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--- 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}