diff --git a/content/book/schmidt20_desig_high_perfor_mechat_third_revis_edition.md b/content/book/schmidt20_desig_high_perfor_mechat_third_revis_edition.md index f425f79..6d90df8 100644 --- a/content/book/schmidt20_desig_high_perfor_mechat_third_revis_edition.md +++ b/content/book/schmidt20_desig_high_perfor_mechat_third_revis_edition.md @@ -8,7 +8,7 @@ Tags : [Reference Books]({{< relref "reference_books" >}}), [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}}) Reference -: ([Schmidt, Schitter, and Rankers 2020](#org6f01bfb)) +: ([Schmidt, Schitter, and Rankers 2020](#org9aaa5b5)) Author(s) : Schmidt, R. M., Schitter, G., & Rankers, A. @@ -17,30 +17,30 @@ Year : 2020 -## 2 Applied Physics in Mechatronic Systems {#2-applied-physics-in-mechatronic-systems} +## Applied Physics in Mechatronic Systems {#applied-physics-in-mechatronic-systems} ### Introduction {#introduction} -### 2.1 Mechanics {#2-dot-1-mechanics} +### Mechanics {#mechanics} > The core of a mechatronic system is its mechanical construction and in spite of many decade of excellent designs, optimizing the mechanical structure in strength, mass and endurance, the mechanical behavior will always remain the limiting factor of the performance of any mechatronic system. -#### 2.1.1 Coordinate Systems {#2-dot-1-dot-1-coordinate-systems} +#### Coordinate Systems {#coordinate-systems} -##### 2.1.1.1 Cartesian Coordinate System {#2-dot-1-dot-1-dot-1-cartesian-coordinate-system} +##### Cartesian Coordinate System {#cartesian-coordinate-system} -##### 2.1.1.2 Generalised Coordinate System {#2-dot-1-dot-1-dot-2-generalised-coordinate-system} +##### Generalised Coordinate System {#generalised-coordinate-system} -##### 2.1.1.3 Modal Coordinate System {#2-dot-1-dot-1-dot-3-modal-coordinate-system} +##### Modal Coordinate System {#modal-coordinate-system} -#### 2.1.2 Force and Motion {#2-dot-1-dot-2-force-and-motion} +#### Force and Motion {#force-and-motion} > _Statics_ deals with the stress levels that are present in the mechanical system when (quasi-)static forces are exerted on it. > It analyses the linear and non-linear strain effects that are caused by elastic and plastic deformation under these stress levels. @@ -50,329 +50,329 @@ Year > The relation between angles and positions is often non-linear in such a mechanism, because of the changing angles, and controlling these often requires special precautions to overcome the inherent non-linearities by linearisation around actual position and adapting the optimal settings of the controller to each position. -##### 2.1.2.1 Galilei and Newton's Laws of Motion {#2-dot-1-dot-2-dot-1-galilei-and-newton-s-laws-of-motion} +##### Galilei and Newton's Laws of Motion {#galilei-and-newton-s-laws-of-motion} -##### 2.1.2.2 Hooke's Law of Elasticity {#2-dot-1-dot-2-dot-2-hooke-s-law-of-elasticity} +##### Hooke's Law of Elasticity {#hooke-s-law-of-elasticity} -##### 2.1.2.3 Lagrange Equations of Motion {#2-dot-1-dot-2-dot-3-lagrange-equations-of-motion} +##### Lagrange Equations of Motion {#lagrange-equations-of-motion} -### 2.2 Electricity and Magnetism {#2-dot-2-electricity-and-magnetism} +### Electricity and Magnetism {#electricity-and-magnetism} -#### 2.2.1 Electric Field {#2-dot-2-dot-1-electric-field} +#### Electric Field {#electric-field} - + {{< figure src="/ox-hugo/schmidt20_electrical_field.svg" caption="Figure 1: Charges have an electric field" >}} -##### 2.2.1.1 Potential Difference and Capacitance {#2-dot-2-dot-1-dot-1-potential-difference-and-capacitance} +##### Potential Difference and Capacitance {#potential-difference-and-capacitance} -##### 2.2.1.2 Electric Current in Conductive Material {#2-dot-2-dot-1-dot-2-electric-current-in-conductive-material} +##### Electric Current in Conductive Material {#electric-current-in-conductive-material} -#### 2.2.2 Magnetism and the Maxwell Equations {#2-dot-2-dot-2-magnetism-and-the-maxwell-equations} +#### Magnetism and the Maxwell Equations {#magnetism-and-the-maxwell-equations} -#### 2.2.3 Electric Sources and Elements {#2-dot-2-dot-3-electric-sources-and-elements} +#### Electric Sources and Elements {#electric-sources-and-elements} -##### 2.2.3.1 Voltage Source {#2-dot-2-dot-3-dot-1-voltage-source} +##### Voltage Source {#voltage-source} -##### 2.2.3.2 Summary on Voltage and Current {#2-dot-2-dot-3-dot-2-summary-on-voltage-and-current} +##### Summary on Voltage and Current {#summary-on-voltage-and-current} -##### 2.2.3.3 Electric Power {#2-dot-2-dot-3-dot-3-electric-power} +##### Electric Power {#electric-power} -##### 2.2.3.4 Ohm's Law {#2-dot-2-dot-3-dot-4-ohm-s-law} +##### Ohm's Law {#ohm-s-law} -##### 2.2.3.5 Practical Values and Summary {#2-dot-2-dot-3-dot-5-practical-values-and-summary} +##### Practical Values and Summary {#practical-values-and-summary} -### 2.3 Signal Theory and Wave Propagation {#2-dot-3-signal-theory-and-wave-propagation} +### Signal Theory and Wave Propagation {#signal-theory-and-wave-propagation} -#### 2.3.1 The Concept of Frequency {#2-dot-3-dot-1-the-concept-of-frequency} +#### The Concept of Frequency {#the-concept-of-frequency} -##### 2.3.1.1 Random Signals or Noise {#2-dot-3-dot-1-dot-1-random-signals-or-noise} +##### Random Signals or Noise {#random-signals-or-noise} -##### 2.3.1.2 Power of Alternating Signals {#2-dot-3-dot-1-dot-2-power-of-alternating-signals} +##### Power of Alternating Signals {#power-of-alternating-signals} -#### 2.3.2 Use of Complex Numbers {#2-dot-3-dot-2-use-of-complex-numbers} +#### Use of Complex Numbers {#use-of-complex-numbers} -##### 2.3.2.1 Dynamic Impedance and Ohm's Law {#2-dot-3-dot-2-dot-1-dynamic-impedance-and-ohm-s-law} +##### Dynamic Impedance and Ohm's Law {#dynamic-impedance-and-ohm-s-law} -##### 2.3.2.2 Power in Dynamic Impedance {#2-dot-3-dot-2-dot-2-power-in-dynamic-impedance} +##### Power in Dynamic Impedance {#power-in-dynamic-impedance} -##### 2.3.2.3 Capacitive Impedance {#2-dot-3-dot-2-dot-3-capacitive-impedance} +##### Capacitive Impedance {#capacitive-impedance} -##### 2.3.2.4 Inductive Impedance {#2-dot-3-dot-2-dot-4-inductive-impedance} +##### Inductive Impedance {#inductive-impedance} -#### 2.3.3 Energy Propagation in Waves {#2-dot-3-dot-3-energy-propagation-in-waves} +#### Energy Propagation in Waves {#energy-propagation-in-waves} -##### 2.3.3.1 Mechanical Waves {#2-dot-3-dot-3-dot-1-mechanical-waves} +##### Mechanical Waves {#mechanical-waves} -##### 2.3.3.2 Wave Equation {#2-dot-3-dot-3-dot-2-wave-equation} +##### Wave Equation {#wave-equation} -##### 2.3.3.3 Electromagnetic Waves {#2-dot-3-dot-3-dot-3-electromagnetic-waves} +##### Electromagnetic Waves {#electromagnetic-waves} -##### 2.3.3.4 Reflection of Waves {#2-dot-3-dot-3-dot-4-reflection-of-waves} +##### Reflection of Waves {#reflection-of-waves} -##### 2.3.3.5 Standing Waves {#2-dot-3-dot-3-dot-5-standing-waves} +##### Standing Waves {#standing-waves} -#### 2.3.4 Fourier Decomposition of Alternating Signals {#2-dot-3-dot-4-fourier-decomposition-of-alternating-signals} +#### Fourier Decomposition of Alternating Signals {#fourier-decomposition-of-alternating-signals} -##### 2.3.4.1 Fourier in the frequency-domain {#2-dot-3-dot-4-dot-1-fourier-in-the-frequency-domain} +##### Fourier in the frequency-domain {#fourier-in-the-frequency-domain} -##### 2.3.4.2 Triangle Waveform {#2-dot-3-dot-4-dot-2-triangle-waveform} +##### Triangle Waveform {#triangle-waveform} -##### 2.3.4.3 Sawtooth Waveform {#2-dot-3-dot-4-dot-3-sawtooth-waveform} +##### Sawtooth Waveform {#sawtooth-waveform} -##### 2.3.4.4 Square Waveform {#2-dot-3-dot-4-dot-4-square-waveform} +##### Square Waveform {#square-waveform} -##### 2.3.4.5 Non-Continuous Alternating Signals {#2-dot-3-dot-4-dot-5-non-continuous-alternating-signals} +##### Non-Continuous Alternating Signals {#non-continuous-alternating-signals} -### 2.4 Dynamic System Analysis and Modelling {#2-dot-4-dynamic-system-analysis-and-modelling} +### Dynamic System Analysis and Modelling {#dynamic-system-analysis-and-modelling} -#### 2.4.0.1 Laplace-Transform {#2-dot-4-dot-0-dot-1-laplace-transform} +#### Laplace-Transform {#laplace-transform} -##### 2.4.0.2 Poles and Zeros {#2-dot-4-dot-0-dot-2-poles-and-zeros} +##### Poles and Zeros {#poles-and-zeros} -##### 2.4.0.3 Order of a Dynamic System {#2-dot-4-dot-0-dot-3-order-of-a-dynamic-system} +##### Order of a Dynamic System {#order-of-a-dynamic-system} -#### 2.4.1 Dynamic Responses in the time-domain {#2-dot-4-dot-1-dynamic-responses-in-the-time-domain} +#### Dynamic Responses in the time-domain {#dynamic-responses-in-the-time-domain} -##### 2.4.1.1 Step Response {#2-dot-4-dot-1-dot-1-step-response} +##### Step Response {#step-response} -##### 2.4.1.2 Impulse Response {#2-dot-4-dot-1-dot-2-impulse-response} +##### Impulse Response {#impulse-response} -##### 2.4.1.3 Impulse Response and Pole Location {#2-dot-4-dot-1-dot-3-impulse-response-and-pole-location} +##### Impulse Response and Pole Location {#impulse-response-and-pole-location} -#### 2.4.2 Dynamic Responses in the frequency-domain {#2-dot-4-dot-2-dynamic-responses-in-the-frequency-domain} +#### Dynamic Responses in the frequency-domain {#dynamic-responses-in-the-frequency-domain} -##### 2.4.2.1 Frequency or Fourier-Domain Responses {#2-dot-4-dot-2-dot-1-frequency-or-fourier-domain-responses} +##### Frequency or Fourier-Domain Responses {#frequency-or-fourier-domain-responses} -##### 2.4.2.2 Domain Notation of Dynamic Functions {#2-dot-4-dot-2-dot-2-domain-notation-of-dynamic-functions} +##### Domain Notation of Dynamic Functions {#domain-notation-of-dynamic-functions} -##### 2.4.2.3 Frequency Response Plots {#2-dot-4-dot-2-dot-3-frequency-response-plots} +##### Frequency Response Plots {#frequency-response-plots} -##### 2.4.2.4 Bode Plot {#2-dot-4-dot-2-dot-4-bode-plot} +##### Bode Plot {#bode-plot} -##### 2.4.2.5 Nyquist Plot {#2-dot-4-dot-2-dot-5-nyquist-plot} +##### Nyquist Plot {#nyquist-plot} -##### 2.4.2.6 Limitation to LTI Systems {#2-dot-4-dot-2-dot-6-limitation-to-lti-systems} +##### Limitation to LTI Systems {#limitation-to-lti-systems} -## 3 Dynamics of Motion Systems {#3-dynamics-of-motion-systems} +## Dynamics of Motion Systems {#dynamics-of-motion-systems} ### Introduction {#introduction} -### 3.1 Stiffness {#3-dot-1-stiffness} +### Stiffness {#stiffness} -#### 3.1.1 Importance of Stiffness for Precision {#3-dot-1-dot-1-importance-of-stiffness-for-precision} +#### Importance of Stiffness for Precision {#importance-of-stiffness-for-precision} -#### 3.1.2 Active Stiffness {#3-dot-1-dot-2-active-stiffness} +#### Active Stiffness {#active-stiffness} -### 3.2 Mass-Spring Systems with Damping {#3-dot-2-mass-spring-systems-with-damping} +### Mass-Spring Systems with Damping {#mass-spring-systems-with-damping} -#### 3.2.1 Dynamic Compliance {#3-dot-2-dot-1-dynamic-compliance} +#### Dynamic Compliance {#dynamic-compliance} -##### 3.2.1.1 Compliance of a Spring {#3-dot-2-dot-1-dot-1-compliance-of-a-spring} +##### Compliance of a Spring {#compliance-of-a-spring} -##### 3.2.1.2 Compliance of a Damper {#3-dot-2-dot-1-dot-2-compliance-of-a-damper} +##### Compliance of a Damper {#compliance-of-a-damper} -##### 3.2.1.3 Compliance of a Body {#3-dot-2-dot-1-dot-3-compliance-of-a-body} +##### Compliance of a Body {#compliance-of-a-body} -##### 3.2.1.4 Dynamic Stiffness {#3-dot-2-dot-1-dot-4-dynamic-stiffness} +##### Dynamic Stiffness {#dynamic-stiffness} -##### 3.2.1.5 Lumping the Dynamic Elements {#3-dot-2-dot-1-dot-5-lumping-the-dynamic-elements} +##### Lumping the Dynamic Elements {#lumping-the-dynamic-elements} -#### 3.2.2 Transfer Function of Compliance {#3-dot-2-dot-2-transfer-function-of-compliance} +#### Transfer Function of Compliance {#transfer-function-of-compliance} -##### 3.2.2.1 Damped Mass-Spring System. {#3-dot-2-dot-2-dot-1-damped-mass-spring-system-dot} +##### Damped Mass-Spring System. {#damped-mass-spring-system-dot} -##### 3.2.2.2 Magnitude {#3-dot-2-dot-2-dot-2-magnitude} +##### Magnitude {#magnitude} -##### 3.2.2.3 Phase {#3-dot-2-dot-2-dot-3-phase} +##### Phase {#phase} -##### 3.2.2.4 Bode Plot {#3-dot-2-dot-2-dot-4-bode-plot} +##### Bode Plot {#bode-plot} -#### 3.2.3 Effects of Damping {#3-dot-2-dot-3-effects-of-damping} +#### Effects of Damping {#effects-of-damping} -##### 3.2.3.1 Damped Resonance and Aperiodic Damping {#3-dot-2-dot-3-dot-1-damped-resonance-and-aperiodic-damping} +##### Damped Resonance and Aperiodic Damping {#damped-resonance-and-aperiodic-damping} -##### 3.2.3.2 Poles and Critical Damping {#3-dot-2-dot-3-dot-2-poles-and-critical-damping} +##### Poles and Critical Damping {#poles-and-critical-damping} -##### 3.2.3.3 Quality-Factor Q and Energy in Resonance {#3-dot-2-dot-3-dot-3-quality-factor-q-and-energy-in-resonance} +##### Quality-Factor Q and Energy in Resonance {#quality-factor-q-and-energy-in-resonance} -#### 3.2.4 Transmissibility {#3-dot-2-dot-4-transmissibility} +#### Transmissibility {#transmissibility} -#### 3.2.5 Fourth-Order Dynamic System {#3-dot-2-dot-5-fourth-order-dynamic-system} +#### Fourth-Order Dynamic System {#fourth-order-dynamic-system} -##### 3.2.5.1 Analytical Description {#3-dot-2-dot-5-dot-1-analytical-description} +##### Analytical Description {#analytical-description} -##### 3.2.5.2 Multiplicative Expression {#3-dot-2-dot-5-dot-2-multiplicative-expression} +##### Multiplicative Expression {#multiplicative-expression} -##### 3.2.5.3 Effect of Different Mass Ratios {#3-dot-2-dot-5-dot-3-effect-of-different-mass-ratios} +##### Effect of Different Mass Ratios {#effect-of-different-mass-ratios} -### 3.3 Modal Decomposition {#3-dot-3-modal-decomposition} +### Modal Decomposition {#modal-decomposition} -#### 3.3.1 Eigenmodes of Two-Body Mass-Spring System {#3-dot-3-dot-1-eigenmodes-of-two-body-mass-spring-system} +#### Eigenmodes of Two-Body Mass-Spring System {#eigenmodes-of-two-body-mass-spring-system} -#### 3.3.2 Theory of Modal Decomposition {#3-dot-3-dot-2-theory-of-modal-decomposition} +#### Theory of Modal Decomposition {#theory-of-modal-decomposition} -##### 3.3.2.1 Multi Degree of Freedom Equation of Motion {#3-dot-3-dot-2-dot-1-multi-degree-of-freedom-equation-of-motion} +##### Multi Degree of Freedom Equation of Motion {#multi-degree-of-freedom-equation-of-motion} -##### 3.3.2.2 Eigenvalues and Eigenvectors {#3-dot-3-dot-2-dot-2-eigenvalues-and-eigenvectors} +##### Eigenvalues and Eigenvectors {#eigenvalues-and-eigenvectors} -##### 3.3.2.3 Modal Coordinates {#3-dot-3-dot-2-dot-3-modal-coordinates} +##### Modal Coordinates {#modal-coordinates} -##### 3.3.2.4 Resulting Transfer Function {#3-dot-3-dot-2-dot-4-resulting-transfer-function} +##### Resulting Transfer Function {#resulting-transfer-function} -#### 3.3.3 Graphical Representation of Mode-Shapes {#3-dot-3-dot-3-graphical-representation-of-mode-shapes} +#### Graphical Representation of Mode-Shapes {#graphical-representation-of-mode-shapes} -##### 3.3.3.1 Traditional Representation {#3-dot-3-dot-3-dot-1-traditional-representation} +##### Traditional Representation {#traditional-representation} -##### 3.3.3.2 Lever Representation {#3-dot-3-dot-3-dot-2-lever-representation} +##### Lever Representation {#lever-representation} -##### 3.3.3.3 General System {#3-dot-3-dot-3-dot-3-general-system} +##### General System {#general-system} -##### 3.3.3.4 User-Defined Physical DOF {#3-dot-3-dot-3-dot-4-user-defined-physical-dof} +##### User-Defined Physical DOF {#user-defined-physical-dof} -#### 3.3.4 Physical Meaning of Modal Parameters {#3-dot-3-dot-4-physical-meaning-of-modal-parameters} +#### Physical Meaning of Modal Parameters {#physical-meaning-of-modal-parameters} -##### 3.3.4.1 Two-Body Mass-Spring System {#3-dot-3-dot-4-dot-1-two-body-mass-spring-system} +##### Two-Body Mass-Spring System {#two-body-mass-spring-system} -##### 3.3.4.2 Planar Flexibly Guided System {#3-dot-3-dot-4-dot-2-planar-flexibly-guided-system} +##### Planar Flexibly Guided System {#planar-flexibly-guided-system} -#### 3.3.5 A Pragmatic View on Sensitivity Analysis {#3-dot-3-dot-5-a-pragmatic-view-on-sensitivity-analysis} +#### A Pragmatic View on Sensitivity Analysis {#a-pragmatic-view-on-sensitivity-analysis} -##### 3.3.5.1 Example of Two Body Mass-Spring System {#3-dot-3-dot-5-dot-1-example-of-two-body-mass-spring-system} +##### Example of Two Body Mass-Spring System {#example-of-two-body-mass-spring-system} -##### 3.3.5.2 Example of Slightly Damped Resonance {#3-dot-3-dot-5-dot-2-example-of-slightly-damped-resonance} +##### Example of Slightly Damped Resonance {#example-of-slightly-damped-resonance} -#### 3.3.6 Suspension and Rigid-Body Modes {#3-dot-3-dot-6-suspension-and-rigid-body-modes} +#### Suspension and Rigid-Body Modes {#suspension-and-rigid-body-modes} -##### 3.3.6.1 Quasi Rigid-Body Suspension mode {#3-dot-3-dot-6-dot-1-quasi-rigid-body-suspension-mode} +##### Quasi Rigid-Body Suspension mode {#quasi-rigid-body-suspension-mode} -### 3.4 Mechanical Frequency Response {#3-dot-4-mechanical-frequency-response} +### Mechanical Frequency Response {#mechanical-frequency-response} -#### 3.4.1 Multiple eigenmodes {#3-dot-4-dot-1-multiple-eigenmodes} +#### Multiple eigenmodes {#multiple-eigenmodes} -#### 3.4.2 Characteristic Frequency Responses {#3-dot-4-dot-2-characteristic-frequency-responses} +#### Characteristic Frequency Responses {#characteristic-frequency-responses} -##### 3.4.2.1 Frequency Response Type I {#3-dot-4-dot-2-dot-1-frequency-response-type-i} +##### Frequency Response Type I {#frequency-response-type-i} -##### 3.4.2.2 Frequency Response Type II {#3-dot-4-dot-2-dot-2-frequency-response-type-ii} +##### Frequency Response Type II {#frequency-response-type-ii} -##### 3.4.2.3 Frequency Response Type III {#3-dot-4-dot-2-dot-3-frequency-response-type-iii} +##### Frequency Response Type III {#frequency-response-type-iii} -##### 3.4.2.4 Frequency Response Type IV {#3-dot-4-dot-2-dot-4-frequency-response-type-iv} +##### Frequency Response Type IV {#frequency-response-type-iv} -#### 3.4.3 Example Systems with Type I/II/IV Response {#3-dot-4-dot-3-example-systems-with-type-i-ii-iv-response} +#### Example Systems with Type I/II/IV Response {#example-systems-with-type-i-ii-iv-response} -##### 3.4.3.1 Planar Moving Body on Compliant Spring {#3-dot-4-dot-3-dot-1-planar-moving-body-on-compliant-spring} +##### Planar Moving Body on Compliant Spring {#planar-moving-body-on-compliant-spring} -##### 3.4.3.2 H-drive Waferstage {#3-dot-4-dot-3-dot-2-h-drive-waferstage} +##### H-drive Waferstage {#h-drive-waferstage} -### 3.5 Summary on Dynamics {#3-dot-5-summary-on-dynamics} +### Summary on Dynamics {#summary-on-dynamics} In this chapter some important lessons have been learned, which are summarised as follows: @@ -392,221 +392,340 @@ Finally it can be concluded, that these insights help in designing actively cont -## 4 Motion Control {#4-motion-control} +## Motion Control {#motion-control} ### Introduction {#introduction} -### 4.1 A Walk around the Control Loop {#4-dot-1-a-walk-around-the-control-loop} +### A Walk around the Control Loop {#a-walk-around-the-control-loop} -{{< figure src="/ox-hugo/schmidt20_walk_control_loop.svg" >}} +Figure [2](#orgee3bd80) shows a basic control loop of a positioning system. +First, the A/D and D/A converters are used to translate analog signals into time-discrete digital signals and vice versa. +Secondly, the impact locations of several disturbances are shown, which play a large role in determining what reqwuirements the controller needs to fulfil. +The core of the control system is the _plant_, which is the physical system that needs to be controlled. + + +
+ Table 1: + Symbols used in Figure 2 +
+ +| Symbol | Meaning | Unit | +|------------|--------------------------------------|------| +| \\(r\\) | Reference signal | [m] | +| \\(r\_f\\) | Filtered reference signal | [m] | +| \\(e\\) | Error signal | [m] | +| \\(u\\) | Control force that should be applied | [N] | +| \\(v\\) | Real force that is applied | [N] | +| \\(x\\) | Plant output motion | [m] | +| \\(y\\) | Measured output motion | [m] | +| \\(y\_m\\) | Measurement value | [m] | + + + +{{< figure src="/ox-hugo/schmidt20_walk_control_loop.svg" caption="Figure 2: Block diagram of a motion control system, including feedforward and feedback control." >}} + +The plant combines the mechanical structure, amplifiers and actuators, as they all deal with energy conversion in close interaction (Figure [3](#org22eead3)). +They interact in both directions in such a way that each element not only determines the input of the next element, but also influences the previous element by its dynamic load. + + + +{{< figure src="/ox-hugo/schmidt20_energy_actuator_system.svg" caption="Figure 3: The energy converting part of a mechatronic system consists of a the amplifier, the actuator and the mechanical structure." >}} -#### 4.1.1 Poles and Zeros in Motion Control {#4-dot-1-dot-1-poles-and-zeros-in-motion-control} +#### Poles and Zeros in Motion Control {#poles-and-zeros-in-motion-control} + +Any transfer function derived from a system can be represented with poles \\(p\_n\\) and zeros \\(z\_m\\): + +\begin{equation} +G(s) = \frac{(s-z\_1)(s-z\_2)\dots(s-z\_m)}{(s-p\_1)(s-p\_2)\dots(s-p\_n)} +\end{equation} + +with \\(m < n\\). + +The number of poles is an indicator of the order of the dynamic system, corresponding to the number of states (position and velocity) and the number of energy containers (mass, spring). +All real system are _strictly proper_ with more poles and zeros. +Even though zeros can not create instability, the term _unstable zeros_ is given to zeros in the right half of the Laplace-plane (positive real term) for two reasons: + +- inverting