From 221e9605b9687aa10cb1326708ba2d94fd7f789e Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Sun, 11 Oct 2026 10:33:38 +0200 Subject: [PATCH] Update content - 2026-10-11 --- ..._vibrat_contr_activ_struc_fourt_edition.md | 1033 ++------------ ..._high_perfor_mechat_third_revis_edition.md | 1236 +---------------- content/book/wardle15_ultra_precis_bearin.md | 10 +- content/zettels/heat_transfer.md | 2 +- content/zettels/system_identification.md | 2 +- 5 files changed, 86 insertions(+), 2197 deletions(-) diff --git a/content/book/preumont18_vibrat_contr_activ_struc_fourt_edition.md b/content/book/preumont18_vibrat_contr_activ_struc_fourt_edition.md index cc1255c..5d2f5a4 100644 --- a/content/book/preumont18_vibrat_contr_activ_struc_fourt_edition.md +++ b/content/book/preumont18_vibrat_contr_activ_struc_fourt_edition.md @@ -18,6 +18,22 @@ Author(s) Year : 2018 +
+\( +\newcommand{\SI}[2]{#1\,#2} +% Simulate SIunitx +\newcommand{\ang}[1]{#1^{\circ}} +\newcommand{\degree}{^{\circ}} +\newcommand{\radian}{\text{rad}} +\newcommand{\percent}{\%} +\newcommand{\decibel}{\text{dB}} +\newcommand{\per}{/} +% Bug with subequations +\newcommand{\eatLabel}[2]{} +\newenvironment{subequations}{\eatLabel}{} +\) +
+ ## Introduction {#introduction} @@ -253,7 +269,7 @@ The general form of the equation of motion governing the dynamic equilibrium bet
-\begin{equation} +\begin{equation}\label{eq:general\_eom} M \ddot{x} + C \dot{x} + K x = f \end{equation} @@ -269,7 +285,7 @@ The damping matrix \\(C\\) represents the various dissipation mechanisms in the
-\begin{equation} +\begin{equation}\label{eq:rayleigh\_damping} C = \alpha M + \beta K \end{equation} @@ -311,7 +327,7 @@ Let perform a change of variable from physical coordinates \\(x\\) to modal coor
-\begin{equation} +\begin{equation}\label{eq:modal\_cov} x = \Phi z \end{equation} @@ -337,7 +353,7 @@ And we obtain decoupled modal equations \ref{eq:modal\_eom}.
-\begin{equation} +\begin{equation}\label{eq:modal\_eom} \ddot{z} + 2 \xi \Omega \dot{z} + \Omega^2 z = z^{-1} \Phi^T f \end{equation} @@ -349,7 +365,7 @@ with:
-Typical values of the modal damping ratio are summarized on table . +Typical values of the modal damping ratio are summarized on table [Table 2](#table--tab:damping-ratio).
@@ -382,7 +398,7 @@ Where \\(G(\omega)\\) is called the **Dynamic flexibility Matrix**: From the modal expansion of the dynamic flexibility matrix can be obtained by coordinate transformation \\(x = \phi z\\) and we obtain: -\begin{equation} +\begin{equation}\label{eq:dynamic\_flexibility\_modal} G(\omega) = \sum\_{i=1}^n \frac{\phi\_i \phi\_i^T}{\mu\_i \omega\_i^2} D\_i(\omega) \end{equation} @@ -390,7 +406,7 @@ With: - \\(D\_i(\omega)\\) is the dynamic amplification factor of mode \\(i\\) given by -\begin{equation} +\begin{equation}\label{eq:dynamic\_amplification} D\_i(\omega) = \frac{1}{1 - \omega^2/\omega\_i^2 + 2 j \xi\_i \omega/\omega\_i} \end{equation} @@ -406,9 +422,6 @@ And \\(G(\omega)\\) can be rewritten on terms of the **low frequency modes only* The quasi-static correction of the high frequency modes \\(R\\) is called the **residual mode**. This introduces a **feedthrough** component in the transfer matrix. -#### Structure with Rigid Body Modes {#structure-with-rigid-body-modes} - - ### Collocated Control System {#collocated-control-system}
@@ -475,7 +488,7 @@ By looking at [Figure 7](#figure--fig:collocated-control-frf), we see that negle The open-loop transfer function of a lighly damped structure with a collocated actuator/sensor pair can be written: -\begin{equation} +\begin{equation}\label{eq:frf\_lighly\_damped\_collocated} G(s) = G\_0 \frac{\Pi\_i(s^2/z\_i^2 + 2 \xi\_i s/z\_i + 1)}{\Pi\_j(s^2/\omega\_j^2 + 2 \xi\_j s /\omega\_j + 1)} \end{equation} @@ -521,7 +534,7 @@ We note: **Faraday's law**: -\begin{equation} +\begin{equation}\label{eq:vc\_first\_equation} e = 2\pi n r B v = T v \end{equation} @@ -529,7 +542,7 @@ With \\(T = 2\pi n r B\\) is the **transducer constant**. **Lorentz force law**: -\begin{equation} +\begin{equation}\label{eq:vc\_second\_equation} f = -i 2\pi n r B = - T i \end{equation} @@ -562,7 +575,7 @@ The transfer function between the total force and the current \\(i\\) applied to
-\begin{equation} +\begin{equation}\label{eq:proof\_mass\_eq} \frac{F}{i} = \frac{-s^2 T}{s^2 + 2\xi\_p \omega\_p s + \omega\_p^2} \end{equation} @@ -595,7 +608,7 @@ If \\(x\_0\\) is the displacement of the support and if the voice coil is open ( By using the two equations, we obtain: -\begin{equation} +\begin{equation}\label{eq:geophone} \frac{e}{\dot{x\_0}} = \frac{-s^2 T}{s^2 + 2\xi\_p\omega\_p s + \omega\_p^2} \end{equation} @@ -630,8 +643,8 @@ With: - \\(f\\) is the force applied to the mechanical terminals - \\(v\\) is the velocity of the mechanical part - \\(Z\_e\\) is the blocked electrical impedance (for \\(v=0\\)) -- \\(T\_{em}\\) is the transduction coefficient representing the electromotive force (in \\(\si{\volt\second\per\meter}\\)) -- \\(T\_{me}\\) is the transduction coefficient representing the force acting on the mechanical terminals to balance the electromagnetic force induced per unit current input (in \\(\si{\newton\per\ampere}\\)) +- \\(T\_{em}\\) is the transduction coefficient representing the electromotive force (in \\(Vs/m\\)) +- \\(T\_{me}\\) is the transduction coefficient representing the force acting on the mechanical terminals to balance the electromagnetic force induced per unit current input (in \\(N/A\\)) - \\(Z\_m\\) is the mechanical impedance measured when \\(i=0\\) Equation \ref{eq:gen\_trans\_e} shows that the voltage across the electrical terminals of any electromechanical transducer is the sum of a contribution proportional to the current applied and a contribution proportional to the velocity of the mechanical terminals. @@ -641,7 +654,7 @@ To do so, the bridge circuit as shown on [Figure 15](#figure--fig:bridge-circuit We can show that -\begin{equation} +\begin{equation}\label{eq:bridge\_eq} V\_4 - V\_2 = \frac{-Z\_b T\_{em}}{Z\_e + Z\_b} v \end{equation} @@ -684,7 +697,7 @@ We here consider a transducer made of one-dimensional piezoelectric material.
