Classical update of content

2020-07-30 10:43:47 +02:00 · 2020-07-30 10:43:47 +02:00 · fb209652b3
commit fb209652b3
parent 408df4315d
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--- a/content/article/claeyssen07_amplif_piezoel_actuat.md
+++ b/content/article/claeyssen07_amplif_piezoel_actuat.md
@ -9,7 +9,7 @@ Tags


 Reference
-: <sup id="5decd2b31c4a9842b80c58b56f96590a"><a class="reference-link" href="#claeyssen07_amplif_piezoel_actuat" title="Frank Claeyssen, Le Letty, Barillot, \&amp; Sosnicki, Amplified Piezoelectric Actuators: Static \&amp; Dynamic  Applications, {Ferroelectrics}, v(1), 3-14 (2007).">(Frank Claeyssen {\it et al.}, 2007)</a></sup>
+: ([Claeyssen et al. 2007](#org3151b14))

 Author(s)
 : Claeyssen, F., Letty, R. L., Barillot, F., & Sosnicki, O.
@ -17,5 +17,24 @@ Author(s)
 Year
 : 2007

-# Bibliography
-<a class="bibtex-entry" id="claeyssen07_amplif_piezoel_actuat">Claeyssen, F., Letty, R. L., Barillot, F., & Sosnicki, O., *Amplified piezoelectric actuators: static \& dynamic applications*, Ferroelectrics, *351(1)*, 3–14 (2007).  http://dx.doi.org/10.1080/00150190701351865</a> [↩](#5decd2b31c4a9842b80c58b56f96590a)
+The amplified piezo actuator APA is an external leveraged actuator based on a shell used both for the ceramic **pre stress** and for the ceramic **motion magnification**.
+
+It is based on low voltage multilayer piezoelectric ceramics (PZT type).
+In static conditions, their free strain \\(S\_p\\) is typically 0.1% when driven at 150 V.
+
+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.
+
+Piezoceramics can bear large compressive stress but they can not bear tensile forces with a good reliability.
+The usual way to solve this limitation consists in prestressing the ceramics by maintaining a compressive stress.
+This introduces another force limit: if the internal dynamic forces are above the prestress, the actuator is endangered because of the ceramic goes in tensile stress and also the ceramic stack looses contact with the shell interface.
+
+For many APA actuators, the amplitude of maximal applicable external force is close to half the actuator blocked force.
+
+The maximum dynamic force achievable by the actuator is determined by the prestress.
+The prestress design allows a peak force equal to half the blocked force.
+
+
+## Bibliography {#bibliography}
+
+<a id="org3151b14"></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/content/article/fleming10_nanop_system_with_force_feedb.md
+++ b/content/article/fleming10_nanop_system_with_force_feedb.md
@ -8,7 +8,7 @@ Tags
 : [Sensor Fusion]({{< relref "sensor_fusion" >}}), [Force Sensors]({{< relref "force_sensors" >}})

 Reference
-: <sup id="c823f68dd2a72b9667a61b3c046b4731"><a class="reference-link" href="#fleming10_nanop_system_with_force_feedb" title="Fleming, Nanopositioning System With Force Feedback for  High-Performance Tracking and Vibration Control, {IEEE/ASME Transactions on Mechatronics}, v(3), 433-447 (2010).">(Fleming, 2010)</a></sup>
+: ([Fleming 2010](#org37731c2))

 Author(s)
 : Fleming, A.
@ -16,7 +16,8 @@ Author(s)
 Year
 : 2010

-Summary:
+
+## Summary {#summary}

 -   The noise generated by a piezoelectric force sensor is much less than a capacitive sensor
 -   Dynamical model of a piezoelectric stack actuator and piezoelectric force sensor
@ -30,7 +31,7 @@ Summary:

 ## Model of a multi-layer monolithic piezoelectric stack actuator {#model-of-a-multi-layer-monolithic-piezoelectric-stack-actuator}

-<a id="org3f4c96b"></a>
+<a id="orgae51a2c"></a>

 {{< figure src="/ox-hugo/fleming10_piezo_model.png" caption="Figure 1: Schematic of a multi-layer monolithic piezoelectric stack actuator model" >}}

@ -112,11 +113,13 @@ As piezoelectric sensors have a capacitive source impedance, the sensor noise de
 The current noise density of a general purpose LM833 FET-input op-amp is \\(0.5\ pA/\sqrt{\text{Hz}}\\).
 The capacitance of a piezoelectric stack is typically between \\(1 \mu F\\) and \\(100 \mu F\\).

-# Bibliography
-<a class="bibtex-entry" id="fleming10_nanop_system_with_force_feedb">Fleming, A., *Nanopositioning system with force feedback for high-performance tracking and vibration control*, IEEE/ASME Transactions on Mechatronics, *15(3)*, 433–447 (2010).  http://dx.doi.org/10.1109/tmech.2009.2028422</a> [↩](#c823f68dd2a72b9667a61b3c046b4731)
+
+## Bibliography {#bibliography}
+
+<a id="org37731c2"></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>.


 ## Backlinks {#backlinks}

-   [Actuators]({{< relref "actuators" >}})
 -   [Force Sensors]({{< relref "force_sensors" >}})
+-   [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
--- a/content/book/fleming14_desig_model_contr_nanop_system.md
+++ b/content/book/fleming14_desig_model_contr_nanop_system.md
@ -9,7 +9,7 @@ Tags


 Reference
-: <sup id="1851788e0c4aa5b06afe3362c73ea5eb"><a href="#fleming14_desig_model_contr_nanop_system" title="Andrew Fleming \&amp; Kam Leang, Design, Modeling and Control of Nanopositioning Systems, Springer International Publishing (2014).">(Andrew Fleming \& Kam Leang, 2014)</a></sup>
+: ([Fleming and Leang 2014](#org2385d08))

 Author(s)
 : Fleming, A. J., & Leang, K. K.
@ -17,5 +17,850 @@ Author(s)
 Year
 : 2014

