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@@ -19,714 +19,7 @@ Year
: 2014
## Introduction to Nanotechnology {#introduction-to-nanotechnology}
## Introduction to Nanopositioning {#introduction-to-nanopositioning}
## Scanning Probe Microscopy {#scanning-probe-microscopy}
## Challenges with Nanopositioning Systems {#challenges-with-nanopositioning-systems}
### Hysteresis {#hysteresis}
### Creep {#creep}
### Thermal Drift {#thermal-drift}
### Mechanical Resonance {#mechanical-resonance}
## Control of Nanopositioning Systems {#control-of-nanopositioning-systems}
### Feedback Control {#feedback-control}
### Feedforward Control {#feedforward-control}
## Book Summary {#book-summary}
### Assumed Knowledge {#assumed-knowledge}
### Content Summary {#content-summary}
## References {#references}
## The Piezoelectric Effect {#the-piezoelectric-effect}
## Piezoelectric Compositions {#piezoelectric-compositions}
## Manufacturing Piezoelectric Ceramics {#manufacturing-piezoelectric-ceramics}
## Piezoelectric Transducers {#piezoelectric-transducers}
## Application Considerations {#application-considerations}
## Response of Piezoelectric Actuators {#response-of-piezoelectric-actuators}
## Modeling Creep and Vibration in Piezoelectric Actuators {#modeling-creep-and-vibration-in-piezoelectric-actuators}
## Chapter Summary {#chapter-summary}
## References {#references}
## Piezoelectric Tube Nanopositioners {#piezoelectric-tube-nanopositioners}
### 63mm Piezoelectric Tube {#63mm-piezoelectric-tube}
### 40mm Piezoelectric Tube Nanopositioner {#40mm-piezoelectric-tube-nanopositioner}
## Piezoelectric Stack Nanopositioners {#piezoelectric-stack-nanopositioners}
### Phyisk Instrumente P-734 Nanopositioner {#phyisk-instrumente-p-734-nanopositioner}
### Phyisk Instrumente P-733.3DD Nanopositioner {#phyisk-instrumente-p-733-dot-3dd-nanopositioner}
### Vertical Nanopositioners {#vertical-nanopositioners}
### Rotational Nanopositioners {#rotational-nanopositioners}
### Low Temperature and UHV Nanopositioners {#low-temperature-and-uhv-nanopositioners}
### Tilting Nanopositioners {#tilting-nanopositioners}
### Optical Objective Nanopositioners {#optical-objective-nanopositioners}
## References {#references}
## Introduction {#introduction}
## Operating Environment {#operating-environment}
## Methods for Actuation {#methods-for-actuation}
## Flexure Hinges {#flexure-hinges}
### Introduction {#introduction}
### Types of Flexures {#types-of-flexures}
### Flexure Hinge Compliance Equations {#flexure-hinge-compliance-equations}
### Stiff Out-of-Plane Flexure Designs {#stiff-out-of-plane-flexure-designs}
### Failure Considerations {#failure-considerations}
### Finite Element Approach for Flexure Design {#finite-element-approach-for-flexure-design}
## Material Considerations {#material-considerations}
### Materials for Flexure and Platform Design {#materials-for-flexure-and-platform-design}
### Thermal Stability of Materials {#thermal-stability-of-materials}
## Manufacturing Techniques {#manufacturing-techniques}
## Design Example: A High-Speed Serial-Kinematic Nanopositioner {#design-example-a-high-speed-serial-kinematic-nanopositioner}
### State-of-the-Art Designs {#state-of-the-art-designs}
### Tradeoffs and Limitations in Speed {#tradeoffs-and-limitations-in-speed}
### Serial- Versus Parallel-Kinematic Configurations {#serial-versus-parallel-kinematic-configurations}
### Piezoactuator Considerations {#piezoactuator-considerations}
### Preloading Piezo-Stack Actuators {#preloading-piezo-stack-actuators}
### Flexure Design for Lateral Positioning {#flexure-design-for-lateral-positioning}
### Design of Vertical Stage {#design-of-vertical-stage}
### Fabrication and Assembly {#fabrication-and-assembly}
### Drive Electronics {#drive-electronics}
\*\*\*\*0 Experimental Results
## Chapter Summary {#chapter-summary}
## References {#references}
## Introduction {#introduction}
## Sensor Characteristics {#sensor-characteristics}
### Calibration and Nonlinearity {#calibration-and-nonlinearity}
### Drift and Stability {#drift-and-stability}
### Bandwidth {#bandwidth}
### Noise {#noise}
### Resolution {#resolution}
### Combining Errors {#combining-errors}
### Metrological Traceability {#metrological-traceability}
## Nanometer Position Sensors {#nanometer-position-sensors}
### Resistive Strain Sensors {#resistive-strain-sensors}
### Piezoresistive Strain Sensors {#piezoresistive-strain-sensors}
### Piezoelectric Strain Sensors {#piezoelectric-strain-sensors}
### Capacitive Sensors {#capacitive-sensors}
### MEMs Capacitive and Thermal Sensors {#mems-capacitive-and-thermal-sensors}
### Eddy-Current Sensors {#eddy-current-sensors}
### Linear Variable Displacement Transformers {#linear-variable-displacement-transformers}
### Laser Interferometers {#laser-interferometers}
### Linear Encoders {#linear-encoders}
## Comparison and Summary {#comparison-and-summary}
## Outlook and Future Requirements {#outlook-and-future-requirements}
## References {#references}
## Introduction {#introduction}
## Shunt Circuit Modeling {#shunt-circuit-modeling}
### Open-Loop {#open-loop}
### Shunt