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help: help:
@echo "Usage: make <command>" @echo "Usage: make <command>"
@echo " hugo - Export the org files to the Hugo website (~/Sites/website)" @echo " hugo - Export the org files to the Hugo website (org-hugo-base-dir)"
hugo: hugo:
@files=$$(grep -rli --include='*.org' --exclude-dir=.git '^#+hugo_base_dir:' . | sort); \ @files=$$(grep -rli --include='*.org' --exclude-dir=.git '^#+hugo_section:' . | sort); \
if [ -z "$$files" ]; then echo "No Org file with #+hugo_base_dir found"; exit 1; fi; \ if [ -z "$$files" ]; then echo "No Org file with #+hugo_section found"; exit 1; fi; \
for f in $$files; do \ for f in $$files; do \
echo "==> Exporting $$f"; \ echo "==> Exporting $$f"; \
emacsclient -e "(with-current-buffer (find-file-noselect \"$(CURDIR)/$${f#./}\") (org-hugo-export-wim-to-md))" > /dev/null || exit 1; \ emacsclient -e "(with-current-buffer (find-file-noselect \"$(CURDIR)/$${f#./}\") (org-hugo-export-wim-to-md))" > /dev/null || exit 1; \
index.org
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#+TITLE: Active Damping of Rotating Platforms using Integral Force Feedback #+TITLE: Active Damping of Rotating Platforms using Integral Force Feedback
#+hugo_section: research
#+hugo_bundle: dehaeze21_activ_dampin_rotat_platf_using
#+export_file_name: _index
#+hugo_custom_front_matter: :venue "Engineering Research Express" :year 2021 :pubtype "journal"
#+hugo_custom_front_matter: :doi "10.1088/2631-8695/abe803"
#+hugo_custom_front_matter: :code "https://git.tdehaeze.xyz/tdehaeze/dehaeze21_activ_dampin_rotat_platf_using"
:DRAWER: :DRAWER:
#+SUBTITLE: Dehaeze Thomas, Collette Christophe #+SUBTITLE: Dehaeze Thomas, Collette Christophe
@@ -55,10 +61,3 @@ Dehaeze, T., & Collette, C., Active damping of rotating platforms using integral
:UNNUMBERED: t :UNNUMBERED: t
:END: :END:
The Matlab scripts that permits to obtain all the results presented in the paper are accessible [[file:matlab/index.org][here]]. The Matlab scripts that permits to obtain all the results presented in the paper are accessible [[file:matlab/index.org][here]].
* Figures ([[file:tikz/index.org][link]])
:PROPERTIES:
:UNNUMBERED: t
:END:
All the figures in the paper are generated using either [[https://sourceforge.net/projects/pgf/][TikZ]] or [[https://inkscape.org/][Inkscape]]. The code snippets that was used to generate the figures are accessible [[file:tikz/index.org][here]].
journal/paper.tex
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% Created 2021-08-27 ven. 18:43 % Created 2025-11-27 Thu 16:56
% Intended LaTeX compiler: pdflatex % Intended LaTeX compiler: pdflatex
\documentclass[10pt]{iopart} \documentclass[10pt]{iopart}
@@ -15,8 +15,10 @@
\usetikzlibrary{shapes.misc,arrows,arrows.meta} \usetikzlibrary{shapes.misc,arrows,arrows.meta}
\usepackage[square,comma,sort&compress,numbers]{natbib} \usepackage[square,comma,sort&compress,numbers]{natbib}
\renewcommand{\bibsection}{\section*{References}} \renewcommand{\bibsection}{\section*{References}}
\date{}
\title{}
\usepackage{biblatex}
\begin{document} \begin{document}
\title{Active damping of rotating platforms using integral force feedback} \title{Active damping of rotating platforms using integral force feedback}
@@ -42,30 +44,34 @@ The results reveal that, despite their different implementations, both modified
\maketitle \maketitle
% Two Columns output % Two Columns output
\ioptwocol \ioptwocol
\section{Introduction} \section{Introduction}
\label{sec:introduction} \label{sec:introduction}
There is an increasing need to reduce the undesirable vibration of sensitive equipment in many different fields such as in aerospace industry \cite{hanieh03_activ_stewar,hauge04_sensor_contr_space_based_six,souleille18_concep_activ_mount_space_applic}, semi conductor industry \cite{yoshioka01_activ_microv_isolat_system_hi}, microscopy \cite{lan08_activ_vibrat_isolat_long_range,fleming15_low_order_dampin_track_contr}, gravitational wave detectors \cite{matichard15_seism_isolat_advan_ligo} and particles accelerators \cite{collette10_activ_quadr_stabil_futur_linear_partic_collid,dehaeze18_sampl_stabil_for_tomog_exper}. There is an increasing need to reduce the undesirable vibration of sensitive equipment in many different fields such as in aerospace industry \cite{hanieh03_activ_stewar,hauge04_sensor_contr_space_based_six,souleille18_concep_activ_mount_space_applic}, semi conductor industry \cite{yoshioka01_activ_microv_isolat_system_hi}, microscopy \cite{lan08_activ_vibrat_isolat_long_range,fleming15_low_order_dampin_track_contr}, gravitational wave detectors \cite{matichard15_seism_isolat_advan_ligo} and particles accelerators \cite{collette10_activ_quadr_stabil_futur_linear_partic_collid,dehaeze18_sampl_stabil_for_tomog_exper}.
A common method to reduce vibration is to mount the sensitive equipment on a suspended platform which attenuates the vibrations above the frequency of the suspension modes \cite{reilly06_critic,poel10_explor_activ_hard_mount_vibrat}. \par A common method to reduce vibration is to mount the sensitive equipment on a suspended platform which attenuates the vibrations above the frequency of the suspension modes \cite{reilly06_critic,poel10_explor_activ_hard_mount_vibrat}. \par
In order to further decrease the residual vibrations, active damping can be used for reducing the magnification of the response in the vicinity of the resonances \cite{collette11_review_activ_vibrat_isolat_strat}. In order to further decrease the residual vibrations, active damping can be used for reducing the magnification of the response in the vicinity of the resonances \cite{collette11_review_activ_vibrat_isolat_strat}.
Many active damping techniques have been developed over the years such as Positive Position Feedback (PPF) \cite{lin06_distur_atten_precis_hexap_point,fanson90_posit_posit_feedb_contr_large_space_struc}, Integral Force Feedback (IFF) \cite{preumont91_activ} and Direct Velocity Feedback (DVF) \cite{karnopp74_vibrat_contr_using_semi_activ_force_gener,serrand00_multic_feedb_contr_isolat_base_excit_vibrat,preumont02_force_feedb_versus_accel_feedb}. \par Many active damping techniques have been developed over the years such as Positive Position Feedback (PPF) \cite{lin06_distur_atten_precis_hexap_point,fanson90_posit_posit_feedb_contr_large_space_struc}, Integral Force Feedback (IFF) \cite{preumont91_activ} and Direct Velocity Feedback (DVF) \cite{karnopp74_vibrat_contr_using_semi_activ_force_gener,serrand00_multic_feedb_contr_isolat_base_excit_vibrat,preumont02_force_feedb_versus_accel_feedb}. \par
In \cite{preumont92_activ_dampin_by_local_force}, the IFF control scheme has been proposed, where a force sensor, a force actuator and an integral controller are used to directly augment the damping of a mechanical system. In \cite{preumont92_activ_dampin_by_local_force}, the IFF control scheme has been proposed, where a force sensor, a force actuator and an integral controller are used to directly augment the damping of a mechanical system.
When the force sensor is collocated with the actuator, the open-loop transfer function has alternating poles and zeros which facilitate to guarantee the stability of the closed loop system \cite{preumont02_force_feedb_versus_accel_feedb}. When the force sensor is collocated with the actuator, the open-loop transfer function has alternating poles and zeros which facilitate to guarantee the stability of the closed loop system \cite{preumont02_force_feedb_versus_accel_feedb}.
It was latter shown that this property holds for multiple collated actuator/sensor pairs \cite{preumont08_trans_zeros_struc_contr_with}. \par It was latter shown that this property holds for multiple collated actuator/sensor pairs \cite{preumont08_trans_zeros_struc_contr_with}. \par
The main advantages of IFF over other active damping techniques are the guaranteed stability even in presence of flexible dynamics, good performances and robustness properties \cite{preumont02_force_feedb_versus_accel_feedb}. \par The main advantages of IFF over other active damping techniques are the guaranteed stability even in presence of flexible dynamics, good performances and robustness properties \cite{preumont02_force_feedb_versus_accel_feedb}. \par
Several improvements of the classical IFF have been proposed, such as adding a feed-through term to increase the achievable damping \cite{teo15_optim_integ_force_feedb_activ_vibrat_contr} or adding an high pass filter to recover the loss of compliance at low frequency \cite{chesne16_enhan_dampin_flexib_struc_using_force_feedb}. Several improvements of the classical IFF have been proposed, such as adding a feed-through term to increase the achievable damping \cite{teo15_optim_integ_force_feedb_activ_vibrat_contr} or adding an high pass filter to recover the loss of compliance at low frequency \cite{chesne16_enhan_dampin_flexib_struc_using_force_feedb}.
Recently, an \(\mathcal{H}_\infty\) optimization criterion has been used to derive optimal gains for the IFF controller \cite{zhao19_optim_integ_force_feedb_contr}. \par Recently, an \(\mathcal{H}_\infty\) optimization criterion has been used to derive optimal gains for the IFF controller \cite{zhao19_optim_integ_force_feedb_contr}. \par
However, when the platform is rotating, gyroscopic effects alter the system dynamics and IFF cannot be applied as is. However, when the platform is rotating, gyroscopic effects alter the system dynamics and IFF cannot be applied as is.
The purpose of this paper is to study how the IFF strategy can be adapted to deal with these gyroscopic effects. \par The purpose of this paper is to study how the IFF strategy can be adapted to deal with these gyroscopic effects. \par
The paper is structured as follows. The paper is structured as follows.
Section \ref{sec:dynamics} presents a simple model of a rotating suspended platform that will be used throughout this study. Section \ref{sec:dynamics} presents a simple model of a rotating suspended platform that will be used throughout this study.
Section \ref{sec:iff} explains how the unconditional stability of IFF is lost due to gyroscopic effects induced by the rotation. Section \ref{sec:iff} explains how the unconditional stability of IFF is lost due to gyroscopic effects induced by the rotation.
Section \ref{sec:iff_hpf} suggests a simple modification of the control law such that damping can be added to the suspension modes in a robust way. Section \ref{sec:iff_hpf} suggests a simple modification of the control law such that damping can be added to the suspension modes in a robust way.
Section \ref{sec:iff_kp} proposes to add springs in parallel with the force sensors to regain the unconditional stability of IFF. Section \ref{sec:iff_kp} proposes to add springs in parallel with the force sensors to regain the unconditional stability of IFF.
Section \ref{sec:comparison} compares both proposed modifications to the classical IFF in terms of damping authority and closed-loop system behavior. Section \ref{sec:comparison} compares both proposed modifications to the classical IFF in terms of damping authority and closed-loop system behavior.
\section{Dynamics of Rotating Platforms} \section{Dynamics of Rotating Platforms}
\label{sec:dynamics} \label{sec:dynamics}
In order to study how the rotation affects the use of IFF, a model of a suspended platform on top of a rotating stage is used. In order to study how the rotation affects the use of IFF, a model of a suspended platform on top of a rotating stage is used.
@@ -86,6 +92,7 @@ Two reference frames are used: an inertial frame \((\vec{i}_x, \vec{i}_y, \vec{i
The position of the payload is represented by \((d_u, d_v, 0)\) expressed in the rotating frame. The position of the payload is represented by \((d_u, d_v, 0)\) expressed in the rotating frame.
\par \par
To obtain the equations of motion for the system represented in Figure \ref{fig:system}, the Lagrangian equations are used: To obtain the equations of motion for the system represented in Figure \ref{fig:system}, the Lagrangian equations are used:
\begin{equation} \begin{equation}
\label{eq:lagrangian_equations} \label{eq:lagrangian_equations}
@@ -120,6 +127,7 @@ The uniform rotation of the system induces two gyroscopic effects as shown in Eq
One can verify that without rotation (\(\Omega = 0\)) the system becomes equivalent to two uncoupled one degree of freedom mass-spring-damper systems. One can verify that without rotation (\(\Omega = 0\)) the system becomes equivalent to two uncoupled one degree of freedom mass-spring-damper systems.
\par \par
To study the dynamics of the system, the differential equations of motions \eqref{eq:eom_coupled} are converted into the Laplace domain and the \(2 \times 2\) transfer function matrix \(\mathbf{G}_d\) from \(\begin{bmatrix}F_u & F_v\end{bmatrix}\) to \(\begin{bmatrix}d_u & d_v\end{bmatrix}\) in Eq. \eqref{eq:Gd_mimo_tf} is obtained. To study the dynamics of the system, the differential equations of motions \eqref{eq:eom_coupled} are converted into the Laplace domain and the \(2 \times 2\) transfer function matrix \(\mathbf{G}_d\) from \(\begin{bmatrix}F_u & F_v\end{bmatrix}\) to \(\begin{bmatrix}d_u & d_v\end{bmatrix}\) in Eq. \eqref{eq:Gd_mimo_tf} is obtained.