-\begin{subequations} +\begin{subequations}\label{eq:piezo\_eq} \begin{align} D & = \epsilon^T E + d\_{33} T\\\\ S & = d\_{33} E + s^E T @@ -708,28 +721,36 @@ With: The set of equations \ref{eq:piezo\_eq} can be written in a matrix form: -\begin{equation} -\begin{bmatrix}D\\\S\end{bmatrix} -= +\begin{equation}\label{eq:piezo\_eq\_matrix} \begin{bmatrix} -\epsilon^T & d\_{33}\\\\ -d\_{33} & s^E + D \\\\ + S +\end{bmatrix} = \begin{bmatrix} + \epsilon^T & d\_{33}\\\\ + d\_{33} & s^E +\end{bmatrix} +\begin{bmatrix} + E \\\\ + T \end{bmatrix} -\begin{bmatrix}E\\\T\end{bmatrix} \end{equation} Where \\((E, T)\\) are the independent variables and \\((D, S)\\) are the dependent variable. If \\((E, S)\\) are taken as independant variables: -\begin{equation} -\begin{bmatrix}D\\\T\end{bmatrix} -= +\begin{equation}\label{eq:piezo\_eq\_matrix\_bis} \begin{bmatrix} -\epsilon^T(1-k^2) & e\_{33}\\\\ --e\_{33} & c^E + D \\\\ + T +\end{bmatrix} = \begin{bmatrix} + \epsilon^T(1-k^2) & e\_{33}\\\\ + -e\_{33} & c^E +\end{bmatrix} +\begin{bmatrix} + E \\\\ + S \end{bmatrix} -\begin{bmatrix}E\\\S\end{bmatrix} \end{equation} With: @@ -739,7 +760,7 @@ With:
-\begin{equation} +\begin{equation}\label{eq:electromechanical\_coupling\_factor} k^2 = \frac{{d\_{33}}^2}{s^E \epsilon^T} = \frac{{e\_{33}}^2}{c^E \epsilon^T} \end{equation} @@ -750,14 +771,18 @@ It measures the efficiency of the conversion of the mechanical energy into elect If one assumes that all the electrical and mechanical quantities are uniformly distributed in a linear transducer formed by a **stack** (see [Figure 17](#figure--fig:piezo-stack)) of \\(n\\) disks of thickness \\(t\\) and cross section \\(A\\), the global constitutive equations of the transducer are obtained by integrating \ref{eq:piezo\_eq\_matrix\_bis} over the volume of the transducer: -\begin{equation} -\begin{bmatrix}Q\\\\Delta\end{bmatrix} -= +\begin{equation}\label{eq:piezo\_stack\_eq} \begin{bmatrix} -C & nd\_{33}\\\\ -nd\_{33} & 1/K\_a + Q \\\\ + \Delta +\end{bmatrix} = \begin{bmatrix} + C & nd\_{33} \\\\ + nd\_{33} & 1/K\_a +\end{bmatrix} +\begin{bmatrix} + V \\\\ + f \end{bmatrix} -\begin{bmatrix}V\\\f\end{bmatrix} \end{equation} where @@ -775,15 +800,19 @@ where Equation \ref{eq:piezo\_stack\_eq} can be inverted to obtain -\begin{equation} -\begin{bmatrix}V\\\f\end{bmatrix} -= -\frac{K\_a}{C(1-k^2)} +\begin{equation}\label{eq:piezo\_stack\_eq\_inv} \begin{bmatrix} -1/K\_a & -nd\_{33}\\\\ --nd\_{33} & C + V \\\\ + f +\end{bmatrix} = \frac{K\_a}{C(1-k^2)} +\begin{bmatrix} + 1/K\_a & -nd\_{33} \\\\ + -nd\_{33} & C +\end{bmatrix} +\begin{bmatrix} + Q \\\\ + \Delta \end{bmatrix} -\begin{bmatrix}Q\\\\Delta\end{bmatrix} \end{equation} @@ -793,7 +822,7 @@ Let us write the total stored electromechanical energy of a discrete piezoelectr The total power delivered to the transducer is the sum of electric power \\(V i\\) and the mechanical power \\(f \dot{\Delta}\\). The net work of the transducer is -\begin{equation} +\begin{equation}\label{eq:piezo\_work} dW = V i dt + f \dot{\Delta} dt = V dQ + f d\Delta \end{equation} @@ -803,7 +832,7 @@ The total power delivered to the transducer is the sum of electric power \\(V i\ By integrating equation \ref{eq:piezo\_work} and using the constitutive equations \ref{eq:piezo\_stack\_eq\_inv}, we obtain the analytical expression of the stored electromechanical energy for the discrete transducer: -\begin{equation} +\begin{equation}\label{eq:piezo\_stack\_work} W\_e(\Delta, Q) = \frac{Q^2}{2 C (1 - k^2)} - \frac{n d\_{33} K\_a}{C(1-k^2)} Q\Delta + \frac{K\_a}{1-k^2}\frac{\Delta^2}{2} \end{equation} @@ -840,7 +869,7 @@ The force acting on the mass is negative of that acting on the transducer, \\(f From the constitutive equations, one finds -\begin{equation} +\begin{equation}\label{eq:piezo\_stack\_admittance} \frac{I}{V} = s C (1-k^2) \frac{s^2 + z^2}{s^2 + p^2} \end{equation} @@ -849,7 +878,7 @@ where the poles and zeros are respectively And one can see that -\begin{equation} +\begin{equation}\label{eq:distance\_p\_z} \frac{z^2 - p^2}{z^2} = k^2 \end{equation} @@ -860,687 +889,9 @@ Equation \ref{eq:distance\_p\_z} constitutes a practical way to determine the el {{< figure src="/ox-hugo/preumont18_piezo_admittance_curve.png" caption="Figure 20: Typical admittance FRF of the transducer" >}} -## Piezoelectric Beam, Plate and Truss {#piezoelectric-beam-plate-and-truss} - - -### Piezoelectric Material {#piezoelectric-material} - - -#### Constitutive Relations {#constitutive-relations} - - -#### Coenergy Density Function {#coenergy-density-function} - - -### Hamilton's Principle {#hamilton-s-principle} - - -### Piezoelectric Beam Actuator {#piezoelectric-beam-actuator} - - -#### Hamilton's Principle {#hamilton-s-principle} - - -#### Piezoelectric Loads {#piezoelectric-loads} - - -### Laminar Sensor {#laminar-sensor} - - -#### Current and Charge Amplifiers {#current-and-charge-amplifiers} - - -#### Distributed Sensor Output {#distributed-sensor-output} - - -#### Charge Amplifier Dynamics {#charge-amplifier-dynamics} - - -### Spatial Modal Filters {#spatial-modal-filters} - - -#### Modal Actuator {#modal-actuator} - - -#### Modal Sensor {#modal-sensor} - - -### Active Beam with Collocated Actuator/Sensor {#active-beam-with-collocated-actuator-sensor} - - -#### Frequency Response Function {#frequency-response-function} - - -#### Pole-Zero Pattern {#pole-zero-pattern} - - -#### Modal Truncation {#modal-truncation} - - -### Admittance of a Beam with a Piezoelectric Patch {#admittance-of-a-beam-with-a-piezoelectric-patch} - - -### Piezoelectric Laminate {#piezoelectric-laminate} - - -#### Two-Dimensional Constitutive Equations {#two-dimensional-constitutive-equations} - - -#### Kirchhoff Theory {#kirchhoff-theory} - - -#### Stiffness Matrix of a Multilayer Elastic Laminate {#stiffness-matrix-of-a-multilayer-elastic-laminate} - - -#### Multilayer Laminate with a Piezoelectric Layer {#multilayer-laminate-with-a-piezoelectric-layer} - - -#### Equivalent Piezoelectric Loads {#equivalent-piezoelectric-loads} - - -#### Sensor Output {#sensor-output} - - -#### Beam Model Versus Plate Model {#beam-model-versus-plate-model} - - -#### Additional Remarks {#additional-remarks} - - -### Active Truss {#active-truss} - - -#### Open-Loop Transfer Function {#open-loop-transfer-function} - - -#### Admittance Function {#admittance-function} - - -### Finite Element Formulation {#finite-element-formulation} - - -### Problems {#problems} - - -### References {#references} - - -## Passive Damping with Piezoelectric Transducers {#passive-damping-with-piezoelectric-transducers} - - -### Introduction {#introduction} - - -### Resistive Shunting {#resistive-shunting} - - -### Inductive Shunting {#inductive-shunting} - - -#### Equal Peak Design {#equal-peak-design} - - -#### Robustness of the Equal Peak Design {#robustness-of-the-equal-peak-design} - - -### Switched Shunt {#switched-shunt} - - -#### Equivalent Damping Ratio {#equivalent-damping-ratio} - - -## BKMK Collocated Versus Non-collocated Control {#bkmk-collocated-versus-non-collocated-control} - - -### Pole-Zero Flipping {#pole-zero-flipping} - -
- -The Root Locus shows, in a graphical form, the evolution of the poles of the closed-loop system as a function of the scalar gain \\(g\\) applied to the compensator. -The Root Locus is the locus of the solution \\(s\\) of the closed loop characteristic equation \\(1 + gG(s)H(s) = 0\\) when \\(g\\) goes from zero to infinity. - -