-# Bibliography
-<a id="fleming14_desig_model_contr_nanop_system"></a>Fleming, A. J., & Leang, K. K., *Design, modeling and control of nanopositioning systems* (2014), : Springer International Publishing. [↩](#1851788e0c4aa5b06afe3362c73ea5eb)
+
+## 1 Introduction {#1-introduction}
+
+
+### 1.1 Introduction to Nanotechnology {#1-dot-1-introduction-to-nanotechnology}
+
+
+### 1.2 Introduction to Nanopositioning {#1-dot-2-introduction-to-nanopositioning}
+
+
+### 1.3 Scanning Probe Microscopy {#1-dot-3-scanning-probe-microscopy}
+
+
+### 1.4 Challenges with Nanopositioning Systems {#1-dot-4-challenges-with-nanopositioning-systems}
+
+
+#### 1.4.1 Hysteresis {#1-dot-4-dot-1-hysteresis}
+
+
+#### 1.4.2 Creep {#1-dot-4-dot-2-creep}
+
+
+#### 1.4.3 Thermal Drift {#1-dot-4-dot-3-thermal-drift}
+
+
+#### 1.4.4 Mechanical Resonance {#1-dot-4-dot-4-mechanical-resonance}
+
+
+### 1.5 Control of Nanopositioning Systems {#1-dot-5-control-of-nanopositioning-systems}
+
+
+#### 1.5.1 Feedback Control {#1-dot-5-dot-1-feedback-control}
+
+
+#### 1.5.2 Feedforward Control {#1-dot-5-dot-2-feedforward-control}
+
+
+### 1.6 Book Summary {#1-dot-6-book-summary}
+
+
+#### 1.6.1 Assumed Knowledge {#1-dot-6-dot-1-assumed-knowledge}
+
+
+#### 1.6.2 Content Summary {#1-dot-6-dot-2-content-summary}
+
+
+### References {#references}
+
+
+## 2 Piezoelectric Transducers {#2-piezoelectric-transducers}
+
+
+### 2.1 The Piezoelectric Effect {#2-dot-1-the-piezoelectric-effect}
+
+
+### 2.2 Piezoelectric Compositions {#2-dot-2-piezoelectric-compositions}
+
+
+### 2.3 Manufacturing Piezoelectric Ceramics {#2-dot-3-manufacturing-piezoelectric-ceramics}
+
+
+### 2.4 Piezoelectric Transducers {#2-dot-4-piezoelectric-transducers}
+
+
+### 2.5 Application Considerations {#2-dot-5-application-considerations}
+
+
+#### 2.5.1 Mounting {#2-dot-5-dot-1-mounting}
+
+
+#### 2.5.2 Stroke Versus Force {#2-dot-5-dot-2-stroke-versus-force}
+
+
+#### 2.5.3 Preload and Flexures {#2-dot-5-dot-3-preload-and-flexures}
+
+
+#### 2.5.4 Electrical Considerations {#2-dot-5-dot-4-electrical-considerations}
+
+
+#### 2.5.5 Self-Heating Considerations {#2-dot-5-dot-5-self-heating-considerations}
+
+
+### 2.6 Response of Piezoelectric Actuators {#2-dot-6-response-of-piezoelectric-actuators}
+
+
+#### 2.6.1 Hysteresis {#2-dot-6-dot-1-hysteresis}
+
+
+#### 2.6.2 Creep {#2-dot-6-dot-2-creep}
+
+
+#### 2.6.3 Temperature Dependence {#2-dot-6-dot-3-temperature-dependence}
+
+
+#### 2.6.4 Vibrational Dynamics {#2-dot-6-dot-4-vibrational-dynamics}
+
+
+#### 2.6.5 Electrical Bandwidth {#2-dot-6-dot-5-electrical-bandwidth}
+
+
+### 2.7 Modeling Creep and Vibration in Piezoelectric Actuators {#2-dot-7-modeling-creep-and-vibration-in-piezoelectric-actuators}
+
+
+### 2.8 Chapter Summary {#2-dot-8-chapter-summary}
+
+
+### References {#references}
+
+
+## 3 Types of Nanopositioners {#3-types-of-nanopositioners}
+
+
+### 3.1 Piezoelectric Tube Nanopositioners {#3-dot-1-piezoelectric-tube-nanopositioners}
+
+
+#### 3.1.1 63mm Piezoelectric Tube {#3-dot-1-dot-1-63mm-piezoelectric-tube}
+
+
+#### 3.1.2 40mm Piezoelectric Tube Nanopositioner {#3-dot-1-dot-2-40mm-piezoelectric-tube-nanopositioner}
+
+
+### 3.2 Piezoelectric Stack Nanopositioners {#3-dot-2-piezoelectric-stack-nanopositioners}
+
+
+#### 3.2.1 Phyisk Instrumente P-734 Nanopositioner {#3-dot-2-dot-1-phyisk-instrumente-p-734-nanopositioner}
+
+
+#### 3.2.2 Phyisk Instrumente P-733.3DD Nanopositioner {#3-dot-2-dot-2-phyisk-instrumente-p-733-dot-3dd-nanopositioner}
+
+
+#### 3.2.3 Vertical Nanopositioners {#3-dot-2-dot-3-vertical-nanopositioners}
+
+
+#### 3.2.4 Rotational Nanopositioners {#3-dot-2-dot-4-rotational-nanopositioners}
+
+
+#### 3.2.5 Low Temperature and UHV Nanopositioners {#3-dot-2-dot-5-low-temperature-and-uhv-nanopositioners}
+
+
+#### 3.2.6 Tilting Nanopositioners {#3-dot-2-dot-6-tilting-nanopositioners}
+
+
+#### 3.2.7 Optical Objective Nanopositioners {#3-dot-2-dot-7-optical-objective-nanopositioners}
+
+
+### References {#references}
+
+
+## 4 Mechanical Design: Flexure-Based Nanopositioners {#4-mechanical-design-flexure-based-nanopositioners}
+
+
+### 4.1 Introduction {#4-dot-1-introduction}
+
+
+### 4.2 Operating Environment {#4-dot-2-operating-environment}
+
+
+### 4.3 Methods for Actuation {#4-dot-3-methods-for-actuation}
+
+
+### 4.4 Flexure Hinges {#4-dot-4-flexure-hinges}
+
+
+#### 4.4.1 Introduction {#4-dot-4-dot-1-introduction}
+
+
+#### 4.4.2 Types of Flexures {#4-dot-4-dot-2-types-of-flexures}
+
+
+#### 4.4.3 Flexure Hinge Compliance Equations {#4-dot-4-dot-3-flexure-hinge-compliance-equations}
+
+
+#### 4.4.4 Stiff Out-of-Plane Flexure Designs {#4-dot-4-dot-4-stiff-out-of-plane-flexure-designs}
+
+
+#### 4.4.5 Failure Considerations {#4-dot-4-dot-5-failure-considerations}
+
+
+#### 4.4.6 Finite Element Approach for Flexure Design {#4-dot-4-dot-6-finite-element-approach-for-flexure-design}
+
+
+### 4.5 Material Considerations {#4-dot-5-material-considerations}
+
+
+#### 4.5.1 Materials for Flexure and Platform Design {#4-dot-5-dot-1-materials-for-flexure-and-platform-design}
+
+
+#### 4.5.2 Thermal Stability of Materials {#4-dot-5-dot-2-thermal-stability-of-materials}
+
+
+### 4.6 Manufacturing Techniques {#4-dot-6-manufacturing-techniques}
+
+
+### 4.7 Design Example: A High-Speed Serial-Kinematic Nanopositioner {#4-dot-7-design-example-a-high-speed-serial-kinematic-nanopositioner}
+
+
+#### 4.7.1 State-of-the-Art Designs {#4-dot-7-dot-1-state-of-the-art-designs}
+
+
+#### 4.7.2 Tradeoffs and Limitations in Speed {#4-dot-7-dot-2-tradeoffs-and-limitations-in-speed}
+
+
+#### 4.7.3 Serial- Versus Parallel-Kinematic Configurations {#4-dot-7-dot-3-serial-versus-parallel-kinematic-configurations}
+
+
+#### 4.7.4 Piezoactuator Considerations {#4-dot-7-dot-4-piezoactuator-considerations}
+
+
+#### 4.7.5 Preloading Piezo-Stack Actuators {#4-dot-7-dot-5-preloading-piezo-stack-actuators}
+
+
+#### 4.7.6 Flexure Design for Lateral Positioning {#4-dot-7-dot-6-flexure-design-for-lateral-positioning}
+
+
+#### 4.7.7 Design of Vertical Stage {#4-dot-7-dot-7-design-of-vertical-stage}
+
+
+#### 4.7.8 Fabrication and Assembly {#4-dot-7-dot-8-fabrication-and-assembly}
+
+
+#### 4.7.9 Drive Electronics {#4-dot-7-dot-9-drive-electronics}
+
+
+#### 4.7.10 Experimental Results {#4-dot-7-dot-10-experimental-results}
+
+
+### 4.8 Chapter Summary {#4-dot-8-chapter-summary}
+
+
+### References {#references}
+
+
+## 5 Position Sensors {#5-position-sensors}
+
+
+### 5.1 Introduction {#5-dot-1-introduction}
+
+
+### 5.2 Sensor Characteristics {#5-dot-2-sensor-characteristics}
+
+
+#### 5.2.1 Calibration and Nonlinearity {#5-dot-2-dot-1-calibration-and-nonlinearity}
+
+
+#### 5.2.2 Drift and Stability {#5-dot-2-dot-2-drift-and-stability}
+
+
+#### 5.2.3 Bandwidth {#5-dot-2-dot-3-bandwidth}
+
+
+#### 5.2.4 Noise {#5-dot-2-dot-4-noise}
+
+
+#### 5.2.5 Resolution {#5-dot-2-dot-5-resolution}
+
+
+#### 5.2.6 Combining Errors {#5-dot-2-dot-6-combining-errors}
+
+
+#### 5.2.7 Metrological Traceability {#5-dot-2-dot-7-metrological-traceability}
+
+
+### 5.3 Nanometer Position Sensors {#5-dot-3-nanometer-position-sensors}
+
+
+#### 5.3.1 Resistive Strain Sensors {#5-dot-3-dot-1-resistive-strain-sensors}
+
+
+#### 5.3.2 Piezoresistive Strain Sensors {#5-dot-3-dot-2-piezoresistive-strain-sensors}
+
+
+#### 5.3.3 Piezoelectric Strain Sensors {#5-dot-3-dot-3-piezoelectric-strain-sensors}
+
+
+#### 5.3.4 Capacitive Sensors {#5-dot-3-dot-4-capacitive-sensors}
+
+
+#### 5.3.5 MEMs Capacitive and Thermal Sensors {#5-dot-3-dot-5-mems-capacitive-and-thermal-sensors}
+
+
+#### 5.3.6 Eddy-Current Sensors {#5-dot-3-dot-6-eddy-current-sensors}
+
+
+#### 5.3.7 Linear Variable Displacement Transformers {#5-dot-3-dot-7-linear-variable-displacement-transformers}
+
+
+#### 5.3.8 Laser Interferometers {#5-dot-3-dot-8-laser-interferometers}
+
+
+#### 5.3.9 Linear Encoders {#5-dot-3-dot-9-linear-encoders}
+
+
+### 5.4 Comparison and Summary {#5-dot-4-comparison-and-summary}
+
+
+### 5.5 Outlook and Future Requirements {#5-dot-5-outlook-and-future-requirements}
+
+
+### References {#references}
+
+
+## 6 Shunt Control {#6-shunt-control}
+
+
+### 6.1 Introduction {#6-dot-1-introduction}
+
+
+### 6.2 Shunt Circuit Modeling {#6-dot-2-shunt-circuit-modeling}
+
+
+#### 6.2.1 Open-Loop {#6-dot-2-dot-1-open-loop}
+
+
+#### 6.2.2 Shunt Damping {#6-dot-2-dot-2-shunt-damping}
+
+
+### 6.3 Implementation {#6-dot-3-implementation}
+
+
+### 6.4 Experimental Results {#6-dot-4-experimental-results}
+
+
+#### 6.4.1 Tube Dynamics {#6-dot-4-dot-1-tube-dynamics}
+
+
+#### 6.4.2 Amplifier Performance {#6-dot-4-dot-2-amplifier-performance}
+
+
+#### 6.4.3 Shunt Damping Performance {#6-dot-4-dot-3-shunt-damping-performance}
+
+
+### 6.5 Chapter Summary {#6-dot-5-chapter-summary}
+
+
+### References {#references}
+
+
+## 7 Feedback Control {#7-feedback-control}
+
+
+### 7.1 Introduction {#7-dot-1-introduction}
+
+
+### 7.2 Experimental Setup {#7-dot-2-experimental-setup}
+
+
+### 7.3 PI Control {#7-dot-3-pi-control}
+
+
+### 7.4 PI Control with Notch Filters {#7-dot-4-pi-control-with-notch-filters}
+
+
+### 7.5 PI Control with IRC Damping {#7-dot-5-pi-control-with-irc-damping}
+
+
+### 7.6 Performance Comparison {#7-dot-6-performance-comparison}
+
+
+### 7.7 Noise and Resolution {#7-dot-7-noise-and-resolution}
+
+
+### 7.8 Analog Implementation {#7-dot-8-analog-implementation}
+
+
+### 7.9 Application to AFM Imaging {#7-dot-9-application-to-afm-imaging}
+
+
+### 7.10 Repetitive Control {#7-dot-10-repetitive-control}
+
+
+#### 7.10.1 Introduction {#7-dot-10-dot-1-introduction}
+
+
+#### 7.10.2 Repetitive Control Concept and Stability Considerations {#7-dot-10-dot-2-repetitive-control-concept-and-stability-considerations}
+
+
+#### 7.10.3 Dual-Stage Repetitive Control {#7-dot-10-dot-3-dual-stage-repetitive-control}
+
+
+#### 7.10.4 Handling Hysteresis {#7-dot-10-dot-4-handling-hysteresis}
+
+
+#### 7.10.5 Design and Implementation {#7-dot-10-dot-5-design-and-implementation}
+
+
+#### 7.10.6 Experimental Results and Discussion {#7-dot-10-dot-6-experimental-results-and-discussion}
+
+
+### 7.11 Summary {#7-dot-11-summary}
+
+
+### References {#references}
+
+
+## 8 Force Feedback Control {#8-force-feedback-control}
+
+
+### 8.1 Introduction {#8-dot-1-introduction}
+
+
+### 8.2 Modeling {#8-dot-2-modeling}
+
+
+#### 8.2.1 Actuator Dynamics {#8-dot-2-dot-1-actuator-dynamics}
+
+
+#### 8.2.2 Sensor Dynamics {#8-dot-2-dot-2-sensor-dynamics}
+
+
+#### 8.2.3 Sensor Noise {#8-dot-2-dot-3-sensor-noise}
+
+
+#### 8.2.4 Mechanical Dynamics {#8-dot-2-dot-4-mechanical-dynamics}
+
+
+#### 8.2.5 System Properties {#8-dot-2-dot-5-system-properties}
+
+
+#### 8.2.6 Example System {#8-dot-2-dot-6-example-system}
+
+
+### 8.3 Damping Control {#8-dot-3-damping-control}
+
+
+### 8.4 Tracking Control {#8-dot-4-tracking-control}
+
+
+#### 8.4.1 Relationship Between Force and Displacement {#8-dot-4-dot-1-relationship-between-force-and-displacement}
+
+
+#### 8.4.2 Integral Displacement Feedback {#8-dot-4-dot-2-integral-displacement-feedback}
+
+
+#### 8.4.3 Direct Tracking Control {#8-dot-4-dot-3-direct-tracking-control}
+
+
+#### 8.4.4 Dual Sensor Feedback {#8-dot-4-dot-4-dual-sensor-feedback}
+
+
+#### 8.4.5 Low Frequency Bypass {#8-dot-4-dot-5-low-frequency-bypass}
+
+
+#### 8.4.6 Feedforward Inputs {#8-dot-4-dot-6-feedforward-inputs}