an unstable zero will result in an unstable pole +- it indicates non-minimum phase behavior, meaning a larger negative phase shift than would be expected from the slope of the amplitude Bode plot. + +It also shows a counter intuitive step response, because the initial motion is directed opposite to the direction of the force. + +It is usually caused by the non-collocated sensor in respect to the actuator. +In reality all mechatronic feedback systems have not perfectly collocated sensors and as a consequence they may show some level of non-minimum phase behaviour. +Fortunately the effect is mostly so small that it can be neglected. -#### 4.1.2 Overview Feedforward Control {#4-dot-1-dot-2-overview-feedforward-control} +#### Overview Feedforward Control {#overview-feedforward-control} + +{{< figure src="/ox-hugo/schmidt20_feedforward_control_diagram.svg" >}} + +Feedforward control is a very useful and preferred first step in the control of a complex dynamic motion system as it provides the following advantages: + +- **Less feedback required**: the better the feedforward part is performing the smaller the feedback error will need to be corrected further errors. This is the most important reason that feedforward control is always applied to the maximum accuracy possible in fast high precision motion systems. +- **No sensor required**: no sensor information is fed back to the system, which means that a sensor can be left out, thus reducing the cost of pure feedforward controlled systems. +- **Predictable movement**: if the reference signal (trajectory) is known in advance, the phase-lag and time delay in the system can be predicted and therefore compensated. +- **No introduction of instability**: the poles of the controlled system are not changed by feedforward control. Therefore no instability can be introduced. +- **No feeding back of sensor noise**: in precision motion systems, positioning noise is a critical point that always has to be considered in the control design. The lack of a sensor avoid insertion of the measurement noise in the system. + +The drawbacks and limitations of feedforward control are: + +- **Limitation to inverted low-pass minimum-phase characteristic**: it is not possible nor wise to create a controller with a very high gain at very high frequencies. Inverting unstable zeros for a non-minimum phase system would create an unstable controller. +- **The plant has to be stable**: Unstable systems cannot be controlled with pure feedforward control. +- **No compensation of model uncertainties**: Variations in the system dynamics, such as shifting of the resonance frequency or variation of the damping, are not monitored and therefore not accounted for in feedforward control. +- **Can only compensate for known disturbances**: Disturbances of the motion system can only be compensated if they can be measured. -##### 4.1.2.1 Summary of Feedforward Control {#4-dot-1-dot-2-dot-1-summary-of-feedforward-control} +#### Overview Feedback Control {#overview-feedback-control} + +{{< figure src="/ox-hugo/schmidt20_feedback_control_diagram.svg" >}} + +Feedback is an addition to feedforward control with the following benefits: + +- **Stabilization of unstable systems**: As feedback control enables to determine the place of the closed-loop poles of the controlled system, unstable poles can be stabilised. +- **Reduction of the effect of disturbances**: Disturbances of the controlled motion system are observed in the sensor signal, and therefore the feedback controller can compensate for them. +- **Handling of uncertainties**: Feedback controlled systems can also be designed for _robustness_, which means that the stability and performance requirements are guaranteed even for parameter variations of the controlled mechatronic system. + +Also, some pitfalls have to be dealt with: + +- **A sensor is required**: The feedback loop is closed, based on the information from a sensor. Therefore, feedback control can be only as good as the quality of the sensor signal allows. In precision positioning systems accurate sensors are required with high resolution and fast response, which are very costly. The measurement and sensing system often takes a substantial part of the total systems budget. +- **Limited reaction speed**: A feedback controller only reacts on difference between the reference signal and the measured system status, which means that the error has to occur first before the controller can correct for it. +- **Feedback of noise**: By closing the loop, the positioning noise of the motion system as well as sensor noise are also fed back, which has to be considered at the system and control design. +- **Can introduce instability**: Just as feedback control can stabilize an unstable system, it can also destabilize a stable plant. +- **Can increase errors**: With higher order systems feedback will reduce errors in the frequency band where the loop-gain is larger than one and increase errors just outside that band. -#### 4.1.3 Overview Feedback Control {#4-dot-1-dot-3-overview-feedback-control} +#### Summary {#summary} + + +
+ Table 2: + Summary of Feedback and Feedforward control +
+ +| | **Advantages** | **Limitations** | +|-----------------|-----------------------------------------|--------------------------------------------------------------| +| **Feedback** | Stabilization of unstable systems | A sensor is required | +| | Reduction of the effect of disturbances | Limited reaction speed | +| | Handling of uncertainties | Feedback of noise | +| | | Can introduce instability | +| | | Can increase errors | +| **Feedforward** | Less feedback required | Limitation to inverted low-pass minimum-phase characteristic | +| | No sensor required | The plant has to be stable | +| | Predictable movement | No compensation of model uncertainties | +| | No introduction of instability | Can only compensate for known disturbances | +| | No feeding back of sensor noise | | -##### 4.1.3.1 Summary of Feedback Control {#4-dot-1-dot-3-dot-1-summary-of-feedback-control} +### Feedforward Control {#feedforward-control} -### 4.2 Feedforward Control {#4-dot-2-feedforward-control} +#### Model-Based Feedforward Control {#model-based-feedforward-control} -#### 4.2.1 Model-Based Feedforward Control {#4-dot-2-dot-1-model-based-feedforward-control} +#### Input-Shaping {#input-shaping} -#### 4.2.2 Input-Shaping {#4-dot-2-dot-2-input-shaping} +#### Adaptive Feedforward Control {#adaptive-feedforward-control} -#### 4.2.3 Adaptive Feedforward Control {#4-dot-2-dot-3-adaptive-feedforward-control} +#### Trajectory Profile Generation {#trajectory-profile-generation} + +The limitations of the actuators and electronics in a controlled motion system are usually related to limitations in the derivatives over time of the position: + +- \\(dx/dt\\) = Velocity +- \\(d^2x/dt^2\\) = Acceleration +- \\(d^3x/dt^3\\) = Jerk +- \\(d^4x/dt^4\\) = Snap + +Of at least the levels of Jerk and preferable also Snap should be limited. +The standard method to cope with these limitations involves shaping the input of a mechatronic motion system by means of _trajectory profile generation_ or _path-planning_. + +Figure [4](#org473e6fa) shows a fourth order trajectory profile of a displacement, which means that all derivatives including the fourth derivative are defined in the path planning. +A third order trajectory would show a square profile for the jerk indicating an infinite Snap and the round of the acceleration would be gone. +A second order trajectory would show a square acceleration profile with infinite Jerk and sharp edges on the velocity. + + + +{{< figure src="/ox-hugo/schmidt20_trajectory_profile.svg" caption="Figure 4: Figure caption" >}} -#### 4.2.4 Trajectory Profile Generation {#4-dot-2-dot-4-trajectory-profile-generation} - - -### 4.3 Feedback Control {#4-dot-3-feedback-control} +### Feedback Control {#feedback-control} > On might say that a high value of the unity-gain crossover frequency and corresponding high-frequency bandwidth limit is rather an unwanted side-effect of the required high loop-gain at lower frequencies, than a target for the design of a control system as such. -#### 4.3.1 Sensitivity to Input Signals {#4-dot-3-dot-1-sensitivity-to-input-signals} +#### Sensitivity to Input Signals {#sensitivity-to-input-signals} -##### 4.3.1.1 Sensitivity Functions {#4-dot-3-dot-1-dot-1-sensitivity-functions} +##### Sensitivity Functions {#sensitivity-functions} -##### 4.3.1.2 Real Feedback Error Sensitivity {#4-dot-3-dot-1-dot-2-real-feedback-error-sensitivity} +##### Real Feedback Error Sensitivity {#real-feedback-error-sensitivity} -#### 4.3.2 Stability and Robustness in Feedback Control {#4-dot-3-dot-2-stability-and-robustness-in-feedback-control} +#### Stability and Robustness in Feedback Control {#stability-and-robustness-in-feedback-control} -##### 4.3.2.1 Stability margins {#4-dot-3-dot-2-dot-1-stability-margins} +##### Stability margins {#stability-margins} -### 4.4 PID Feedback Control {#4-dot-4-pid-feedback-control} +### PID Feedback Control {#pid-feedback-control} -#### 4.4.1 PID-Control of a Compact-Disc Player {#4-dot-4-dot-1-pid-control-of-a-compact-disc-player} +#### PID-Control of a Compact-Disc Player {#pid-control-of-a-compact-disc-player} -##### 4.4.1.1 Relevant Sensitivity Functions {#4-dot-4-dot-1-dot-1-relevant-sensitivity-functions} +##### Relevant Sensitivity Functions {#relevant-sensitivity-functions} -##### 4.4.1.2 Proportional Feedback {#4-dot-4-dot-1-dot-2-proportional-feedback} +##### Proportional Feedback {#proportional-feedback} -##### 4.4.1.3 Proportional-Differential Feedback {#4-dot-4-dot-1-dot-3-proportional-differential-feedback} +##### Proportional-Differential Feedback {#proportional-differential-feedback} -##### 4.4.1.4 Limiting the Differentiating Action {#4-dot-4-dot-1-dot-4-limiting-the-differentiating-action} +##### Limiting the Differentiating Action {#limiting-the-differentiating-action} -##### 4.4.1.5 Adding I-Control {#4-dot-4-dot-1-dot-5-adding-i-control} +##### Adding I-Control {#adding-i-control} -#### 4.4.2 PID-Control of a Spring Supported Mass {#4-dot-4-dot-2-pid-control-of-a-spring-supported-mass} +#### PID-Control of a Spring Supported Mass {#pid-control-of-a-spring-supported-mass} -##### 4.4.2.1 P-Control {#4-dot-4-dot-2-dot-1-p-control} +##### P-Control {#p-control} -##### 4.4.2.2 D-Control {#4-dot-4-dot-2-dot-2-d-control} +##### D-Control {#d-control} -##### 4.4.2.3 I-Control {#4-dot-4-dot-2-dot-3-i-control} +##### I-Control {#i-control} -##### 4.4.2.4 Sensitivity Function Graphs {#4-dot-4-dot-2-dot-4-sensitivity-function-graphs} +##### Sensitivity Function Graphs {#sensitivity-function-graphs} -#### 4.4.3 Limitations and Side Effects of PID-Feedback Control {#4-dot-4-dot-3-limitations-and-side-effects-of-pid-feedback-control} +#### Limitations