diff --git a/content/book/fleming14_desig_model_contr_nanop_system.md b/content/book/fleming14_desig_model_contr_nanop_system.md index 30d64ae..45149f8 100644 --- a/content/book/fleming14_desig_model_contr_nanop_system.md +++ b/content/book/fleming14_desig_model_contr_nanop_system.md @@ -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} @@ -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}