Its elements are shown in Eq. \eqref{eq:Gd_indiv_el}. Its elements are shown in Eq. \eqref{eq:Gd_indiv_el}.
@@ -158,6 +166,7 @@ For all further numerical analysis in this study, we consider \(\omega_0 = \SI{1
Even though no system with such parameters will be encountered in practice, conclusions can be drawn relative to these parameters such that they can be generalized to any other set of parameters. Even though no system with such parameters will be encountered in practice, conclusions can be drawn relative to these parameters such that they can be generalized to any other set of parameters.
\par \par
The poles of \(\mathbf{G}_d\) are the complex solutions \(p\) of Eq. \eqref{eq:poles}. The poles of \(\mathbf{G}_d\) are the complex solutions \(p\) of Eq. \eqref{eq:poles}.
\begin{equation} \begin{equation}
@@ -220,7 +229,6 @@ For \(\Omega > \omega_0\), the low frequency pair of complex conjugate poles \(p
\caption{\label{fig:plant_compare_rotating_speed}Bode plots for \(\mathbf{G}_d\) for several rotational speed \(\Omega\)} \caption{\label{fig:plant_compare_rotating_speed}Bode plots for \(\mathbf{G}_d\) for several rotational speed \(\Omega\)}
\centering \centering
\end{figure} \end{figure}
\section{Decentralized Integral Force Feedback} \section{Decentralized Integral Force Feedback}
\label{sec:iff} \label{sec:iff}
In order to apply IFF to the rotating system, force sensors are added in series with the two actuators (Figure \ref{fig:system_iff}). In order to apply IFF to the rotating system, force sensors are added in series with the two actuators (Figure \ref{fig:system_iff}).
@@ -240,6 +248,7 @@ The control diagram is schematically shown in Figure \ref{fig:control_diagram_if
\end{figure} \end{figure}
\par \par
The forces \(\begin{bmatrix}f_u & f_v\end{bmatrix}\) measured by the two force sensors represented in Figure \ref{fig:system_iff} are described by Eq. \eqref{eq:measured_force}. The forces \(\begin{bmatrix}f_u & f_v\end{bmatrix}\) measured by the two force sensors represented in Figure \ref{fig:system_iff} are described by Eq. \eqref{eq:measured_force}.
\begin{equation} \begin{equation}
\label{eq:measured_force} \label{eq:measured_force}
@@ -298,6 +307,7 @@ This can be explained as follows: a constant force \(F_u\) induces a small displ
\end{figure} \end{figure}
\par \par
\label{sec:iff_pure_int} \label{sec:iff_pure_int}
The two IFF controllers \(K_{F}\) consist of a pure integrator as shown in Eq. \eqref{eq:Kf_pure_int} where \(g\) is a scalar representing the gain of the controller. The two IFF controllers \(K_{F}\) consist of a pure integrator as shown in Eq. \eqref{eq:Kf_pure_int} where \(g\) is a scalar representing the gain of the controller.
\begin{equation} \begin{equation}
@@ -326,7 +336,6 @@ The control system is thus canceling the spring forces which makes the suspended
In order to apply decentralized IFF to rotating platforms, two solutions are proposed to deal with this instability problem. In order to apply decentralized IFF to rotating platforms, two solutions are proposed to deal with this instability problem.
The first one consists of slightly modifying the control law (Section \ref{sec:iff_hpf}) while the second one consists of adding springs in parallel with the force sensors (Section \ref{sec:iff_kp}). The first one consists of slightly modifying the control law (Section \ref{sec:iff_hpf}) while the second one consists of adding springs in parallel with the force sensors (Section \ref{sec:iff_kp}).
\section{Integral Force Feedback with High Pass Filter} \section{Integral Force Feedback with High Pass Filter}
\label{sec:iff_hpf} \label{sec:iff_hpf}
As was explained in the previous section, the instability comes in part from the high gain at low frequency caused by the pure integrators. As was explained in the previous section, the instability comes in part from the high gain at low frequency caused by the pure integrators.
@@ -344,6 +353,7 @@ This modification of the IFF controller is typically done to avoid saturation as
This is however not the case in this study as it will become clear in the next section. This is however not the case in this study as it will become clear in the next section.
\par \par
The loop gains, \(K_F(s)\) times the direct dynamics \(f_u/F_u\), with and without the added HPF are shown in Figure \ref{fig:loop_gain_modified_iff}. The loop gains, \(K_F(s)\) times the direct dynamics \(f_u/F_u\), with and without the added HPF are shown in Figure \ref{fig:loop_gain_modified_iff}.
The effect of the added HPF limits the low frequency gain as expected. The effect of the added HPF limits the low frequency gain as expected.
@@ -370,6 +380,7 @@ It is interesting to note that \(g_{\text{max}}\) also corresponds to the contro
\end{figure} \end{figure}
\par \par
Two parameters can be tuned for the modified controller in Eq. \eqref{eq:IFF_LHF}: the gain \(g\) and the pole's location \(\omega_i\). Two parameters can be tuned for the modified controller in Eq. \eqref{eq:IFF_LHF}: the gain \(g\) and the pole's location \(\omega_i\).
The optimal values of \(\omega_i\) and \(g\) are here considered as the values for which the damping of all the closed-loop poles are simultaneously maximized. The optimal values of \(\omega_i\) and \(g\) are here considered as the values for which the damping of all the closed-loop poles are simultaneously maximized.
@@ -397,7 +408,6 @@ Three regions can be observed:
\item \(0.02 < \omega_i/\omega_0 < 0.2\): the attainable damping ratio is maximized and is reached for \(g \approx 2\) \item \(0.02 < \omega_i/\omega_0 < 0.2\): the attainable damping ratio is maximized and is reached for \(g \approx 2\)
\item \(0.2 < \omega_i/\omega_0\): the added damping decreases as \(\omega_i/\omega_0\) increases. \item \(0.2 < \omega_i/\omega_0\): the added damping decreases as \(\omega_i/\omega_0\) increases.
\end{itemize} \end{itemize}
\section{Integral Force Feedback with Parallel Springs} \section{Integral Force Feedback with Parallel Springs}
\label{sec:iff_kp} \label{sec:iff_kp}
In this section additional springs in parallel with the force sensors are added to counteract the negative stiffness induced by the gyroscopic effects. In this section additional springs in parallel with the force sensors are added to counteract the negative stiffness induced by the gyroscopic effects.
@@ -413,6 +423,7 @@ The parallel stiffness \(k_p\) then corresponds to the mechanical amplification
\end{figure} \end{figure}
\par \par
The forces measured by the two force sensors represented in Figure \ref{fig:system_parallel_springs} are described by Eq. \eqref{eq:measured_force_kp}. The forces measured by the two force sensors represented in Figure \ref{fig:system_parallel_springs} are described by Eq. \eqref{eq:measured_force_kp}.
\begin{equation} \begin{equation}
@@ -476,6 +487,7 @@ It is shown that if the added stiffness is higher than the maximum negative stif
\end{figure} \end{figure}
\par \par
Even though the parallel stiffness \(k_p\) has no impact on the open-loop poles (as the overall stiffness \(k\) is kept constant), it has a large impact on the transmission zeros. Even though the parallel stiffness \(k_p\) has no impact on the open-loop poles (as the overall stiffness \(k\) is kept constant), it has a large impact on the transmission zeros.
Moreover, as the attainable damping is generally proportional to the distance between poles and zeros \cite{preumont18_vibrat_contr_activ_struc_fourt_edition}, the parallel stiffness \(k_p\) is foreseen to have a large impact on the attainable damping. Moreover, as the attainable damping is generally proportional to the distance between poles and zeros \cite{preumont18_vibrat_contr_activ_struc_fourt_edition}, the parallel stiffness \(k_p\) is foreseen to have a large impact on the attainable damping.
@@ -497,7 +509,6 @@ This is confirmed by the Figure \ref{fig:opt_damp_alpha} where the attainable cl
\includegraphics[scale=1,scale=0.95]{figs/fig16.pdf} \includegraphics[scale=1,scale=0.95]{figs/fig16.pdf}
\caption{\label{fig:opt_damp_alpha}Optimal damping ratio \(\xi_\text{opt}\) and the corresponding optimal gain \(g_\text{opt}\) as a function of \(\alpha\)} \caption{\label{fig:opt_damp_alpha}Optimal damping ratio \(\xi_\text{opt}\) and the corresponding optimal gain \(g_\text{opt}\) as a function of \(\alpha\)}
\end{figure} \end{figure}
\section{Comparison and Discussion} \section{Comparison and Discussion}
\label{sec:comparison} \label{sec:comparison}
In order to overcome the instability issue of the classical IFF strategy when applied to rotating platforms, two modifications of IFF have been proposed in Sections \ref{sec:iff_hpf} and \ref{sec:iff_kp}. In order to overcome the instability issue of the classical IFF strategy when applied to rotating platforms, two modifications of IFF have been proposed in Sections \ref{sec:iff_hpf} and \ref{sec:iff_kp}.
@@ -507,6 +518,7 @@ For the following comparisons, the cut-off frequency for the HPF is set to \(\om
These values are chosen based on the discussion about optimal parameters. These values are chosen based on the discussion about optimal parameters.
\par \par
Figure \ref{fig:comp_root_locus} shows the Root Locus plots for the two proposed IFF modifications. Figure \ref{fig:comp_root_locus} shows the Root Locus plots for the two proposed IFF modifications.
While the two pairs of complex conjugate open-loop poles are identical for both techniques, the transmission zeros are not. While the two pairs of complex conjugate open-loop poles are identical for both techniques, the transmission zeros are not.
This means that the closed-loop behavior of both systems will differ when large control gains are used. This means that the closed-loop behavior of both systems will differ when large control gains are used.
@@ -523,6 +535,7 @@ It is interesting to note that the maximum added damping is very similar for bot
\end{figure} \end{figure}
\par \par
The two proposed techniques are now compared in terms of closed-loop transmissibility and compliance. The two proposed techniques are now compared in terms of closed-loop transmissibility and compliance.
The transmissibility is here defined as the transfer function from a displacement of the rotating stage along \(\vec{i}_x\) to the displacement of the payload along the same direction. The transmissibility is here defined as the transfer function from a displacement of the rotating stage along \(\vec{i}_x\) to the displacement of the payload along the same direction.
@@ -557,7 +570,6 @@ It is also confirmed that these two techniques can significantly damp the suspen
On can see in Figure \ref{fig:comp_transmissibility} that the problem of the degradation of the transmissibility at high frequency when using passive damping techniques is overcome by the use of IFF. On can see in Figure \ref{fig:comp_transmissibility} that the problem of the degradation of the transmissibility at high frequency when using passive damping techniques is overcome by the use of IFF.
The addition of the HPF or the use of the parallel stiffness also permits to limit the degradation of the compliance as compared with classical IFF (Figure \ref{fig:comp_compliance}). The addition of the HPF or the use of the parallel stiffness also permits to limit the degradation of the compliance as compared with classical IFF (Figure \ref{fig:comp_compliance}).
\section{Conclusion} \section{Conclusion}
\label{sec:conclusion} \label{sec:conclusion}
@@ -575,15 +587,12 @@ It was shown that if the stiffness \(k_p\) of the additional springs is larger t
While having very different implementations, both proposed modifications are very similar when it comes to the attainable damping and the obtained closed loop system behavior. While having very different implementations, both proposed modifications are very similar when it comes to the attainable damping and the obtained closed loop system behavior.
Future work will focus on the experimental validation of the proposed IFF modifications. Future work will focus on the experimental validation of the proposed IFF modifications.
\section*{Data Availability} \section*{Data Availability}
Matlab \cite{matlab20} was used for this study. Matlab \cite{matlab20} was used for this study.
The source code is available under a MIT License and archived in Zenodo \cite{dehaeze20_activ_dampin_rotat_posit_platf}. The source code is available under a MIT License and archived in Zenodo \cite{dehaeze20_activ_dampin_rotat_posit_platf}.
\section*{Acknowledgments} \section*{Acknowledgments}
This research benefited from a FRIA grant (grant number: FC 31597) from the French Community of Belgium. This research benefited from a FRIA grant (grant number: FC 31597) from the French Community of Belgium.
This paper is based on a paper previously presented at the ISMA conference \cite{dehaeze20_activ_dampin_rotat_platf_integ_force_feedb}. This paper is based on a paper previously presented at the ISMA conference \cite{dehaeze20_activ_dampin_rotat_platf_integ_force_feedb}.
\bibliographystyle{iopart-num} \bibliographystyle{iopart-num}
\bibliography{ref} \bibliography{ref}
\end{document} \end{document}
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matlab/index.org
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@@ -1,4 +1,7 @@
#+TITLE: Active Damping of Rotating Platforms using Integral Force Feedback - Matlab Computation #+TITLE: Active Damping of Rotating Platforms using Integral Force Feedback - Matlab Computation
#+hugo_section: research/dehaeze21_activ_dampin_rotat_platf_using
#+hugo_bundle: matlab
#+export_file_name: index
:DRAWER: :DRAWER:
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ../index.html
@@ -25,14 +28,8 @@
#+PROPERTY: header-args:matlab+ :output-dir figs #+PROPERTY: header-args:matlab+ :output-dir figs
:END: :END:
#+begin_export html
<hr>
<p>This report is also available as a <a href="./index.pdf">pdf</a>.</p>
<hr>
#+end_export
* Introduction :ignore: * Introduction :ignore:
This document gathers the Matlab code used to for the conference paper cite:dehaeze20_activ_dampin_rotat_platf_integ_force_feedb and the journal paper cite:dehaeze21_activ_dampin_rotat_platf_using. This document gathers the Matlab code used to for the conference paper [[cite:&dehaeze20_activ_dampin_rotat_platf_integ_force_feedb]] and the journal paper [[cite:&dehaeze21_activ_dampin_rotat_platf_using]].