- -If the open-loop transfer function is written -\\[ G(s)H(s) = k \frac{\Pi\_{i=1}^{m} (s - z\_i)}{\Pi\_{i=1}^{n} (s - p\_i)} \\] -The locus goes from the poles \\(p\_i\\) (for \\(g=0\\)) to the zeros \\(z\_i\\) (as \\(g \rightarrow \infty\\)). - - -### The Two-Mass Problem {#the-two-mass-problem} - - -#### Collocated Control {#collocated-control} - - -#### Non-collocated Control {#non-collocated-control} - - -### Notch Filter {#notch-filter} - - -### Effect of Pole-Zero Flipping on the Bode Plots {#effect-of-pole-zero-flipping-on-the-bode-plots} - - -### Nearly Collocated Control System {#nearly-collocated-control-system} - - -### Non-collocated Control Systems {#non-collocated-control-systems} - - -### The Role of Damping {#the-role-of-damping} - - -## Active Damping with Collocated System {#active-damping-with-collocated-system} - - -### Introduction {#introduction} - -The role of active damping is to increase the negative real parts of system poles wile maintaining the natural frequencies essentially unchanged. - -Active damping requires relatively little control effort; this is why it is also called Low Authority Control (LAC). -Other control strategies which fully relocate the closed loop poles are called High Autority Control (HAC). - - -### Lead Control {#lead-control} - -\\[H(s) = g \frac{s+z}{z+p} \quad p \gg z \\] - -It produces a phase lead in the frequency band between \\(z\\) and \\(p\\), bringing active damping to all the modes belonging to \\(z < \omega\_i < p\\). - -The closed-loop poles start at the open-llop poles for \\(g=0\\) and go to the open-loop zeros for \\(g\rightarrow\infty\\). - -The controller does not have any roll-off, but the roll-off of the structure is enough to guarantee gain stability at high frequency. - - -### Direct Velocity Feedback (DVF) {#direct-velocity-feedback--dvf} - -This is a particular case of the Lead controller as \\(z\rightarrow 0\\) and \\(p\rightarrow\infty\\). - -Structure: -\\[M \ddot{x} + K x = b u\\] - -Output is a velocity sensor: -\\[y = b^T \dot{x}\\] - -Control: -\\[u = -g y\\] - - -### Positive Position Feedback (PPF) {#positive-position-feedback--ppf} - -Sometimes the plant does not have a roll-off of \\(-40dB/\text{decade}\\), then we can use a second-order PPF: -\\[H(s) = \frac{-g}{s^2 + 2 \xi\_f \omega\_f s + {\omega\_f}^2}\\] - - -### Integral Force Feedback (IFF) {#integral-force-feedback--iff} - - -### Duality Between the Lead and the IFF Controllers {#duality-between-the-lead-and-the-iff-controllers} - - -#### Root Locus of a Single Mode {#root-locus-of-a-single-mode} - - -#### Open-Loop Poles and Zeros {#open-loop-poles-and-zeros} - - -### Actuator and Sensor Dynamics {#actuator-and-sensor-dynamics} - - -### Decentralized Control with Collocated Pairs {#decentralized-control-with-collocated-pairs} - - -#### Cross talk {#cross-talk} - - -#### Force Actuator and Displacement Sensor {#force-actuator-and-displacement-sensor} - - -#### Displacement Actuator and Force Sensor {#displacement-actuator-and-force-sensor} - - -### Proof of Equation (7.18)–(7.32) {#proof-of-equation--7-dot-18----7-dot-32} - - -## Vibration Isolation {#vibration-isolation} - - -### Introduction {#introduction} - - -### Relaxation Isolator {#relaxation-isolator} - - -#### Electromagnetic Realization {#electromagnetic-realization} - - -### Active Isolation {#active-isolation} - - -#### Sky-Hook Damper {#sky-hook-damper} - - -#### Integral Force Feedback {#integral-force-feedback} - - -### Flexible Body {#flexible-body} - - -#### Free-Free Beam with Isolator {#free-free-beam-with-isolator} - - -### Payload Isolation in Spacecraft {#payload-isolation-in-spacecraft} - - -#### Interaction Isolator/Attitude Control {#interaction-isolator-attitude-control} - - -#### Gough–Stewart Platform {#gough-stewart-platform} - - -### Six-Axis Isolator {#six-axis-isolator} - - -#### Relaxation Isolator {#relaxation-isolator} - - -#### Integral Force Feedback {#integral-force-feedback} - - -#### Spherical Joints, Modal Spread {#spherical-joints-modal-spread} - - -### Active Versus Passive {#active-versus-passive} - - -### Car Suspension {#car-suspension} - - -## State Space Approach {#state-space-approach} - - -### Introduction {#introduction} - - -### State Space Description {#state-space-description} - - -#### Single Degree of Freedom Oscillator {#single-degree-of-freedom-oscillator} - - -#### Flexible Structure {#flexible-structure} - - -#### Inverted Pendulum {#inverted-pendulum} - - -### System Transfer Function {#system-transfer-function} - - -#### Poles and Zeros {#poles-and-zeros} - - -### Pole Placement by State Feedback {#pole-placement-by-state-feedback} - - -#### Example: Oscillator {#example-oscillator} - - -### Linear Quadratic Regulator {#linear-quadratic-regulator} - - -#### Symmetric Root Locus {#symmetric-root-locus} - - -#### Inverted Pendulum {#inverted-pendulum} - - -### Observer Design {#observer-design} - - -### Kalman Filter {#kalman-filter} - - -#### Inverted Pendulum {#inverted-pendulum} - - -### Reduced-Order Observer {#reduced-order-observer} - - -#### Oscillator {#oscillator} - - -#### Inverted Pendulum {#inverted-pendulum} - - -### Separation Principle {#separation-principle} - - -### Transfer Function of the Compensator {#transfer-function-of-the-compensator} - - -#### The Two-Mass Problem {#the-two-mass-problem} - - -## Analysis and Synthesis in the Frequency Domain {#analysis-and-synthesis-in-the-frequency-domain} - - -### Gain and Phase Margins {#gain-and-phase-margins} - - -### Nyquist Criterion {#nyquist-criterion} - - -#### Cauchy's Principle {#cauchy-s-principle} - - -#### Nyquist Stability Criterion {#nyquist-stability-criterion} - - -### Nichols Chart {#nichols-chart} - - -### Feedback Specification for SISO Systems {#feedback-specification-for-siso-systems} - - -#### Sensitivity {#sensitivity} - - -#### Tracking Error {#tracking-error} - - -#### Performance Specification {#performance-specification} - - -#### Unstructured Uncertainty {#unstructured-uncertainty} - - -#### Robust Performance and Robust Stability {#robust-performance-and-robust-stability} - - -### Bode Gain–Phase Relationships {#bode-gain-phase-relationships} - - -### The Bode Ideal Cutoff {#the-bode-ideal-cutoff} - - -### Non-minimum Phase Systems {#non-minimum-phase-systems} - - -### Usual Compensators {#usual-compensators} - - -#### System Type {#system-type} - - -#### Lead Compensator {#lead-compensator} - - -#### PI Compensator {#pi-compensator} - - -#### Lag Compensator {#lag-compensator} - - -#### PID Compensator {#pid-compensator} - - -### Multivariable Systems {#multivariable-systems} - - -#### Performance Specification {#performance-specification} - - -#### Small Gain Theorem {#small-gain-theorem} - - -#### Stability Robustness Tests {#stability-robustness-tests} - - -#### Residual Dynamics {#residual-dynamics} - - -## Optimal Control {#optimal-control} - - -### Introduction {#introduction} - - -### Quadratic Integral {#quadratic-integral} - - -### Deterministic LQR {#deterministic-lqr} - - -### Stochastic Response to a White Noise {#stochastic-response-to-a-white-noise} - - -#### Remark {#remark} - - -### Stochastic LQR {#stochastic-lqr} - - -### Asymptotic Behavior of the Closed Loop {#asymptotic-behavior-of-the-closed-loop} - - -### Prescribed Degree of Stability {#prescribed-degree-of-stability} - - -### Gain and Phase Margins of the LQR {#gain-and-phase-margins-of-the-lqr} - - -### Full State Observer {#full-state-observer} - - -#### Covariance of the Reconstruction Error {#covariance-of-the-reconstruction-error} - - -### Kalman Filter (KF) {#kalman-filter--kf} - - -### Linear Quadratic Gaussian (LQG) {#linear-quadratic-gaussian--lqg} - - -### Duality {#duality} - - -### Spillover {#spillover} - - -#### Spillover Reduction {#spillover-reduction} - - -### Loop Transfer Recovery (LTR) {#loop-transfer-recovery--ltr} - - -### Integral Control with State Feedback {#integral-control-with-state-feedback} - - -### Frequency Shaping {#frequency-shaping} - -Weakness of LQG: - -- use frequency independant cost function -- use noise statistics with uniform distribution - -To overcome the weakness => frequency shaping either by: - -- considering a frequency dependant cost function -- using colored noise statistics - - -#### Frequency-Shaped Cost Functionals {#frequency-shaped-cost-functionals} - - -#### Noise Model {#noise-model} - - -## Controllability and Observability {#controllability-and-observability} - - -### Introduction {#introduction} - - -#### Definitions {#definitions} - - -### Controllability and Observability Matrices {#controllability-and-observability-matrices} - - -### Examples {#examples} - - -#### Cart with Two Inverted Pendulums {#cart-with-two-inverted-pendulums} - - -#### Double Inverted Pendulum {#double-inverted-pendulum} - - -#### Two d.o.f. Oscillator {#two-d-dot-o-dot-f-dot-oscillator} - - -### State Transformation {#state-transformation} - - -#### Control Canonical Form {#control-canonical-form} - - -#### Left and Right Eigenvectors {#left-and-right-eigenvectors} - - -#### Diagonal Form {#diagonal-form} - - -### PBH Test {#pbh-test} - - -### Residues {#residues} - - -### Example {#example} - - -### Sensitivity {#sensitivity} - - -### Controllability and Observability Gramians {#controllability-and-observability-gramians} - - -### Internally Balanced Coordinates {#internally-balanced-coordinates} - - -### Model Reduction {#model-reduction} - - -#### Transfer Equivalent Realization {#transfer-equivalent-realization} - - -#### Internally Balanced Realization {#internally-balanced-realization} - - -#### Example {#example} - - -## Stability {#stability} - - -### Introduction {#introduction} - - -#### Phase Portrait {#phase-portrait} - - -### Linear Systems {#linear-systems} - - -#### Routh--Hurwitz Criterion {#routh-hurwitz-criterion} - - -### Lyapunov's Direct Method {#lyapunov-s-direct-method} - - -#### Introductory Example {#introductory-example} - - -#### Stability Theorem {#stability-theorem} - - -#### Asymptotic Stability Theorem {#asymptotic-stability-theorem} - - -#### Lasalle's Theorem {#lasalle-s-theorem} - - -#### Geometric Interpretation {#geometric-interpretation} - - -#### Instability Theorem {#instability-theorem} - - -### Lyapunov Functions for Linear Systems {#lyapunov-functions-for-linear-systems} - - -### Lyapunov's Indirect Method {#lyapunov-s-indirect-method} - - -### An Application to Controller Design {#an-application-to-controller-design} - - -### Energy Absorbing Controls {#energy-absorbing-controls} - - ## Applications {#applications} -### Digital Implementation {#digital-implementation} - - -#### Sampling, Aliasing, and Prefiltering {#sampling-aliasing-and-prefiltering} - - -#### Zero-Order Hold, Computational Delay {#zero-order-hold-computational-delay} - - -#### Quantization {#quantization} - - -#### Discretization of a Continuous Controller {#discretization-of-a-continuous-controller} - - -### Active Damping of a Truss Structure {#active-damping-of-a-truss-structure} - - -#### Actuator Placement {#actuator-placement} - - -#### Implementation, Experimental Results {#implementation-experimental-results} - - -### Active Damping Generic Interface {#active-damping-generic-interface} - - -#### Active Damping {#active-damping} - - -#### Experiment {#experiment} - - -#### Pointing and Position Control {#pointing-and-position-control} - - -### Active Damping of a Plate {#active-damping-of-a-plate} - - -#### Control Design {#control-design} - - -### Active Damping of a Stiff Beam {#active-damping-of-a-stiff-beam} - - -#### System Design {#system-design} - - ### The HAC/LAC Strategy {#the-hac-lac-strategy} In active structures for precision engineering applications, the control system is used to reduce the effect of transient and steady-state disturbances on the controlled variables. @@ -1574,234 +925,6 @@ This approach has the following advantages: #### Results {#results} -### Vibroacoustics: Volume Displacement Sensors {#vibroacoustics-volume-displacement-sensors} - - -#### QWSIS Sensor {#qwsis-sensor} - - -#### Discrete Array Sensor {#discrete-array-sensor} - - -#### Spatial Aliasing {#spatial-aliasing} - - -#### Distributed Sensor {#distributed-sensor} - - -## Tendon Control of Cable Structures {#tendon-control-of-cable-structures} - - -### Introduction {#introduction} - - -### Tendon Control of Strings and Cables {#tendon-control-of-strings-and-cables} - - -### Active Damping Strategy {#active-damping-strategy} - - -### Basic Experiment {#basic-experiment} - - -### Linear Theory of Decentralized Active Damping {#linear-theory-of-decentralized-active-damping} - - -### Guyed Truss Experiment {#guyed-truss-experiment} - - -### Microprecision Interferometer Testbed {#microprecision-interferometer-testbed} - - -### Free-Floating Truss Experiment {#free-floating-truss-experiment} - - -### Application to Cable-Stayed Bridges {#application-to-cable-stayed-bridges} - - -#### Laboratory Experiment {#laboratory-experiment} - - -#### Control of Parametric Resonance {#control-of-parametric-resonance} - - -#### Large Scale Experiment {#large-scale-experiment} - - -### Application to Suspension Bridges {#application-to-suspension-bridges} - - -#### Footbridge {#footbridge} - - -#### Laboratory Experiment {#laboratory-experiment} - - -## Active Control of Large Telescopes: Adaptive Optics {#active-control-of-large-telescopes-adaptive-optics} - - -### Introduction {#introduction} - - -#### Wavefront Sensor {#wavefront-sensor} - - -#### Zernike Modes {#zernike-modes} - - -#### Fried Length, Seeing {#fried-length-seeing} - - -#### Kolmogorov Turbulence Model {#kolmogorov-turbulence-model} - - -#### Strehl Ratio {#strehl-ratio} - - -#### Power Spectral Density of the Zernike Modes {#power-spectral-density-of-the-zernike-modes} - - -### Deformable Mirror for Adaptive Optics {#deformable-mirror-for-adaptive-optics} - - -#### Stoney Formula {#stoney-formula} - - -#### Stroke Versus Natural Frequency {#stroke-versus-natural-frequency} - - -### Feedback Control of an AO Mirror {#feedback-control-of-an-ao-mirror} - - -#### Quasi-static Control {#quasi-static-control} - - -#### Control of the Mirror Based on the Jacobian {#control-of-the-mirror-based-on-the-jacobian} - - -#### Control of Zernike Modes {#control-of-zernike-modes} - - -### Dynamic Response of the AO Mirror {#dynamic-response-of-the-ao-mirror} - - -#### Dynamic Model of the Mirror {#dynamic-model-of-the-mirror} - - -#### Control-Structure Interaction {#control-structure-interaction} - - -#### Passive Damping {#passive-damping} - - -#### Active Damping {#active-damping} - - -### Miscellaneous {#miscellaneous} - - -#### Segmented AO Mirror {#segmented-ao-mirror} - - -#### Initial Curvature of the AO Mirror {#initial-curvature-of-the-ao-mirror} - - -## Active Control of Large Telescopes: Active Optics {#active-control-of-large-telescopes-active-optics} - - -### Introduction {#introduction} - - -### Monolithic Primary Mirror {#monolithic-primary-mirror} - - -### Segmented Primary Mirror {#segmented-primary-mirror} - - -### SVD Controller {#svd-controller} - - -#### Loop Shaping of the SVD Controller {#loop-shaping-of-the-svd-controller} - - -### Dynamics of a Segmented Mirror {#dynamics-of-a-segmented-mirror} - - -### Control-Structure Interaction {#control-structure-interaction} - - -#### SISO System {#siso-system} - - -#### MIMO System {#mimo-system} - - -#### Spillover Alleviation {#spillover-alleviation} - - -### Scaling Rules {#scaling-rules} - - -#### Static Deflection Under Gravity {#static-deflection-under-gravity} - - -#### First Resonance Frequency {#first-resonance-frequency} - - -#### Control Bandwidth {#control-bandwidth} - - -## Adaptive Thin Shell Space Reflectors {#adaptive-thin-shell-space-reflectors} - - -### Introduction {#introduction} - - -### Adaptive Plates Versus Adaptive Shells {#adaptive-plates-versus-adaptive-shells} - - -### Adaptive Spherical Shell {#adaptive-spherical-shell} - - -### Quasi-static Control: Hierarchical Approach {#quasi-static-control-hierarchical-approach} - - -### Petal Configuration {#petal-configuration} - - -### MATS Demonstrator {#mats-demonstrator} - - -#### Manufacturing of the Demonstrator {#manufacturing-of-the-demonstrator} - - -## Semi-active Control {#semi-active-control} - - -### Introduction {#introduction} - - -### Magneto-Rheological Fluids {#magneto-rheological-fluids} - - -### MR Devices {#mr-devices} - - -### Semi-active Suspension {#semi-active-suspension} - - -#### Semi-active Devices {#semi-active-devices} - - -### Narrow-Band Disturbance {#narrow-band-disturbance} - - -#### Quarter-Car Semi-active Suspension {#quarter-car-semi-active-suspension} - - -### Problems {#problems} - - ## Bibliography {#bibliography}