and Side Effects of PID-Feedback Control {#limitations-and-side-effects-of-pid-feedback-control} -##### 4.4.3.1 Increased Sensitivity, the Waterbed Effect {#4-dot-4-dot-3-dot-1-increased-sensitivity-the-waterbed-effect} +##### Increased Sensitivity, the Waterbed Effect {#increased-sensitivity-the-waterbed-effect} -##### 4.4.3.2 Integrator Wind-Up and Delays {#4-dot-4-dot-3-dot-2-integrator-wind-up-and-delays} +##### Integrator Wind-Up and Delays {#integrator-wind-up-and-delays} -#### 4.4.4 PID-Control of a Fourth-Order Dynamic System {#4-dot-4-dot-4-pid-control-of-a-fourth-order-dynamic-system} +#### PID-Control of a Fourth-Order Dynamic System {#pid-control-of-a-fourth-order-dynamic-system} -##### 4.4.4.1 Controlling a Type III Dynamic System {#4-dot-4-dot-4-dot-1-controlling-a-type-iii-dynamic-system} +##### Controlling a Type III Dynamic System {#controlling-a-type-iii-dynamic-system} -##### 4.4.4.2 Passive Damping {#4-dot-4-dot-4-dot-2-passive-damping} +##### Passive Damping {#passive-damping} -##### 4.4.4.3 Shifting the Phase {#4-dot-4-dot-4-dot-3-shifting-the-phase} +##### Shifting the Phase {#shifting-the-phase} -#### 4.4.5 PID-Control of a Piezoelectric Actuator {#4-dot-4-dot-5-pid-control-of-a-piezoelectric-actuator} +#### PID-Control of a Piezoelectric Actuator {#pid-control-of-a-piezoelectric-actuator} -##### 4.4.5.1 Creating a Fourth-Order System {#4-dot-4-dot-5-dot-1-creating-a-fourth-order-system} +##### Creating a Fourth-Order System {#creating-a-fourth-order-system} -#### 4.4.6 PID-Control of a Magnetic Bearing {#4-dot-4-dot-6-pid-control-of-a-magnetic-bearing} +#### PID-Control of a Magnetic Bearing {#pid-control-of-a-magnetic-bearing} -##### 4.4.6.1 Frequency Response {#4-dot-4-dot-6-dot-1-frequency-response} +##### Frequency Response {#frequency-response} -##### 4.4.6.2 Positive Stiffness by P-Control {#4-dot-4-dot-6-dot-2-positive-stiffness-by-p-control} +##### Positive Stiffness by P-Control {#positive-stiffness-by-p-control} -##### 4.4.6.3 D-Control and Pole Placement {#4-dot-4-dot-6-dot-3-d-control-and-pole-placement} +##### D-Control and Pole Placement {#d-control-and-pole-placement} -##### 4.4.6.4 I-control for Reduced Sensitivity {#4-dot-4-dot-6-dot-4-i-control-for-reduced-sensitivity} +##### I-control for Reduced Sensitivity {#i-control-for-reduced-sensitivity} -#### 4.4.7 Optimisation by Loop-Shaping Design {#4-dot-4-dot-7-optimisation-by-loop-shaping-design} +#### Optimisation by Loop-Shaping Design {#optimisation-by-loop-shaping-design} -##### 4.4.7.1 Optimal Value of Alpha {#4-dot-4-dot-7-dot-1-optimal-value-of-alpha} +##### Optimal Value of Alpha {#optimal-value-of-alpha} -##### 4.4.7.2 Additional Low-Pass Filtering {#4-dot-4-dot-7-dot-2-additional-low-pass-filtering} +##### Additional Low-Pass Filtering {#additional-low-pass-filtering} -##### 4.4.7.3 Notching Filters {#4-dot-4-dot-7-dot-3-notching-filters} +##### Notching Filters {#notching-filters} -##### 4.4.7.4 Peaking and Shelving Filters {#4-dot-4-dot-7-dot-4-peaking-and-shelving-filters} +##### Peaking and Shelving Filters {#peaking-and-shelving-filters} -#### 4.4.8 Design Steps for PID-control {#4-dot-4-dot-8-design-steps-for-pid-control} +#### Design Steps for PID-control {#design-steps-for-pid-control} -### 4.5 Digital Signal Processing - The Z-Domain {#4-dot-5-digital-signal-processing-the-z-domain} +### Digital Signal Processing - The Z-Domain {#digital-signal-processing-the-z-domain} -#### 4.5.1 Continuous Time versus Discrete Time {#4-dot-5-dot-1-continuous-time-versus-discrete-time} +#### Continuous Time versus Discrete Time {#continuous-time-versus-discrete-time} + -#### 4.5.2 Sampling of Continuous Signals {#4-dot-5-dot-2-sampling-of-continuous-signals} +{{< figure src="/ox-hugo/schmidt20_digital_implementation.svg" caption="Figure 5: Overview of a digital implementation of a feedback controller, emphasising the analog-to-digital and digital-to-analog converters with their required analogue filters" >}} -#### 4.5.3 Digital Number Representation {#4-dot-5-dot-3-digital-number-representation} +#### Sampling of Continuous Signals {#sampling-of-continuous-signals} -##### 4.5.3.1 Fixed Point Arithmetic {#4-dot-5-dot-3-dot-1-fixed-point-arithmetic} +#### Digital Number Representation {#digital-number-representation} +{{< figure src="/ox-hugo/schmidt20_digital_number_representation.svg" >}} -##### 4.5.3.2 Floating Point Arithmetic {#4-dot-5-dot-3-dot-2-floating-point-arithmetic} +#### Digital Filter Theory {#digital-filter-theory} -#### 4.5.4 Digital Filter Theory {#4-dot-5-dot-4-digital-filter-theory} +##### Z-Transform and Difference Equations {#z-transform-and-difference-equations} -##### 4.5.4.1 Z-Transform and Difference Equations {#4-dot-5-dot-4-dot-1-z-transform-and-difference-equations} +#### Finite Impulse Response (FIR) Filter {#finite-impulse-response--fir--filter} -#### 4.5.5 Finite Impulse Response (FIR) Filter {#4-dot-5-dot-5-finite-impulse-response--fir--filter} +#### Infinite Impulse Response (IIR) Filter {#infinite-impulse-response--iir--filter} -#### 4.5.6 Infinite Impulse Response (IIR) Filter {#4-dot-5-dot-6-infinite-impulse-response--iir--filter} +#### Converting Continuous to Discrete-Time Filters {#converting-continuous-to-discrete-time-filters} -#### 4.5.7 Converting Continuous to Discrete-Time Filters {#4-dot-5-dot-7-converting-continuous-to-discrete-time-filters} +### State-Space Feedback Control {#state-space-feedback-control} -### 4.6 State-Space Feedback Control {#4-dot-6-state-space-feedback-control} +#### State-Space in Relation to Motion Control {#state-space-in-relation-to-motion-control} -#### 4.6.1 State-Space in Relation to Motion Control {#4-dot-6-dot-1-state-space-in-relation-to-motion-control} +##### Mechanical Dynamic System in State-Space {#mechanical-dynamic-system-in-state-space} -##### 4.6.1.1 Mechanical Dynamic System in State-Space {#4-dot-6-dot-1-dot-1-mechanical-dynamic-system-in-state-space} +##### PID-Control Feedback in State-Space {#pid-control-feedback-in-state-space} -##### 4.6.1.2 PID-Control Feedback in State-Space {#4-dot-6-dot-1-dot-2-pid-control-feedback-in-state-space} +#### State Feedback {#state-feedback} -#### 4.6.2 State Feedback {#4-dot-6-dot-2-state-feedback} +##### System Identification {#system-identification} -##### 4.6.2.1 System Identification {#4-dot-6-dot-2-dot-1-system-identification} +##### State Estimation {#state-estimation} -##### 4.6.2.2 State Estimation {#4-dot-6-dot-2-dot-2-state-estimation} +##### Additional Remarks on State-Space Control {#additional-remarks-on-state-space-control} -##### 4.6.2.3 Additional Remarks on State-Space Control {#4-dot-6-dot-2-dot-3-additional-remarks-on-state-space-control} - -### 4.7 Conclusion on Motion Control {#4-dot-7-conclusion-on-motion-control} +### Conclusion on Motion Control {#conclusion-on-motion-control} Motion control is essential for Precision Mechatronic Systems and consists of two complementary elements: @@ -619,941 +738,941 @@ Motion control is essential for Precision Mechatronic Systems and consists of tw -## 5 Electromechanic Actuators {#5-electromechanic-actuators} +## Electromechanic Actuators {#electromechanic-actuators} ### Introduction {#introduction} -### 5.1 Electromagnetics {#5-dot-1-electromagnetics} +### Electromagnetics {#electromagnetics} -#### 5.1.1 Hopkinson's Law {#5-dot-1-dot-1-hopkinson-s-law} +#### Hopkinson's Law {#hopkinson-s-law} -##### 5.1.1.1 Practical Aspects of Hopkinson's Law {#5-dot-1-dot-1-dot-1-practical-aspects-of-hopkinson-s-law} +##### Practical Aspects of Hopkinson's Law {#practical-aspects-of-hopkinson-s-law} -##### 5.1.1.2 Magnetic Energy {#5-dot-1-dot-1-dot-2-magnetic-energy} +##### Magnetic Energy {#magnetic-energy} -#### 5.1.2 Ferromagnetic Materials {#5-dot-1-dot-2-ferromagnetic-materials} +#### Ferromagnetic Materials {#ferromagnetic-materials} -##### 5.1.2.1 Coil with Ferromagnetic Yoke {#5-dot-1-dot-2-dot-1-coil-with-ferromagnetic-yoke} +##### Coil with Ferromagnetic Yoke {#coil-with-ferromagnetic-yoke} -##### 5.1.2.2 Magnetisation Curve {#5-dot-1-dot-2-dot-2-magnetisation-curve} +##### Magnetisation Curve {#magnetisation-curve} -##### 5.1.2.3 Permanent Magnets {#5-dot-1-dot-2-dot-3-permanent-magnets} +##### Permanent Magnets {#permanent-magnets} -#### 5.1.3 Creating a Magnetic Field in an Air-Gap {#5-dot-1-dot-3-creating-a-magnetic-field-in-an-air-gap} +#### Creating a Magnetic Field in an Air-Gap {#creating-a-magnetic-field-in-an-air-gap} -##### 5.1.3.1 Optimal Use of Permanent Magnet Material {#5-dot-1-dot-3-dot-1-optimal-use-of-permanent-magnet-material} +##### Optimal Use of Permanent Magnet Material {#optimal-use-of-permanent-magnet-material} -##### 5.1.3.2 Flat Magnets Reduce Fringing Flux {#5-dot-1-dot-3-dot-2-flat-magnets-reduce-fringing-flux} +##### Flat Magnets Reduce Fringing Flux {#flat-magnets-reduce-fringing-flux} -##### 5.1.3.3 Low Cost Loudspeaker Magnet {#5-dot-1-dot-3-dot-3-low-cost-loudspeaker-magnet} +##### Low Cost Loudspeaker Magnet {#low-cost-loudspeaker-magnet} -### 5.2 Lorentz Actuator {#5-dot-2-lorentz-actuator} +### Lorentz Actuator {#lorentz-actuator} -#### 5.2.1 Lorentz Force {#5-dot-2-dot-1-lorentz-force} +#### Lorentz Force {#lorentz-force} -##### 5.2.1.1 Force from Flux-Linkage {#5-dot-2-dot-1-dot-1-force-from-flux-linkage} +##### Force from Flux-Linkage {#force-from-flux-linkage} -#### 5.2.2 The Lorentz actuator as a Generator {#5-dot-2-dot-2-the-lorentz-actuator-as-a-generator} +#### The Lorentz actuator as a Generator {#the-lorentz-actuator-as-a-generator} -#### 5.2.3 Improving the Force of a Lorentz Actuator {#5-dot-2-dot-3-improving-the-force-of-a-lorentz-actuator} +#### Improving the Force of a Lorentz Actuator {#improving-the-force-of-a-lorentz-actuator} -##### 5.2.3.1 The Moving-Coil Loudspeaker Actuator {#5-dot-2-dot-3-dot-1-the-moving-coil-loudspeaker-actuator} +##### The Moving-Coil Loudspeaker Actuator {#the-moving-coil-loudspeaker-actuator} -#### 5.2.4 Position Dependency of the Lorentz Force {#5-dot-2-dot-4-position-dependency-of-the-lorentz-force} +#### Position Dependency of the Lorentz Force {#position-dependency-of-the-lorentz-force} -##### 5.2.4.1 Over-Hung and Under-Hung Coil {#5-dot-2-dot-4-dot-1-over-hung-and-under-hung-coil} +##### Over-Hung and Under-Hung Coil {#over-hung-and-under-hung-coil} -#### 5.2.5 Electronic Commutation {#5-dot-2-dot-5-electronic-commutation} +#### Electronic Commutation {#electronic-commutation} -##### 5.2.5.1 Three-Phase Electronic Control {#5-dot-2-dot-5-dot-1-three-phase-electronic-control} +##### Three-Phase Electronic Control {#three-phase-electronic-control} -#### 5.2.6 Figures of Merit of a Lorentz Actuator {#5-dot-2-dot-6-figures-of-merit-of-a-lorentz-actuator} +#### Figures of Merit of a Lorentz Actuator {#figures-of-merit-of-a-lorentz-actuator} -### 