It is structured in several sections: It is structured in several sections:
- Section [[sec:system_description]]: presents a simple model of a rotating suspended platform that will be used throughout this study. - Section [[sec:system_description]]: presents a simple model of a rotating suspended platform that will be used throughout this study.
@@ -42,7 +39,7 @@ It is structured in several sections:
- Section [[sec:comparison]]: compares both proposed modifications to the classical IFF in terms of damping authority and closed-loop system behavior. - Section [[sec:comparison]]: compares both proposed modifications to the classical IFF in terms of damping authority and closed-loop system behavior.
- Section [[sec:notations]]: contains the notations used for both the Matlab code and the paper - Section [[sec:notations]]: contains the notations used for both the Matlab code and the paper
The matlab code is accessible on [[https://zenodo.org/record/3894343][Zonodo]] and [[https://github.com/tdehaeze/dehaeze20_contr_stewa_platf][Github]] cite:dehaeze20_activ_dampin_rotat_posit_platf. It can also be download as a =.zip= file [[file:matlab.zip][here]]. The matlab code is accessible on [[https://zenodo.org/record/3894343][Zonodo]] and [[https://github.com/tdehaeze/dehaeze20_contr_stewa_platf][Github]] [[cite:&dehaeze20_activ_dampin_rotat_posit_platf]]. It can also be download as a =.zip= file [[file:matlab.zip][here]].
To run the Matlab code, go in the =matlab= directory and run the following Matlab files corresponding to each section. To run the Matlab code, go in the =matlab= directory and run the following Matlab files corresponding to each section.
@@ -80,7 +77,7 @@ The system consists of one 2 degree of freedom translation stage on top of a spi
#+name: fig:system #+name: fig:system
#+caption: Schematic of the studied system #+caption: Schematic of the studied system
[[file:figs-paper/system.png]] [[file:figs/fig04.png]]
The control inputs are the forces applied by the actuators of the translation stage ($F_u$ and $F_v$). The control inputs are the forces applied by the actuators of the translation stage ($F_u$ and $F_v$).
As the translation stage is rotating around the Z axis due to the spindle, the forces are applied along $\vec{i}_u$ and $\vec{i}_v$. As the translation stage is rotating around the Z axis due to the spindle, the forces are applied along $\vec{i}_u$ and $\vec{i}_v$.
@@ -439,7 +436,7 @@ Two identical controllers $K_F$ are used to feedback each of the sensed force to
#+name: fig:system_iff #+name: fig:system_iff
#+caption: System with added Force Sensor in series with the actuators #+caption: System with added Force Sensor in series with the actuators
[[file:figs-paper/system_iff.png]] [[file:figs/fig01.png]]
** Matlab Init :noexport:ignore: ** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
@@ -1180,7 +1177,7 @@ In this section additional springs in parallel with the force sensors are added
#+name: fig:system_parallel_springs #+name: fig:system_parallel_springs
#+caption: Studied system with additional springs in parallel with the actuators and force sensors #+caption: Studied system with additional springs in parallel with the actuators and force sensors
[[file:figs-paper/system_parallel_springs.png]] [[file:figs/fig12.png]]
In order to keep the overall stiffness $k = k_a + k_p$ constant, a scalar parameter $\alpha$ ($0 \le \alpha < 1$) is defined to describe the fraction of the total stiffness in parallel with the actuator and force sensor In order to keep the overall stiffness $k = k_a + k_p$ constant, a scalar parameter $\alpha$ ($0 \le \alpha < 1$) is defined to describe the fraction of the total stiffness in parallel with the actuator and force sensor
\begin{equation} \begin{equation}
tikz/config.html
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<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-11-12 jeu. 10:40 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>LaTeX Configuration for Tikz export</title>
<meta name="generator" content="Org mode" />
<meta name="author" content="Thomas Dehaeze" />
<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
</head>
<body>
<div id="org-div-home-and-up">
<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
</div><div id="content">
<h1 class="title">LaTeX Configuration for Tikz export</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org867af51">1. Packages</a></li>
<li><a href="#org0ce4790">2. Tikz related packages</a></li>
<li><a href="#org8bcc408">3. Tikz Libraries</a></li>
<li><a href="#orgde57bbd">4. PGF Plot libraries and config</a></li>
<li><a href="#org94164aa">5. Setup size of figures</a></li>
<li><a href="#org502b962">6. Setup Arrows style</a></li>
<li><a href="#orgf6c80f8">7. Colors</a></li>
<li><a href="#org6bc9bcf">8. Control</a>
<ul>
<li><a href="#org1d11095">8.1. Blocks</a></li>
<li><a href="#org2c3854c">8.2. Branches</a></li>
<li><a href="#orgf96b1b7">8.3. Hand Writen Style</a></li>
<li><a href="#org37871dd">8.4. DAC</a></li>
<li><a href="#orgbe02fb3">8.5. ADC</a></li>
<li><a href="#org1589875">8.6. Gain</a></li>
<li><a href="#orgbda9747">8.7. Add / Substract / Divide / Multiply block</a></li>
</ul>
</li>
<li><a href="#org419f26c">9. Plots</a>
<ul>
<li><a href="#org1e09080">9.1. Grid</a></li>
<li><a href="#orgfbf200f">9.2. Lines</a></li>
<li><a href="#orgb0c9fcd">9.3. Ticks</a></li>
<li><a href="#org6657c23">9.4. Size</a></li>
<li><a href="#org834808f">9.5. Label</a></li>
<li><a href="#org3d4f938">9.6. Legend</a></li>
<li><a href="#org834d8fb">9.7. Upper and Lower bounds</a></li>
<li><a href="#org006768d">9.8. Pole</a></li>
<li><a href="#org4d0b582">9.9. Zero</a></li>
</ul>
</li>
<li><a href="#orgf4cc3ee">10. Mechanical</a>
<ul>
<li><a href="#orge4f0590">10.1. Spring</a></li>
<li><a href="#org5b9134f">10.2. Coil</a></li>
<li><a href="#orgd2347a6">10.3. Damper</a></li>
<li><a href="#orgdd8b774">10.4. Actuator</a></li>
<li><a href="#orgbf79dfb">10.5. Ground</a></li>
<li><a href="#org29f9d60">10.6. Force Sensor</a></li>
<li><a href="#org1e03e32">10.7. Inertial Sensor</a></li>
<li><a href="#orgeae9e18">10.8. Axis Rotator</a></li>
<li><a href="#orgc22a8c6">10.9. Cross</a></li>
<li><a href="#org2167d13">10.10. Piezoelectric actuator</a></li>
<li><a href="#org2ae4369">10.11. Voice coil</a></li>
</ul>
</li>
<li><a href="#org3730519">11. Optics</a></li>
<li><a href="#org0b6e57a">12. Misc</a></li>
</ul>
</div>
</div>
<div id="outline-container-org867af51" class="outline-2">
<h2 id="org867af51"><span class="section-number-2">1</span> Packages</h2>
<div class="outline-text-2" id="text-1">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>[<span class="org-variable-name">utf8</span>]{<span class="org-function-name">inputenc</span>}
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>[<span class="org-variable-name">T1</span>]{<span class="org-function-name">fontenc</span>}
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>[<span class="org-variable-name">french, english</span>]{<span class="org-function-name">babel</span>} <span class="org-comment">% Last language is main language</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">lmodern</span>} <span class="org-comment">% Latin Modern Font</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">gensymb</span>} <span class="org-comment">% Generic symbols for both text and math mode</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">standalone</span>} <span class="org-comment">% Used to generate standalone Tikz</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">amsmath</span>} <span class="org-comment">% Main math Package</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">mathtools</span>} <span class="org-comment">% Extension package to amsmath</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">amsthm</span>} <span class="org-comment">% Typesetting theorems (AMS style)</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">amsfonts</span>} <span class="org-comment">% More fonts from the AMS</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">textcomp</span>} <span class="org-comment">% provide many text symbols</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">steinmetz</span>} <span class="org-comment">% For phase symbol</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">xstring</span>} <span class="org-comment">% Utils to manipulate strings</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">etoolbox</span>} <span class="org-comment">% Add basic if/then</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">esvect</span>} <span class="org-comment">% Beautyfull vectors</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">graphicx</span>} <span class="org-comment">% Enhanced support for graphics</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">grffile</span>} <span class="org-comment">% Used by matlab2tikz</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">microtype</span>} <span class="org-comment">% typographic tuning</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">setspace</span>} <span class="org-comment">% for line spacing, e.g. </span><span class="org-font-latex-sedate"><span class="org-comment">\onehalfspacing</span></span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">tabularx</span>} <span class="org-comment">% table features</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">enumitem</span>} <span class="org-comment">% for simple list modifications</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">booktabs</span>} <span class="org-comment">% better table support</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">stackengine</span>} <span class="org-comment">%</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>[<span class="org-variable-name">load-configurations=abbreviations</span>]{<span class="org-function-name">siunitx</span>} <span class="org-comment">% SI units</span>
<span class="org-font-latex-sedate">\sisetup</span>{
locale = US,
detect-all,
range-phrase=--,
range-units=single
}
</pre>
</div>
</div>
</div>
<div id="outline-container-org0ce4790" class="outline-2">
<h2 id="org0ce4790"><span class="section-number-2">2</span> Tikz related packages</h2>
<div class="outline-text-2" id="text-2">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">tikz</span>} <span class="org-comment">% Tikz</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">tikzscale</span>} <span class="org-comment">% Used to scale Tikz graphics</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">adjustbox</span>} <span class="org-comment">% Used to proper positioning of tikz pictures</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">circuitikz</span>} <span class="org-comment">% Draw electronic circuits</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">pgfpages</span>} <span class="org-comment">% Needed to use notes</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">pgfplots</span>} <span class="org-comment">% Used to plot functions</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org8bcc408" class="outline-2">
<h2 id="org8bcc408"><span class="section-number-2">3</span> Tikz Libraries</h2>
<div class="outline-text-2" id="text-3">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\usetikzlibrary</span>{arrows} <span class="org-comment">% Arrow tip library</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{arrows.meta} <span class="org-comment">% Add some arrows</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{calc} <span class="org-comment">% The library allows advanced Coordinate Calculations</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{intersections} <span class="org-comment">% calculate intersections of paths</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{matrix} <span class="org-comment">%</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{patterns} <span class="org-comment">%</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{shapes} <span class="org-comment">% Defines circle and rectangle</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{shapes.geometric} <span class="org-comment">% Use for the shape diamond and isosceles triangle</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{snakes} <span class="org-comment">% snake=coil and snake=zigzag using segment amplitude=10pt</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{positioning} <span class="org-comment">% Additional options for placing nodes</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{3d} <span class="org-comment">% Plot 3D shapes</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{spy} <span class="org-comment">% Creating a magnified area</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{decorations.text} <span class="org-comment">% Used to make text follows a curve</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{decorations.pathmorphing} <span class="org-comment">% deformation of a path</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{decorations.markings} <span class="org-comment">% Used for spring and damper</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{babel} <span class="org-comment">% A tiny library that make the interaction with the babel package easier</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{plotmarks} <span class="org-comment">% This library defines a number of plot marks</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{fit} <span class="org-comment">% Used to make rectangle as nodes by specifying two points</span>
<span class="org-font-latex-sedate">\usetikzlibrary</span>{backgrounds} <span class="org-comment">% Used to put things under others</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orgde57bbd" class="outline-2">
<h2 id="orgde57bbd"><span class="section-number-2">4</span> PGF Plot libraries and config</h2>