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 441ed21..b04fc25 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 @@ -419,171 +419,6 @@ The values are given in [Table 1](#table--tab:relation-slope-decade) for a decad ## Dynamics of Motion Systems {#dynamics-of-motion-systems} -### Introduction {#introduction} - - -### Stiffness {#stiffness} - - -#### Importance of Stiffness for Precision {#importance-of-stiffness-for-precision} - - -#### Active Stiffness {#active-stiffness} - - -### Mass-Spring Systems with Damping {#mass-spring-systems-with-damping} - - -#### Dynamic Compliance {#dynamic-compliance} - - -##### Compliance of a Spring {#compliance-of-a-spring} - - -##### Compliance of a Damper {#compliance-of-a-damper} - - -##### Compliance of a Body {#compliance-of-a-body} - - -##### Dynamic Stiffness {#dynamic-stiffness} - - -##### Lumping the Dynamic Elements {#lumping-the-dynamic-elements} - - -#### Transfer Function of Compliance {#transfer-function-of-compliance} - - -##### Damped Mass-Spring System. {#damped-mass-spring-system-dot} - - -##### Magnitude {#magnitude} - - -##### Phase {#phase} - - -##### Bode Plot {#bode-plot} - - -#### Effects of Damping {#effects-of-damping} - - -##### Damped Resonance and Aperiodic Damping {#damped-resonance-and-aperiodic-damping} - - -##### Poles and Critical Damping {#poles-and-critical-damping} - - -##### Quality-Factor Q and Energy in Resonance {#quality-factor-q-and-energy-in-resonance} - - -#### Transmissibility {#transmissibility} - - -#### Fourth-Order Dynamic System {#fourth-order-dynamic-system} - - -##### Analytical Description {#analytical-description} - - -##### Multiplicative Expression {#multiplicative-expression} - - -##### Effect of Different Mass Ratios {#effect-of-different-mass-ratios} - - -### Modal Decomposition {#modal-decomposition} - - -#### Eigenmodes of Two-Body Mass-Spring System {#eigenmodes-of-two-body-mass-spring-system} - - -#### Theory of Modal Decomposition {#theory-of-modal-decomposition} - - -##### Multi Degree of Freedom Equation of Motion {#multi-degree-of-freedom-equation-of-motion} - - -##### Eigenvalues and Eigenvectors {#eigenvalues-and-eigenvectors} - - -##### Modal Coordinates {#modal-coordinates} - - -##### Resulting Transfer Function {#resulting-transfer-function} - - -#### Graphical Representation of Mode-Shapes {#graphical-representation-of-mode-shapes} - - -##### Traditional Representation {#traditional-representation} - - -##### Lever Representation {#lever-representation} - - -##### General System {#general-system} - - -##### User-Defined Physical DOF {#user-defined-physical-dof} - - -#### Physical Meaning of Modal Parameters {#physical-meaning-of-modal-parameters} - - -##### Two-Body Mass-Spring System {#two-body-mass-spring-system} - - -##### Planar Flexibly Guided System {#planar-flexibly-guided-system} - - -#### A Pragmatic View on Sensitivity Analysis {#a-pragmatic-view-on-sensitivity-analysis} - - -##### Example of Two Body Mass-Spring System {#example-of-two-body-mass-spring-system} - - -##### Example of Slightly Damped Resonance {#example-of-slightly-damped-resonance} - - -#### Suspension and Rigid-Body Modes {#suspension-and-rigid-body-modes} - - -##### Quasi Rigid-Body Suspension mode {#quasi-rigid-body-suspension-mode} - - -### Mechanical Frequency Response {#mechanical-frequency-response} - - -#### Multiple eigenmodes {#multiple-eigenmodes} - - -#### Characteristic Frequency Responses {#characteristic-frequency-responses} - - -##### Frequency Response Type I {#frequency-response-type-i} - - -##### Frequency Response Type II {#frequency-response-type-ii} - - -##### Frequency Response Type III {#frequency-response-type-iii} - - -##### Frequency Response Type IV {#frequency-response-type-iv} - - -#### Example Systems with Type I/II/IV Response {#example-systems-with-type-i-ii-iv-response} - - -##### Planar Moving Body on Compliant Spring {#planar-moving-body-on-compliant-spring} - - -##### H-drive Waferstage {#h-drive-waferstage} - - ### Summary on Dynamics {#summary-on-dynamics}
@@ -619,7 +454,7 @@ The core of the control system is the _plant_, which is the physical system that
Table 3: - Symbols used in 3 + Symbols used in 3
| Symbol | Meaning | Unit | @@ -1028,102 +863,6 @@ In more complicated control systems, it remains useful to also use the Nyquist p {{< figure src="/ox-hugo/schmidt20_phase_gain_margin_bode.svg" caption="Figure 13: The gain and phase margin in the Bode plot" >}} -### PID Feedback Control {#pid-feedback-control} - - -#### PID-Control of a Compact-Disc Player {#pid-control-of-a-compact-disc-player} - - -##### Relevant Sensitivity Functions {#relevant-sensitivity-functions} - - -##### Proportional Feedback {#proportional-feedback} - - -##### Proportional-Differential Feedback {#proportional-differential-feedback} - - -##### Limiting the Differentiating Action {#limiting-the-differentiating-action} - - -##### Adding I-Control {#adding-i-control} - - -#### PID-Control of a Spring Supported Mass {#pid-control-of-a-spring-supported-mass} - - -##### P-Control {#p-control} - - -##### D-Control {#d-control} - - -##### I-Control {#i-control} - - -##### Sensitivity Function Graphs {#sensitivity-function-graphs} - - -#### Limitations and Side Effects of PID-Feedback Control {#limitations-and-side-effects-of-pid-feedback-control} - - -##### Increased Sensitivity, the Waterbed Effect {#increased-sensitivity-the-waterbed-effect} - - -##### Integrator Wind-Up and Delays {#integrator-wind-up-and-delays} - - -#### PID-Control of a Fourth-Order Dynamic System {#pid-control-of-a-fourth-order-dynamic-system} - - -##### Controlling a Type III Dynamic System {#controlling-a-type-iii-dynamic-system} - - -##### Passive Damping {#passive-damping} - - -##### Shifting the Phase {#shifting-the-phase} - - -#### PID-Control of a Piezoelectric Actuator {#pid-control-of-a-piezoelectric-actuator} - - -##### Creating a Fourth-Order System {#creating-a-fourth-order-system} - - -#### PID-Control of a Magnetic Bearing {#pid-control-of-a-magnetic-bearing} - - -##### Frequency Response {#frequency-response} - - -##### Positive Stiffness by P-Control {#positive-stiffness-by-p-control} - - -##### D-Control and Pole Placement {#d-control-and-pole-placement} - - -##### I-control for Reduced Sensitivity {#i-control-for-reduced-sensitivity} - - -#### Optimisation by Loop-Shaping Design {#optimisation-by-loop-shaping-design} - - -##### Optimal Value of Alpha {#optimal-value-of-alpha} - - -##### Additional Low-Pass Filtering {#additional-low-pass-filtering} - - -##### Notching Filters {#notching-filters} - - -##### Peaking and Shelving Filters {#peaking-and-shelving-filters} - - -#### Design Steps for PID-control {#design-steps-for-pid-control} - - ### Digital Signal Processing - The Z-Domain {#digital-signal-processing-the-z-domain} Most modern controllers operate with digital processors in the discrete time domain, also called the _Z-domain_, which allows to create filters by combining scaled sampled data at fixed intervals. @@ -1243,30 +982,6 @@ The storage register is divided into three groups, as shown in [Figure 15](#figu #### Converting Continuous to Discrete-Time Filters {#converting-continuous-to-discrete-time-filters} -### State-Space Feedback Control {#state-space-feedback-control} - - -#### State-Space in Relation to Motion Control {#state-space-in-relation-to-motion-control} - - -##### Mechanical Dynamic System in State-Space {#mechanical-dynamic-system-in-state-space} - - -##### PID-Control Feedback in State-Space {#pid-control-feedback-in-state-space} - - -#### State Feedback {#state-feedback} - - -##### System Identification {#system-identification} - - -##### State Estimation {#state-estimation} - - -##### Additional Remarks on State-Space Control {#additional-remarks-on-state-space-control} - - ### Conclusion on Motion Control {#conclusion-on-motion-control}
@@ -1282,955 +997,6 @@ Motion control is essential for Precision Mechatronic Systems and consists of tw