5.3 Variable Reluctance Actuation {#5-dot-3-variable-reluctance-actuation} +### Variable Reluctance Actuation {#variable-reluctance-actuation} -#### 5.3.1 Reluctance Force in Lorentz Actuator {#5-dot-3-dot-1-reluctance-force-in-lorentz-actuator} +#### Reluctance Force in Lorentz Actuator {#reluctance-force-in-lorentz-actuator} -##### 5.3.1.1 Eddy-Current Ring {#5-dot-3-dot-1-dot-1-eddy-current-ring} +##### Eddy-Current Ring {#eddy-current-ring} -##### 5.3.1.2 Ironless Stator {#5-dot-3-dot-1-dot-2-ironless-stator} +##### Ironless Stator {#ironless-stator} -#### 5.3.2 Analytical Derivation of Reluctance Force {#5-dot-3-dot-2-analytical-derivation-of-reluctance-force} +#### Analytical Derivation of Reluctance Force {#analytical-derivation-of-reluctance-force} -#### 5.3.3 Variable Reluctance Actuator. {#5-dot-3-dot-3-variable-reluctance-actuator-dot} +#### Variable Reluctance Actuator. {#variable-reluctance-actuator-dot} -##### 5.3.3.1 Electromagnetic Relay {#5-dot-3-dot-3-dot-1-electromagnetic-relay} +##### Electromagnetic Relay {#electromagnetic-relay} -##### 5.3.3.2 Magnetic Attraction Force {#5-dot-3-dot-3-dot-2-magnetic-attraction-force} +##### Magnetic Attraction Force {#magnetic-attraction-force} -#### 5.3.4 Permanent Magnet Biased Reluctance Actuator {#5-dot-3-dot-4-permanent-magnet-biased-reluctance-actuator} +#### Permanent Magnet Biased Reluctance Actuator {#permanent-magnet-biased-reluctance-actuator} -##### 5.3.4.1 Double Variable Reluctance Actuator {#5-dot-3-dot-4-dot-1-double-variable-reluctance-actuator} +##### Double Variable Reluctance Actuator {#double-variable-reluctance-actuator} -##### 5.3.4.2 Constant Common Flux {#5-dot-3-dot-4-dot-2-constant-common-flux} +##### Constant Common Flux {#constant-common-flux} -##### 5.3.4.3 Combining two Sources of Magnetic Flux {#5-dot-3-dot-4-dot-3-combining-two-sources-of-magnetic-flux} +##### Combining two Sources of Magnetic Flux {#combining-two-sources-of-magnetic-flux} -##### 5.3.4.4 Hybrid Force Calculation {#5-dot-3-dot-4-dot-4-hybrid-force-calculation} +##### Hybrid Force Calculation {#hybrid-force-calculation} -##### 5.3.4.5 Magnetic Bearings {#5-dot-3-dot-4-dot-5-magnetic-bearings} +##### Magnetic Bearings {#magnetic-bearings} -#### 5.3.5 Active Linearisation of the Reluctance Force {#5-dot-3-dot-5-active-linearisation-of-the-reluctance-force} +#### Active Linearisation of the Reluctance Force {#active-linearisation-of-the-reluctance-force} -### 5.4 Application of Electromagnetic Actuators {#5-dot-4-application-of-electromagnetic-actuators} +### Application of Electromagnetic Actuators {#application-of-electromagnetic-actuators} -#### 5.4.1 Electrical Interface Properties {#5-dot-4-dot-1-electrical-interface-properties} +#### Electrical Interface Properties {#electrical-interface-properties} -##### 5.4.1.1 Dynamic Effects of Self-Inductance {#5-dot-4-dot-1-dot-1-dynamic-effects-of-self-inductance} +##### Dynamic Effects of Self-Inductance {#dynamic-effects-of-self-inductance} -##### 5.4.1.2 Limitation of the \`\`Jerk'' {#5-dot-4-dot-1-dot-2-limitation-of-the-jerk} +##### Limitation of the \`\`Jerk'' {#limitation-of-the-jerk} -##### 5.4.1.3 Electromagnetic Damping {#5-dot-4-dot-1-dot-3-electromagnetic-damping} +##### Electromagnetic Damping {#electromagnetic-damping} -#### 5.4.2 Comparison of three Electromagnetic Actuators {#5-dot-4-dot-2-comparison-of-three-electromagnetic-actuators} +#### Comparison of three Electromagnetic Actuators {#comparison-of-three-electromagnetic-actuators} -##### 5.4.2.1 Force-Constants {#5-dot-4-dot-2-dot-1-force-constants} +##### Force-Constants {#force-constants} -##### 5.4.2.2 Figures of Merit Including Mass {#5-dot-4-dot-2-dot-2-figures-of-merit-including-mass} +##### Figures of Merit Including Mass {#figures-of-merit-including-mass} -##### 5.4.2.3 Stiffness {#5-dot-4-dot-2-dot-3-stiffness} +##### Stiffness {#stiffness} -##### 5.4.2.4 Repeatability and Predictability {#5-dot-4-dot-2-dot-4-repeatability-and-predictability} +##### Repeatability and Predictability {#repeatability-and-predictability} -##### 5.4.2.5 Dynamic Effects on the Control Loop {#5-dot-4-dot-2-dot-5-dynamic-effects-on-the-control-loop} +##### Dynamic Effects on the Control Loop {#dynamic-effects-on-the-control-loop} -### 5.5 Piezoelectric Actuators {#5-dot-5-piezoelectric-actuators} +### Piezoelectric Actuators {#piezoelectric-actuators} -#### 5.5.1 Piezoelectricity {#5-dot-5-dot-1-piezoelectricity} +#### Piezoelectricity {#piezoelectricity} -##### 5.5.1.1 Poling {#5-dot-5-dot-1-dot-1-poling} +##### Poling {#poling} -##### 5.5.1.2 Tapping the Bound Charge by Electrodes {#5-dot-5-dot-1-dot-2-tapping-the-bound-charge-by-electrodes} +##### Tapping the Bound Charge by Electrodes {#tapping-the-bound-charge-by-electrodes} -#### 5.5.2 Transducer Models {#5-dot-5-dot-2-transducer-models} +#### Transducer Models {#transducer-models} -#### 5.5.3 Nonlinearity of Piezoelectric Actuators {#5-dot-5-dot-3-nonlinearity-of-piezoelectric-actuators} +#### Nonlinearity of Piezoelectric Actuators {#nonlinearity-of-piezoelectric-actuators} -##### 5.5.3.1 Creep {#5-dot-5-dot-3-dot-1-creep} +##### Creep {#creep} -##### 5.5.3.2 Hysteresis {#5-dot-5-dot-3-dot-2-hysteresis} +##### Hysteresis {#hysteresis} -##### 5.5.3.3 Aging {#5-dot-5-dot-3-dot-3-aging} +##### Aging {#aging} -#### 5.5.4 Mechanical Considerations {#5-dot-5-dot-4-mechanical-considerations} +#### Mechanical Considerations {#mechanical-considerations} -##### 5.5.4.1 Piezoelectric Actuator Stiffness {#5-dot-5-dot-4-dot-1-piezoelectric-actuator-stiffness} +##### Piezoelectric Actuator Stiffness {#piezoelectric-actuator-stiffness} -##### 5.5.4.2 Actuator Types {#5-dot-5-dot-4-dot-2-actuator-types} +##### Actuator Types {#actuator-types} -##### 5.5.4.3 Long Range Actuation by Friction {#5-dot-5-dot-4-dot-3-long-range-actuation-by-friction} +##### Long Range Actuation by Friction {#long-range-actuation-by-friction} -##### 5.5.4.4 Actuator Integration {#5-dot-5-dot-4-dot-4-actuator-integration} +##### Actuator Integration {#actuator-integration} -##### 5.5.4.5 Mechanical Amplification {#5-dot-5-dot-4-dot-5-mechanical-amplification} +##### Mechanical Amplification {#mechanical-amplification} -##### 5.5.4.6 Multiple Motion Directions by Stacking {#5-dot-5-dot-4-dot-6-multiple-motion-directions-by-stacking} +##### Multiple Motion Directions by Stacking {#multiple-motion-directions-by-stacking} -#### 5.5.5 Electrical Considerations {#5-dot-5-dot-5-electrical-considerations} +#### Electrical Considerations {#electrical-considerations} -##### 5.5.5.1 Charge vs. Voltage Control {#5-dot-5-dot-5-dot-1-charge-vs-dot-voltage-control} +##### Charge vs. Voltage Control {#charge-vs-dot-voltage-control} -##### 5.5.5.2 Self-Sensing Actuation {#5-dot-5-dot-5-dot-2-self-sensing-actuation} +##### Self-Sensing Actuation {#self-sensing-actuation} -### 5.6 Choosing the right Actuator Type {#5-dot-6-choosing-the-right-actuator-type} +### Choosing the right Actuator Type {#choosing-the-right-actuator-type} -## 6 Analogue Electronics in Mechatronic Systems {#6-analogue-electronics-in-mechatronic-systems} +## Analogue Electronics in Mechatronic Systems {#analogue-electronics-in-mechatronic-systems} ### Introduction {#introduction} -### 6.1 Passive Linear Electronics {#6-dot-1-passive-linear-electronics} +### Passive Linear Electronics {#passive-linear-electronics} -#### 6.1.1 Network Theory and Laws {#6-dot-1-dot-1-network-theory-and-laws} +#### Network Theory and Laws {#network-theory-and-laws} -##### 6.1.1.1 Voltage Source {#6-dot-1-dot-1-dot-1-voltage-source} +##### Voltage Source {#voltage-source} -##### 6.1.1.2 Current Source {#6-dot-1-dot-1-dot-2-current-source} +##### Current Source {#current-source} -##### 6.1.1.3 Theorem of Norton and Thevenin {#6-dot-1-dot-1-dot-3-theorem-of-norton-and-thevenin} +##### Theorem of Norton and Thevenin {#theorem-of-norton-and-thevenin} -##### 6.1.1.4 Kirchhoff's Laws {#6-dot-1-dot-1-dot-4-kirchhoff-s-laws} +##### Kirchhoff's Laws {#kirchhoff-s-laws} -##### 6.1.1.5 Impedances in Series or Parallel {#6-dot-1-dot-1-dot-5-impedances-in-series-or-parallel} +##### Impedances in Series or Parallel {#impedances-in-series-or-parallel} -##### 6.1.1.6 Voltage Divider {#6-dot-1-dot-1-dot-6-voltage-divider} +##### Voltage Divider {#voltage-divider} -##### 6.1.1.7 Maximum Power of a Real Voltage Source {#6-dot-1-dot-1-dot-7-maximum-power-of-a-real-voltage-source} +##### Maximum Power of a Real Voltage Source {#maximum-power-of-a-real-voltage-source} -#### 6.1.2 Impedances in Electronic Circuits {#6-dot-1-dot-2-impedances-in-electronic-circuits} +#### Impedances in Electronic Circuits {#impedances-in-electronic-circuits} -##### 6.1.2.1 Resistors {#6-dot-1-dot-2-dot-1-resistors} +##### Resistors {#resistors} -##### 6.1.2.2 Capacitors {#6-dot-1-dot-2-dot-2-capacitors} +##### Capacitors {#capacitors} -##### 6.1.2.3 Inductors {#6-dot-1-dot-2-dot-3-inductors} +##### Inductors {#inductors} -#### 6.1.3 Passive Filters {#6-dot-1-dot-3-passive-filters} +#### Passive Filters {#passive-filters} -##### 6.1.3.1 Passive First-Order RC-Filters {#6-dot-1-dot-3-dot-1-passive-first-order-rc-filters} +##### Passive First-Order RC-Filters {#passive-first-order-rc-filters} -##### 6.1.3.2 Passive Higher-Order RC-Filters {#6-dot-1-dot-3-dot-2-passive-higher-order-rc-filters} +##### Passive Higher-Order RC-Filters {#passive-higher-order-rc-filters} -##### 6.1.3.3 Passive LCR-Filters {#6-dot-1-dot-3-dot-3-passive-lcr-filters} +##### Passive LCR-Filters {#passive-lcr-filters} -#### 6.1.4 Mechanical-Electrical Dynamic Analogy {#6-dot-1-dot-4-mechanical-electrical-dynamic-analogy} +#### Mechanical-Electrical Dynamic Analogy {#mechanical-electrical-dynamic-analogy} -### 6.2 Semiconductors and Active Electronics {#6-dot-2-semiconductors-and-active-electronics} +### Semiconductors and Active Electronics {#semiconductors-and-active-electronics} -#### 6.2.1 Basic Discrete Semiconductors {#6-dot-2-dot-1-basic-discrete-semiconductors} +#### Basic Discrete Semiconductors {#basic-discrete-semiconductors} -##### 6.2.1.1 Semiconductor Diode {#6-dot-2-dot-1-dot-1-semiconductor-diode} +##### Semiconductor Diode {#semiconductor-diode} -##### 6.2.1.2 Bipolar Transistors {#6-dot-2-dot-1-dot-2-bipolar-transistors} +##### Bipolar Transistors {#bipolar-transistors} -##### 6.2.1.3 MOSFET {#6-dot-2-dot-1-dot-3-mosfet} +##### MOSFET {#mosfet} -##### 6.2.1.4 Other Discrete Semiconductors {#6-dot-2-dot-1-dot-4-other-discrete-semiconductors} +##### Other Discrete Semiconductors {#other-discrete-semiconductors} -#### 6.2.2 Single Transistor Linear Amplifiers {#6-dot-2-dot-2-single-transistor-linear-amplifiers} +#### Single Transistor Linear Amplifiers {#single-transistor-linear-amplifiers} -##### 6.2.2.1 Emitter Follower {#6-dot-2-dot-2-dot-1-emitter-follower} +##### Emitter