<div class="outline-text-2" id="text-4">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\usepgfplotslibrary</span>{patchplots}
<span class="org-font-latex-sedate">\usepgfplotslibrary</span>{groupplots}
<span class="org-font-latex-sedate">\pgfplotsset</span>{compat=newest}
<span class="org-font-latex-sedate">\pgfplotsset</span>{plot coordinates/math parser=false}
</pre>
</div>
</div>
</div>
<div id="outline-container-org94164aa" class="outline-2">
<h2 id="org94164aa"><span class="section-number-2">5</span> Setup size of figures</h2>
<div class="outline-text-2" id="text-5">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\newlength</span></span>{<span class="org-font-latex-sedate"><span class="org-function-name">\fheight</span></span>}
<span class="org-font-latex-sedate"><span class="org-keyword">\newlength</span></span>{<span class="org-font-latex-sedate"><span class="org-function-name">\fwidth</span></span>}
<span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span>{<span class="org-font-latex-sedate"><span class="org-variable-name">\fwidth</span></span>}{<span class="org-variable-name">85mm</span>}
<span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span>{<span class="org-font-latex-sedate"><span class="org-variable-name">\fheight</span></span>}{<span class="org-variable-name">112mm</span>}
</pre>
</div>
</div>
</div>
<div id="outline-container-org502b962" class="outline-2">
<h2 id="org502b962"><span class="section-number-2">6</span> Setup Arrows style</h2>
<div class="outline-text-2" id="text-6">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{&gt;=Stealth}
<span class="org-comment-delimiter">% </span><span class="org-comment">Setup default Linewidth</span>
<span class="org-font-latex-sedate">\tikzset</span>{every path/.style={line width=1pt}}
</pre>
</div>
</div>
</div>
<div id="outline-container-orgf6c80f8" class="outline-2">
<h2 id="orgf6c80f8"><span class="section-number-2">7</span> Colors</h2>
<div class="outline-text-2" id="text-7">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">xcolor</span>}<span class="org-comment">% Color extension</span>
<span class="org-font-latex-sedate">\definecolor</span>{colorblack}{rgb}{0, 0, 0}
<span class="org-font-latex-sedate">\definecolor</span>{colorblue}{rgb}{0, 0.4470, 0.7410}
<span class="org-font-latex-sedate">\definecolor</span>{colorred}{rgb}{0.8500, 0.3250, 0.0980}
<span class="org-font-latex-sedate">\definecolor</span>{coloryellow}{rgb}{0.9290, 0.6940, 0.1250}
<span class="org-font-latex-sedate">\definecolor</span>{colorpurple}{rgb}{0.4940, 0.1840, 0.5560}
<span class="org-font-latex-sedate">\definecolor</span>{colorgreen}{rgb}{0.4660, 0.6740, 0.1880}
<span class="org-font-latex-sedate">\definecolor</span>{colorcyan}{rgb}{0.3010, 0.7450, 0.9330}
<span class="org-font-latex-sedate">\definecolor</span>{colorbordeau}{rgb}{0.6350, 0.0780, 0.1840}
<span class="org-comment-delimiter">% </span><span class="org-comment">Main color</span>
<span class="org-font-latex-sedate">\definecolor</span>{maincolor}{RGB}{89, 9, 38}
<span class="org-font-latex-sedate">\definecolor</span>{secondcolor}{RGB}{20, 9, 89}
</pre>
</div>
</div>
</div>
<div id="outline-container-org6bc9bcf" class="outline-2">
<h2 id="org6bc9bcf"><span class="section-number-2">8</span> Control</h2>
<div class="outline-text-2" id="text-8">
</div>
<div id="outline-container-org1d11095" class="outline-3">
<h3 id="org1d11095"><span class="section-number-3">8.1</span> Blocks</h3>
<div class="outline-text-3" id="text-8-1">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
block/.style n args={2}{<span class="org-comment">%</span>
draw,
fill=white,
minimum width = #1,
minimum height = #2,
},
block/.default={1.2cm}{1.0cm}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-org2c3854c" class="outline-3">
<h3 id="org2c3854c"><span class="section-number-3">8.2</span> Branches</h3>
<div class="outline-text-3" id="text-8-2">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzstyle</span>{branch}=[fill,shape=circle,minimum size=4pt,inner sep=0pt]
<span class="org-font-latex-sedate">\tikzstyle</span>{-&gt;top}=[-{Stealth[color=black, scale=0.8]}, draw=white, double=black, double distance=1pt, line width=1pt]
<span class="org-font-latex-sedate">\tikzstyle</span>{&lt;-top}=[{stealth[color=black, scale=0.8]}-, draw=white, double=black, double distance=1pt, line width=1pt]
</pre>
</div>
</div>
</div>
<div id="outline-container-orgf96b1b7" class="outline-3">
<h3 id="orgf96b1b7"><span class="section-number-3">8.3</span> Hand Writen Style</h3>
<div class="outline-text-3" id="text-8-3">
<p>
Usefull for schematic plots
</p>
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzstyle</span>{handwriten}=[decorate,decoration={random steps,amplitude=0.1pt,segment length=0.8pt}]
</pre>
</div>
</div>
</div>
<div id="outline-container-org37871dd" class="outline-3">
<h3 id="org37871dd"><span class="section-number-3">8.4</span> DAC</h3>
<div class="outline-text-3" id="text-8-4">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
DAC/.style={<span class="org-comment">%</span>
draw,
signal,
}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-orgbe02fb3" class="outline-3">
<h3 id="orgbe02fb3"><span class="section-number-3">8.5</span> ADC</h3>
<div class="outline-text-3" id="text-8-5">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
ADC/.style={<span class="org-comment">%</span>
draw,
signal,
signal to = west,
}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-org1589875" class="outline-3">
<h3 id="org1589875"><span class="section-number-3">8.6</span> Gain</h3>
<div class="outline-text-3" id="text-8-6">
<p>
Maybe use <code>isosceles</code> instead of regular polygon?
</p>
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
gain right/.style={<span class="org-comment">%</span>
draw,
regular polygon,
regular polygon sides = 3,
inner sep = 2pt,
shape border rotate=-90
},
gain left/.style={<span class="org-comment">%</span>
draw,
regular polygon,
regular polygon sides = 3,
inner sep = 2pt,
shape border rotate=90
},
gain top/.style={<span class="org-comment">%</span>
draw,
regular polygon,
regular polygon sides = 3,
inner sep = 2pt,
shape border rotate=0
},
gain bottom/.style={<span class="org-comment">%</span>
draw,
regular polygon,
regular polygon sides = 3,
inner sep = 2pt,
shape border rotate=180
},
}
</pre>
</div>
</div>
</div>
<div id="outline-container-orgbda9747" class="outline-3">
<h3 id="orgbda9747"><span class="section-number-3">8.7</span> Add / Substract / Divide / Multiply block</h3>
<div class="outline-text-3" id="text-8-7">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">% Add block with Circled operations</span>
addc/.style n args={5}{<span class="org-comment">%</span>
draw,
fill=white,
circle,
outer sep = 0pt,
inner sep = 0pt,
minimum size = 2em,
execute at begin node={<span class="org-font-latex-sedate"><span class="org-keyword">\LARGE</span></span><span class="org-type"> </span><span class="org-type"><span class="org-font-latex-math">$#1$</span></span>},
append after command={<span class="org-font-latex-sedate">\pgfextra</span>{<span class="org-font-latex-sedate">\let\mainnode</span>=<span class="org-font-latex-sedate">\tikzlastnode</span>}
<span class="org-font-latex-sedate">\ifx</span>#2<span class="org-font-latex-sedate">\empty\else</span>
node[draw, circle, outer sep=6pt, inner sep=0pt, above left] at (<span class="org-font-latex-sedate">\mainnode</span>.west) {<span class="org-font-latex-math">$#2$</span>}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\fi</span>
<span class="org-font-latex-sedate">\ifx</span>#3<span class="org-font-latex-sedate">\empty\else</span>
node[draw, circle, outer sep=6pt, inner sep=0pt, above right] at (<span class="org-font-latex-sedate">\mainnode</span>.north) {<span class="org-font-latex-math">$#3$</span>}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\fi</span>
<span class="org-font-latex-sedate">\ifx</span>#4<span class="org-font-latex-sedate">\empty\else</span>
node[draw, circle, outer sep=6pt, inner sep=0pt, below right] at (<span class="org-font-latex-sedate">\mainnode</span>.east) {<span class="org-font-latex-math">$#4$</span>}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\fi</span>
<span class="org-font-latex-sedate">\ifx</span>#5<span class="org-font-latex-sedate">\empty\else</span>
node[draw, circle, outer sep=6pt, inner sep=0pt, below left] at (<span class="org-font-latex-sedate">\mainnode</span>.south) {<span class="org-font-latex-math">$#5$</span>}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\fi</span>
}
},
addc/.default={+}{}{}{}{},
}
</pre>
</div>
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">% Add Block</span>
addb/.style n args={5}{<span class="org-comment">%</span>
draw,
fill=white,
circle,
outer sep = 0pt,
inner sep = 0pt,
minimum size = 2em,
execute at begin node={<span class="org-font-latex-sedate"><span class="org-keyword">\LARGE</span></span><span class="org-type"> </span><span class="org-type"><span class="org-font-latex-math">$#1$</span></span>},
append after command={<span class="org-font-latex-sedate">\pgfextra</span>{<span class="org-font-latex-sedate">\let\mainnode</span>=<span class="org-font-latex-sedate">\tikzlastnode</span>}
<span class="org-font-latex-sedate">\ifx</span>#2<span class="org-font-latex-sedate">\empty\else</span>
node[outer sep=2pt, inner sep=0pt, above left] at (<span class="org-font-latex-sedate">\mainnode</span>.west) {<span class="org-font-latex-math">$#2$</span>}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\fi</span>
<span class="org-font-latex-sedate">\ifx</span>#3<span class="org-font-latex-sedate">\empty\else</span>
node[outer sep=2pt, inner sep=0pt, above right] at (<span class="org-font-latex-sedate">\mainnode</span>.north) {<span class="org-font-latex-math">$#3$</span>}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\fi</span>
<span class="org-font-latex-sedate">\ifx</span>#4<span class="org-font-latex-sedate">\empty\else</span>
node[outer sep=2pt, inner sep=0pt, below right] at (<span class="org-font-latex-sedate">\mainnode</span>.east) {<span class="org-font-latex-math">$#4$</span>}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\fi</span>
<span class="org-font-latex-sedate">\ifx</span>#5<span class="org-font-latex-sedate">\empty\else</span>
node[outer sep=2pt, inner sep=0pt, below left] at (<span class="org-font-latex-sedate">\mainnode</span>.south) {<span class="org-font-latex-math">$#5$</span>}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\fi</span>
}
},
addb/.default={+}{}{}{}{},
}
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org419f26c" class="outline-2">
<h2 id="org419f26c"><span class="section-number-2">9</span> Plots</h2>
<div class="outline-text-2" id="text-9">
</div>
<div id="outline-container-org1e09080" class="outline-3">
<h3 id="org1e09080"><span class="section-number-3">9.1</span> Grid</h3>
<div class="outline-text-3" id="text-9-1">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\pgfplotsset</span>{grid style={black}}
<span class="org-font-latex-sedate">\pgfplotsset</span>{major grid style={black!30!white}}
<span class="org-font-latex-sedate">\pgfplotsset</span>{minor grid style={black!10!white}}
<span class="org-font-latex-sedate">\pgfplotsset</span>{xmajorgrids}
<span class="org-font-latex-sedate">\pgfplotsset</span>{ymajorgrids}
</pre>
</div>
</div>
</div>
<div id="outline-container-orgfbf200f" class="outline-3">
<h3 id="orgfbf200f"><span class="section-number-3">9.2</span> Lines</h3>
<div class="outline-text-3" id="text-9-2">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\pgfplotsset</span>{separate axis lines=false} <span class="org-comment">% draw axis as rectangle and not as 4 lines</span>
<span class="org-font-latex-sedate">\pgfplotsset</span>{every outer x axis line/.append style={black}}
<span class="org-font-latex-sedate">\pgfplotsset</span>{every outer y axis line/.append style={black}}
<span class="org-font-latex-sedate">\pgfplotsset</span>{axis background/.style={fill=white}}
<span class="org-font-latex-sedate">\pgfplotsset</span>{axis x line*=bottom} <span class="org-comment">% solid line on the bottom with thin on the top</span>
<span class="org-font-latex-sedate">\pgfplotsset</span>{axis y line*=left} <span class="org-comment">% solid line on the left with thin on the right</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orgb0c9fcd" class="outline-3">
<h3 id="orgb0c9fcd"><span class="section-number-3">9.3</span> Ticks</h3>
<div class="outline-text-3" id="text-9-3">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\pgfplotsset</span>{every y tick label/.append style={font=<span class="org-font-latex-sedate">\color</span>{black}}}
<span class="org-font-latex-sedate">\pgfplotsset</span>{every y tick/.append style={black}}
<span class="org-font-latex-sedate">\pgfplotsset</span>{every x tick label/.append style={font=<span class="org-font-latex-sedate">\color</span>{black}}}
<span class="org-font-latex-sedate">\pgfplotsset</span>{every x tick/.append style={black}}
</pre>
</div>
</div>
</div>
<div id="outline-container-org6657c23" class="outline-3">
<h3 id="org6657c23"><span class="section-number-3">9.4</span> Size</h3>
<div class="outline-text-3" id="text-9-4">
<p>
If <code>scale only axis=false</code> (the default), pgfplots will try to produce the desired width including labels, titles and ticks.
</p>
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\pgfplotsset</span>{scale only axis=true}
</pre>
</div>
</div>
</div>
<div id="outline-container-org834808f" class="outline-3">
<h3 id="org834808f"><span class="section-number-3">9.5</span> Label</h3>
<div class="outline-text-3" id="text-9-5">
<p>
Used to align all of ylabel of one figure.