-## Electromechanic Actuators {#electromechanic-actuators} - - -### Introduction {#introduction} - - -### Electromagnetics {#electromagnetics} - - -#### Hopkinson's Law {#hopkinson-s-law} - - -##### Practical Aspects of Hopkinson's Law {#practical-aspects-of-hopkinson-s-law} - - -##### Magnetic Energy {#magnetic-energy} - - -#### Ferromagnetic Materials {#ferromagnetic-materials} - - -##### Coil with Ferromagnetic Yoke {#coil-with-ferromagnetic-yoke} - - -##### Magnetisation Curve {#magnetisation-curve} - - -##### Permanent Magnets {#permanent-magnets} - - -#### Creating a Magnetic Field in an Air-Gap {#creating-a-magnetic-field-in-an-air-gap} - - -##### Optimal Use of Permanent Magnet Material {#optimal-use-of-permanent-magnet-material} - - -##### Flat Magnets Reduce Fringing Flux {#flat-magnets-reduce-fringing-flux} - - -##### Low Cost Loudspeaker Magnet {#low-cost-loudspeaker-magnet} - - -### Lorentz Actuator {#lorentz-actuator} - - -#### Lorentz Force {#lorentz-force} - - -##### Force from Flux-Linkage {#force-from-flux-linkage} - - -#### The Lorentz actuator as a Generator {#the-lorentz-actuator-as-a-generator} - - -#### Improving the Force of a Lorentz Actuator {#improving-the-force-of-a-lorentz-actuator} - - -##### The Moving-Coil Loudspeaker Actuator {#the-moving-coil-loudspeaker-actuator} - - -#### Position Dependency of the Lorentz Force {#position-dependency-of-the-lorentz-force} - - -##### Over-Hung and Under-Hung Coil {#over-hung-and-under-hung-coil} - - -#### Electronic Commutation {#electronic-commutation} - - -##### Three-Phase Electronic Control {#three-phase-electronic-control} - - -#### Figures of Merit of a Lorentz Actuator {#figures-of-merit-of-a-lorentz-actuator} - - -### Variable Reluctance Actuation {#variable-reluctance-actuation} - - -#### Reluctance Force in Lorentz Actuator {#reluctance-force-in-lorentz-actuator} - - -##### Eddy-Current Ring {#eddy-current-ring} - - -##### Ironless Stator {#ironless-stator} - - -#### Analytical Derivation of Reluctance Force {#analytical-derivation-of-reluctance-force} - - -#### Variable Reluctance Actuator. {#variable-reluctance-actuator-dot} - - -##### Electromagnetic Relay {#electromagnetic-relay} - - -##### Magnetic Attraction Force {#magnetic-attraction-force} - - -#### Permanent Magnet Biased Reluctance Actuator {#permanent-magnet-biased-reluctance-actuator} - - -##### Double Variable Reluctance Actuator {#double-variable-reluctance-actuator} - - -##### Constant Common Flux {#constant-common-flux} - - -##### Combining two Sources of Magnetic Flux {#combining-two-sources-of-magnetic-flux} - - -##### Hybrid Force Calculation {#hybrid-force-calculation} - - -##### Magnetic Bearings {#magnetic-bearings} - - -#### Active Linearisation of the Reluctance Force {#active-linearisation-of-the-reluctance-force} - - -### Application of Electromagnetic Actuators {#application-of-electromagnetic-actuators} - - -#### Electrical Interface Properties {#electrical-interface-properties} - - -##### Dynamic Effects of Self-Inductance {#dynamic-effects-of-self-inductance} - - -##### Limitation of the \`\`Jerk'' {#limitation-of-the-jerk} - - -##### Electromagnetic Damping {#electromagnetic-damping} - - -#### Comparison of three Electromagnetic Actuators {#comparison-of-three-electromagnetic-actuators} - - -##### Force-Constants {#force-constants} - - -##### Figures of Merit Including Mass {#figures-of-merit-including-mass} - - -##### Stiffness {#stiffness} - - -##### Repeatability and Predictability {#repeatability-and-predictability} - - -##### Dynamic Effects on the Control Loop {#dynamic-effects-on-the-control-loop} - - -### Piezoelectric Actuators {#piezoelectric-actuators} - - -#### Piezoelectricity {#piezoelectricity} - - -##### Poling {#poling} - - -##### Tapping the Bound Charge by Electrodes {#tapping-the-bound-charge-by-electrodes} - - -#### Transducer Models {#transducer-models} - - -#### Nonlinearity of Piezoelectric Actuators {#nonlinearity-of-piezoelectric-actuators} - - -##### Creep {#creep} - - -##### Hysteresis {#hysteresis} - - -##### Aging {#aging} - - -#### Mechanical Considerations {#mechanical-considerations} - - -##### Piezoelectric Actuator Stiffness {#piezoelectric-actuator-stiffness} - - -##### Actuator Types {#actuator-types} - - -##### Long Range Actuation by Friction {#long-range-actuation-by-friction} - - -##### Actuator Integration {#actuator-integration} - - -##### Mechanical Amplification {#mechanical-amplification} - - -##### Multiple Motion Directions by Stacking {#multiple-motion-directions-by-stacking} - - -#### Electrical Considerations {#electrical-considerations} - - -##### Charge vs. Voltage Control {#charge-vs-dot-voltage-control} - - -##### Self-Sensing Actuation {#self-sensing-actuation} - - -### Choosing the right Actuator Type {#choosing-the-right-actuator-type} - - -## Analogue Electronics in Mechatronic Systems {#analogue-electronics-in-mechatronic-systems} - - -### Introduction {#introduction} - - -### Passive Linear Electronics {#passive-linear-electronics} - - -#### Network Theory and Laws {#network-theory-and-laws} - - -##### Voltage Source {#voltage-source} - - -##### Current Source {#current-source} - - -##### Theorem of Norton and Thevenin {#theorem-of-norton-and-thevenin} - - -##### Kirchhoff's Laws {#kirchhoff-s-laws} - - -##### Impedances in Series or Parallel {#impedances-in-series-or-parallel} - - -##### Voltage Divider {#voltage-divider} - - -##### Maximum Power of a Real Voltage Source {#maximum-power-of-a-real-voltage-source} - - -#### Impedances in Electronic Circuits {#impedances-in-electronic-circuits} - - -##### Resistors {#resistors} - - -##### Capacitors {#capacitors} - - -##### Inductors {#inductors} - - -#### Passive Filters {#passive-filters} - - -##### Passive First-Order RC-Filters {#passive-first-order-rc-filters} - - -##### Passive Higher-Order RC-Filters {#passive-higher-order-rc-filters} - - -##### Passive LCR-Filters {#passive-lcr-filters} - - -#### Mechanical-Electrical Dynamic Analogy {#mechanical-electrical-dynamic-analogy} - - -### Semiconductors and Active Electronics {#semiconductors-and-active-electronics} - - -#### Basic Discrete Semiconductors {#basic-discrete-semiconductors} - - -##### Semiconductor Diode {#semiconductor-diode} - - -##### Bipolar Transistors {#bipolar-transistors} - - -##### MOSFET {#mosfet} - - -##### Other Discrete Semiconductors {#other-discrete-semiconductors} - - -#### Single Transistor Linear Amplifiers {#single-transistor-linear-amplifiers} - - -##### Emitter Follower {#emitter-follower} - - -##### Voltage Amplifier {#voltage-amplifier} - - -##### Differential Amplifier {#differential-amplifier} - - -#### Operational Amplifier {#operational-amplifier} - - -##### Basic Operational Amplifier Design {#basic-operational-amplifier-design} - - -##### Operational Amplifier with Feedback {#operational-amplifier-with-feedback} - - -#### Linear Amplifiers with Operational Amplifiers {#linear-amplifiers-with-operational-amplifiers} - - -##### Design Rules {#design-rules} - - -##### Non-Inverting Amplifier {#non-inverting-amplifier} - - -##### Inverting Amplifier {#inverting-amplifier} - - -##### Adding and Subtracting Signals {#adding-and-subtracting-signals} - - -##### Transimpedance Amplifier {#transimpedance-amplifier} - - -##### Transconductance Amplifier {#transconductance-amplifier} - - -#### Active Electronic Filters {#active-electronic-filters} - - -##### Integrator and First-Order Low-Pass {#integrator-and-first-order-low-pass} - - -##### Differentiator and First-Order High-Pass {#differentiator-and-first-order-high-pass} - - -#### Analogue PID-Controller {#analogue-pid-controller} - - -##### PID Transfer Function {#pid-transfer-function} - - -##### PID Control Gains {#pid-control-gains} - - -##### High-Speed PID-Control {#high-speed-pid-control} - - -#### Higher-order Electronic Filters {#higher-order-electronic-filters} - - -##### Second-Order Low-Pass Filter {#second-order-low-pass-filter} - - -##### Different Types of Active Filters {#different-types-of-active-filters} - - -#### Ideal and Real Operational Amplifiers {#ideal-and-real-operational-amplifiers} - - -##### Open-Loop Voltage Gain {#open-loop-voltage-gain} - - -##### Dynamic Limitations {#dynamic-limitations} - - -##### Input Related Limitations {#input-related-limitations} - - -##### Power Supply and Output Limitations {#power-supply-and-output-limitations} - - -#### Closing Remarks on Low-Power Electronics {#closing-remarks-on-low-power-electronics} - - -### Power Amplifiers for Motion Control {#power-amplifiers-for-motion-control} - - -#### Required Properties for Actuator Drive {#required-properties-for-actuator-drive} - - -##### Power