Damping {#shunt-damping}
## Implementation {#implementation}
## Experimental Results {#experimental-results}
### Tube Dynamics {#tube-dynamics}
### Amplifier Performance {#amplifier-performance}
### Shunt Damping Performance {#shunt-damping-performance}
## Chapter Summary {#chapter-summary}
## References {#references}
## Introduction {#introduction}
## Experimental Setup {#experimental-setup}
## PI Control {#pi-control}
## PI Control with Notch Filters {#pi-control-with-notch-filters}
## PI Control with IRC Damping {#pi-control-with-irc-damping}
## Performance Comparison {#performance-comparison}
## Noise and Resolution {#noise-and-resolution}
## Analog Implementation {#analog-implementation}
## Application to AFM Imaging {#application-to-afm-imaging}
## References {#references}
## Introduction {#introduction}
## Modeling {#modeling}
### Actuator Dynamics {#actuator-dynamics}
### Sensor Dynamics {#sensor-dynamics}
### Sensor Noise {#sensor-noise}
### Mechanical Dynamics {#mechanical-dynamics}
### System Properties {#system-properties}
### Example System {#example-system}
## Damping Control {#damping-control}
## Tracking Control {#tracking-control}
### Relationship Between Force and Displacement {#relationship-between-force-and-displacement}
### Integral Displacement Feedback {#integral-displacement-feedback}
### Direct Tracking Control {#direct-tracking-control}
### Dual Sensor Feedback {#dual-sensor-feedback}
### Low Frequency Bypass {#low-frequency-bypass}
### Feedforward Inputs {#feedforward-inputs}
### Higher-Order Modes {#higher-order-modes}
## Experimental Results {#experimental-results}
### Experimental Nanopositioner {#experimental-nanopositioner}
### Actuators and Force Sensors {#actuators-and-force-sensors}
### Control Design {#control-design}
### Noise Performance {#noise-performance}
## Chapter Summary {#chapter-summary}
## References {#references}
## Why Feedforward? {#why-feedforward}
## Modeling for Feedforward Control {#modeling-for-feedforward-control}
## Feedforward Control of Dynamics and Hysteresis {#feedforward-control-of-dynamics-and-hysteresis}
### Simple DC-Gain Feedforward Control {#simple-dc-gain-feedforward-control}
### An Inversion-Based Feedforward Approach for Linear Dynamics {#an-inversion-based-feedforward-approach-for-linear-dynamics}
### Frequency-Weighted Inversion: The Optimal Inverse {#frequency-weighted-inversion-the-optimal-inverse}
### Application to AFM Imaging {#application-to-afm-imaging}
## Feedforward and Feedback Control {#feedforward-and-feedback-control}
### Application to AFM Imaging {#application-to-afm-imaging}
## Iterative Feedforward Control {#iterative-feedforward-control}
### The ILC Problem {#the-ilc-problem}
### Model-Based ILC {#model-based-ilc}
### Nonlinear ILC {#nonlinear-ilc}
### Conclusions {#conclusions}
## References {#references}
## 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}
## 11.1 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}
## 12.1 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}
## 13.1 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}
## Electrical Considerations {#electrical-considerations}
### Amplifier and Piezo electrical models {#amplifier-and-piezo-electrical-models}
## Amplifier and Piezo electrical models {#amplifier-and-piezo-electrical-models}
<a id="figure--fig:fleming14-amplifier-model"></a>
@@ -755,7 +48,7 @@ with:
- \\(\xi = \frac{R\_s \sqrt{L C\_p}}{2 L}\\)
### Amplifier small-signal Bandwidth {#amplifier-small-signal-bandwidth}
## Amplifier small-signal Bandwidth {#amplifier-small-signal-bandwidth}
The most obvious bandwidth limitation is the small-signal bandwidth of the amplifier.
@@ -799,7 +92,7 @@ It is however usually quite high compare to \\(\omega\_c\\) as shown in [Table 2
| L = 2500 nH | 320 kHz | 100 kHz | 32 kHz |
### Amplifier maximum slew rate {#amplifier-maximum-slew-rate}
## Amplifier maximum slew rate {#amplifier-maximum-slew-rate}
Further bandwidth restrictions are imposed by the maximum **slew rate** of the amplifier.
This is the maximum rate at which the output voltage can change and is usually expressed in \\(V/\mu s\\).
@@ -817,7 +110,7 @@ If a 300kHz sine wave is to be reproduced with an amplitude of 10V, the required
When dealing with capacitive loads, **the current limit is usually exceed well before the slew rate limit**.
### Current and Power Limitations {#current-and-power-limitations}
## Current and Power Limitations {#current-and-power-limitations}
When driving the actuator off-resonance, the current delivered to a piezoelectric actuator is approximately:
\\[ I\_L(s) = V\_L(s) C\_p s \\]
@@ -838,7 +131,7 @@ For sinusoidal signals, the maximum positive and negative current is equal to:
| f = 300 kHz | 1.9 A | 19 A | 190 A |
### Chapter Summary {#chapter-summary}
## Summary {#summary}
The bandwidth limitations of standard piezoelectric drives were identified as:
@@ -848,9 +141,6 @@ The bandwidth limitations of standard piezoelectric drives were identified as:
- High cable and connector inductance
### References {#references}
## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">