</p>
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\pgfplotsset</span>{ylabel absolute}
</pre>
</div>
</div>
</div>
<div id="outline-container-org3d4f938" class="outline-3">
<h3 id="org3d4f938"><span class="section-number-3">9.6</span> Legend</h3>
<div class="outline-text-3" id="text-9-6">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-comment-delimiter">% </span><span class="org-comment">https://tex.stackexchange.com/questions/54794/using-a-pgfplots-style-legend-in-a-plain-old-tikzpicture#54834</span>
<span class="org-comment-delimiter">% </span><span class="org-comment">argument #1: any options</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\newenvironment</span></span>{<span class="org-function-name">customlegend</span>}[<span class="org-variable-name">1</span>][]{<span class="org-function-name"><span class="org-comment">%</span></span>
<span class="org-function-name"> </span><span class="org-font-latex-sedate"><span class="org-function-name">\begingroup</span></span>
<span class="org-function-name"> </span><span class="org-function-name"><span class="org-comment">% inits/clears the lists (which might be populated from previous</span></span>
<span class="org-function-name"> </span><span class="org-function-name"><span class="org-comment">% axes):</span></span>
<span class="org-function-name"> </span><span class="org-font-latex-sedate"><span class="org-function-name">\csname</span></span><span class="org-function-name"> pgfplots@init@cleared@structures</span><span class="org-font-latex-sedate"><span class="org-function-name">\endcsname</span></span>
<span class="org-function-name"> </span><span class="org-font-latex-sedate"><span class="org-function-name">\pgfplotsset</span></span><span class="org-function-name">{#1}</span><span class="org-function-name"><span class="org-comment">%</span></span>
}{<span class="org-function-name"><span class="org-comment">%</span></span>
<span class="org-function-name"> </span><span class="org-function-name"><span class="org-comment">% draws the legend:</span></span>
<span class="org-function-name"> </span><span class="org-font-latex-sedate"><span class="org-function-name">\csname</span></span><span class="org-function-name"> pgfplots@createlegend</span><span class="org-font-latex-sedate"><span class="org-function-name">\endcsname</span></span>
<span class="org-function-name"> </span><span class="org-font-latex-sedate"><span class="org-function-name">\endgroup</span></span>
}<span class="org-comment">%</span>
<span class="org-comment-delimiter">% </span><span class="org-comment">makes </span><span class="org-font-latex-sedate"><span class="org-comment">\addlegendimage</span></span><span class="org-comment"> available (typically only available within an</span>
<span class="org-comment-delimiter">% </span><span class="org-comment">axis environment):</span>
<span class="org-font-latex-sedate">\def\addlegendimage</span>{<span class="org-font-latex-sedate">\csname</span> pgfplots@addlegendimage<span class="org-font-latex-sedate">\endcsname</span>}
<span class="org-comment-delimiter">% </span><span class="org-comment">definition to insert numbers</span>
<span class="org-comment-delimiter">% </span><span class="org-font-latex-sedate"><span class="org-comment">\pgfkeys</span></span><span class="org-comment">{/pgfplots/number in legend/.style={%</span>
<span class="org-comment-delimiter">% </span><span class="org-comment">/pgfplots/legend image code/.code={%</span>
<span class="org-comment-delimiter">% </span><span class="org-font-latex-sedate"><span class="org-comment">\node</span></span><span class="org-comment"> at (0.125,-0.0225){#1}; % &lt;= changed x value</span>
<span class="org-comment-delimiter">% </span><span class="org-comment">},%</span>
<span class="org-comment-delimiter">% </span><span class="org-comment">},</span>
<span class="org-comment-delimiter">% </span><span class="org-comment">}</span>
<span class="org-font-latex-sedate">\pgfplotsset</span>{
every legend to name picture/.style={west}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-org834d8fb" class="outline-3">
<h3 id="org834d8fb"><span class="section-number-3">9.7</span> Upper and Lower bounds</h3>
<div class="outline-text-3" id="text-9-7">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzstyle</span>{upperbound}=[line cap=round, postaction={decorate,draw,decoration={border, segment length=0.2cm, amplitude=0.3cm, angle=60}}]
<span class="org-font-latex-sedate">\tikzstyle</span>{lowerbound}=[line cap=round, postaction={decorate,draw,decoration={border, segment length=0.2cm, amplitude=0.3cm, angle=-60}}]
</pre>
</div>
<p>
And we add the corresdonding
</p>
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\pgfplotsset</span>{
/pgfplots/upperbound/.style 1 args={
legend image code/.code={
<span class="org-font-latex-sedate">\draw</span>[##1, upperbound]
plot coordinates {
(0cm,0cm)
(0.6cm,0cm)
}
}
}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-org006768d" class="outline-3">
<h3 id="org006768d"><span class="section-number-3">9.8</span> Pole</h3>
<div class="outline-text-3" id="text-9-8">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
pole/.style{<span class="org-comment">%</span>
color=red,
cross out,
draw,
inner sep=0pt,
outer sep=0pt,
minimum size=#1pt
},
pole/.default={4}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-org4d0b582" class="outline-3">
<h3 id="org4d0b582"><span class="section-number-3">9.9</span> Zero</h3>
<div class="outline-text-3" id="text-9-9">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
zero/.style{<span class="org-comment">%</span>
color=red,
circle,
draw,
inner sep=0pt,
outer sep=0pt,
minimum size=#1pt
},
zero/.default={4}
}
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-orgf4cc3ee" class="outline-2">
<h2 id="orgf4cc3ee"><span class="section-number-2">10</span> Mechanical</h2>
<div class="outline-text-2" id="text-10">
</div>
<div id="outline-container-orge4f0590" class="outline-3">
<h3 id="orge4f0590"><span class="section-number-3">10.1</span> Spring</h3>
<div class="outline-text-3" id="text-10-1">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
spring/.style={<span class="org-comment">%</span>
thick,
decoration={
zigzag,
pre length = #1cm,
post length = #1cm,
segment length = 6
},
decorate
},
spring/.default={0.2}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-org5b9134f" class="outline-3">
<h3 id="org5b9134f"><span class="section-number-3">10.2</span> Coil</h3>
<div class="outline-text-3" id="text-10-2">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
coil/.style n args={2}{<span class="org-comment">%</span>
thick,
decoration={
coil,
pre length = #1cm,
post length = #2cm,
segment length = 4
},
decorate
},
coil/.default={0.3}{0.3}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-orgd2347a6" class="outline-3">
<h3 id="orgd2347a6"><span class="section-number-3">10.3</span> Damper</h3>
<div class="outline-text-3" id="text-10-3">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
damper/.style n args={2}{<span class="org-comment">%</span>
thick,
decoration={markings, mark connection node=dmp, mark=at position 0.5 with {
<span class="org-font-latex-sedate">\node</span> (dmp) [thick,
inner sep = 0pt,
transform shape,
rotate =-90,
minimum width = #1pt,
minimum height = #2pt,
draw=none] {};
<span class="org-font-latex-sedate">\draw</span> [thick] (<span class="org-font-latex-math">$(dmp.north east)+(0.6*#2pt,0)$</span>) -- (dmp.south east) -- (dmp.south west) -- (<span class="org-font-latex-math">$(dmp.north west)+(0.6*#2pt,0)$</span>);
<span class="org-font-latex-sedate">\draw</span> [thick] (<span class="org-font-latex-math">$(dmp.north)+(0,-0.3*#1pt)$</span>) -- (<span class="org-font-latex-math">$(dmp.north)+(0,0.3*#1pt)$</span>);
}
},
decorate
},
damper/.default={12}{3}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-orgdd8b774" class="outline-3">
<h3 id="orgdd8b774"><span class="section-number-3">10.4</span> Actuator</h3>
<div class="outline-text-3" id="text-10-4">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
actuator/.style n args={2}{<span class="org-comment">%</span>
thick,
draw=none,
decoration={
markings,
mark connection node=my node,
mark=at position .5 with {
<span class="org-font-latex-sedate">\node</span> [draw, inner sep=0pt, minimum width=#1cm, minimum height=#2cm,
transform shape, fill=white] (my node) {};
},
mark=at position .0 with {
<span class="org-font-latex-sedate">\draw</span>[&lt;-] (0, 0) -- (my node);
},
mark=at position 1.0 with {
<span class="org-font-latex-sedate">\draw</span>[&lt;-] (0, 0) -- (my node);
}
},
decorate
},
actuator/.default={0.5}{0.2}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-orgbf79dfb" class="outline-3">
<h3 id="orgbf79dfb"><span class="section-number-3">10.5</span> Ground</h3>
<div class="outline-text-3" id="text-10-5">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
ground/.style n args={2}{<span class="org-comment">%</span>
fill,
pattern = north east lines,
draw = none,
anchor = north,
minimum width = #1cm,
minimum height = #2cm,
append after command={
(<span class="org-font-latex-sedate">\tikzlastnode</span>.north west) edge (<span class="org-font-latex-sedate">\tikzlastnode</span>.north east)
}
},
ground/.default={2.5}{0.3}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-org29f9d60" class="outline-3">
<h3 id="org29f9d60"><span class="section-number-3">10.6</span> Force Sensor</h3>
<div class="outline-text-3" id="text-10-6">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
forcesensor/.style n args={2}{<span class="org-comment">%</span>
rectangle,
outer sep=0pt,
inner sep=0pt,
draw=black,
fill=white!60!black,
anchor=south,
minimum width =#1cm,
minimum height=#2cm,
append after command={
[every edge/.append style={
thick,
black,
}]
(<span class="org-font-latex-sedate">\tikzlastnode</span>.north west) edge (<span class="org-font-latex-sedate">\tikzlastnode</span>.south east)
(<span class="org-font-latex-sedate">\tikzlastnode</span>.north east) edge (<span class="org-font-latex-sedate">\tikzlastnode</span>.south west)
}
},
forcesensor/.default={2.0}{0.5}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-org1e03e32" class="outline-3">
<h3 id="org1e03e32"><span class="section-number-3">10.7</span> Inertial Sensor</h3>
<div class="outline-text-3" id="text-10-7">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
inertialsensor/.style={<span class="org-comment">%</span>
rectangle,
outer sep=0pt,
inner sep=0pt,
draw=black,
fill=white!60!black,
anchor=south east,
minimum size=#1cm,
append after command={
[every edge/.append style={
thick,
black,
}]
(<span class="org-font-latex-sedate">\tikzlastnode</span>.north west) edge (<span class="org-font-latex-sedate">\tikzlastnode</span>.south east)
(<span class="org-font-latex-sedate">\tikzlastnode</span>.north east) edge (<span class="org-font-latex-sedate">\tikzlastnode</span>.south west)
}
},
inertialsensor/.default={0.3}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-orgeae9e18" class="outline-3">
<h3 id="orgeae9e18"><span class="section-number-3">10.8</span> Axis Rotator</h3>
<div class="outline-text-3" id="text-10-8">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\newcommand</span></span>{<span class="org-font-latex-sedate"><span class="org-function-name">\AxisRotator</span></span>}[<span class="org-variable-name">1</span>][<span class="org-variable-name">rotate=0</span>]{<span class="org-function-name"><span class="org-comment">%</span></span>
<span class="org-function-name"> </span><span class="org-font-latex-sedate"><span class="org-function-name">\tikz</span></span><span class="org-function-name"> [x=0.1cm,y=0.30cm,-stealth,#1] </span><span class="org-font-latex-sedate"><span class="org-function-name">\draw</span></span><span class="org-function-name"> (0,0) arc (-150:150:1 and 1);</span><span class="org-function-name"><span class="org-comment">%</span></span>
}
</pre>
</div>
</div>
</div>
<div id="outline-container-orgc22a8c6" class="outline-3">
<h3 id="orgc22a8c6"><span class="section-number-3">10.9</span> Cross</h3>
<div class="outline-text-3" id="text-10-9">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzstyle</span>{cross}=[path picture={
<span class="org-font-latex-sedate">\draw</span>[black]
(path picture bounding box.south east) -- (path picture bounding box.north west) (path picture bounding box.south west) -- (path picture bounding box.north east);
}]
</pre>
</div>
</div>
</div>
<div id="outline-container-org2167d13" class="outline-3">
<h3 id="org2167d13"><span class="section-number-3">10.10</span> Piezoelectric actuator</h3>
<div class="outline-text-3" id="text-10-10">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
piezo/.style n args={3}{<span class="org-comment">%</span>
draw,
rectangle,
minimum width = #1cm,
minimum height = #2cm,
fill=blue!10!white,
anchor=center,
append after command={
[every edge/.append style={
thick,
black,
}]
<span class="org-font-latex-sedate">\foreach</span> <span class="org-font-latex-sedate">\i</span> in {1,...,#3}{
(<span class="org-font-latex-math">${</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\i</span></span><span class="org-font-latex-math">/(1+#3)}*(</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tikzlastnode</span></span><span class="org-font-latex-math">.north west)+{(1+#3-</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\i</span></span><span class="org-font-latex-math">)/(1+#3)}*(</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tikzlastnode</span></span><span class="org-font-latex-math">.south west)+0.1*(#1,0)$</span>) edge (<span class="org-font-latex-math">${</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\i</span></span><span class="org-font-latex-math">/(1+#3)}*(</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tikzlastnode</span></span><span class="org-font-latex-math">.north east)+{(1+#3-</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\i</span></span><span class="org-font-latex-math">)/(1+#3)}*(</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tikzlastnode</span></span><span class="org-font-latex-math">.south east)-0.1*(#1,0)$</span>)
}
}
},
piezo/.default={2}{4}{10}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-org2ae4369" class="outline-3">
<h3 id="org2ae4369"><span class="section-number-3">10.11</span> Voice coil</h3>