Follower {#emitter-follower} -##### 6.2.2.2 Voltage Amplifier {#6-dot-2-dot-2-dot-2-voltage-amplifier} +##### Voltage Amplifier {#voltage-amplifier} -##### 6.2.2.3 Differential Amplifier {#6-dot-2-dot-2-dot-3-differential-amplifier} +##### Differential Amplifier {#differential-amplifier} -#### 6.2.3 Operational Amplifier {#6-dot-2-dot-3-operational-amplifier} +#### Operational Amplifier {#operational-amplifier} -##### 6.2.3.1 Basic Operational Amplifier Design {#6-dot-2-dot-3-dot-1-basic-operational-amplifier-design} +##### Basic Operational Amplifier Design {#basic-operational-amplifier-design} -##### 6.2.3.2 Operational Amplifier with Feedback {#6-dot-2-dot-3-dot-2-operational-amplifier-with-feedback} +##### Operational Amplifier with Feedback {#operational-amplifier-with-feedback} -#### 6.2.4 Linear Amplifiers with Operational Amplifiers {#6-dot-2-dot-4-linear-amplifiers-with-operational-amplifiers} +#### Linear Amplifiers with Operational Amplifiers {#linear-amplifiers-with-operational-amplifiers} -##### 6.2.4.1 Design Rules {#6-dot-2-dot-4-dot-1-design-rules} +##### Design Rules {#design-rules} -##### 6.2.4.2 Non-Inverting Amplifier {#6-dot-2-dot-4-dot-2-non-inverting-amplifier} +##### Non-Inverting Amplifier {#non-inverting-amplifier} -##### 6.2.4.3 Inverting Amplifier {#6-dot-2-dot-4-dot-3-inverting-amplifier} +##### Inverting Amplifier {#inverting-amplifier} -##### 6.2.4.4 Adding and Subtracting Signals {#6-dot-2-dot-4-dot-4-adding-and-subtracting-signals} +##### Adding and Subtracting Signals {#adding-and-subtracting-signals} -##### 6.2.4.5 Transimpedance Amplifier {#6-dot-2-dot-4-dot-5-transimpedance-amplifier} +##### Transimpedance Amplifier {#transimpedance-amplifier} -##### 6.2.4.6 Transconductance Amplifier {#6-dot-2-dot-4-dot-6-transconductance-amplifier} +##### Transconductance Amplifier {#transconductance-amplifier} -#### 6.2.5 Active Electronic Filters {#6-dot-2-dot-5-active-electronic-filters} +#### Active Electronic Filters {#active-electronic-filters} -##### 6.2.5.1 Integrator and First-Order Low-Pass {#6-dot-2-dot-5-dot-1-integrator-and-first-order-low-pass} +##### Integrator and First-Order Low-Pass {#integrator-and-first-order-low-pass} -##### 6.2.5.2 Differentiator and First-Order High-Pass {#6-dot-2-dot-5-dot-2-differentiator-and-first-order-high-pass} +##### Differentiator and First-Order High-Pass {#differentiator-and-first-order-high-pass} -#### 6.2.6 Analogue PID-Controller {#6-dot-2-dot-6-analogue-pid-controller} +#### Analogue PID-Controller {#analogue-pid-controller} -##### 6.2.6.1 PID Transfer Function {#6-dot-2-dot-6-dot-1-pid-transfer-function} +##### PID Transfer Function {#pid-transfer-function} -##### 6.2.6.2 PID Control Gains {#6-dot-2-dot-6-dot-2-pid-control-gains} +##### PID Control Gains {#pid-control-gains} -##### 6.2.6.3 High-Speed PID-Control {#6-dot-2-dot-6-dot-3-high-speed-pid-control} +##### High-Speed PID-Control {#high-speed-pid-control} -#### 6.2.7 Higher-order Electronic Filters {#6-dot-2-dot-7-higher-order-electronic-filters} +#### Higher-order Electronic Filters {#higher-order-electronic-filters} -##### 6.2.7.1 Second-Order Low-Pass Filter {#6-dot-2-dot-7-dot-1-second-order-low-pass-filter} +##### Second-Order Low-Pass Filter {#second-order-low-pass-filter} -##### 6.2.7.2 Different Types of Active Filters {#6-dot-2-dot-7-dot-2-different-types-of-active-filters} +##### Different Types of Active Filters {#different-types-of-active-filters} -#### 6.2.8 Ideal and Real Operational Amplifiers {#6-dot-2-dot-8-ideal-and-real-operational-amplifiers} +#### Ideal and Real Operational Amplifiers {#ideal-and-real-operational-amplifiers} -##### 6.2.8.1 Open-Loop Voltage Gain {#6-dot-2-dot-8-dot-1-open-loop-voltage-gain} +##### Open-Loop Voltage Gain {#open-loop-voltage-gain} -##### 6.2.8.2 Dynamic Limitations {#6-dot-2-dot-8-dot-2-dynamic-limitations} +##### Dynamic Limitations {#dynamic-limitations} -##### 6.2.8.3 Input Related Limitations {#6-dot-2-dot-8-dot-3-input-related-limitations} +##### Input Related Limitations {#input-related-limitations} -##### 6.2.8.4 Power Supply and Output Limitations {#6-dot-2-dot-8-dot-4-power-supply-and-output-limitations} +##### Power Supply and Output Limitations {#power-supply-and-output-limitations} -#### 6.2.9 Closing Remarks on Low-Power Electronics {#6-dot-2-dot-9-closing-remarks-on-low-power-electronics} +#### Closing Remarks on Low-Power Electronics {#closing-remarks-on-low-power-electronics} -### 6.3 Power Amplifiers for Motion Control {#6-dot-3-power-amplifiers-for-motion-control} +### Power Amplifiers for Motion Control {#power-amplifiers-for-motion-control} -#### 6.3.1 Required Properties for Actuator Drive {#6-dot-3-dot-1-required-properties-for-actuator-drive} +#### Required Properties for Actuator Drive {#required-properties-for-actuator-drive} -##### 6.3.1.1 Power Delivery Capability {#6-dot-3-dot-1-dot-1-power-delivery-capability} +##### Power Delivery Capability {#power-delivery-capability} -##### 6.3.1.2 Dynamic Properties {#6-dot-3-dot-1-dot-2-dynamic-properties} +##### Dynamic Properties {#dynamic-properties} -##### 6.3.1.3 Linearity, Freedom of Distortion {#6-dot-3-dot-1-dot-3-linearity-freedom-of-distortion} +##### Linearity, Freedom of Distortion {#linearity-freedom-of-distortion} -##### 6.3.1.4 Voltage or Current Drive {#6-dot-3-dot-1-dot-4-voltage-or-current-drive} +##### Voltage or Current Drive {#voltage-or-current-drive} -##### 6.3.1.5 Efficiency {#6-dot-3-dot-1-dot-5-efficiency} +##### Efficiency {#efficiency} -##### 6.3.1.6 Four-Quadrant Operation {#6-dot-3-dot-1-dot-6-four-quadrant-operation} +##### Four-Quadrant Operation {#four-quadrant-operation} -##### 6.3.1.7 Preferred Power Amplifier Principle {#6-dot-3-dot-1-dot-7-preferred-power-amplifier-principle} +##### Preferred Power Amplifier Principle {#preferred-power-amplifier-principle} -#### 6.3.2 Switched-Mode Power Amplifiers {#6-dot-3-dot-2-switched-mode-power-amplifiers} +#### Switched-Mode Power Amplifiers {#switched-mode-power-amplifiers} -##### 6.3.2.1 Power MOSFET, a Fast High-Power Switch {#6-dot-3-dot-2-dot-1-power-mosfet-a-fast-high-power-switch} +##### Power MOSFET, a Fast High-Power Switch {#power-mosfet-a-fast-high-power-switch} -##### 6.3.2.2 Switching Sequence Generation {#6-dot-3-dot-2-dot-2-switching-sequence-generation} +##### Switching Sequence Generation {#switching-sequence-generation} -##### 6.3.2.3 Voltage Drive Amplifier {#6-dot-3-dot-2-dot-3-voltage-drive-amplifier} +##### Voltage Drive Amplifier {#voltage-drive-amplifier} -##### 6.3.2.4 Energy Flow in the Power Output Stage {#6-dot-3-dot-2-dot-4-energy-flow-in-the-power-output-stage} +##### Energy Flow in the Power Output Stage {#energy-flow-in-the-power-output-stage} -##### 6.3.2.5 Intermediate Conclusions and Other Issues {#6-dot-3-dot-2-dot-5-intermediate-conclusions-and-other-issues} +##### Intermediate Conclusions and Other Issues {#intermediate-conclusions-and-other-issues} -##### 6.3.2.6 Driving the Power MOSFETs {#6-dot-3-dot-2-dot-6-driving-the-power-mosfets} +##### Driving the Power MOSFETs {#driving-the-power-mosfets} -##### 6.3.2.7 Charge Pumping {#6-dot-3-dot-2-dot-7-charge-pumping} +##### Charge Pumping {#charge-pumping} -##### 6.3.2.8 H-Bridge Configuration {#6-dot-3-dot-2-dot-8-h-bridge-configuration} +##### H-Bridge Configuration {#h-bridge-configuration} -##### 6.3.2.9 Output Filter {#6-dot-3-dot-2-dot-9-output-filter} +##### Output Filter {#output-filter} -#### 6.3.3 Resonant-Mode Power Amplifiers {#6-dot-3-dot-3-resonant-mode-power-amplifiers} +#### Resonant-Mode Power Amplifiers {#resonant-mode-power-amplifiers} -##### 6.3.3.1 Switching Sequence of the Output Stage {#6-dot-3-dot-3-dot-1-switching-sequence-of-the-output-stage} +##### Switching Sequence of the Output Stage {#switching-sequence-of-the-output-stage} -##### 6.3.3.2 Lossless Current Sensing {#6-dot-3-dot-3-dot-2-lossless-current-sensing} +##### Lossless Current Sensing {#lossless-current-sensing} -#### 6.3.4 Three-Phase Amplifiers {#6-dot-3-dot-4-three-phase-amplifiers} +#### Three-Phase Amplifiers {#three-phase-amplifiers} -##### 6.3.4.1 Concept of Three-Phase Amplifier {#6-dot-3-dot-4-dot-1-concept-of-three-phase-amplifier} +##### Concept of Three-Phase Amplifier {#concept-of-three-phase-amplifier} -##### 6.3.4.2 Three-Phase Switching Power Stages {#6-dot-3-dot-4-dot-2-three-phase-switching-power-stages} +##### Three-Phase Switching Power Stages {#three-phase-switching-power-stages} -#### 6.3.5 Some Last Remarks on Power Electronics {#6-dot-3-dot-5-some-last-remarks-on-power-electronics} +#### Some Last Remarks on Power Electronics {#some-last-remarks-on-power-electronics} -## 7 Optics in Mechatronic Systems {#7-optics-in-mechatronic-systems} +## Optics in Mechatronic Systems {#optics-in-mechatronic-systems} ### Introduction {#introduction} -### 7.1 Properties of Light and Light Sources {#7-dot-1-properties-of-light-and-light-sources} +### Properties of Light and Light Sources {#properties-of-light-and-light-sources} -#### 7.1.1 Light Generation by Thermal Radiation {#7-dot-1-dot-1-light-generation-by-thermal-radiation} +#### Light Generation by Thermal Radiation {#light-generation-by-thermal-radiation} -#### 7.1.2 Photons by Electron Energy State Variation {#7-dot-1-dot-2-photons-by-electron-energy-state-variation} +#### Photons by Electron Energy State Variation {#photons-by-electron-energy-state-variation} -##### 7.1.2.1 Light Emitting Diodes {#7-dot-1-dot-2-dot-1-light-emitting-diodes} +##### Light Emitting Diodes {#light-emitting-diodes} -##### 7.1.2.2 Laser as an Ideal Light Source {#7-dot-1-dot-2-dot-2-laser-as-an-ideal-light-source} +##### Laser as an Ideal Light Source {#laser-as-an-ideal-light-source} -#### 7.1.3 Useful Power from a Light Source {#7-dot-1-dot-3-useful-power-from-a-light-source} +#### Useful Power from a Light Source {#useful-power-from-a-light-source} -##### 7.1.3.1 Radiant Emittance and Irradiance {#7-dot-1-dot-3-dot-1-radiant-emittance-and-irradiance} +##### Radiant Emittance and Irradiance {#radiant-emittance-and-irradiance} -##### 7.1.3.2 Radiance {#7-dot-1-dot-3-dot-2-radiance} +##### Radiance {#radiance} -##### 7.1.3.3 Etendue {#7-dot-1-dot-3-dot-3-etendue} +##### Etendue {#etendue} -### 7.2 Reflection and Refraction {#7-dot-2-reflection-and-refraction} +### Reflection and Refraction {#reflection-and-refraction} -#### 7.2.1 Reflection and Refraction according to the Least Time {#7-dot-2-dot-1-reflection-and-refraction-according-to-the-least-time} +#### Reflection and Refraction according to the Least Time {#reflection-and-refraction-according-to-the-least-time} -##### 7.2.1.1 Partial Reflection and Refraction {#7-dot-2-dot-1-dot-1-partial-reflection-and-refraction} +##### Partial Reflection and Refraction {#partial-reflection-and-refraction} -#### 7.2.2 Concept of Wavefront {#7-dot-2-dot-2-concept-of-wavefront} +#### Concept of Wavefront {#concept-of-wavefront} -##### 7.2.2.1 A Wavefront is Not Real {#7-dot-2-dot-2-dot-1-a-wavefront-is-not-real} +##### A Wavefront is Not Real {#a-wavefront-is-not-real} -### 7.3 Geometric Optics {#7-dot-3-geometric-optics} +### Geometric Optics {#geometric-optics} -#### 7.3.1 Imaging with Refractive Lens Elements {#7-dot-3-dot-1-imaging-with-refractive-lens-elements} +#### Imaging with Refractive Lens Elements {#imaging-with-refractive-lens-elements} -##### 7.3.1.1 Sign Conventions {#7-dot-3-dot-1-dot-1-sign-conventions} +##### Sign Conventions {#sign-conventions} -##### 7.3.1.2 Real Lens Elements {#7-dot-3-dot-1-dot-2-real-lens-elements} +##### Real Lens Elements {#real-lens-elements} -##### 7.3.1.3 Magnification {#7-dot-3-dot-1-dot-3-magnification} +##### Magnification {#magnification} -#### 7.3.2 Aberrations {#7-dot-3-dot-2-aberrations} +#### Aberrations {#aberrations} -##### 7.3.2.1 Spherical Aberration {#7-dot-3-dot-2-dot-1-spherical-aberration} +##### Spherical Aberration {#spherical-aberration} -##### 7.3.2.2 Astigmatism {#7-dot-3-dot-2-dot-2-astigmatism} +##### Astigmatism {#astigmatism} -##### 7.3.2.3 Coma {#7-dot-3-dot-2-dot-3-coma} +##### Coma {#coma} -##### 7.3.2.4 Geometric and Chromatic Aberrations {#7-dot-3-dot-2-dot-4-geometric-and-chromatic-aberrations} +##### Geometric and Chromatic Aberrations {#geometric-and-chromatic-aberrations} -#### 7.3.3 Combining Multiple Optical Elements {#7-dot-3-dot-3-combining-multiple-optical-elements} +#### Combining Multiple Optical Elements {#combining-multiple-optical-elements} -##### 7.3.3.1 Combining Two Positive Lenses {#7-dot-3-dot-3-dot-1-combining-two-positive-lenses} +##### Combining Two Positive Lenses {#combining-two-positive-lenses} -#### 7.3.4 Aperture Stop and Pupil {#7-dot-3-dot-4-aperture-stop-and-pupil} +#### Aperture Stop and Pupil {#aperture-stop-and-pupil} -#### 7.3.5 Telecentricity {#7-dot-3-dot-5-telecentricity} +#### Telecentricity {#telecentricity} -##### 7.3.5.1 Pupil, Aperture and Lens Dimensions {#7-dot-3-dot-5-dot-1-pupil-aperture-and-lens-dimensions} +##### Pupil, Aperture and Lens Dimensions {#pupil-aperture-and-lens-dimensions} -##### 7.3.5.2 Practical Applications and Constraints {#7-dot-3-dot-5-dot-2-practical-applications-and-constraints} +##### Practical Applications and Constraints {#practical-applications-and-constraints} -### 7.4 Physical Optics {#7-dot-4-physical-optics} +### Physical Optics {#physical-optics} -#### 7.4.1 Polarisation {#7-dot-4-dot-1-polarisation} +#### Polarisation {#polarisation} -##### 7.4.1.1 Birefringence {#7-dot-4-dot-1-dot-1-birefringence} +##### Birefringence {#birefringence} -#### 7.4.2 Interference {#7-dot-4-dot-2-interference} +#### Interference {#interference} -##### 7.4.2.1 Fabry-Perot Interferometer {#7-dot-4-dot-2-dot-1-fabry-perot-interferometer} +##### Fabry-Perot Interferometer {#fabry-perot-interferometer} -#### 7.4.3 Diffraction {#7-dot-4-dot-3-diffraction} +#### Diffraction {#diffraction} -##### 7.4.3.1 Amplitude gratings {#7-dot-4-dot-3-dot-1-amplitude-gratings} +##### Amplitude gratings {#amplitude-gratings} -##### 7.4.3.2 Phase Gratings {#7-dot-4-dot-3-dot-2-phase-gratings} +##### Phase Gratings {#phase-gratings} -##### 7.4.3.3 Direction of the Incoming Light {#7-dot-4-dot-3-dot-3-direction-of-the-incoming-light} +##### Direction of the Incoming Light {#direction-of-the-incoming-light} -#### 7.4.4 Imaging Quality based on Diffraction {#7-dot-4-dot-4-imaging-quality-based-on-diffraction} +#### Imaging Quality based on Diffraction {#imaging-quality-based-on-diffraction} -##### 7.4.4.1 Numerical Aperture and f-Number {#7-dot-4-dot-4-dot-1-numerical-aperture-and-f-number} +##### Numerical Aperture and f-Number {#numerical-aperture-and-f-number} -##### 7.4.4.2 Depth of Focus {#7-dot-4-dot-4-dot-2-depth-of-focus} +##### Depth of Focus {#depth-of-focus} -### 7.5 Adaptive Optics {#7-dot-5-adaptive-optics} +### Adaptive Optics {#adaptive-optics} -#### 7.5.1 Thermal Effects in Optical Imaging Systems {#7-dot-5-dot-1-thermal-effects-in-optical-imaging-systems} +#### Thermal Effects in Optical Imaging Systems {#thermal-effects-in-optical-imaging-systems} -#### 7.5.2 Correcting the Wavefront {#7-dot-5-dot-2-correcting-the-wavefront} +#### Correcting the Wavefront {#correcting-the-wavefront} -##### 7.5.2.1 Zernike Polynomials {#7-dot-5-dot-2-dot-1-zernike-polynomials} +##### Zernike Polynomials {#zernike-polynomials} -##### 7.5.2.2 Correcting Zernikes by Adaptive Optics {#7-dot-5-dot-2-dot-2-correcting-zernikes-by-adaptive-optics} +##### Correcting Zernikes by Adaptive Optics {#correcting-zernikes-by-adaptive-optics} -#### 7.5.3 Adaptive Optics Principle of Operation {#7-dot-5-dot-3-adaptive-optics-principle-of-operation} +#### Adaptive Optics Principle of Operation {#adaptive-optics-principle-of-operation} -##### 7.5.3.1 Active Mirrors {#7-dot-5-dot-3-dot-1-active-mirrors} +##### Active Mirrors {#active-mirrors} -## 8 Measurement in Mechatronic Systems {#8-measurement-in-mechatronic-systems} +## Measurement in Mechatronic Systems {#measurement-in-mechatronic-systems} ### Introduction {#introduction} -#### 8.0.1 Measurement Systems {#8-dot-0-dot-1-measurement-systems} +#### Measurement Systems {#measurement-systems} -#### 8.0.2 Errors in Measurement Systems, Uncertainty {#8-dot-0-dot-2-errors-in-measurement-systems-uncertainty} +#### Errors in Measurement Systems, Uncertainty {#errors-in-measurement-systems-uncertainty} -##### 8.0.2.1 Uncertainty in Traceable Measurements {#8-dot-0-dot-2-dot-1-uncertainty-in-traceable-measurements} +##### Uncertainty in Traceable Measurements {#uncertainty-in-traceable-measurements} -#### 8.0.3 Functional Model of a Measurement System Element {#8-dot-0-dot-3-functional-model-of-a-measurement-system-element} +#### Functional Model of a Measurement System Element {#functional-model-of-a-measurement-system-element} -### 8.1 Dynamic Error Budgeting {#8-dot-1-dynamic-error-budgeting} +### Dynamic Error Budgeting {#dynamic-error-budgeting} -#### 8.1.1 Error Statistics in Repeated Measurements {#8-dot-1-dot-1-error-statistics-in-repeated-measurements} +#### Error Statistics in Repeated Measurements {#error-statistics-in-repeated-measurements} -#### 8.1.2 The Normal Distribution {#8-dot-1-dot-2-the-normal-distribution} +#### The Normal Distribution {#the-normal-distribution} -#### 8.1.3 Combining Different Error Sources {#8-dot-1-dot-3-combining-different-error-sources} +#### Combining Different Error Sources {#combining-different-error-sources} -#### 8.1.4 Power Spectral Density and Cumulative Power {#8-dot-1-dot-4-power-spectral-density-and-cumulative-power} +#### Power Spectral Density and Cumulative Power {#power-spectral-density-and-cumulative-power} -#### 8.1.5 Do not use the Cumulative Amplitude Spectrum! {#8-dot-1-dot-5-do-not-use-the-cumulative-amplitude-spectrum} +#### Do not use the Cumulative Amplitude Spectrum! {#do-not-use-the-cumulative-amplitude-spectrum} -#### 8.1.6 Variations in Dynamic Error Budgeting {#8-dot-1-dot-6-variations-in-dynamic-error-budgeting} +#### Variations in Dynamic Error Budgeting {#variations-in-dynamic-error-budgeting} -#### 8.1.7 Sources of Noise and Disturbances {#8-dot-1-dot-7-sources-of-noise-and-disturbances} +#### Sources of Noise and Disturbances {#sources-of-noise-and-disturbances} -##### 8.1.7.1 Mechanical Noise {#8-dot-1-dot-7-dot-1-mechanical-noise} +##### Mechanical Noise {#mechanical-noise} -##### 8.1.7.2 Electronic Noise {#8-dot-1-dot-7-dot-2-electronic-noise} +##### Electronic Noise {#electronic-noise} -### 8.2 Sensor Signal Sensitivity {#8-dot-2-sensor-signal-sensitivity} +### Sensor Signal Sensitivity {#sensor-signal-sensitivity} -#### 8.2.1 Sensing Element {#8-dot-2-dot-1-sensing-element} +#### Sensing Element {#sensing-element} -#### 8.2.2 Converting an Impedance into an Electric Signal {#8-dot-2-dot-2-converting-an-impedance-into-an-electric-signal} +#### Converting an Impedance into an Electric Signal {#converting-an-impedance-into-an-electric-signal} -##### 8.2.2.1 Wheatstone Bridge {#8-dot-2-dot-2-dot-1-wheatstone-bridge} +##### Wheatstone Bridge {#wheatstone-bridge} -#### 8.2.3 Electronic Interconnection of Sensitive Signals {#8-dot-2-dot-3-electronic-interconnection-of-sensitive-signals} +#### Electronic Interconnection of Sensitive Signals {#electronic-interconnection-of-sensitive-signals} -##### 8.2.3.1 Magnetic Disturbances {#8-dot-2-dot-3-dot-1-magnetic-disturbances} +##### Magnetic Disturbances {#magnetic-disturbances} -##### 8.2.3.2 Capacitive Disturbances {#8-dot-2-dot-3-dot-2-capacitive-disturbances} +##### Capacitive Disturbances {#capacitive-disturbances} -##### 8.2.3.3 Ground Loops {#8-dot-2-dot-3-dot-3-ground-loops} +##### Ground Loops {#ground-loops} -### 8.3 Signal Conditioning {#8-dot-3-signal-conditioning} +### Signal Conditioning {#signal-conditioning} -#### 8.3.1 Instrumentation Amplifier {#8-dot-3-dot-1-instrumentation-amplifier} +#### Instrumentation Amplifier {#instrumentation-amplifier} -#### 8.3.2 Filtering and Modulation {#8-dot-3-dot-2-filtering-and-modulation} +#### Filtering and Modulation {#filtering-and-modulation} -##### 8.3.2.1 AM with Square Wave Carrier {#8-dot-3-dot-2-dot-1-am-with-square-wave-carrier} +##### AM with Square Wave Carrier {#am-with-square-wave-carrier} -##### 8.3.2.2 AM with Sinusoidal Carrier {#8-dot-3-dot-2-dot-2-am-with-sinusoidal-carrier} +##### AM with Sinusoidal Carrier {#am-with-sinusoidal-carrier} -### 8.4 Signal Processing {#8-dot-4-signal-processing} +### Signal Processing {#signal-processing} -#### 8.4.1 Schmitt Trigger {#8-dot-4-dot-1-schmitt-trigger} +#### Schmitt Trigger {#schmitt-trigger} -#### 8.4.2 Digital Representation of Measurement Data {#8-dot-4-dot-2-digital-representation-of-measurement-data} +#### Digital Representation of Measurement Data {#digital-representation-of-measurement-data} -##### 8.4.2.1 Gray Code {#8-dot-4-dot-2-dot-1-gray-code} +##### Gray Code {#gray-code} -##### 8.4.2.2 Sampling of Analogue Values {#8-dot-4-dot-2-dot-2-sampling-of-analogue-values} +##### Sampling of Analogue Values {#sampling-of-analogue-values} -##### 8.4.2.3 Nyquist-Shannon Theorem {#8-dot-4-dot-2-dot-3-nyquist-shannon-theorem} +##### Nyquist-Shannon Theorem {#nyquist-shannon-theorem} -##### 8.4.2.4 Filtering to Prevent Aliasing {#8-dot-4-dot-2-dot-4-filtering-to-prevent-aliasing} +##### Filtering to Prevent Aliasing {#filtering-to-prevent-aliasing} -#### 8.4.3 Analogue-to-Digital Converters {#8-dot-4-dot-3-analogue-to-digital-converters} +#### Analogue-to-Digital Converters {#analogue-to-digital-converters} -##### 8.4.3.1 Dual-Slope ADC {#8-dot-4-dot-3-dot-1-dual-slope-adc} +##### Dual-Slope ADC {#dual-slope-adc} -##### 8.4.3.2 Successive-Approximation ADC {#8-dot-4-dot-3-dot-2-successive-approximation-adc} +##### Successive-Approximation