+
+
+#### 8.4.7 Higher-Order Modes {#8-dot-4-dot-7-higher-order-modes}
+
+
+### 8.5 Experimental Results {#8-dot-5-experimental-results}
+
+
+#### 8.5.1 Experimental Nanopositioner {#8-dot-5-dot-1-experimental-nanopositioner}
+
+
+#### 8.5.2 Actuators and Force Sensors {#8-dot-5-dot-2-actuators-and-force-sensors}
+
+
+#### 8.5.3 Control Design {#8-dot-5-dot-3-control-design}
+
+
+#### 8.5.4 Noise Performance {#8-dot-5-dot-4-noise-performance}
+
+
+### 8.6 Chapter Summary {#8-dot-6-chapter-summary}
+
+
+### References {#references}
+
+
+## 9 Feedforward Control {#9-feedforward-control}
+
+
+### 9.1 Why Feedforward? {#9-dot-1-why-feedforward}
+
+
+### 9.2 Modeling for Feedforward Control {#9-dot-2-modeling-for-feedforward-control}
+
+
+### 9.3 Feedforward Control of Dynamics and Hysteresis {#9-dot-3-feedforward-control-of-dynamics-and-hysteresis}
+
+
+#### 9.3.1 Simple DC-Gain Feedforward Control {#9-dot-3-dot-1-simple-dc-gain-feedforward-control}
+
+
+#### 9.3.2 An Inversion-Based Feedforward Approach  for Linear Dynamics {#9-dot-3-dot-2-an-inversion-based-feedforward-approach-for-linear-dynamics}
+
+
+#### 9.3.3 Frequency-Weighted Inversion: The Optimal Inverse {#9-dot-3-dot-3-frequency-weighted-inversion-the-optimal-inverse}
+
+
+#### 9.3.4 Application to AFM Imaging {#9-dot-3-dot-4-application-to-afm-imaging}
+
+
+### 9.4 Feedforward and Feedback Control {#9-dot-4-feedforward-and-feedback-control}
+
+
+#### 9.4.1 Application to AFM Imaging {#9-dot-4-dot-1-application-to-afm-imaging}
+
+
+### 9.5 Iterative Feedforward Control {#9-dot-5-iterative-feedforward-control}
+
+
+#### 9.5.1 The ILC Problem {#9-dot-5-dot-1-the-ilc-problem}
+
+
+#### 9.5.2 Model-Based ILC {#9-dot-5-dot-2-model-based-ilc}
+
+
+#### 9.5.3 Nonlinear ILC {#9-dot-5-dot-3-nonlinear-ilc}
+
+
+#### 9.5.4 Conclusions {#9-dot-5-dot-4-conclusions}
+
+
+### References {#references}
+
+
+## 10 Command Shaping {#10-command-shaping}
+
+
+### 10.1 Introduction {#10-dot-1-introduction}
+
+
+#### 10.1.1 Background {#10-dot-1-dot-1-background}
+
+
+#### 10.1.2 The Optimal Periodic Input {#10-dot-1-dot-2-the-optimal-periodic-input}
+
+
+### 10.2 Signal Optimization {#10-dot-2-signal-optimization}
+
+
+### 10.3 Frequency Domain Cost Functions {#10-dot-3-frequency-domain-cost-functions}
+
+
+#### 10.3.1 Background: Discrete Fourier Series {#10-dot-3-dot-1-background-discrete-fourier-series}
+
+
+#### 10.3.2 Minimizing Signal Power {#10-dot-3-dot-2-minimizing-signal-power}
+
+
+#### 10.3.3 Minimizing Frequency Weighted Power {#10-dot-3-dot-3-minimizing-frequency-weighted-power}
+
+
+#### 10.3.4 Minimizing Velocity and Acceleration {#10-dot-3-dot-4-minimizing-velocity-and-acceleration}
+
+
+#### 10.3.5 Single-Sided Frequency Domain Calculations {#10-dot-3-dot-5-single-sided-frequency-domain-calculations}
+
+
+### 10.4 Time Domain Cost Function {#10-dot-4-time-domain-cost-function}
+
+
+#### 10.4.1 Minimum Velocity {#10-dot-4-dot-1-minimum-velocity}
+
+
+#### 10.4.2 Minimum Acceleration {#10-dot-4-dot-2-minimum-acceleration}
+
+
+#### 10.4.3 Frequency Weighted Objectives {#10-dot-4-dot-3-frequency-weighted-objectives}
+
+
+### 10.5 Application to Scan Generation {#10-dot-5-application-to-scan-generation}
+
+
+#### 10.5.1 Choosing β and K {#10-dot-5-dot-1-choosing-β-and-k}
+
+
+#### 10.5.2 Improving Feedback and Feedforward Controllers {#10-dot-5-dot-2-improving-feedback-and-feedforward-controllers}
+
+
+### 10.6 Comparison to Other Techniques {#10-dot-6-comparison-to-other-techniques}
+
+
+### 10.7 Experimental Application {#10-dot-7-experimental-application}
+
+
+### 10.8 Chapter Summary {#10-dot-8-chapter-summary}
+
+
+### References {#references}
+
+
+## 11 Hysteresis Modeling and Control {#11-hysteresis-modeling-and-control}
+
+
+### 11.1 Introduction {#11-dot-1-introduction}
+
+
+### 11.2 Modeling Hysteresis {#11-dot-2-modeling-hysteresis}
+
+
+#### 11.2.1 Simple Polynomial Model {#11-dot-2-dot-1-simple-polynomial-model}
+
+
+#### 11.2.2 Maxwell Slip Model {#11-dot-2-dot-2-maxwell-slip-model}
+
+
+#### 11.2.3 Duhem Model {#11-dot-2-dot-3-duhem-model}
+
+
+#### 11.2.4 Preisach Model {#11-dot-2-dot-4-preisach-model}
+
+
+#### 11.2.5 Classical Prandlt-Ishlinksii Model {#11-dot-2-dot-5-classical-prandlt-ishlinksii-model}
+
+
+### 11.3 Feedforward Hysteresis Compensation {#11-dot-3-feedforward-hysteresis-compensation}
+
+
+#### 11.3.1 Feedforward Control Using the Presiach Model {#11-dot-3-dot-1-feedforward-control-using-the-presiach-model}
+
+
+#### 11.3.2 Feedforward Control Using the Prandlt-Ishlinksii Model {#11-dot-3-dot-2-feedforward-control-using-the-prandlt-ishlinksii-model}
+
+
+### 11.4 Chapter Summary {#11-dot-4-chapter-summary}
+
+
+### References {#references}
+
+
+## 12 Charge Drives {#12-charge-drives}
+
+
+### 12.1 Introduction {#12-dot-1-introduction}
+
+
+### 12.2 Charge Drives {#12-dot-2-charge-drives}
+
+
+### 12.3 Application to Piezoelectric Stack Nanopositioners {#12-dot-3-application-to-piezoelectric-stack-nanopositioners}
+
+
+### 12.4 Application to Piezoelectric Tube Nanopositioners {#12-dot-4-application-to-piezoelectric-tube-nanopositioners}
+
+
+### 12.5 Alternative Electrode Configurations {#12-dot-5-alternative-electrode-configurations}
+
+
+#### 12.5.1 Grounded Internal Electrode {#12-dot-5-dot-1-grounded-internal-electrode}
+
+
+#### 12.5.2 Quartered Internal Electrode {#12-dot-5-dot-2-quartered-internal-electrode}
+
+
+### 12.6 Charge Versus Voltage {#12-dot-6-charge-versus-voltage}
+
+
+#### 12.6.1 Advantages {#12-dot-6-dot-1-advantages}
+
+
+#### 12.6.2 Disadvantages {#12-dot-6-dot-2-disadvantages}
+
+
+### 12.7 Impact on Closed-Loop Control {#12-dot-7-impact-on-closed-loop-control}
+
+
+### 12.8 Chapter Summary {#12-dot-8-chapter-summary}
+
+
+### References {#references}
+
+
+## 13 Noise in Nanopositioning Systems {#13-noise-in-nanopositioning-systems}
+
+
+### 13.1 Introduction {#13-dot-1-introduction}
+
+
+### 13.2 Review of Random Processes {#13-dot-2-review-of-random-processes}
+
+
+#### 13.2.1 Probability Distributions {#13-dot-2-dot-1-probability-distributions}
+
+
+#### 13.2.2 Expected Value, Moments, Variance, and RMS {#13-dot-2-dot-2-expected-value-moments-variance-and-rms}
+
+
+#### 13.2.3 Gaussian Random Variables {#13-dot-2-dot-3-gaussian-random-variables}
+
+
+#### 13.2.4 Continuous Random Processes {#13-dot-2-dot-4-continuous-random-processes}
+
+
+#### 13.2.5 Joint Density Functions and Stationarity {#13-dot-2-dot-5-joint-density-functions-and-stationarity}
+
+
+#### 13.2.6 Correlation Functions {#13-dot-2-dot-6-correlation-functions}
+
+
+#### 13.2.7 Gaussian Random Processes {#13-dot-2-dot-7-gaussian-random-processes}
+
+
+#### 13.2.8 Power Spectral Density {#13-dot-2-dot-8-power-spectral-density}
+
+
+#### 13.2.9 Filtered Random Processes {#13-dot-2-dot-9-filtered-random-processes}
+
+
+#### 13.2.10 White Noise {#13-dot-2-dot-10-white-noise}
+
+
+#### 13.2.11 Spectral Density in V/sqrtHz {#13-dot-2-dot-11-spectral-density-in-v-sqrthz}
+
+
+#### 13.2.12 Single- and Double-Sided Spectra {#13-dot-2-dot-12-single-and-double-sided-spectra}
+
+
+### 13.3 Resolution and Noise {#13-dot-3-resolution-and-noise}
+
+
+### 13.4 Sources of Nanopositioning Noise {#13-dot-4-sources-of-nanopositioning-noise}
+
+
+#### 13.4.1 Sensor Noise {#13-dot-4-dot-1-sensor-noise}
+
+
+#### 13.4.2 External Noise {#13-dot-4-dot-2-external-noise}
+
+
+#### 13.4.3 Amplifier Noise {#13-dot-4-dot-3-amplifier-noise}
+
+
+### 13.5 Closed-Loop Position Noise {#13-dot-5-closed-loop-position-noise}
+
+
+#### 13.5.1 Noise Sensitivity Functions {#13-dot-5-dot-1-noise-sensitivity-functions}
+
+
+#### 13.5.2 Closed-Loop Position Noise Spectral Density {#13-dot-5-dot-2-closed-loop-position-noise-spectral-density}
+
+
+#### 13.5.3 Closed-Loop Noise Approximations with Integral Control {#13-dot-5-dot-3-closed-loop-noise-approximations-with-integral-control}
+
+
+#### 13.5.4 Closed-Loop Position Noise Variance {#13-dot-5-dot-4-closed-loop-position-noise-variance}
+
+
+#### 13.5.5 A Note on Units {#13-dot-5-dot-5-a-note-on-units}
+
+
+### 13.6 Simulation Examples {#13-dot-6-simulation-examples}
+
+
+#### 13.6.1 Integral Controller Noise Simulation {#13-dot-6-dot-1-integral-controller-noise-simulation}
+
+
+#### 13.6.2 Noise Simulation with Inverse Model Controller {#13-dot-6-dot-2-noise-simulation-with-inverse-model-controller}
+
+
+#### 13.6.3 Feedback Versus Feedforward Control {#13-dot-6-dot-3-feedback-versus-feedforward-control}
+
+
+### 13.7 Practical Frequency Domain Noise Measurements {#13-dot-7-practical-frequency-domain-noise-measurements}
+
+
+#### 13.7.1 Preamplification {#13-dot-7-dot-1-preamplification}
+
+
+#### 13.7.2 Spectrum Estimation {#13-dot-7-dot-2-spectrum-estimation}
+
+
+#### 13.7.3 Direct Measurement of Position Noise {#13-dot-7-dot-3-direct-measurement-of-position-noise}
+
+
+#### 13.7.4 Measurement of the External Disturbance {#13-dot-7-dot-4-measurement-of-the-external-disturbance}
+
+
+### 13.8 Experimental Demonstration {#13-dot-8-experimental-demonstration}
+
+
+### 13.9 Time-Domain Noise Measurements {#13-dot-9-time-domain-noise-measurements}
+
+
+#### 13.9.1 Total Integrated Noise {#13-dot-9-dot-1-total-integrated-noise}
+
+
+#### 13.9.2 Estimating the Position Noise {#13-dot-9-dot-2-estimating-the-position-noise}
+
+
+#### 13.9.3 Practical Considerations {#13-dot-9-dot-3-practical-considerations}
+
+
+#### 13.9.4 Experimental Demonstration {#13-dot-9-dot-4-experimental-demonstration}
+
+
+### 13.10 A Simple Method for Measuring the Resolution  of Nanopositioning Systems {#13-dot-10-a-simple-method-for-measuring-the-resolution-of-nanopositioning-systems}
+
+
+### 13.11 Techniques for Improving Resolution {#13-dot-11-techniques-for-improving-resolution}
+
+
+### 13.12 Chapter Summary {#13-dot-12-chapter-summary}
+
+
+### References {#references}
+
+
+## 14 Electrical Considerations {#14-electrical-considerations}
+
+
+### 14.1 Introduction {#14-dot-1-introduction}
+
+
+### 14.2 Bandwidth Limitations {#14-dot-2-bandwidth-limitations}
+
+
+#### 14.2.1 Passive Bandwidth Limitations {#14-dot-2-dot-1-passive-bandwidth-limitations}
+
+
+#### 14.2.2 Amplifier Bandwidth {#14-dot-2-dot-2-amplifier-bandwidth}
+
+
+#### 14.2.3 Current and Power Limitations {#14-dot-2-dot-3-current-and-power-limitations}
+
+
+### 14.3 Dual-Amplifier {#14-dot-3-dual-amplifier}
+
+
+#### 14.3.1 Circuit Operation {#14-dot-3-dot-1-circuit-operation}
+
+
+#### 14.3.2 Range Considerations {#14-dot-3-dot-2-range-considerations}
+
+
+### 14.4 Electrical Design {#14-dot-4-electrical-design}
+
+
+#### 14.4.1 High-Voltage Stage {#14-dot-4-dot-1-high-voltage-stage}
+
+
+#### 14.4.2 Low-Voltage Stage {#14-dot-4-dot-2-low-voltage-stage}
+
+
+#### 14.4.3 Cabling and Interconnects {#14-dot-4-dot-3-cabling-and-interconnects}
+
+
+### 14.5 Chapter Summary {#14-dot-5-chapter-summary}
+
+
+### References {#references}
+
+
+## Bibliography {#bibliography}
+
+<a id="org2385d08"></a>Fleming, Andrew J., and Kam K. Leang. 2014. _Design, Modeling and Control of Nanopositioning Systems_. Advances in Industrial Control. Springer International Publishing. <https://doi.org/10.1007/978-3-319-06617-2>.
--- a/content/book/hatch00_vibrat_matlab_ansys.md
+++ b/content/book/hatch00_vibrat_matlab_ansys.md
@ -8,7 +8,7 @@ Tags
 : [Finite Element Model]({{< relref "finite_element_model" >}})