<div class="outline-text-3" id="text-10-11">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\def\voicecoil</span>#1#2#3{
<span class="org-comment">% ======================</span>
<span class="org-comment">% Parameters</span>
<span class="org-comment">% ======================</span>
<span class="org-font-latex-sedate">\def\voicecoilw</span>{#1} <span class="org-comment">% Total Width</span>
<span class="org-font-latex-sedate">\def\voicecoilh</span>{#2} <span class="org-comment">% Total Height</span>
<span class="org-font-latex-sedate">\def\magnetw</span>{<span class="org-font-latex-sedate">\voicecoilw</span>} <span class="org-comment">% Width of the magnet</span>
<span class="org-font-latex-sedate">\def\magneth</span>{<span class="org-font-latex-sedate">\voicecoilh</span>/1.4} <span class="org-comment">% Height of the magnet</span>
<span class="org-font-latex-sedate">\def\magnetwb</span>{0.15*<span class="org-font-latex-sedate">\magnetw</span>} <span class="org-comment">% Width of the borders of the magnet</span>
<span class="org-font-latex-sedate">\def\magnetmw</span>{0.15*<span class="org-font-latex-sedate">\magnetw</span>} <span class="org-comment">% Width of the middle part of the magnet</span>
<span class="org-font-latex-sedate">\def\magnetwg</span>{0.5*<span class="org-font-latex-sedate">\magnetw</span>} <span class="org-comment">% Width of the gap of the magnet</span>
<span class="org-font-latex-sedate">\def\magnethl</span>{<span class="org-font-latex-sedate">\magnetwb</span>} <span class="org-comment">% Height of the low part of the magnet</span>
<span class="org-font-latex-sedate">\def\magnetmh</span>{0.15*<span class="org-font-latex-sedate">\magneth</span>} <span class="org-comment">% Height of the middle part of the magnet</span>
<span class="org-font-latex-sedate">\def\magnethg</span>{0.2*<span class="org-font-latex-sedate">\magneth</span>} <span class="org-comment">% Height of the gap of the magnet</span>
<span class="org-comment">% ======================</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[shift={(0.5*<span class="org-font-latex-sedate">\voicecoilw</span>, 0.5*<span class="org-font-latex-sedate">\voicecoilh</span>)}, rotate=#3, shift={(0, -0.5*<span class="org-font-latex-sedate">\voicecoilh</span>)}]
<span class="org-comment">% ======================</span>
<span class="org-comment">% Magnet</span>
<span class="org-comment">% ======================</span>
<span class="org-font-latex-sedate">\draw</span>[fill=white] (0, 0) -| ++(0.5*<span class="org-font-latex-sedate">\magnetw</span>, <span class="org-font-latex-sedate">\magneth</span>) -| ++(-0.5*<span class="org-font-latex-sedate">\magnetw</span>+0.5*<span class="org-font-latex-sedate">\magnetwg</span>, -<span class="org-font-latex-sedate">\magnethg</span>) -| (0.5*<span class="org-font-latex-sedate">\magnetw</span>-<span class="org-font-latex-sedate">\magnetwb</span>, <span class="org-font-latex-sedate">\magnethl</span>) -| (-0.5*<span class="org-font-latex-sedate">\magnetw</span>+<span class="org-font-latex-sedate">\magnetwb</span>, <span class="org-font-latex-sedate">\magneth</span>-<span class="org-font-latex-sedate">\magnethg</span>) -| (-0.5*<span class="org-font-latex-sedate">\magnetwg</span>, <span class="org-font-latex-sedate">\magneth</span>) -| (-0.5*<span class="org-font-latex-sedate">\magnetw</span>, 0) -- (cycle);
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[shift={(0, <span class="org-font-latex-sedate">\magnethl</span>)}]
<span class="org-font-latex-sedate">\draw</span>[fill=red] (-0.5*<span class="org-font-latex-sedate">\magnetmw</span>, 0) rectangle (0.5*<span class="org-font-latex-sedate">\magnetmw</span>, <span class="org-font-latex-sedate">\magnetmh</span>);
<span class="org-font-latex-sedate">\draw</span>[fill=blue] (-0.5*<span class="org-font-latex-sedate">\magnetmw</span>, <span class="org-font-latex-sedate">\magnetmh</span>) rectangle (0.5*<span class="org-font-latex-sedate">\magnetmw</span>, 2*<span class="org-font-latex-sedate">\magnetmh</span>);
<span class="org-comment">% Top conductive Magnet</span>
<span class="org-font-latex-sedate">\draw</span>[fill=white] (-0.5*<span class="org-font-latex-sedate">\magnetmw</span>, 2*<span class="org-font-latex-sedate">\magnetmh</span>) -| (0.5*<span class="org-font-latex-sedate">\magnetmw</span>, -<span class="org-font-latex-sedate">\magnethl</span>+<span class="org-font-latex-sedate">\magneth</span>-<span class="org-font-latex-sedate">\magnethg</span>) -| ++(0.1, <span class="org-font-latex-sedate">\magnethg</span>) -| ++(-0.2-<span class="org-font-latex-sedate">\magnetmw</span>, -<span class="org-font-latex-sedate">\magnethg</span>) -| (-0.5*<span class="org-font-latex-sedate">\magnetmw</span>, <span class="org-font-latex-sedate">\magnetmh</span>);
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-comment">% ======================</span>
<span class="org-comment">% ======================</span>
<span class="org-comment">% Coil</span>
<span class="org-comment">% ======================</span>
<span class="org-font-latex-sedate">\pgfmathsetmacro</span>{<span class="org-font-latex-sedate">\coilwidth</span>}{0.5*0.5*<span class="org-font-latex-sedate">\magnetmw</span>+0.5*0.1+0.25*<span class="org-font-latex-sedate">\magnetwg</span>}<span class="org-comment">%</span>
<span class="org-font-latex-sedate">\draw</span>[] ( <span class="org-font-latex-sedate">\coilwidth</span>, 0.5*<span class="org-font-latex-sedate">\magneth</span>) -- ++(0, 0.7*<span class="org-font-latex-sedate">\magneth</span>);
<span class="org-font-latex-sedate">\draw</span>[] (-<span class="org-font-latex-sedate">\coilwidth</span>, 0.5*<span class="org-font-latex-sedate">\magneth</span>) -- ++(0, 0.7*<span class="org-font-latex-sedate">\magneth</span>);
<span class="org-comment">% Point on the coil</span>
<span class="org-font-latex-sedate">\foreach</span> <span class="org-font-latex-sedate">\x</span> in {0,1,...,9}
{
<span class="org-font-latex-sedate">\node</span>[circle,inner sep=0.6pt,fill] at ( <span class="org-font-latex-sedate">\coilwidth</span>, <span class="org-font-latex-sedate">\x</span>*0.7*<span class="org-font-latex-sedate">\magneth</span>/10+0.5*<span class="org-font-latex-sedate">\magneth</span>);
<span class="org-font-latex-sedate">\node</span>[circle,inner sep=0.6pt,fill] at (-<span class="org-font-latex-sedate">\coilwidth</span>, <span class="org-font-latex-sedate">\x</span>*0.7*<span class="org-font-latex-sedate">\magneth</span>/10+0.5*<span class="org-font-latex-sedate">\magneth</span>);
}
<span class="org-font-latex-sedate">\draw</span>[fill=white] (-0.5*<span class="org-font-latex-sedate">\magnetw</span>, 1.2*<span class="org-font-latex-sedate">\magneth</span>) rectangle ++(<span class="org-font-latex-sedate">\magnetw</span>, <span class="org-font-latex-sedate">\magnethg</span>);
<span class="org-comment">% ======================</span>
<span class="org-comment">% ======================</span>
<span class="org-comment">% Coordinates</span>
<span class="org-comment">% ======================</span>
<span class="org-comment">% Force</span>
<span class="org-font-latex-sedate">\coordinate</span>[] (vc_force) at (0, <span class="org-font-latex-sedate">\magneth</span>-0.5*<span class="org-font-latex-sedate">\magnethg</span>);
<span class="org-comment">% Coil</span>
<span class="org-font-latex-sedate">\coordinate</span>[] (vc_coil) at (0, <span class="org-font-latex-sedate">\voicecoilh</span>);
<span class="org-comment">% Magnet</span>
<span class="org-font-latex-sedate">\coordinate</span>[] (vc_magnet) at (0, 0);
<span class="org-comment">% Coil Wires</span>
<span class="org-font-latex-sedate">\coordinate</span>[] (vc_wire_one) at ( <span class="org-font-latex-sedate">\coilwidth</span>, 1.2*<span class="org-font-latex-sedate">\magneth</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (vc_wire_two) at (-<span class="org-font-latex-sedate">\coilwidth</span>, 1.2*<span class="org-font-latex-sedate">\magneth</span>);
<span class="org-comment">% ======================</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
}
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org3730519" class="outline-2">
<h2 id="org3730519"><span class="section-number-2">11</span> Optics</h2>
<div class="outline-text-2" id="text-11">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
-&gt;-/.style={
decoration={
markings,
mark = at position #1 with {<span class="org-font-latex-sedate">\arrow</span>{&gt;}
}
},
postaction={decorate}
}
}
<span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
-&lt;-/.style={
decoration={
markings,
mark = at position #1 with {<span class="org-font-latex-sedate">\arrow</span>{&lt;}
}
},
postaction={decorate}
}
}
</pre>
</div>
</div>
</div>
<div id="outline-container-org0b6e57a" class="outline-2">
<h2 id="org0b6e57a"><span class="section-number-2">12</span> Misc</h2>
<div class="outline-text-2" id="text-12">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
labelc/.style= {<span class="org-comment">%</span>
draw,
fill=white,
shape=circle,
inner sep=2pt,
outer sep=6pt,
}
}
</pre>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2020-11-12 jeu. 10:40</p>
</div>
</body>
</html>
tikz/config.org
-689
View File
@@ -1,689 +0,0 @@
#+TITLE: LaTeX Configuration for Tikz export
:drawer:
#+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP: ../index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
#+PROPERTY: header-args:latex+ :tangle config.tex
#+PROPERTY: header-args:latex+ :exports code
:end:
* Packages
#+begin_src latex
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[french, english]{babel} % Last language is main language
\usepackage{lmodern} % Latin Modern Font
\usepackage{gensymb} % Generic symbols for both text and math mode
\usepackage{standalone} % Used to generate standalone Tikz
\usepackage{amsmath} % Main math Package
\usepackage{mathtools} % Extension package to amsmath
\usepackage{amsthm} % Typesetting theorems (AMS style)
\usepackage{amsfonts} % More fonts from the AMS
\usepackage{textcomp} % provide many text symbols
\usepackage{steinmetz} % For phase symbol
\usepackage{xstring} % Utils to manipulate strings
\usepackage{etoolbox} % Add basic if/then
\usepackage{esvect} % Beautyfull vectors
\usepackage{graphicx} % Enhanced support for graphics
\usepackage{grffile} % Used by matlab2tikz
\usepackage{microtype} % typographic tuning
\usepackage{setspace} % for line spacing, e.g. \onehalfspacing
\usepackage{tabularx} % table features
\usepackage{enumitem} % for simple list modifications
\usepackage{booktabs} % better table support
\usepackage{stackengine} %
\usepackage[load-configurations=abbreviations]{siunitx} % SI units
\sisetup{
locale = US,
detect-all,
range-phrase=--,
range-units=single
}
#+end_src
* Tikz related packages
#+begin_src latex
\usepackage{tikz} % Tikz
\usepackage{tikzscale} % Used to scale Tikz graphics
\usepackage{adjustbox} % Used to proper positioning of tikz pictures
\usepackage{circuitikz} % Draw electronic circuits
\usepackage{pgfpages} % Needed to use notes
\usepackage{pgfplots} % Used to plot functions
#+end_src
* Tikz Libraries
#+begin_src latex
\usetikzlibrary{arrows} % Arrow tip library
\usetikzlibrary{arrows.meta} % Add some arrows
\usetikzlibrary{calc} % The library allows advanced Coordinate Calculations
\usetikzlibrary{intersections} % calculate intersections of paths
\usetikzlibrary{matrix} %
\usetikzlibrary{patterns} %
\usetikzlibrary{shapes} % Defines circle and rectangle
\usetikzlibrary{shapes.geometric} % Use for the shape diamond and isosceles triangle
\usetikzlibrary{snakes} % snake=coil and snake=zigzag using segment amplitude=10pt
\usetikzlibrary{positioning} % Additional options for placing nodes
\usetikzlibrary{3d} % Plot 3D shapes
\usetikzlibrary{spy} % Creating a magnified area
\usetikzlibrary{decorations.text} % Used to make text follows a curve
\usetikzlibrary{decorations.pathmorphing} % deformation of a path
\usetikzlibrary{decorations.markings} % Used for spring and damper
\usetikzlibrary{babel} % A tiny library that make the interaction with the babel package easier
\usetikzlibrary{plotmarks} % This library defines a number of plot marks
\usetikzlibrary{fit} % Used to make rectangle as nodes by specifying two points
\usetikzlibrary{backgrounds} % Used to put things under others
#+end_src
* PGF Plot libraries and config
#+begin_src latex
\usepgfplotslibrary{patchplots}
\usepgfplotslibrary{groupplots}
\pgfplotsset{compat=newest}
\pgfplotsset{plot coordinates/math parser=false}
#+end_src
* Setup size of figures
#+begin_src latex
\newlength{\fheight}
\newlength{\fwidth}
\setlength{\fwidth}{85mm}
\setlength{\fheight}{112mm}
#+end_src
* Setup Arrows style
#+begin_src latex
\tikzset{>=Stealth}
% Setup default Linewidth
\tikzset{every path/.style={line width=1pt}}
#+end_src
* Colors
#+begin_src latex
\usepackage{xcolor}% Color extension
\definecolor{colorblack}{rgb}{0, 0, 0}
\definecolor{colorblue}{rgb}{0, 0.4470, 0.7410}
\definecolor{colorred}{rgb}{0.8500, 0.3250, 0.0980}
\definecolor{coloryellow}{rgb}{0.9290, 0.6940, 0.1250}
\definecolor{colorpurple}{rgb}{0.4940, 0.1840, 0.5560}
\definecolor{colorgreen}{rgb}{0.4660, 0.6740, 0.1880}
\definecolor{colorcyan}{rgb}{0.3010, 0.7450, 0.9330}
\definecolor{colorbordeau}{rgb}{0.6350, 0.0780, 0.1840}
% Main color
\definecolor{maincolor}{RGB}{89, 9, 38}
\definecolor{secondcolor}{RGB}{20, 9, 89}
#+end_src
* Control
** Blocks
#+begin_src latex
\tikzset{%
block/.style n args={2}{%
draw,
fill=white,
minimum width = #1,
minimum height = #2,
},
block/.default={1.2cm}{1.0cm}
}
#+end_src
** TODO Branches
#+begin_src latex
\tikzstyle{branch}=[fill,shape=circle,minimum size=4pt,inner sep=0pt]
\tikzstyle{->top}=[-{Stealth[color=black, scale=0.8]}, draw=white, double=black, double distance=1pt, line width=1pt]
\tikzstyle{<-top}=[{stealth[color=black, scale=0.8]}-, draw=white, double=black, double distance=1pt, line width=1pt]
#+end_src
** TODO Hand Writen Style
Usefull for schematic plots
#+begin_src latex
\tikzstyle{handwriten}=[decorate,decoration={random steps,amplitude=0.1pt,segment length=0.8pt}]
#+end_src
** DAC
#+begin_src latex
\tikzset{%
DAC/.style={%
draw,
signal,
}
}
#+end_src
** ADC
#+begin_src latex
\tikzset{%
ADC/.style={%
draw,
signal,
signal to = west,
}
}
#+end_src
** TODO Gain
Maybe use =isosceles= instead of regular polygon?