Delivery Capability {#power-delivery-capability} - - -##### Dynamic Properties {#dynamic-properties} - - -##### Linearity, Freedom of Distortion {#linearity-freedom-of-distortion} - - -##### Voltage or Current Drive {#voltage-or-current-drive} - - -##### Efficiency {#efficiency} - - -##### Four-Quadrant Operation {#four-quadrant-operation} - - -##### Preferred Power Amplifier Principle {#preferred-power-amplifier-principle} - - -#### Switched-Mode Power Amplifiers {#switched-mode-power-amplifiers} - - -##### Power MOSFET, a Fast High-Power Switch {#power-mosfet-a-fast-high-power-switch} - - -##### Switching Sequence Generation {#switching-sequence-generation} - - -##### Voltage Drive Amplifier {#voltage-drive-amplifier} - - -##### Energy Flow in the Power Output Stage {#energy-flow-in-the-power-output-stage} - - -##### Intermediate Conclusions and Other Issues {#intermediate-conclusions-and-other-issues} - - -##### Driving the Power MOSFETs {#driving-the-power-mosfets} - - -##### Charge Pumping {#charge-pumping} - - -##### H-Bridge Configuration {#h-bridge-configuration} - - -##### Output Filter {#output-filter} - - -#### Resonant-Mode Power Amplifiers {#resonant-mode-power-amplifiers} - - -##### Switching Sequence of the Output Stage {#switching-sequence-of-the-output-stage} - - -##### Lossless Current Sensing {#lossless-current-sensing} - - -#### Three-Phase Amplifiers {#three-phase-amplifiers} - - -##### Concept of Three-Phase Amplifier {#concept-of-three-phase-amplifier} - - -##### Three-Phase Switching Power Stages {#three-phase-switching-power-stages} - - -#### Some Last Remarks on Power Electronics {#some-last-remarks-on-power-electronics} - - -## Optics in Mechatronic Systems {#optics-in-mechatronic-systems} - - -### Introduction {#introduction} - - -### Properties of Light and Light Sources {#properties-of-light-and-light-sources} - - -#### Light Generation by Thermal Radiation {#light-generation-by-thermal-radiation} - - -#### Photons by Electron Energy State Variation {#photons-by-electron-energy-state-variation} - - -##### Light Emitting Diodes {#light-emitting-diodes} - - -##### Laser as an Ideal Light Source {#laser-as-an-ideal-light-source} - - -#### Useful Power from a Light Source {#useful-power-from-a-light-source} - - -##### Radiant Emittance and Irradiance {#radiant-emittance-and-irradiance} - - -##### Radiance {#radiance} - - -##### Etendue {#etendue} - - -### Reflection and Refraction {#reflection-and-refraction} - - -#### Reflection and Refraction according to the Least Time {#reflection-and-refraction-according-to-the-least-time} - - -##### Partial Reflection and Refraction {#partial-reflection-and-refraction} - - -#### Concept of Wavefront {#concept-of-wavefront} - - -##### A Wavefront is Not Real {#a-wavefront-is-not-real} - - -### Geometric Optics {#geometric-optics} - - -#### Imaging with Refractive Lens Elements {#imaging-with-refractive-lens-elements} - - -##### Sign Conventions {#sign-conventions} - - -##### Real Lens Elements {#real-lens-elements} - - -##### Magnification {#magnification} - - -#### Aberrations {#aberrations} - - -##### Spherical Aberration {#spherical-aberration} - - -##### Astigmatism {#astigmatism} - - -##### Coma {#coma} - - -##### Geometric and Chromatic Aberrations {#geometric-and-chromatic-aberrations} - - -#### Combining Multiple Optical Elements {#combining-multiple-optical-elements} - - -##### Combining Two Positive Lenses {#combining-two-positive-lenses} - - -#### Aperture Stop and Pupil {#aperture-stop-and-pupil} - - -#### Telecentricity {#telecentricity} - - -##### Pupil, Aperture and Lens Dimensions {#pupil-aperture-and-lens-dimensions} - - -##### Practical Applications and Constraints {#practical-applications-and-constraints} - - -### Physical Optics {#physical-optics} - - -#### Polarisation {#polarisation} - - -##### Birefringence {#birefringence} - - -#### Interference {#interference} - - -##### Fabry-Perot Interferometer {#fabry-perot-interferometer} - - -#### Diffraction {#diffraction} - - -##### Amplitude gratings {#amplitude-gratings} - - -##### Phase Gratings {#phase-gratings} - - -##### Direction of the Incoming Light {#direction-of-the-incoming-light} - - -#### Imaging Quality based on Diffraction {#imaging-quality-based-on-diffraction} - - -##### Numerical Aperture and f-Number {#numerical-aperture-and-f-number} - - -##### Depth of Focus {#depth-of-focus} - - -### Adaptive Optics {#adaptive-optics} - - -#### Thermal Effects in Optical Imaging Systems {#thermal-effects-in-optical-imaging-systems} - - -#### Correcting the Wavefront {#correcting-the-wavefront} - - -##### Zernike Polynomials {#zernike-polynomials} - - -##### Correcting Zernikes by Adaptive Optics {#correcting-zernikes-by-adaptive-optics} - - -#### Adaptive Optics Principle of Operation {#adaptive-optics-principle-of-operation} - - -##### Active Mirrors {#active-mirrors} - - -## Measurement in Mechatronic Systems {#measurement-in-mechatronic-systems} - - -### Introduction {#introduction} - - -#### Measurement Systems {#measurement-systems} - - -#### Errors in Measurement Systems, Uncertainty {#errors-in-measurement-systems-uncertainty} - - -##### Uncertainty in Traceable Measurements {#uncertainty-in-traceable-measurements} - - -#### Functional Model of a Measurement System Element {#functional-model-of-a-measurement-system-element} - - -### Dynamic Error Budgeting {#dynamic-error-budgeting} - - -#### Error Statistics in Repeated Measurements {#error-statistics-in-repeated-measurements} - - -#### The Normal Distribution {#the-normal-distribution} - - -#### Combining Different Error Sources {#combining-different-error-sources} - - -#### Power Spectral Density and Cumulative Power {#power-spectral-density-and-cumulative-power} - -{{< figure src="/ox-hugo/schmidt20_psd_cps.svg" >}} - - -#### Do not use the Cumulative Amplitude Spectrum! {#do-not-use-the-cumulative-amplitude-spectrum} - - -#### Variations in Dynamic Error Budgeting {#variations-in-dynamic-error-budgeting} - - -#### Sources of Noise and Disturbances {#sources-of-noise-and-disturbances} - - -##### Mechanical Noise {#mechanical-noise} - - -##### Electronic Noise {#electronic-noise} - - -### Sensor Signal Sensitivity {#sensor-signal-sensitivity} - - -#### Sensing Element {#sensing-element} - - -#### Converting an Impedance into an Electric Signal {#converting-an-impedance-into-an-electric-signal} - - -##### Wheatstone Bridge {#wheatstone-bridge} - - -#### Electronic Interconnection of Sensitive Signals {#electronic-interconnection-of-sensitive-signals} - -{{< figure src="/ox-hugo/schmidt20_signal_interference.svg" >}} - -{{< figure src="/ox-hugo/schmidt20_cable_topology.svg" >}} - -{{< figure src="/ox-hugo/schmidt20_electrostatic_shielding.svg" >}} - - -##### Magnetic Disturbances {#magnetic-disturbances} - - -##### Capacitive Disturbances {#capacitive-disturbances} - - -##### Ground Loops {#ground-loops} - -{{< figure src="/ox-hugo/schmidt20_ground_loops.svg" >}} - - -### Signal Conditioning {#signal-conditioning} - - -#### Instrumentation Amplifier {#instrumentation-amplifier} - - -#### Filtering and Modulation {#filtering-and-modulation} - - -##### AM with Square Wave Carrier {#am-with-square-wave-carrier} - - -##### AM with Sinusoidal Carrier {#am-with-sinusoidal-carrier} - - -### Signal Processing {#signal-processing} - - -#### Schmitt Trigger {#schmitt-trigger} - -{{< figure src="/ox-hugo/schmidt20_schmitt_trigger.svg" >}} - - -#### Digital Representation of Measurement Data {#digital-representation-of-measurement-data} - - -##### Gray Code {#gray-code} - -{{< figure src="/ox-hugo/schmidt20_gray_code.svg" >}} - - -##### Sampling of Analogue Values {#sampling-of-analogue-values} - - -##### Nyquist-Shannon Theorem {#nyquist-shannon-theorem} - - -##### Filtering to Prevent Aliasing {#filtering-to-prevent-aliasing} - - -#### Analogue-to-Digital Converters {#analogue-to-digital-converters} - - -##### Dual-Slope ADC {#dual-slope-adc} - - -##### Successive-Approximation ADC {#successive-approximation-adc} - - -##### Sigma-Delta ADC {#sigma-delta-adc} - - -##### ADC Latency in a Feedback Loop {#adc-latency-in-a-feedback-loop} - - -#### Connecting the