ADC {#successive-approximation-adc} -##### 8.4.3.3 Sigma-Delta ADC {#8-dot-4-dot-3-dot-3-sigma-delta-adc} +##### Sigma-Delta ADC {#sigma-delta-adc} -##### 8.4.3.4 ADC Latency in a Feedback Loop {#8-dot-4-dot-3-dot-4-adc-latency-in-a-feedback-loop} +##### ADC Latency in a Feedback Loop {#adc-latency-in-a-feedback-loop} -#### 8.4.4 Connecting the Less Sensitive Elements {#8-dot-4-dot-4-connecting-the-less-sensitive-elements} +#### Connecting the Less Sensitive Elements {#connecting-the-less-sensitive-elements} -##### 8.4.4.1 Characteristic Impedance {#8-dot-4-dot-4-dot-1-characteristic-impedance} +##### Characteristic Impedance {#characteristic-impedance} -##### 8.4.4.2 Non-Galvanic Connection {#8-dot-4-dot-4-dot-2-non-galvanic-connection} +##### Non-Galvanic Connection {#non-galvanic-connection} -### 8.5 Short-Range Motion Sensors {#8-dot-5-short-range-motion-sensors} +### Short-Range Motion Sensors {#short-range-motion-sensors} -#### 8.5.1 Optical Sensors {#8-dot-5-dot-1-optical-sensors} +#### Optical Sensors {#optical-sensors} -##### 8.5.1.1 Position Sensitive Detectors {#8-dot-5-dot-1-dot-1-position-sensitive-detectors} +##### Position Sensitive Detectors {#position-sensitive-detectors} -##### 8.5.1.2 Optical Deflectometer {#8-dot-5-dot-1-dot-2-optical-deflectometer} +##### Optical Deflectometer {#optical-deflectometer} -#### 8.5.2 Capacitive Position Sensors {#8-dot-5-dot-2-capacitive-position-sensors} +#### Capacitive Position Sensors {#capacitive-position-sensors} -##### 8.5.2.1 Linearising by Differential Measurement {#8-dot-5-dot-2-dot-1-linearising-by-differential-measurement} +##### Linearising by Differential Measurement {#linearising-by-differential-measurement} -##### 8.5.2.2 Accuracy Limits and Improvements {#8-dot-5-dot-2-dot-2-accuracy-limits-and-improvements} +##### Accuracy Limits and Improvements {#accuracy-limits-and-improvements} -##### 8.5.2.3 Sensing to Conductive Moving Plate {#8-dot-5-dot-2-dot-3-sensing-to-conductive-moving-plate} +##### Sensing to Conductive Moving Plate {#sensing-to-conductive-moving-plate} -#### 8.5.3 Inductive Position Sensors {#8-dot-5-dot-3-inductive-position-sensors} +#### Inductive Position Sensors {#inductive-position-sensors} -##### 8.5.3.1 Linear Variable Differential Transformer {#8-dot-5-dot-3-dot-1-linear-variable-differential-transformer} +##### Linear Variable Differential Transformer {#linear-variable-differential-transformer} -##### 8.5.3.2 Eddy-Current Sensors {#8-dot-5-dot-3-dot-2-eddy-current-sensors} +##### Eddy-Current Sensors {#eddy-current-sensors} -#### 8.5.4 Pneumatic Proximity Sensor or Air-Gage {#8-dot-5-dot-4-pneumatic-proximity-sensor-or-air-gage} +#### Pneumatic Proximity Sensor or Air-Gage {#pneumatic-proximity-sensor-or-air-gage} -### 8.6 Measurement of Mechanical Dynamics {#8-dot-6-measurement-of-mechanical-dynamics} +### Measurement of Mechanical Dynamics {#measurement-of-mechanical-dynamics} -#### 8.6.1 Measurement of Force and Strain {#8-dot-6-dot-1-measurement-of-force-and-strain} +#### Measurement of Force and Strain {#measurement-of-force-and-strain} -##### 8.6.1.1 Strain Gages {#8-dot-6-dot-1-dot-1-strain-gages} +##### Strain Gages {#strain-gages} -##### 8.6.1.2 Fibre Bragg Grating Strain Measurement {#8-dot-6-dot-1-dot-2-fibre-bragg-grating-strain-measurement} +##### Fibre Bragg Grating Strain Measurement {#fibre-bragg-grating-strain-measurement} -#### 8.6.2 Velocity Measurement {#8-dot-6-dot-2-velocity-measurement} +#### Velocity Measurement {#velocity-measurement} -##### 8.6.2.1 Geophone {#8-dot-6-dot-2-dot-1-geophone} +##### Geophone {#geophone} -#### 8.6.3 Accelerometers {#8-dot-6-dot-3-accelerometers} +#### Accelerometers {#accelerometers} -##### 8.6.3.1 Closed-Loop Feedback Accelerometer {#8-dot-6-dot-3-dot-1-closed-loop-feedback-accelerometer} +##### Closed-Loop Feedback Accelerometer {#closed-loop-feedback-accelerometer} -##### 8.6.3.2 Piezoelectric Accelerometer {#8-dot-6-dot-3-dot-2-piezoelectric-accelerometer} +##### Piezoelectric Accelerometer {#piezoelectric-accelerometer} -##### 8.6.3.3 MEMS Accelerometer {#8-dot-6-dot-3-dot-3-mems-accelerometer} +##### MEMS Accelerometer {#mems-accelerometer} -### 8.7 Optical Long-Range Incremental Position Sensors {#8-dot-7-optical-long-range-incremental-position-sensors} +### Optical Long-Range Incremental Position Sensors {#optical-long-range-incremental-position-sensors} -#### 8.7.1 Linear Optical Encoders {#8-dot-7-dot-1-linear-optical-encoders} +#### Linear Optical Encoders {#linear-optical-encoders} -##### 8.7.1.1 Interpolation {#8-dot-7-dot-1-dot-1-interpolation} +##### Interpolation {#interpolation} -##### 8.7.1.2 Vernier Resolution Enhancement {#8-dot-7-dot-1-dot-2-vernier-resolution-enhancement} +##### Vernier Resolution Enhancement {#vernier-resolution-enhancement} -##### 8.7.1.3 Interferometric Optical Encoder {#8-dot-7-dot-1-dot-3-interferometric-optical-encoder} +##### Interferometric Optical Encoder {#interferometric-optical-encoder} -##### 8.7.1.4 Concluding Remarks on Linear Encoders {#8-dot-7-dot-1-dot-4-concluding-remarks-on-linear-encoders} +##### Concluding Remarks on Linear Encoders {#concluding-remarks-on-linear-encoders} -#### 8.7.2 Laser Interferometer Measurement Systems {#8-dot-7-dot-2-laser-interferometer-measurement-systems} +#### Laser Interferometer Measurement Systems {#laser-interferometer-measurement-systems} -##### 8.7.2.1 Homodyne Distance Interferometry {#8-dot-7-dot-2-dot-1-homodyne-distance-interferometry} +##### Homodyne Distance Interferometry {#homodyne-distance-interferometry} -##### 8.7.2.2 Heterodyne Distance Interferometry {#8-dot-7-dot-2-dot-2-heterodyne-distance-interferometry} +##### Heterodyne Distance Interferometry {#heterodyne-distance-interferometry} -##### 8.7.2.3 Measurement Uncertainty {#8-dot-7-dot-2-dot-3-measurement-uncertainty} +##### Measurement Uncertainty {#measurement-uncertainty} -##### 8.7.2.4 Configurations {#8-dot-7-dot-2-dot-4-configurations} +##### Configurations {#configurations} -##### 8.7.2.5 Multi-Axis Laser Interferometers {#8-dot-7-dot-2-dot-5-multi-axis-laser-interferometers} +##### Multi-Axis Laser Interferometers {#multi-axis-laser-interferometers} -#### 8.7.3 Mechanical Aspects {#8-dot-7-dot-3-mechanical-aspects} +#### Mechanical Aspects {#mechanical-aspects} -##### 8.7.3.1 Abbe Error {#8-dot-7-dot-3-dot-1-abbe-error} +##### Abbe Error {#abbe-error} -## 9 Precision Positioning in Wafer Scanners {#9-precision-positioning-in-wafer-scanners} +## Precision Positioning in Wafer Scanners {#precision-positioning-in-wafer-scanners} ### Introduction {#introduction} -### 9.1 The Waferscanner {#9-dot-1-the-waferscanner} +### The Waferscanner {#the-waferscanner} -#### 9.1.1 Requirements on Precision {#9-dot-1-dot-1-requirements-on-precision} +#### Requirements on Precision {#requirements-on-precision} -### 9.2 Dynamic Architecture {#9-dot-2-dynamic-architecture} +### Dynamic Architecture {#dynamic-architecture} -#### 9.2.1 Balance Masses {#9-dot-2-dot-1-balance-masses} +#### Balance Masses {#balance-masses} -#### 9.2.2 Vibration Isolation {#9-dot-2-dot-2-vibration-isolation} +#### Vibration Isolation {#vibration-isolation} -##### 9.2.2.1 Eigendynamics of the Sensitive Parts {#9-dot-2-dot-2-dot-1-eigendynamics-of-the-sensitive-parts} +##### Eigendynamics of the Sensitive Parts {#eigendynamics-of-the-sensitive-parts} -### 9.3 Zero-Stiffness Stage Actuation {#9-dot-3-zero-stiffness-stage-actuation} +### Zero-Stiffness Stage Actuation {#zero-stiffness-stage-actuation} -#### 9.3.1 Waferstage Actuation Concept {#9-dot-3-dot-1-waferstage-actuation-concept} +#### Waferstage Actuation Concept {#waferstage-actuation-concept} -##### 9.3.1.1 Waferstepper Long-Range Lorentz Actuator {#9-dot-3-dot-1-dot-1-waferstepper-long-range-lorentz-actuator} +##### Waferstepper Long-Range Lorentz Actuator {#waferstepper-long-range-lorentz-actuator} -##### 9.3.1.2 Multi-Axis Positioning {#9-dot-3-dot-1-dot-2-multi-axis-positioning} +##### Multi-Axis Positioning {#multi-axis-positioning} -##### 9.3.1.3 Long- and Short-Stroke Actuation {#9-dot-3-dot-1-dot-3-long-and-short-stroke-actuation} +##### Long- and Short-Stroke Actuation {#long-and-short-stroke-actuation} -#### 9.3.2 Full Magnetic Levitation {#9-dot-3-dot-2-full-magnetic-levitation} +#### Full Magnetic Levitation {#full-magnetic-levitation} -#### 9.3.3 Acceleration Limits of Reticle Stage {#9-dot-3-dot-3-acceleration-limits-of-reticle-stage} +#### Acceleration Limits of Reticle Stage {#acceleration-limits-of-reticle-stage} -### 9.4 Position Measurement {#9-dot-4-position-measurement} +### Position Measurement {#position-measurement} -#### 9.4.1 Alignment Sensor {#9-dot-4-dot-1-alignment-sensor} +#### Alignment Sensor {#alignment-sensor} -#### 9.4.2 Keeping the Wafer in Focus {#9-dot-4-dot-2-keeping-the-wafer-in-focus} +#### Keeping the Wafer in Focus {#keeping-the-wafer-in-focus} -#### 9.4.3 Dual-Stage Measurement and Exposure {#9-dot-4-dot-3-dual-stage-measurement-and-exposure} +#### Dual-Stage Measurement and Exposure {#dual-stage-measurement-and-exposure} -#### 9.4.4 Long-Range Incremental Measurement System {#9-dot-4-dot-4-long-range-incremental-measurement-system} +#### Long-Range Incremental Measurement System {#long-range-incremental-measurement-system} -##### 9.4.4.1 Real-Time Metrology Loop {#9-dot-4-dot-4-dot-1-real-time-metrology-loop} +##### Real-Time Metrology Loop {#real-time-metrology-loop} -### 9.5 Motion Control {#9-dot-5-motion-control} +### Motion Control {#motion-control} -#### 9.5.1 Feedforward and Feedback Control {#9-dot-5-dot-1-feedforward-and-feedback-control} +#### Feedforward and Feedback Control {#feedforward-and-feedback-control} -##### 9.5.1.1 Thermal, The Final Frontier {#9-dot-5-dot-1-dot-1-thermal-the-final-frontier} +##### Thermal, The Final Frontier {#thermal-the-final-frontier} -#### 9.5.2 The Mass Dilemma {#9-dot-5-dot-2-the-mass-dilemma} +#### The Mass Dilemma {#the-mass-dilemma} > A reduced mass requires improved system dynamics that enable a higher control bandwidth to compensate for the increase sensitivity for external vibrations. -### 9.6 Future Developments in IC Lithography {#9-dot-6-future-developments-in-ic-lithography} +### Future Developments in IC Lithography {#future-developments-in-ic-lithography} -### 9.7 Main Design Rules for Precision {#9-dot-7-main-design-rules-for-precision} +### Main Design Rules for Precision {#main-design-rules-for-precision} ## Bibliography {#bibliography} -Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2020. _The Design of High Performance Mechatronics - Third Revised Edition_. Ios Press. +Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2020. _The Design of High Performance Mechatronics - Third Revised Edition_. 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