 Reference
-: <sup id="484c4fad309f6b0e866a7cacf4653d74"><a class="reference-link" href="#hatch00_vibrat_matlab_ansys" title="Hatch, Vibration simulation using MATLAB and ANSYS, CRC Press (2000).">(Hatch, 2000)</a></sup>
+: ([Hatch 2000](#org26212b4))

 Author(s)
 : Hatch, M. R.
@ -21,14 +21,14 @@ Matlab Code form the book is available [here](https://in.mathworks.com/matlabcen

 ## Introduction {#introduction}

-<a id="org4692204"></a>
+<a id="org660282e"></a>

 The main goal of this book is to show how to take results of large dynamic finite element models and build small Matlab state space dynamic mechanical models for use in control system models.


 ### Modal Analysis {#modal-analysis}

-The diagram in Figure [1](#org6569db5) shows the methodology for analyzing a lightly damped structure using normal modes.
+The diagram in Figure [1](#org7e10f92) shows the methodology for analyzing a lightly damped structure using normal modes.

 <div class="important">
  <div></div>
@ -46,7 +46,7 @@ The steps are:

 </div>

-<a id="org6569db5"></a>
+<a id="org7e10f92"></a>

 {{< figure src="/ox-hugo/hatch00_modal_analysis_flowchart.png" caption="Figure 1: Modal analysis method flowchart" >}}

@ -58,7 +58,7 @@ Because finite element models usually have a very large number of states, an imp
 <div class="important">
  <div></div>

-Figure [2](#org2fb61c6) shows such process, the steps are:
+Figure [2](#org1c1177f) shows such process, the steps are:

 -   start with the finite element model
 -   compute the eigenvalues and eigenvectors (as many as dof in the model)
@ -71,14 +71,14 @@ Figure [2](#org2fb61c6) shows such process, the steps are:

 </div>

-<a id="org2fb61c6"></a>
+<a id="org1c1177f"></a>

 {{< figure src="/ox-hugo/hatch00_model_reduction_chart.png" caption="Figure 2: Model size reduction flowchart" >}}


 ### Notations {#notations}

-Tables [3](#org3e528f9), [2](#table--tab:notations-eigen-vectors-values) and [3](#table--tab:notations-stiffness-mass) summarize the notations of this document.
+Tables [3](#org437cc66), [2](#table--tab:notations-eigen-vectors-values) and [3](#table--tab:notations-stiffness-mass) summarize the notations of this document.

 <a id="table--tab:notations-modes-nodes"></a>
 <div class="table-caption">
@ -127,22 +127,22 @@ Tables [3](#org3e528f9), [2](#table--tab:notations-eigen-vectors-values) and [3]

 ## Zeros in SISO Mechanical Systems {#zeros-in-siso-mechanical-systems}

-<a id="org2522018"></a>
+<a id="orgf7c45a9"></a>
 The origin and influence of poles are clear: they represent the resonant frequencies of the system, and for each resonance frequency, a mode shape can be defined to describe the motion at that frequency.

 We here which to give an intuitive understanding for **when to expect zeros in SISO mechanical systems** and **how to predict the frequencies at which they will occur**.

-Figure [3](#org3e528f9) shows a series arrangement of masses and springs, with a total of \\(n\\) masses and \\(n+1\\) springs.
+Figure [3](#org437cc66) shows a series arrangement of masses and springs, with a total of \\(n\\) masses and \\(n+1\\) springs.
 The degrees of freedom are numbered from left to right, \\(z\_1\\) through \\(z\_n\\).

-<a id="org3e528f9"></a>
+<a id="org437cc66"></a>

 {{< figure src="/ox-hugo/hatch00_n_dof_zeros.png" caption="Figure 3: n dof system showing various SISO input/output configurations" >}}

 <div class="important">
  <div></div>

-<sup id="2169677da08094824a29bd3231ea1264"><a class="reference-link" href="#miu93_mechat" title="Denny Miu, Mechatronics: Electromechanics and Contromechanics, Springer-Verlag New York (1993).">(Denny Miu, 1993)</a></sup> shows that the zeros of any particular transfer function are the poles of the constrained system to the left and/or right of the system defined by constraining the one or two dof's defining the transfer function.
+([Miu 1993](#org44eae27)) shows that the zeros of any particular transfer function are the poles of the constrained system to the left and/or right of the system defined by constraining the one or two dof's defining the transfer function.

 The resonances of the "overhanging appendages" of the constrained system create the zeros.

@ -151,12 +151,12 @@ The resonances of the "overhanging appendages" of the constrained system create

 ## State Space Analysis {#state-space-analysis}

-<a id="orgd09cb02"></a>
+<a id="orgc7d1453"></a>


 ## Modal Analysis {#modal-analysis}

-<a id="orga858b43"></a>
+<a id="orgaec588e"></a>

 Lightly damped structures are typically analyzed with the "normal mode" method described in this section.

@ -196,9 +196,9 @@ Summarizing the modal analysis method of analyzing linear mechanical systems and

 #### Equation of Motion {#equation-of-motion}

-Let's consider the model shown in Figure [4](#orgc897d6a) with \\(k\_1 = k\_2 = k\\), \\(m\_1 = m\_2 = m\_3 = m\\) and \\(c\_1 = c\_2 = 0\\).
+Let's consider the model shown in Figure [4](#org7d4f157) with \\(k\_1 = k\_2 = k\\), \\(m\_1 = m\_2 = m\_3 = m\\) and \\(c\_1 = c\_2 = 0\\).

-<a id="orgc897d6a"></a>
+<a id="org7d4f157"></a>

 {{< figure src="/ox-hugo/hatch00_undamped_tdof_model.png" caption="Figure 4: Undamped tdof model" >}}

@ -297,17 +297,17 @@ One then find:
  \end{bmatrix}
 \end{equation}

-Virtual interpretation of the eigenvectors are shown in Figures [5](#org40e1b2b), [6](#orgbe3ed46) and [7](#org766efd1).
+Virtual interpretation of the eigenvectors are shown in Figures [5](#org102195c), [6](#org8c88cc4) and [7](#org033aa75).

-<a id="org40e1b2b"></a>
+<a id="org102195c"></a>

 {{< figure src="/ox-hugo/hatch00_tdof_mode_1.png" caption="Figure 5: Rigid-Body Mode, 0rad/s" >}}

-<a id="orgbe3ed46"></a>
+<a id="org8c88cc4"></a>

 {{< figure src="/ox-hugo/hatch00_tdof_mode_2.png" caption="Figure 6: Second Model, Middle Mass Stationary, 1rad/s" >}}

-<a id="org766efd1"></a>
+<a id="org033aa75"></a>

 {{< figure src="/ox-hugo/hatch00_tdof_mode_3.png" caption="Figure 7: Third Mode, 1.7rad/s" >}}

@ -346,9 +346,9 @@ There are many options for change of basis, but we will show that **when eigenve
 The n-uncoupled equations in the principal coordinate system can then be solved for the responses in the principal coordinate system using the well known solutions for the single dof systems.
 The n-responses in the principal coordinate system can then be **transformed back** to the physical coordinate system to provide the actual response in physical coordinate.

-This procedure is schematically shown in Figure [8](#org9c058ac).
+This procedure is schematically shown in Figure [8](#org137f17c).

-<a id="org9c058ac"></a>
+<a id="org137f17c"></a>

 {{< figure src="/ox-hugo/hatch00_schematic_modal_solution.png" caption="Figure 8: Roadmap for Modal Solution" >}}

@ -696,7 +696,7 @@ Absolute damping is based on making \\(b = 0\\), in which case the percentage of

 ## Frequency Response: Modal Form {#frequency-response-modal-form}

-<a id="org74f8e80"></a>
+<a id="org5db4c17"></a>

 The procedure to obtain the frequency response from a modal form is as follow:

@ -704,9 +704,9 @@ The procedure to obtain the frequency response from a modal form is as follow:
 -   use Laplace transform to obtain the transfer functions in principal coordinates
 -   back-transform the transfer functions to physical coordinates where the individual mode contributions will be evident

-This will be applied to the model shown in Figure [9](#orgbbe5276).
+This will be applied to the model shown in Figure [9](#orgefc4430).

-<a id="orgbbe5276"></a>
+<a id="orgefc4430"></a>

 {{< figure src="/ox-hugo/hatch00_tdof_model.png" caption="Figure 9: tdof undamped model for modal analysis" >}}

@ -888,9 +888,9 @@ Equations \eqref{eq:general_add_tf} and \eqref{eq:general_add_tf_damp} shows tha

 </div>

-Figure [10](#org4f8e313) shows the separate contributions of each mode to the total response \\(z\_1/F\_1\\).
+Figure [10](#org997887a) shows the separate contributions of each mode to the total response \\(z\_1/F\_1\\).