Less Sensitive Elements {#connecting-the-less-sensitive-elements} - - -##### Characteristic Impedance {#characteristic-impedance} - - -##### Non-Galvanic Connection {#non-galvanic-connection} - - -### Short-Range Motion Sensors {#short-range-motion-sensors} - - -#### Optical Sensors {#optical-sensors} - - -##### Position Sensitive Detectors {#position-sensitive-detectors} - - -##### Optical Deflectometer {#optical-deflectometer} - - -#### Capacitive Position Sensors {#capacitive-position-sensors} - - -##### Linearising by Differential Measurement {#linearising-by-differential-measurement} - - -##### Accuracy Limits and Improvements {#accuracy-limits-and-improvements} - - -##### Sensing to Conductive Moving Plate {#sensing-to-conductive-moving-plate} - - -#### Inductive Position Sensors {#inductive-position-sensors} - - -##### Linear Variable Differential Transformer {#linear-variable-differential-transformer} - - -##### Eddy-Current Sensors {#eddy-current-sensors} - - -#### Pneumatic Proximity Sensor or Air-Gage {#pneumatic-proximity-sensor-or-air-gage} - - -### Measurement of Mechanical Dynamics {#measurement-of-mechanical-dynamics} - - -#### Measurement of Force and Strain {#measurement-of-force-and-strain} - - -##### Strain Gages {#strain-gages} - - -##### Fibre Bragg Grating Strain Measurement {#fibre-bragg-grating-strain-measurement} - - -#### Velocity Measurement {#velocity-measurement} - - -##### Geophone {#geophone} - - -#### Accelerometers {#accelerometers} - - -##### Closed-Loop Feedback Accelerometer {#closed-loop-feedback-accelerometer} - - -##### Piezoelectric Accelerometer {#piezoelectric-accelerometer} - - -##### MEMS Accelerometer {#mems-accelerometer} - - -### Optical Long-Range Incremental Position Sensors {#optical-long-range-incremental-position-sensors} - - -#### Linear Optical Encoders {#linear-optical-encoders} - - -##### Interpolation {#interpolation} - - -##### Vernier Resolution Enhancement {#vernier-resolution-enhancement} - - -##### Interferometric Optical Encoder {#interferometric-optical-encoder} - - -##### Concluding Remarks on Linear Encoders {#concluding-remarks-on-linear-encoders} - - -#### Laser Interferometer Measurement Systems {#laser-interferometer-measurement-systems} - - -##### Homodyne Distance Interferometry {#homodyne-distance-interferometry} - - -##### Heterodyne Distance Interferometry {#heterodyne-distance-interferometry} - - -##### Measurement Uncertainty {#measurement-uncertainty} - - -##### Configurations {#configurations} - - -##### Multi-Axis Laser Interferometers {#multi-axis-laser-interferometers} - - -#### Mechanical Aspects {#mechanical-aspects} - - -##### Abbe Error {#abbe-error} - - -## Precision Positioning in Wafer Scanners {#precision-positioning-in-wafer-scanners} - - -### Introduction {#introduction} - - -### The Waferscanner {#the-waferscanner} - - -#### Requirements on Precision {#requirements-on-precision} - - -### Dynamic Architecture {#dynamic-architecture} - - -#### Balance Masses {#balance-masses} - - -#### Vibration Isolation {#vibration-isolation} - - -##### Eigendynamics of the Sensitive Parts {#eigendynamics-of-the-sensitive-parts} - - -### Zero-Stiffness Stage Actuation {#zero-stiffness-stage-actuation} - - -#### Waferstage Actuation Concept {#waferstage-actuation-concept} - - -##### Waferstepper Long-Range Lorentz Actuator {#waferstepper-long-range-lorentz-actuator} - - -##### Multi-Axis Positioning {#multi-axis-positioning} - - -##### Long- and Short-Stroke Actuation {#long-and-short-stroke-actuation} - - -#### Full Magnetic Levitation {#full-magnetic-levitation} - - -#### Acceleration Limits of Reticle Stage {#acceleration-limits-of-reticle-stage} - - -### Position Measurement {#position-measurement} - - -#### Alignment Sensor {#alignment-sensor} - - -#### Keeping the Wafer in Focus {#keeping-the-wafer-in-focus} - - -#### Dual-Stage Measurement and Exposure {#dual-stage-measurement-and-exposure} - - -#### Long-Range Incremental Measurement System {#long-range-incremental-measurement-system} - - -##### Real-Time Metrology Loop {#real-time-metrology-loop} - - -### Motion Control {#motion-control} - - -#### Feedforward and Feedback Control {#feedforward-and-feedback-control} - - -##### Thermal, The Final Frontier {#thermal-the-final-frontier} - - -#### 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. - - -### Future Developments in IC Lithography {#future-developments-in-ic-lithography} - - -### Main Design Rules for Precision {#main-design-rules-for-precision} - - ## Bibliography {#bibliography}
diff --git a/content/book/wardle15_ultra_precis_bearin.md b/content/book/wardle15_ultra_precis_bearin.md index d5959e8..ffaf343 100644 --- a/content/book/wardle15_ultra_precis_bearin.md +++ b/content/book/wardle15_ultra_precis_bearin.md @@ -28,7 +28,7 @@ Causes: **Types of error motion** -A distinction is made between (see Figure ): +A distinction is made between (see [Figure 1](#figure--fig:wardle15-synchronous-asynchronous-schematic)): - motion errors that are harmonic of the basic rotor speed: _synchronous_ motion error - those that are node: _asynchronous_ motion errors @@ -42,19 +42,19 @@ A distinction is made between (see Figure ). +It is displayed as a polar plot of motion error amplitude versus angle of rotation ([Figure 2](#figure--fig:wardle15-typical-error-plot)). {{< figure src="/ox-hugo/wardle15_typical_error_plot.png" caption="Figure 2: Total error motion" >}} -The Synchronous error motion (i.e. error that are harmonics of the rotational speed) can be extracted (Figure ). +The Synchronous error motion (i.e. error that are harmonics of the rotational speed) can be extracted ([Figure 3](#figure--fig:wardle15-synchronous-error-example)). {{< figure src="/ox-hugo/wardle15_synchronous_error_example.png" caption="Figure 3: Synchronous motion error" >}} -It can then be separated into a "_fundamental error motion_" and a "_residual error motion_" (Figure ). +It can then be separated into a "_fundamental error motion_" and a "_residual error motion_" ([Figure 4](#figure--fig:wardle15-fundamental-and-residual-errors)). The fundamental error motion contains only one frequency corresponding to the speed of the rotation of the bearing. For radial measurements, it corresponds to the eccentricity, and is not always significant. @@ -62,7 +62,7 @@ For radial measurements, it corresponds to the eccentricity, and is not always s {{< figure src="/ox-hugo/wardle15_fundamental_and_residual_errors.png" caption="Figure 4: (a) Fundamental error motion; and (b) residual synchronous error motion" >}} -The Asynchronous error motion (Figure ) contains all other motion error frequencies. +The Asynchronous error motion ([Figure 5](#figure--fig:wardle15-asynchronous-error-motion-example)) contains all other motion error frequencies. diff --git a/content/zettels/heat_transfer.md b/content/zettels/heat_transfer.md index f57c8a2..26f7ffb 100644 --- a/content/zettels/heat_transfer.md +++ b/content/zettels/heat_transfer.md @@ -106,7 +106,7 @@ h\_{rad} = \epsilon\_1 \sigma (T\_1^2 + T\_2^2)(T\_1 + T\_2) ### Emissivity {#emissivity} The emissivity of materials highly depend on the surface finish (the more polished, the lower the emissivity). -Some examples are given in . +Some examples are given in [Table 1](#table--tab:emissivity-examples). Gold coating gives also a very low emissivity and is typically used in cryogenic applications. diff --git a/content/zettels/system_identification.md b/content/zettels/system_identification.md index 2921bc5..8ad89b2 100644 --- a/content/zettels/system_identification.md +++ b/content/zettels/system_identification.md @@ -23,7 +23,7 @@ The system is represented in [Figure 1](#figure--fig:siso-identification-schemat The goal of system identification is to compute the transfer function \\(G\\) from known excitation signal \\(u\\) and from a measure of \\(y\_m\\). -There are different ways of obtaining a model \\(G\\) of the system summarized in Table . +There are different ways of obtaining a model \\(G\\) of the system summarized in Table [Table 1](#table--tab:system-identification-model-types). For mechatronics systems, _frequency domain identification_ is the norm.