezoelectric actuators can be driven either using a voltage to charge converter or a [Voltage Amplifier](voltage_amplifier.md). +Limitations of the electronics is discussed in [Design, modeling and control of nanopositioning systems](fleming14_desig_model_contr_nanop_system.md). ## Bibliography {#bibliography} -Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” _Ferroelectrics_ 351 (1):3–14. . +Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” _Ferroelectrics_ 351 (1):3–14. . -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. . +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. . -Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.” +Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”