-<a id="org4f8e313"></a>
+<a id="org997887a"></a>

 {{< figure src="/ox-hugo/hatch00_z11_tf.png" caption="Figure 10: Mode contributions to the transfer function from \\(F\_1\\) to \\(z\_1\\)" >}}

@ -899,16 +899,16 @@ The zeros for SISO transfer functions are the roots of the numerator, however, f

 ## SISO State Space Matlab Model from ANSYS Model {#siso-state-space-matlab-model-from-ansys-model}

-<a id="orgde113bc"></a>
+<a id="orgee24ebb"></a>


 ### Introduction {#introduction}

-In this section is developed a SISO state space Matlab model from an ANSYS cantilever beam model as shown in Figure [11](#orgf61b7cd).
+In this section is developed a SISO state space Matlab model from an ANSYS cantilever beam model as shown in Figure [11](#org64b074d).
 A z direction force is applied at the midpoint of the beam and z displacement at the tip is the output.
 The objective is to provide the smallest Matlab state space model that accurately represents the pertinent dynamics.

-<a id="orgf61b7cd"></a>
+<a id="org64b074d"></a>

 {{< figure src="/ox-hugo/hatch00_cantilever_beam.png" caption="Figure 11: Cantilever beam with forcing function at midpoint" >}}

@ -987,7 +987,7 @@ If sorting of DC gain values is performed prior to the `truncate` operation, the

 ## Ground Acceleration Matlab Model From ANSYS Model {#ground-acceleration-matlab-model-from-ansys-model}

-<a id="org86135e3"></a>
+<a id="org88a2eb8"></a>


 ### Model Description {#model-description}
@ -1001,25 +1001,25 @@ If sorting of DC gain values is performed prior to the `truncate` operation, the

 ## SISO Disk Drive Actuator Model {#siso-disk-drive-actuator-model}

-<a id="org5a61d5f"></a>
+<a id="org9f31aa5"></a>

-In this section we wish to extract a SISO state space model from a Finite Element model representing a Disk Drive Actuator (Figure [12](#orgc2d185d)).
+In this section we wish to extract a SISO state space model from a Finite Element model representing a Disk Drive Actuator (Figure [12](#org594b960)).


 ### Actuator Description {#actuator-description}

-<a id="orgc2d185d"></a>
+<a id="org594b960"></a>

 {{< figure src="/ox-hugo/hatch00_disk_drive_siso_model.png" caption="Figure 12: Drawing of Actuator/Suspension system" >}}

-The primary motion of the actuator is rotation about the pivot bearing, therefore the final model has the coordinate system transformed from a Cartesian x,y,z coordinate system to a Cylindrical \\(r\\), \\(\theta\\) and \\(z\\) system, with the two origins coincident (Figure [13](#orgd4d4d64)).
+The primary motion of the actuator is rotation about the pivot bearing, therefore the final model has the coordinate system transformed from a Cartesian x,y,z coordinate system to a Cylindrical \\(r\\), \\(\theta\\) and \\(z\\) system, with the two origins coincident (Figure [13](#orgb941e2d)).

-<a id="orgd4d4d64"></a>
+<a id="orgb941e2d"></a>

 {{< figure src="/ox-hugo/hatch00_disk_drive_nodes_reduced_model.png" caption="Figure 13: Nodes used for reduced Matlab model. Shown with partial finite element mesh at coil" >}}

 For reduced models, we only require eigenvector information for dof where forces are applied and where displacements are required.
-Figure [13](#orgd4d4d64) shows the nodes used for the reduced Matlab model.
+Figure [13](#orgb941e2d) shows the nodes used for the reduced Matlab model.
 The four nodes 24061, 24066, 24082 and 24087 are located in the center of the coil in the z direction and are used for simulating the VCM force.
 The arrows at the nodes indicate the direction of forces.

@ -1079,7 +1079,7 @@ From Ansys, we have the eigenvalues \\(\omega\_i\\) and eigenvectors \\(\bm{z}\\

 ## Balanced Reduction {#balanced-reduction}

-<a id="org1ed7c19"></a>
+<a id="orgc607ae9"></a>

 In this chapter another method of reducing models, “balanced reduction”, will be introduced and compared with the DC and peak gain ranking methods.

@ -1194,14 +1194,14 @@ The **states to be kept are the states with the largest diagonal terms**.

 ## MIMO Two Stage Actuator Model {#mimo-two-stage-actuator-model}

-<a id="org2ac725c"></a>
+<a id="org03a495e"></a>

-In this section, a MIMO two-stage actuator model is derived from a finite element model (Figure [14](#org781c515)).
+In this section, a MIMO two-stage actuator model is derived from a finite element model (Figure [14](#orgf0d40c4)).


 ### Actuator Description {#actuator-description}

-<a id="org781c515"></a>
+<a id="orgf0d40c4"></a>

 {{< figure src="/ox-hugo/hatch00_disk_drive_mimo_schematic.png" caption="Figure 14: Drawing of actuator/suspension system" >}}

@ -1223,9 +1223,9 @@ Since the same forces are being applied to both piezo elements, they represent t

 ### Ansys Model Description {#ansys-model-description}

-In Figure [15](#org6316e01) are shown the principal nodes used for the model.
+In Figure [15](#org3b2d630) are shown the principal nodes used for the model.

-<a id="org6316e01"></a>
+<a id="org3b2d630"></a>

 {{< figure src="/ox-hugo/hatch00_disk_drive_mimo_ansys.png" caption="Figure 15: Nodes used for reduced Matlab model, shown with partial mesh at coil and piezo element" >}}

@ -1344,11 +1344,11 @@ And we note:
 G = zn * Gp;
 ```

-<a id="org1a720cb"></a>
+<a id="orga327a57"></a>

 {{< figure src="/ox-hugo/hatch00_z13_tf.png" caption="Figure 16: Mode contributions to the transfer function from \\(F\_1\\) to \\(z\_3\\)" >}}

-<a id="org9f278e9"></a>
+<a id="orgcdf4fe9"></a>

 {{< figure src="/ox-hugo/hatch00_z11_tf.png" caption="Figure 17: Mode contributions to the transfer function from \\(F\_1\\) to \\(z\_1\\)" >}}

@ -1446,13 +1446,13 @@ G_f = ss(A, B, C, D);

 ### Simple mode truncation {#simple-mode-truncation}

-Let's plot the frequency of the modes (Figure [18](#orgd322a53)).
+Let's plot the frequency of the modes (Figure [18](#org677de35)).

-<a id="orgd322a53"></a>
+<a id="org677de35"></a>

 {{< figure src="/ox-hugo/hatch00_cant_beam_modes_freq.png" caption="Figure 18: Frequency of the modes" >}}

-<a id="orgb88c298"></a>
+<a id="orgad1205a"></a>

 {{< figure src="/ox-hugo/hatch00_cant_beam_unsorted_dc_gains.png" caption="Figure 19: Unsorted DC Gains" >}}

@ -1521,7 +1521,7 @@ dc_gain = abs(xn(i_input, :).*xn(i_output, :))./(2*pi*f0).^2;
 [dc_gain_sort, index_sort] = sort(dc_gain, 'descend');
 ```

-<a id="orgf4c7beb"></a>
+<a id="org78bca6c"></a>

 {{< figure src="/ox-hugo/hatch00_cant_beam_sorted_dc_gains.png" caption="Figure 20: Sorted DC Gains" >}}

@ -1865,7 +1865,7 @@ wo = gram(G_m, 'o');

 And we plot the diagonal terms

-<a id="orgb83de68"></a>
+<a id="orgdf43aa3"></a>

 {{< figure src="/ox-hugo/hatch00_gramians.png" caption="Figure 21: Observability and Controllability Gramians" >}}

@ -1883,7 +1883,7 @@ We use `balreal` to rank oscillatory states.
 [G_b, G, T, Ti] = balreal(G_m);
 ```

-<a id="org7516695"></a>
+<a id="org09f35b9"></a>

 {{< figure src="/ox-hugo/hatch00_cant_beam_gramian_balanced.png" caption="Figure 22: Sorted values of the Gramian of the balanced realization" >}}

@ -2126,12 +2126,11 @@ pos_frames = pos([1, i_input, i_output], :);
 ```


-## Import super-element from Ansys {#import-super-element-from-ansys}
+## Bibliography {#bibliography}

-# Bibliography
-<a class="bibtex-entry" id="hatch00_vibrat_matlab_ansys">Hatch, M. R., *Vibration simulation using matlab and ansys* (2000), : CRC Press.</a> [↩](#484c4fad309f6b0e866a7cacf4653d74)
+<a id="org26212b4"></a>Hatch, Michael R. 2000. _Vibration Simulation Using MATLAB and ANSYS_. CRC Press.

-<a class="bibtex-entry" id="miu93_mechat">Miu, D. K., *Mechatronics: electromechanics and contromechanics* (1993), : Springer-Verlag New York.</a> [↩](#2169677da08094824a29bd3231ea1264)
+<a id="org44eae27"></a>Miu, Denny K. 1993. _Mechatronics: Electromechanics and Contromechanics_. 1st ed. Mechanical Engineering Series. Springer-Verlag New York.


 ## Backlinks {#backlinks}
--- a/content/zettels/amplified_piezoelectric_actuators.md
+++ b/content/zettels/amplified_piezoelectric_actuators.md
@ -0,0 +1,10 @@
+++
+title = "Amplified Piezoelectric Actuators"
+author = ["Thomas Dehaeze"]
+draft = false
+++
+
+Tags
+: [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
+
+<./biblio/references.bib>
--- a/content/zettels/force_sensors.md
+++ b/content/zettels/force_sensors.md
@ -8,23 +8,36 @@ Tags
 :


-## Dynamics and Noise of a piezoelectric force sensor {#dynamics-and-noise-of-a-piezoelectric-force-sensor}
+## Piezoelectric Force Sensors {#piezoelectric-force-sensors}
+
+
+### Dynamics and Noise of a piezoelectric force sensor {#dynamics-and-noise-of-a-piezoelectric-force-sensor}

 An analysis the dynamics and noise of a piezoelectric force sensor is done in <sup id="c823f68dd2a72b9667a61b3c046b4731"><a class="reference-link" href="#fleming10_nanop_system_with_force_feedb" title="Fleming, Nanopositioning System With Force Feedback for  High-Performance Tracking and Vibration Control, {IEEE/ASME Transactions on Mechatronics}, v(3), 433-447 (2010).">(Fleming, 2010)</a></sup> ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).