#+begin_src latex
\tikzset{%
gain right/.style={%
draw,
regular polygon,
regular polygon sides = 3,
inner sep = 2pt,
shape border rotate=-90
},
gain left/.style={%
draw,
regular polygon,
regular polygon sides = 3,
inner sep = 2pt,
shape border rotate=90
},
gain top/.style={%
draw,
regular polygon,
regular polygon sides = 3,
inner sep = 2pt,
shape border rotate=0
},
gain bottom/.style={%
draw,
regular polygon,
regular polygon sides = 3,
inner sep = 2pt,
shape border rotate=180
},
}
#+end_src
** Add / Substract / Divide / Multiply block
#+begin_src latex
\tikzset{% Add block with Circled operations
addc/.style n args={5}{%
draw,
fill=white,
circle,
outer sep = 0pt,
inner sep = 0pt,
minimum size = 2em,
execute at begin node={\LARGE $#1$},
append after command={\pgfextra{\let\mainnode=\tikzlastnode}
\ifx#2\empty\else
node[draw, circle, outer sep=6pt, inner sep=0pt, above left] at (\mainnode.west) {$#2$}%
\fi
\ifx#3\empty\else
node[draw, circle, outer sep=6pt, inner sep=0pt, above right] at (\mainnode.north) {$#3$}%
\fi
\ifx#4\empty\else
node[draw, circle, outer sep=6pt, inner sep=0pt, below right] at (\mainnode.east) {$#4$}%
\fi
\ifx#5\empty\else
node[draw, circle, outer sep=6pt, inner sep=0pt, below left] at (\mainnode.south) {$#5$}%
\fi
}
},
addc/.default={+}{}{}{}{},
}
#+end_src
#+begin_src latex
\tikzset{% Add Block
addb/.style n args={5}{%
draw,
fill=white,
circle,
outer sep = 0pt,
inner sep = 0pt,
minimum size = 2em,
execute at begin node={\LARGE $#1$},
append after command={\pgfextra{\let\mainnode=\tikzlastnode}
\ifx#2\empty\else
node[outer sep=2pt, inner sep=0pt, above left] at (\mainnode.west) {$#2$}%
\fi
\ifx#3\empty\else
node[outer sep=2pt, inner sep=0pt, above right] at (\mainnode.north) {$#3$}%
\fi
\ifx#4\empty\else
node[outer sep=2pt, inner sep=0pt, below right] at (\mainnode.east) {$#4$}%
\fi
\ifx#5\empty\else
node[outer sep=2pt, inner sep=0pt, below left] at (\mainnode.south) {$#5$}%
\fi
}
},
addb/.default={+}{}{}{}{},
}
#+end_src
* Plots
** Grid
#+begin_src latex
\pgfplotsset{grid style={black}}
\pgfplotsset{major grid style={black!30!white}}
\pgfplotsset{minor grid style={black!10!white}}
\pgfplotsset{xmajorgrids}
\pgfplotsset{ymajorgrids}
#+end_src
** Lines
#+begin_src latex
\pgfplotsset{separate axis lines=false} % draw axis as rectangle and not as 4 lines
\pgfplotsset{every outer x axis line/.append style={black}}
\pgfplotsset{every outer y axis line/.append style={black}}
\pgfplotsset{axis background/.style={fill=white}}
\pgfplotsset{axis x line*=bottom} % solid line on the bottom with thin on the top
\pgfplotsset{axis y line*=left} % solid line on the left with thin on the right
#+end_src
** Ticks
#+begin_src latex
\pgfplotsset{every y tick label/.append style={font=\color{black}}}
\pgfplotsset{every y tick/.append style={black}}
\pgfplotsset{every x tick label/.append style={font=\color{black}}}
\pgfplotsset{every x tick/.append style={black}}
#+end_src
** Size
If =scale only axis=false= (the default), pgfplots will try to produce the desired width including labels, titles and ticks.
#+begin_src latex
\pgfplotsset{scale only axis=true}
#+end_src
** Label
Used to align all of ylabel of one figure.
#+begin_src latex
\pgfplotsset{ylabel absolute}
#+end_src
** Legend
#+begin_src latex
% https://tex.stackexchange.com/questions/54794/using-a-pgfplots-style-legend-in-a-plain-old-tikzpicture#54834
% argument #1: any options
\newenvironment{customlegend}[1][]{%
\begingroup
% inits/clears the lists (which might be populated from previous
% axes):
\csname pgfplots@init@cleared@structures\endcsname
\pgfplotsset{#1}%
}{%
% draws the legend:
\csname pgfplots@createlegend\endcsname
\endgroup
}%
% makes \addlegendimage available (typically only available within an
% axis environment):
\def\addlegendimage{\csname pgfplots@addlegendimage\endcsname}
% definition to insert numbers
% \pgfkeys{/pgfplots/number in legend/.style={%
% /pgfplots/legend image code/.code={%
% \node at (0.125,-0.0225){#1}; % <= changed x value
% },%
% },
% }
\pgfplotsset{
every legend to name picture/.style={west}
}
#+end_src
** Upper and Lower bounds
#+begin_src latex
\tikzstyle{upperbound}=[line cap=round, postaction={decorate,draw,decoration={border, segment length=0.2cm, amplitude=0.3cm, angle=60}}]
\tikzstyle{lowerbound}=[line cap=round, postaction={decorate,draw,decoration={border, segment length=0.2cm, amplitude=0.3cm, angle=-60}}]
#+end_src
And we add the corresdonding
#+begin_src latex
\pgfplotsset{
/pgfplots/upperbound/.style 1 args={
legend image code/.code={
\draw[##1, upperbound]
plot coordinates {
(0cm,0cm)
(0.6cm,0cm)
}
}
}
}
#+end_src
** Pole
#+begin_src latex
\tikzset{%
pole/.style{%
color=red,
cross out,
draw,
inner sep=0pt,
outer sep=0pt,
minimum size=#1pt
},
pole/.default={4}
}
#+end_src
** Zero
#+begin_src latex
\tikzset{%
zero/.style{%
color=red,
circle,
draw,
inner sep=0pt,
outer sep=0pt,
minimum size=#1pt
},
zero/.default={4}
}
#+end_src
* Mechanical
** Spring
#+begin_src latex
\tikzset{%
spring/.style={%
thick,
decoration={
zigzag,
pre length = #1cm,
post length = #1cm,
segment length = 6
},
decorate
},
spring/.default={0.2}
}
#+end_src
** Coil
#+begin_src latex
\tikzset{%
coil/.style n args={2}{%
thick,
decoration={
coil,
pre length = #1cm,
post length = #2cm,
segment length = 4
},
decorate
},
coil/.default={0.3}{0.3}
}
#+end_src
** Damper
#+begin_src latex
\tikzset{%
damper/.style n args={2}{%
thick,
decoration={markings, mark connection node=dmp, mark=at position 0.5 with {
\node (dmp) [thick,
inner sep = 0pt,
transform shape,
rotate =-90,
minimum width = #1pt,
minimum height = #2pt,
draw=none] {};
\draw [thick] ($(dmp.north east)+(0.6*#2pt,0)$) -- (dmp.south east) -- (dmp.south west) -- ($(dmp.north west)+(0.6*#2pt,0)$);
\draw [thick] ($(dmp.north)+(0,-0.3*#1pt)$) -- ($(dmp.north)+(0,0.3*#1pt)$);
}
},
decorate
},
damper/.default={12}{3}
}
#+end_src
** Actuator
#+begin_src latex
\tikzset{%
actuator/.style n args={2}{%
thick,
draw=none,
decoration={
markings,
mark connection node=my node,
mark=at position .5 with {
\node [draw, inner sep=0pt, minimum width=#1cm, minimum height=#2cm,
transform shape, fill=white] (my node) {};
},
mark=at position .0 with {
\draw[<-] (0, 0) -- (my node);
},
mark=at position 1.0 with {
\draw[<-] (0, 0) -- (my node);
}
},
decorate
},
actuator/.default={0.5}{0.2}
}
#+end_src
** Ground
#+begin_src latex
\tikzset{%
ground/.style n args={2}{%
fill,
pattern = north east lines,
draw = none,
anchor = north,
minimum width = #1cm,
minimum height = #2cm,
append after command={
(\tikzlastnode.north west) edge (\tikzlastnode.north east)
}
},
ground/.default={2.5}{0.3}
}
#+end_src
** Force Sensor
#+begin_src latex
\tikzset{%
forcesensor/.style n args={2}{%
rectangle,
outer sep=0pt,
inner sep=0pt,
draw=black,
fill=white!60!black,
anchor=south,
minimum width =#1cm,
minimum height=#2cm,
append after command={
[every edge/.append style={
thick,
black,
}]
(\tikzlastnode.north west) edge (\tikzlastnode.south east)
(\tikzlastnode.north east) edge (\tikzlastnode.south west)
}
},
forcesensor/.default={2.0}{0.5}
}
#+end_src
** Inertial Sensor
#+begin_src latex
\tikzset{%
inertialsensor/.style={%
rectangle,
outer sep=0pt,
inner sep=0pt,
draw=black,
fill=white!60!black,
anchor=south east,
minimum size=#1cm,
append after command={
[every edge/.append style={
thick,
black,
}]
(\tikzlastnode.north west) edge (\tikzlastnode.south east)
(\tikzlastnode.north east) edge (\tikzlastnode.south west)
}
},
inertialsensor/.default={0.3}
}
#+end_src
** Axis Rotator
#+begin_src latex
\newcommand{\AxisRotator}[1][rotate=0]{%
\tikz [x=0.1cm,y=0.30cm,-stealth,#1] \draw (0,0) arc (-150:150:1 and 1);%
}
#+end_src
** Cross
#+begin_src latex
\tikzstyle{cross}=[path picture={
\draw[black]
(path picture bounding box.south east) -- (path picture bounding box.north west) (path picture bounding box.south west) -- (path picture bounding box.north east);
}]
#+end_src
** Piezoelectric actuator
#+begin_src latex
\tikzset{%
piezo/.style n args={3}{%
draw,
rectangle,
minimum width = #1cm,
minimum height = #2cm,
fill=blue!10!white,
anchor=center,
append after command={
[every edge/.append style={
thick,
black,
}]
\foreach \i in {1,...,#3}{
(${\i/(1+#3)}*(\tikzlastnode.north west)+{(1+#3-\i)/(1+#3)}*(\tikzlastnode.south west)+0.1*(#1,0)$) edge (${\i/(1+#3)}*(\tikzlastnode.north east)+{(1+#3-\i)/(1+#3)}*(\tikzlastnode.south east)-0.1*(#1,0)$)
}
}
},
piezo/.default={2}{4}{10}
}
#+end_src
** Voice coil
#+begin_src latex
\def\voicecoil#1#2#3{
% ======================
% Parameters
% ======================
\def\voicecoilw{#1} % Total Width
\def\voicecoilh{#2} % Total Height
\def\magnetw{\voicecoilw} % Width of the magnet
\def\magneth{\voicecoilh/1.4} % Height of the magnet
\def\magnetwb{0.15*\magnetw} % Width of the borders of the magnet
\def\magnetmw{0.15*\magnetw} % Width of the middle part of the magnet
\def\magnetwg{0.5*\magnetw} % Width of the gap of the magnet
\def\magnethl{\magnetwb} % Height of the low part of the magnet
\def\magnetmh{0.15*\magneth} % Height of the middle part of the magnet
\def\magnethg{0.2*\magneth} % Height of the gap of the magnet
% ======================
\begin{scope}[shift={(0.5*\voicecoilw, 0.5*\voicecoilh)}, rotate=#3, shift={(0, -0.5*\voicecoilh)}]
% ======================
% Magnet
% ======================
\draw[fill=white] (0, 0) -| ++(0.5*\magnetw, \magneth) -| ++(-0.5*\magnetw+0.5*\magnetwg, -\magnethg) -| (0.5*\magnetw-\magnetwb, \magnethl) -| (-0.5*\magnetw+\magnetwb, \magneth-\magnethg) -| (-0.5*\magnetwg, \magneth) -| (-0.5*\magnetw, 0) -- (cycle);
\begin{scope}[shift={(0, \magnethl)}]
\draw[fill=red] (-0.5*\magnetmw, 0) rectangle (0.5*\magnetmw, \magnetmh);