-## Manufacturers {#manufacturers}
+### Manufacturers {#manufacturers}

 | Manufacturers | Links                                                         |
 |---------------|---------------------------------------------------------------|
 | PCB           | [link](https://www.pcb.com/products/productfinder.aspx?tx=17) |

+
+### Signal Conditioner {#signal-conditioner}
+
+The voltage generated by the piezoelectric material generally needs to be amplified.
+
+| Manufacturers | Links                                         |
+|---------------|-----------------------------------------------|
+| PCB           | [link](https://www.pcb.com/products?m=482c15) |
+
 # Bibliography
 <a class="bibtex-entry" id="fleming10_nanop_system_with_force_feedb">Fleming, A., *Nanopositioning system with force feedback for high-performance tracking and vibration control*, IEEE/ASME Transactions on Mechatronics, *15(3)*, 433–447 (2010).  http://dx.doi.org/10.1109/tmech.2009.2028422</a> [↩](#c823f68dd2a72b9667a61b3c046b4731)


 ## Backlinks {#backlinks}

-   [Nanopositioning system with force feedback for high-performance tracking and vibration control]({{< relref "fleming10_nanop_system_with_force_feedb" >}})
 -   [Collocated Control]({{< relref "collocated_control" >}})
+-   [Nanopositioning system with force feedback for high-performance tracking and vibration control]({{< relref "fleming10_nanop_system_with_force_feedb" >}})
+-   [Sensors]({{< relref "sensors" >}})
 -   [Position Sensors]({{< relref "position_sensors" >}})
--- a/content/zettels/piezoelectric_actuators.md
+++ b/content/zettels/piezoelectric_actuators.md
@ -13,38 +13,45 @@ Tags

 ### Manufacturers {#manufacturers}

-| Manufacturers       | Links                                                                              |
-|---------------------|------------------------------------------------------------------------------------|
-| Cedrat              | [link](http://www.cedrat-technologies.com/)                                        |
-| PI                  | [link](https://www.physikinstrumente.com/en/)                                      |
-| Piezo System        | [link](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/) |
-| Noliac              | [link](http://www.noliac.com/)                                                     |
-| Thorlabs            | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700)           |
-| PiezoDrive          | [link](https://www.piezodrive.com/actuators/)                                      |
-| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/10.html)                     |
-| CoreMorrow          | [link](http://www.coremorrow.com/en/pro-9-1.html)                                  |
+| Manufacturers       | Links                                                                                                          |
+|---------------------|----------------------------------------------------------------------------------------------------------------|
+| Cedrat              | [link](http://www.cedrat-technologies.com/)                                                                    |
+| PI                  | [link](https://www.physikinstrumente.com/en/)                                                                  |
+| Piezo System        | [link](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/)                             |
+| Noliac              | [link](http://www.noliac.com/)                                                                                 |
+| Thorlabs            | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700)                                       |
+| PiezoDrive          | [link](https://www.piezodrive.com/actuators/)                                                                  |
+| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/10.html)                                                 |
+| CoreMorrow          | [link](http://www.coremorrow.com/en/pro-9-1.html)                                                              |
+| PiezoData           | [link](https://www.piezodata.com/piezo-stack-actuator-2/)                                                      |
+| Queensgate          | [link](https://www.nanopositioning.com/product-category/nanopositioning/nanopositioning-actuators-translators) |


 ### Model {#model}

-A model of a multi-layer monolithic piezoelectric stack actuator is described in <sup id="c823f68dd2a72b9667a61b3c046b4731"><a class="reference-link" href="#fleming10_nanop_system_with_force_feedb" title="Fleming, Nanopositioning System With Force Feedback for  High-Performance Tracking and Vibration Control, {IEEE/ASME Transactions on Mechatronics}, v(3), 433-447 (2010).">(Fleming, 2010)</a></sup> ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
+A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#org7ef2e50)) ([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.
+
+The relation between the applied voltage \\(V\_a\\) to the generated force \\(F\_a\\) is:
+\\[ F\_a = g\_a V\_a, \quad g\_a = d\_{33} n k\_a \\]
+with:
+
+-   \\(d\_{33}\\) is the piezoelectric strain constant [m/V]
+-   \\(n\\) is the number of layers
+-   \\(k\_a\\) is the actuator stiffness [N/m]


 ## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}

-The Amplified Piezo Actuators principle is presented in <sup id="5decd2b31c4a9842b80c58b56f96590a"><a class="reference-link" href="#claeyssen07_amplif_piezoel_actuat" title="Frank Claeyssen, Le Letty, Barillot, \&amp; Sosnicki, Amplified Piezoelectric Actuators: Static \&amp; Dynamic  Applications, {Ferroelectrics}, v(1), 3-14 (2007).">(Frank Claeyssen {\it et al.}, 2007)</a></sup>:
+The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#orgc110fa4)):

 > 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 <sup id="849750850d9986ed326e74bd3c448d03"><a class="reference-link" href="#lucinskis16_dynam_charac" title="@misc{lucinskis16_dynam_charac,
-  author          = {R. Lucinskis and C. Mangeot},
-  title           = {Dynamic Characterization of an amplified piezoelectric
-                  actuator},
-  year            = 2016,
-}">(Lucinskis \& Mangeot, 2016)</a></sup>.
+A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#orge1d2714)).

-<a id="orgd9b1a8d"></a>
+<a id="org5a5d286"></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 class=\"reference-link\" 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).\">(Mingxiang Ling {\it et al.}, 2016)</a></sup>" >}}

@ -57,6 +64,7 @@ A model of an amplified piezoelectric actuator is described in <sup id="84975085
 | Noliac              | [link](http://www.noliac.com/products/actuators/amplified-actuators/)                                                                                                                                                                             |
 | Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F5.html), [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F3.html), [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5Fmtkk.html) |
 | CoreMorrow          | [link](http://www.coremorrow.com/en/pro-13-1.html)                                                                                                                                                                                                |
+| PiezoData           | [link](https://www.piezodata.com/piezoelectric-actuator-amplifier/)                                                                                                                                                                               |


 ## Specifications {#specifications}
@ -121,7 +129,7 @@ with:

 ### Resolution {#resolution}

-The resolution is limited by the noise in the voltage amplified.
+The resolution is limited by the noise in the [Voltage Amplifier]({{< relref "voltage_amplifier" >}}).

 Typical [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}}) of voltage amplifiers is \\(100dB = 10^{5}\\).
 Thus, for a piezoelectric stack with a displacement \\(L\\), the resolution will be
@ -135,53 +143,57 @@ For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolut

 ### Electrical Capacitance {#electrical-capacitance}

-The electrical capacitance gives the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#org3da123f)).
+The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#orgebd19c2)).
+This is due to the fact that voltage amplifier has a limitation on the deliverable current.

-<a id="org3da123f"></a>
+[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="orgebd19c2"></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" >}}


 ## 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](#orgab6e282)).
+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](#orgb64bc37)).

-<a id="orgab6e282"></a>
+<a id="orgb64bc37"></a>

 {{< 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](#orgcf60838)):
+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](#org944d760)):

 \begin{equation}
  \Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
 \end{equation}

-<a id="orgcf60838"></a>
+<a id="org944d760"></a>

 {{< 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](#orga8ee6e8)).
+For piezo actuators, force and displacement are inversely related (Figure [5](#org0a60bcb)).
 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.
+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="orga8ee6e8"></a>
+<a id="org0a60bcb"></a>

 {{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}

-# Bibliography
-<a class="bibtex-entry" id="fleming10_nanop_system_with_force_feedb">Fleming, A., *Nanopositioning system with force feedback for high-performance tracking and vibration control*, IEEE/ASME Transactions on Mechatronics, *15(3)*, 433–447 (2010).  http://dx.doi.org/10.1109/tmech.2009.2028422</a> [↩](#c823f68dd2a72b9667a61b3c046b4731)

-<a class="bibtex-entry" id="claeyssen07_amplif_piezoel_actuat">Claeyssen, F., Letty, R. L., Barillot, F., & Sosnicki, O., *Amplified piezoelectric actuators: static \& dynamic applications*, Ferroelectrics, *351(1)*, 3–14 (2007).  http://dx.doi.org/10.1080/00150190701351865</a> [↩](#5decd2b31c4a9842b80c58b56f96590a)
+## Bibliography {#bibliography}

-<a class="bibtex-entry" id="lucinskis16_dynam_charac">Lucinskis, R., & Mangeot, C. (2016). *Dynamic characterization of an amplified piezoelectric actuator*. Retrieved from [](). .</a> [↩](#849750850d9986ed326e74bd3c448d03)
+<a id="orgc110fa4"></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 class="bibtex-entry" id="ling16_enhan_mathem_model_displ_amplif">Ling, M., Cao, J., Zeng, M., Lin, J., & Inman, D. J., *Enhanced mathematical modeling of the displacement amplification ratio for piezoelectric compliant mechanisms*, Smart Materials and Structures, *25(7)*, 075022 (2016).  http://dx.doi.org/10.1088/0964-1726/25/7/075022</a> [↩](#d9e8b33774f1e65d16bd79114db8ac64)
+<a id="org7ef2e50"></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="orge1d2714"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”


 ## Backlinks {#backlinks}

 -   [Actuators]({{< relref "actuators" >}})
+-   [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
--- a/content/zettels/position_sensors.md
+++ b/content/zettels/position_sensors.md
@ -5,12 +5,12 @@ draft = false
 +++

 Tags
-: [Inertial Sensors]({{< relref "inertial_sensors" >}}), [Force Sensors]({{< relref "force_sensors" >}}), [Sensor Fusion]({{< relref "sensor_fusion" >}})
+: [Inertial Sensors]({{< relref "inertial_sensors" >}}), [Force Sensors]({{< relref "force_sensors" >}}), [Sensor Fusion]({{< relref "sensor_fusion" >}}), [Signal Conditioner]({{< relref "signal_conditioner" >}}), [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})


 ## Reviews of Relative Position Sensors {#reviews-of-relative-position-sensors}

-   Fleming, A. J., A review of nanometer resolution position sensors: operation and performance <sup id="3fb5b61524290e36d639a4fac65703d0"><a class="reference-link" href="#fleming13_review_nanom_resol_posit_sensor" title="Andrew Fleming, A Review of Nanometer Resolution Position Sensors:  Operation and Performance, {Sensors and Actuators A: Physical}, v(nil), 106-126 (2013).">(Andrew Fleming, 2013)</a></sup> ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))
+-   Fleming, A. J., A review of nanometer resolution position sensors: operation and performance ([Fleming 2013](#orgeaf4a0a)) ([Notes]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}}))

 <a id="table--tab:characteristics-relative-sensor"></a>
 <div class="table-caption">
@ -44,8 +44,7 @@ Tags
 | Interferometer | Meters                         |         | 0.5 nm     | >100kHz  | 1 ppm FSR |
 | Encoder        | Meters                         |         | 6 nm       | >100kHz  | 5 ppm FSR |

-
-## Strain Gauge {#strain-gauge}
+Capacitive Sensors and Eddy-Current sensors are compare [here](https://www.lionprecision.com/comparing-capacitive-and-eddy-current-sensors/).


 ## Capacitive Sensor {#capacitive-sensor}
@ -55,42 +54,48 @@ Description:
 -   <http://www.lionprecision.com/tech-library/technotes/cap-0020-sensor-theory.html>
 -   <https://www.lionprecision.com/comparing-capacitive-and-eddy-current-sensors>

-| Manufacturers  | Links                                                                                           |
-|----------------|-------------------------------------------------------------------------------------------------|
-| Micro Sense    | [link](http://www.microsense.net/products-position-sensors.htm)                                 |
-| Micro-Epsilon  | [link](https://www.micro-epsilon.com/displacement-position-sensors/capacitive-sensor/)          |
-| PI             | [link](https://www.physikinstrumente.com/en/technology/sensor-technologies/capacitive-sensors/) |
-| Unipulse       | [link](https://www.unipulse.com/product/ps-ia/)                                                 |
-| Lion-Precision | [link](https://www.lionprecision.com/products/capacitive-sensors)                               |
+| Manufacturers  | Links                                                                                            | Country |
+|----------------|--------------------------------------------------------------------------------------------------|---------|
+| Micro Sense    | [link](http://www.microsense.net/products-position-sensors.htm)                                  | USA     |
+| Micro-Epsilon  | [link](https://www.micro-epsilon.com/displacement-position-sensors/capacitive-sensor/)           | Germany |
+| PI             | [link](https://www.physikinstrumente.com/en/technology/sensor-technologies/capacitive-sensors/)  | Germany |
+| Unipulse       | [link](https://www.unipulse.com/product/ps-ia/)                                                  | Japan   |
+| Lion-Precision | [link](https://www.lionprecision.com/products/capacitive-sensors)                                | USA     |
+| Fogale         | [link](http://www.fogale.fr/brochures.html)                                                      | USA     |
+| Queensgate     | [link](https://www.nanopositioning.com/product-category/nanopositioning/nanopositioning-sensors) | UK      |
+| Capacitec      | [link](https://www.capacitec.com/Displacement-Sensing-Systems)                                   | USA     |


 ## Inductive Sensor (Eddy Current) {#inductive-sensor--eddy-current}

-| Manufacturers  | Links                                                                                    |
-|----------------|------------------------------------------------------------------------------------------|
-| Micro-Epsilon  | [link](https://www.micro-epsilon.com/displacement-position-sensors/eddy-current-sensor/) |
-| Lion Precision | [link](https://www.lionprecision.com/products/eddy-current-sensors)                      |
+| Manufacturers  | Links                                                                                     |         |
+|----------------|-------------------------------------------------------------------------------------------|---------|
+| Micro-Epsilon  | [link](https://www.micro-epsilon.com/displacement-position-sensors/eddy-current-sensor/)  | Germany |
+| Lion Precision | [link](https://www.lionprecision.com/products/eddy-current-sensors)                       | USA     |
+| Cedrat         | [link](https://www.cedrat-technologies.com/en/products/sensors/eddy-current-sensors.html) | France  |
+| Kaman          | [link](https://www.kamansensors.com/product/smt-9700/)                                    | USA     |
+| Keyence        | [link](https://www.keyence.com/ss/products/measure/measurement%5Flibrary/type/inductive/) | USA     |


 ## Inductive Sensor (LVDT) {#inductive-sensor--lvdt}

-| Manufacturers | Links                                                                                      |
-|---------------|--------------------------------------------------------------------------------------------|
-| Micro-Epsilon | [link](https://www.micro-epsilon.com/displacement-position-sensors/inductive-sensor-lvdt/) |
-| Keyence       | [link](https://www.keyence.eu/products/measure/contact-distance-lvdt/gt2/index.jsp)        |
+| Manufacturers | Links                                                                                      | Country |
+|---------------|--------------------------------------------------------------------------------------------|---------|
+| Micro-Epsilon | [link](https://www.micro-epsilon.com/displacement-position-sensors/inductive-sensor-lvdt/) | Germany |
+| Keyence       | [link](https://www.keyence.eu/products/measure/contact-distance-lvdt/gt2/index.jsp)        | USA     |


 ## Interferometers {#interferometers}

-| Manufacturers | Links                                                                                                    |
-|---------------|----------------------------------------------------------------------------------------------------------|
-| Attocube      | [link](http://www.attocube.com/)                                                                         |
-| Zygo          | [link](https://www.zygo.com/?/met/markets/stageposition/zmi/)                                            |
-| Smaract       | [link](https://www.smaract.com/interferometry)                                                           |
-| Qutools       | [link](https://www.qutools.com/qudis/)                                                                   |
-| Renishaw      | [link](https://www.renishaw.com/en/fibre-optic-laser-encoder-products--6594)                             |
-| Sios          | [link](https://sios-de.com/products/length-measurement/laser-interferometer/)                            |
-| Keysight      | [link](https://www.keysight.com/en/pc-1000000393%3Aepsg%3Apgr/laser-heads?nid=-536900395.0&cc=FR&lc=fre) |
+| Manufacturers | Links                                                                                                    | Country |
+|---------------|----------------------------------------------------------------------------------------------------------|---------|
+| Attocube      | [link](http://www.attocube.com/)                                                                         | Germany |
+| Zygo          | [link](https://www.zygo.com/?/met/markets/stageposition/zmi/)                                            | USA     |
+| Smaract       | [link](https://www.smaract.com/interferometry)                                                           | Germany |
+| Qutools       | [link](https://www.qutools.com/qudis/)                                                                   | Germany |
+| Renishaw      | [link](https://www.renishaw.com/en/fibre-optic-laser-encoder-products--6594)                             | UK      |
+| Sios          | [link](https://sios-de.com/products/length-measurement/laser-interferometer/)                            | Germany |
+| Keysight      | [link](https://www.keysight.com/en/pc-1000000393%3Aepsg%3Apgr/laser-heads?nid=-536900395.0&cc=FR&lc=fre) | USA     |

 <div class="table-caption">
  <span class="table-number">Table 3</span>:
@ -103,31 +108,33 @@ Description:
 | Renishaw  | 0.2                          | 1                         | 6                        | 1                                           |
 | Picoscale | 0.2                          | 2                         | 2                        | 1                                           |

-<sup id="7658b1219a4458a62ae8c6f51b767542"><a class="reference-link" href="#jang17_compen_refrac_index_air_laser" title="Yoon-Soo Jang \&amp; Seung-Woo Kim, Compensation of the Refractive Index of Air in Laser  Interferometer for Distance Measurement: a Review, {International Journal of Precision Engineering and
-                  Manufacturing}, v(12), 1881-1890 (2017).">(Yoon-Soo Jang \& Seung-Woo Kim, 2017)</a></sup>
+([Jang and Kim 2017](#org5a2485c))

-<a id="org0399c13"></a>
+<a id="orgdc4dc3c"></a>

 {{< figure src="/ox-hugo/position_sensor_interferometer_precision.png" caption="Figure 1: Expected precision of interferometer as a function of measured distance" >}}


-## Fiber Optic Displacement Sensor {#fiber-optic-displacement-sensor}
+## Linear Encoders {#linear-encoders}

-| Manufacturers | Links                                              |
-|---------------|----------------------------------------------------|
-| Unipulse      | [link](https://www.unipulse.com/product/atw200-2/) |
+| Manufacturers  | Links                                                                 | Country |
+|----------------|-----------------------------------------------------------------------|---------|
+| Heidenhain     | [link](https://www.heidenhain.com/en%5FUS/products/linear-encoders/)  | Germany |
+| MicroE Systems | [link](https://www.celeramotion.com/microe/products/linear-encoders/) | USA     |
+| Renishaw       | [link](https://www.renishaw.com/en/browse-encoder-range--6440)        | UK      |

-# Bibliography
-<a class="bibtex-entry" id="fleming13_review_nanom_resol_posit_sensor">Fleming, A. J., *A review of nanometer resolution position sensors: operation and performance*, Sensors and Actuators A: Physical, *190(nil)*, 106–126 (2013).  http://dx.doi.org/10.1016/j.sna.2012.10.016</a> [↩](#3fb5b61524290e36d639a4fac65703d0)

-<a class="bibtex-entry" id="collette11_review">Collette, C., Artoos, K., Guinchard, M., Janssens, S., Carmona Fernandez, P., & Hauviller, C., *Review of sensors for low frequency seismic vibration measurement* (2011).</a> [↩](#642a18d86de4e062c6afb0f5f20501c4)
+## Bibliography {#bibliography}

-<a class="bibtex-entry" id="jang17_compen_refrac_index_air_laser">Jang, Y., & Kim, S., *Compensation of the refractive index of air in laser interferometer for distance measurement: a review*, International Journal of Precision Engineering and Manufacturing, *18(12)*, 1881–1890 (2017).  http://dx.doi.org/10.1007/s12541-017-0217-y</a> [↩](#7658b1219a4458a62ae8c6f51b767542)
+<a id="orgeaf4a0a"></a>Fleming, Andrew J. 2013. “A Review of Nanometer Resolution Position Sensors: Operation and Performance.” _Sensors and Actuators a: Physical_ 190 (nil):106–26. <https://doi.org/10.1016/j.sna.2012.10.016>.
+
+<a id="org5a2485c"></a>Jang, Yoon-Soo, and Seung-Woo Kim. 2017. “Compensation of the Refractive Index of Air in Laser Interferometer for Distance Measurement: A Review.” _International Journal of Precision Engineering and Manufacturing_ 18 (12):1881–90. <https://doi.org/10.1007/s12541-017-0217-y>.


 ## Backlinks {#backlinks}

 -   [A review of nanometer resolution position sensors: operation and performance]({{< relref "fleming13_review_nanom_resol_posit_sensor" >}})
 -   [Measurement technologies for precision positioning]({{< relref "gao15_measur_techn_precis_posit" >}})
-   [Collocated Control]({{< relref "collocated_control" >}})
 -   [Inertial Sensors]({{< relref "inertial_sensors" >}})
+-   [Sensors]({{< relref "sensors" >}})
+-   [Collocated Control]({{< relref "collocated_control" >}})
--- a/content/zettels/power_spectral_density.md
+++ b/content/zettels/power_spectral_density.md
@ -0,0 +1,17 @@
+++
+title = "Power Spectral Density"
+author = ["Thomas Dehaeze"]
+draft = false
+++
+
+Tags
+: [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})
+
+Tutorial about Power Spectral Density is accessible [here](https://tdehaeze.github.io/spectral-analysis/).
+
+A good article about how to use the `pwelch` function with Matlab ([Schmid 2012](#org8fdb443)).
+
+
+## Bibliography {#bibliography}
+
+<a id="org8fdb443"></a>Schmid, Hanspeter. 2012. “How to Use the FFT and Matlab’s Pwelch Function for Signal and Noise Simulations and Measurements.” _Institute of Microelectronics_.
--- a/content/zettels/shaker.md
+++ b/content/zettels/shaker.md
@ -0,0 +1,17 @@
+++
+title = "Shaker"
+author = ["Thomas Dehaeze"]
+draft = false
+++
+
+Tags
+: [Voice Coil Actuators]({{< relref "voice_coil_actuators" >}})
+
+
+## Manufacturers {#manufacturers}
+
+| Manufacturers | Links                                                             |
+|---------------|-------------------------------------------------------------------|
+| Labsen        | [link](http://labsentec.com.au/category/products/vibrationshock/) |
+
+<./biblio/references.bib>
--- a/content/zettels/signal_conditioner.md
+++ b/content/zettels/signal_conditioner.md
@ -0,0 +1,51 @@
+++
+title = "Signal Conditioner"
+author = ["Thomas Dehaeze"]
+draft = false
+++
+
+Tags
+: [Force Sensors]({{< relref "force_sensors" >}})
+
+Most sensors needs some signal conditioner electronics before digitize the signal.
+Few examples are:
+
+-   Piezoelectric force sensors
+-   Geophone
+-   Thermocouple, ...
+
+The signal conditioning electronics can have different functions:
+
+-   Amplification
+-   Isolation
+-   Filtering
+-   Excitation
+-   Linearization
+
+
+## Charge Amplifier {#charge-amplifier}
+
+| Manufacturers | Links                                                                                                               |
+|---------------|---------------------------------------------------------------------------------------------------------------------|
+| PCB           | [link](https://www.pcb.com/sensors-for-test-measurement/electronics/line-powered-multi-channel-signal-conditioners) |
+
+
+## Voltage Amplifier {#voltage-amplifier}
+
+| Manufacturers | Links                                                            |
+|---------------|------------------------------------------------------------------|
+| Femto         | [link](https://www.femto.de/en/products/voltage-amplifiers.html) |
+
+
+## Current Amplifier {#current-amplifier}
+
+| Manufacturers | Links                                                            |
+|---------------|------------------------------------------------------------------|
+| Femto         | [link](https://www.femto.de/en/products/current-amplifiers.html) |
+
+<./biblio/references.bib>
+
+
+## Backlinks {#backlinks}
+
+-   [Position Sensors]({{< relref "position_sensors" >}})
--- a/content/zettels/signal_to_noise_ratio.md
+++ b/content/zettels/signal_to_noise_ratio.md
@ -7,19 +7,10 @@ draft = false
 Tags
 : [Electronics]({{< relref "electronics" >}}), [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}})

-From <sup id="3b7899e183dba866e6a6419cf820467f"><a href="#jabben07_mechat" title="@phdthesis{jabben07_mechat,
-  author          = {Jabben, Leon},
-  school          = {Delft University},
-  title           = {Mechatronic design of a magnetically suspended rotating
-                  platform},
-  year            = 2007,
-}">@phdthesis{jabben07_mechat,
-  author          = {Jabben, Leon},
-  school          = {Delft University},
-  title           = {Mechatronic design of a magnetically suspended rotating
-                  platform},
-  year            = 2007,
-}</a></sup> (Section 3.3.2):
+
+## SNR to Noise PSD {#snr-to-noise-psd}
+
+From ([Jabben 2007](#orgd8e3764)) (Section 3.3.2):

 > Electronic equipment does most often not come with detailed electric schemes, in which case the PSD should be determined from measurements.
 > In the design phase however, one has to rely on information provided by specification sheets from the manufacturer.
@ -31,5 +22,88 @@ From <sup id="3b7899e183dba866e6a6419cf820467f"><a href="#jabben07_mechat" title
 > \\[ S\_{snr} = \frac{x\_{fr}^2}{8 f\_c C\_{snr}^2} \\]
 > with \\(x\_{fr}\\) the full range of \\(x\\), and \\(C\_{snr}\\) the SNR.

-# Bibliography
-<a id="jabben07_mechat"></a>Jabben, L., *Mechatronic design of a magnetically suspended rotating platform* (Doctoral dissertation) (2007). Delft University, . [↩](#3b7899e183dba866e6a6419cf820467f)
+<div class="examp">
+  <div></div>
+
+Let's take an example.
+
+-   \\(x\_{fr} = 170 V\\)
+-   \\(C\_{snr} = 85 dB\\)
+-   \\(f\_c = 200 Hz\\)
+
+The Power Spectral Density of the output voltage is:
+\\[ S\_{snr} = \frac{170^2}{8 \cdot 200 \cdot {10^{\frac{2 \cdot 85}{20}}}} = 5.7 \cdot 10^{-8}\ V^2/Hz \\]
+
+And the RMS of that noise up to \\(f\_c\\) is:
+\\[ S\_{rms} = \sqrt{S\_{snr} \cdot f\_c} \approx 3.4\ mV \\]
+
+</div>
+
+
+## Convert SNR to Noise RMS value {#convert-snr-to-noise-rms-value}
+
+The RMS value of the noise can be computed from:
+\\[ N\_\text{rms} = 10^{-\frac{S\_{snr}}{20}} S\_\text{rms} \\]
+where \\(S\_{snr}\\) is the SNR in dB and \\(S\_\text{rms}\\) is the RMS value of a sinus taking the full range.
+
+If the full range is \\(\Delta V\\), then:
+\\[ S\_\text{rms} = \frac{\Delta V/2}{\sqrt{2}} \\]
+
+<div class="examp">
+  <div></div>
+
+As an example, let's take a voltage amplifier with a full range of \\(\Delta V = 20V\\) and a SNR of 85dB.
+The RMS value of the noise is then:
+\\[ n\_\text{rms} = 10^{-\frac{S\_{nrs}}{20}} s\_\text{rms} \\]
+
+\\[ n\_\text{rms} = 10^{-\frac{85}{20}} \frac{10}{\sqrt{2}} \approx 0.4 mV\_\text{rms} \\]
+
+</div>
+
+
+## Convert wanted Noise RMS value to required SNR {#convert-wanted-noise-rms-value-to-required-snr}
+
+If the wanted full range and RMS value of the noise are defined, the required SNR can be computed from:
+\\[ S\_{snr} = 20 \log \frac{\text{Signal, rms}}{\text{Noise, rms}} \\]
+
+<div class="examp">
+  <div></div>
+
+Let's say the wanted noise is \\(1 mV, \text{rms}\\) for a full range of \\(20 V\\), the corresponding SNR is:
+\\[ S\_{snr} = 20 \log \frac{\frac{20/2}{\sqrt{2}}}{10^{-3}} \approx 77dB \\]
+
+</div>
+
+
+## Noise Density to RMS noise {#noise-density-to-rms-noise}
+
+From ([Fleming 2010](#org68e05a9)):
+\\[ \text{RMS noise} = \sqrt{2 \times \text{bandwidth}} \times \text{noise density} \\]
+
+If the noise is normally distributed, the RMS value is also the standard deviation \\(\sigma\\).
+The peak to peak amplitude is then approximatively \\(6 \sigma\\).
+
+<div class="exampl">
+  <div></div>
+
+-   noise density = \\(20 pm/\sqrt{Hz}\\)
+-   bandwidth = 100Hz
+
+\\[ \sigma = \sqrt{2 \times 100} \times 20 = 0.28nm RMS \\]
+The peak-to-peak noise will be approximately \\(6 \sigma = 1.7 nm\\)
+
+</div>
+
+
+## Bibliography {#bibliography}
+
+<a id="org68e05a9"></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="orgd8e3764"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.
+
+
+## Backlinks {#backlinks}
+
+-   [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
+-   [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
+-   [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
--- a/content/zettels/slip_rings.md
+++ b/content/zettels/slip_rings.md
@ -0,0 +1,14 @@
+++
+title = "Slip Rings"
+author = ["Thomas Dehaeze"]
+draft = false
+++
+
+Tags
+:
+
+| Manufacturers | Links                           |
+|---------------|---------------------------------|
+| Moflon        | [link](https://www.moflon.com/) |
+
+<./biblio/references.bib>
--- a/content/zettels/voice_coil_actuators.md
+++ b/content/zettels/voice_coil_actuators.md
@ -21,6 +21,7 @@ Tags
 | Beikimco             | [link](http://www.beikimco.com/)             |
 | Electromate          | [link](https://www.electromate.com/)         |
 | Magnetic Innovations | [link](https://www.magneticinnovations.com/) |
+| Monticont            | [link](http://www.moticont.com/)             |


 ## Typical Specifications {#typical-specifications}
--- a/content/zettels/voltage_amplifier.md
+++ b/content/zettels/voltage_amplifier.md
@ -0,0 +1,98 @@
+++
+title = "Voltage Amplifier"
+author = ["Thomas Dehaeze"]
+draft = false
+++
+
+Tags
+: [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}}), [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}}), [Electronics]({{< relref "electronics" >}})
+
+
+## Voltage Amplifiers to drive Capacitive Load {#voltage-amplifiers-to-drive-capacitive-load}
+
+
+### Limitation in Current {#limitation-in-current}
+
+The piezoelectric stack can be represented as a capacitance.
+
+Let's take a capacitance driven by a voltage amplifier (Figure [1](#org0d9f468)).
+
+<a id="org0d9f468"></a>
+
+{{< figure src="/ox-hugo/voltage_amplifier_capacitance.png" caption="Figure 1: Piezoelectric actuator model with a voltage source" >}}
+
+The equation linking the voltage to the current is:
+\\[ I = C \frac{dU}{dt} \\]
+
+Suppose we want to drive the piezo with a voltage:
+\\[ U(t) = U\_0 \sin(\omega\_0 t) \\]
+
+The required current is:
+\\[ I = C U\_0 \omega\_0 \cos(\omega\_0 t) \\]
+
+Thus, for a specified maximum current \\(I\_\text{max}\\), the "power bandwidth" will be:
+\\[ \omega\_{0, \text{max}} = \frac{I\_\text{max}}{C U\_0}, \quad f\_{0, \text{max}} = \frac{I\_\text{max}}{C U\_0} \frac{1}{2 \pi} \\]
+
+-   Below \\(\omega\_{0, \text{max}}\\), a voltage amplitude \\(U\_0\\) can be applied to the piezoelectric load without reaching the maximum current \\(I\_\text{max}\\).
+-   Above \\(\omega\_{0, \text{max}}\\), the maximum current \\(I\_\text{max}\\) is reached and the maximum voltage that can be applied decreases with frequency:
+    \\[ U\_\text{max} = \frac{I\_\text{max}}{\omega C} \\]
+
+The maximum voltage as a function of frequency is shown in Figure [2](#org8625e7c).
+
+```matlab
+Vpkp = 170; % [V]
+Imax = 30e-3; % [A]
+C = 1e-6; % [F]
+
+(1/(2*pi))*Imax/(C * Vpkp/2) % Fmax [Hz]
+```
+
+```text
+56.172
+```
+
+<a id="org8625e7c"></a>
+
+{{< figure src="/ox-hugo/voltage_amplifier_max_V_piezo.png" caption="Figure 2: Maximum voltage as a function of the frequency for \\(C = 1 \mu F\\), \\(I\_\text{max} = 30mA\\) and \\(V\_{pkp} = 170 V\\)" >}}
+
+Similarly, the voltage rise time is determined by the Capacitance of the piezoelectric stack and by the maximum current that the amplifier can deliver:
+\\[ t\_c = \frac{\Delta U C}{I\_\text{max}} \\]
+with \\(t\_c\\) in seconds, \\(\Delta U\\) in volts, \\(C\\) in Farads and \\(I\_\text{max}\\) in Amperes.
+
+If driven at \\(\Delta U = 100V\\), \\(C = 1 \mu F\\) and \\(I\_\text{max} = 1 A\\), then:
+\\[ t\_c = \frac{100 \cdot 10^{-6}}{1} = 0.1 ms \\]
+
+
+### Amplifiers for Low Voltage PZT {#amplifiers-for-low-voltage-pzt}
+
+Piezoelectric Stack Actuators are behaving like capacitor for the Amplifiers.
+
+Specifications are usually:
+
+-   Maximum Current
+-   DC Gain (usually around 10)
+-   Output Noise or [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}})
+
+The bandwidth can be estimated from the Maximum Current and the Capacitance of the Piezoelectric Actuator.
+
+| Manufacturers       | Links                                                                                                                                                   |
+|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------|
+| Piezo Drive         | [link](https://www.piezodrive.com/drivers/)                                                                                                             |
+| Thorlabs            | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=13630)                                                                               |
+| PI                  | [link](https://www.pi-usa.us/en/products/controllers-drivers-motion-control-software/piezo-drivers-controllers-power-supplies-high-voltage-amplifiers/) |
+| Micromega Dynamics  |                                                                                                                                                         |
+| Lab Systems         | [link](https://www.lab-systems.com/products/amplifier/amplifier.html)                                                                                   |
+| Falco System        | [link](https://www.falco-systems.com/products.html)                                                                                                     |
+| Piezomechanics      | [link](https://www.piezomechanik.com/products/)                                                                                                         |
+| Cedrat Technologies | [link](https://www.cedrat-technologies.com/en/products/piezo-controllers/electronic-amplifier-boards.html)                                              |
+| acal                | [link](https://www.acalbfi.com/nl/Electronic-test-and-measurement/High-voltage-amplifiers/c/CAT-06-03)                                                  |
+| Trek                | [link](https://www.trekinc.com/products/HV%5FAmp.asp)                                                                                                   |
+| Madcitylabs         | [link](http://www.madcitylabs.com/piezoactuators.html)                                                                                                  |
+
+<./biblio/references.bib>
+
+
+## Backlinks {#backlinks}
+
+-   [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
+-   [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
--- a/static/ox-hugo/voltage_amplifier_capacitance.png
+++ b/static/ox-hugo/voltage_amplifier_capacitance.png
--- a/static/ox-hugo/voltage_amplifier_max_V_piezo.png
+++ b/static/ox-hugo/voltage_amplifier_max_V_piezo.png