\draw[fill=blue] (-0.5*\magnetmw, \magnetmh) rectangle (0.5*\magnetmw, 2*\magnetmh);
% Top conductive Magnet
\draw[fill=white] (-0.5*\magnetmw, 2*\magnetmh) -| (0.5*\magnetmw, -\magnethl+\magneth-\magnethg) -| ++(0.1, \magnethg) -| ++(-0.2-\magnetmw, -\magnethg) -| (-0.5*\magnetmw, \magnetmh);
\end{scope}
% ======================
% ======================
% Coil
% ======================
\pgfmathsetmacro{\coilwidth}{0.5*0.5*\magnetmw+0.5*0.1+0.25*\magnetwg}%
\draw[] ( \coilwidth, 0.5*\magneth) -- ++(0, 0.7*\magneth);
\draw[] (-\coilwidth, 0.5*\magneth) -- ++(0, 0.7*\magneth);
% Point on the coil
\foreach \x in {0,1,...,9}
{
\node[circle,inner sep=0.6pt,fill] at ( \coilwidth, \x*0.7*\magneth/10+0.5*\magneth);
\node[circle,inner sep=0.6pt,fill] at (-\coilwidth, \x*0.7*\magneth/10+0.5*\magneth);
}
\draw[fill=white] (-0.5*\magnetw, 1.2*\magneth) rectangle ++(\magnetw, \magnethg);
% ======================
% ======================
% Coordinates
% ======================
% Force
\coordinate[] (vc_force) at (0, \magneth-0.5*\magnethg);
% Coil
\coordinate[] (vc_coil) at (0, \voicecoilh);
% Magnet
\coordinate[] (vc_magnet) at (0, 0);
% Coil Wires
\coordinate[] (vc_wire_one) at ( \coilwidth, 1.2*\magneth);
\coordinate[] (vc_wire_two) at (-\coilwidth, 1.2*\magneth);
% ======================
\end{scope}
}
#+end_src
* Optics
#+begin_src latex
\tikzset{%
->-/.style={
decoration={
markings,
mark = at position #1 with {\arrow{>}
}
},
postaction={decorate}
}
}
\tikzset{%
-<-/.style={
decoration={
markings,
mark = at position #1 with {\arrow{<}
}
},
postaction={decorate}
}
}
#+end_src
* Misc
#+begin_src latex
\tikzset{%
labelc/.style= {%
draw,
fill=white,
shape=circle,
inner sep=2pt,
outer sep=6pt,
}
}
#+end_src
tikz/config.tex
-556
View File
@@ -1,556 +0,0 @@
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[french, english]{babel} % Last language is main language
\usepackage{lmodern} % Latin Modern Font
\usepackage{gensymb} % Generic symbols for both text and math mode
\usepackage{standalone} % Used to generate standalone Tikz
\usepackage{amsmath} % Main math Package
\usepackage{mathtools} % Extension package to amsmath
\usepackage{amsthm} % Typesetting theorems (AMS style)
\usepackage{amsfonts} % More fonts from the AMS
\usepackage{textcomp} % provide many text symbols
\usepackage{steinmetz} % For phase symbol
\usepackage{xstring} % Utils to manipulate strings
\usepackage{etoolbox} % Add basic if/then
\usepackage{esvect} % Beautyfull vectors
\usepackage{graphicx} % Enhanced support for graphics
\usepackage{grffile} % Used by matlab2tikz
\usepackage{microtype} % typographic tuning
\usepackage{setspace} % for line spacing, e.g. \onehalfspacing
\usepackage{tabularx} % table features
\usepackage{enumitem} % for simple list modifications
\usepackage{booktabs} % better table support
\usepackage{stackengine} %
\usepackage[load-configurations=abbreviations]{siunitx} % SI units
\sisetup{
locale = US,
detect-all,
range-phrase=--,
range-units=single
}
\usepackage{tikz} % Tikz
\usepackage{tikzscale} % Used to scale Tikz graphics
\usepackage{adjustbox} % Used to proper positioning of tikz pictures
\usepackage{circuitikz} % Draw electronic circuits
\usepackage{pgfpages} % Needed to use notes
\usepackage{pgfplots} % Used to plot functions
\usetikzlibrary{arrows} % Arrow tip library
\usetikzlibrary{arrows.meta} % Add some arrows
\usetikzlibrary{calc} % The library allows advanced Coordinate Calculations
\usetikzlibrary{intersections} % calculate intersections of paths
\usetikzlibrary{matrix} %
\usetikzlibrary{patterns} %
\usetikzlibrary{shapes} % Defines circle and rectangle
\usetikzlibrary{shapes.geometric} % Use for the shape diamond and isosceles triangle
\usetikzlibrary{snakes} % snake=coil and snake=zigzag using segment amplitude=10pt
\usetikzlibrary{positioning} % Additional options for placing nodes
\usetikzlibrary{3d} % Plot 3D shapes
\usetikzlibrary{spy} % Creating a magnified area
\usetikzlibrary{decorations.text} % Used to make text follows a curve
\usetikzlibrary{decorations.pathmorphing} % deformation of a path
\usetikzlibrary{decorations.markings} % Used for spring and damper
\usetikzlibrary{babel} % A tiny library that make the interaction with the babel package easier
\usetikzlibrary{plotmarks} % This library defines a number of plot marks
\usetikzlibrary{fit} % Used to make rectangle as nodes by specifying two points
\usetikzlibrary{backgrounds} % Used to put things under others
\usepgfplotslibrary{patchplots}
\usepgfplotslibrary{groupplots}
\pgfplotsset{compat=newest}
\pgfplotsset{plot coordinates/math parser=false}
\newlength{\fheight}
\newlength{\fwidth}
\setlength{\fwidth}{85mm}
\setlength{\fheight}{112mm}
\tikzset{>=Stealth}
% Setup default Linewidth
\tikzset{every path/.style={line width=1pt}}
\usepackage{xcolor}% Color extension
\definecolor{colorblack}{rgb}{0, 0, 0}
\definecolor{colorblue}{rgb}{0, 0.4470, 0.7410}
\definecolor{colorred}{rgb}{0.8500, 0.3250, 0.0980}
\definecolor{coloryellow}{rgb}{0.9290, 0.6940, 0.1250}
\definecolor{colorpurple}{rgb}{0.4940, 0.1840, 0.5560}
\definecolor{colorgreen}{rgb}{0.4660, 0.6740, 0.1880}
\definecolor{colorcyan}{rgb}{0.3010, 0.7450, 0.9330}
\definecolor{colorbordeau}{rgb}{0.6350, 0.0780, 0.1840}
% Main color
\definecolor{maincolor}{RGB}{89, 9, 38}
\definecolor{secondcolor}{RGB}{20, 9, 89}
\tikzset{%
block/.style n args={2}{%
draw,
fill=white,
minimum width = #1,
minimum height = #2,
},
block/.default={1.2cm}{1.0cm}
}
\tikzstyle{branch}=[fill,shape=circle,minimum size=4pt,inner sep=0pt]
\tikzstyle{->top}=[-{Stealth[color=black, scale=0.8]}, draw=white, double=black, double distance=1pt, line width=1pt]
\tikzstyle{<-top}=[{stealth[color=black, scale=0.8]}-, draw=white, double=black, double distance=1pt, line width=1pt]
\tikzstyle{handwriten}=[decorate,decoration={random steps,amplitude=0.1pt,segment length=0.8pt}]
\tikzset{%
DAC/.style={%
draw,
signal,
}
}
\tikzset{%
ADC/.style={%
draw,
signal,
signal to = west,
}
}
\tikzset{%
gain right/.style={%
draw,
regular polygon,
regular polygon sides = 3,
inner sep = 2pt,
shape border rotate=-90
},
gain left/.style={%
draw,
regular polygon,
regular polygon sides = 3,
inner sep = 2pt,
shape border rotate=90
},
gain top/.style={%
draw,
regular polygon,
regular polygon sides = 3,
inner sep = 2pt,
shape border rotate=0
},
gain bottom/.style={%
draw,
regular polygon,
regular polygon sides = 3,
inner sep = 2pt,
shape border rotate=180
},
}
\tikzset{% Add block with Circled operations
addc/.style n args={5}{%
draw,
fill=white,
circle,
outer sep = 0pt,
inner sep = 0pt,
minimum size = 2em,
execute at begin node={\LARGE $#1$},
append after command={\pgfextra{\let\mainnode=\tikzlastnode}
\ifx#2\empty\else
node[draw, circle, outer sep=6pt, inner sep=0pt, above left] at (\mainnode.west) {$#2$}%
\fi
\ifx#3\empty\else
node[draw, circle, outer sep=6pt, inner sep=0pt, above right] at (\mainnode.north) {$#3$}%
\fi
\ifx#4\empty\else
node[draw, circle, outer sep=6pt, inner sep=0pt, below right] at (\mainnode.east) {$#4$}%
\fi
\ifx#5\empty\else
node[draw, circle, outer sep=6pt, inner sep=0pt, below left] at (\mainnode.south) {$#5$}%
\fi
}
},
addc/.default={+}{}{}{}{},
}
\tikzset{% Add Block
addb/.style n args={5}{%
draw,
fill=white,
circle,
outer sep = 0pt,
inner sep = 0pt,
minimum size = 2em,
execute at begin node={\LARGE $#1$},
append after command={\pgfextra{\let\mainnode=\tikzlastnode}
\ifx#2\empty\else
node[outer sep=2pt, inner sep=0pt, above left] at (\mainnode.west) {$#2$}%
\fi
\ifx#3\empty\else
node[outer sep=2pt, inner sep=0pt, above right] at (\mainnode.north) {$#3$}%
\fi
\ifx#4\empty\else
node[outer sep=2pt, inner sep=0pt, below right] at (\mainnode.east) {$#4$}%
\fi
\ifx#5\empty\else
node[outer sep=2pt, inner sep=0pt, below left] at (\mainnode.south) {$#5$}%
\fi
}
},
addb/.default={+}{}{}{}{},
}
\pgfplotsset{grid style={black}}
\pgfplotsset{major grid style={black!30!white}}
\pgfplotsset{minor grid style={black!10!white}}
\pgfplotsset{xmajorgrids}
\pgfplotsset{ymajorgrids}
\pgfplotsset{separate axis lines=false} % draw axis as rectangle and not as 4 lines
\pgfplotsset{every outer x axis line/.append style={black}}
\pgfplotsset{every outer y axis line/.append style={black}}
\pgfplotsset{axis background/.style={fill=white}}
\pgfplotsset{axis x line*=bottom} % solid line on the bottom with thin on the top
\pgfplotsset{axis y line*=left} % solid line on the left with thin on the right
\pgfplotsset{every y tick label/.append style={font=\color{black}}}
\pgfplotsset{every y tick/.append style={black}}
\pgfplotsset{every x tick label/.append style={font=\color{black}}}
\pgfplotsset{every x tick/.append style={black}}
\pgfplotsset{scale only axis=true}
\pgfplotsset{ylabel absolute}
% https://tex.stackexchange.com/questions/54794/using-a-pgfplots-style-legend-in-a-plain-old-tikzpicture#54834
% argument #1: any options
\newenvironment{customlegend}[1][]{%
\begingroup
% inits/clears the lists (which might be populated from previous
% axes):
\csname pgfplots@init@cleared@structures\endcsname
\pgfplotsset{#1}%
}{%
% draws the legend:
\csname pgfplots@createlegend\endcsname
\endgroup
}%
% makes \addlegendimage available (typically only available within an
% axis environment):
\def\addlegendimage{\csname pgfplots@addlegendimage\endcsname}
% definition to insert numbers
% \pgfkeys{/pgfplots/number in legend/.style={%
% /pgfplots/legend image code/.code={%
% \node at (0.125,-0.0225){#1}; % <= changed x value
% },%
% },
% }
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every legend to name picture/.style={west}
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legend image code/.code={
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\tikzset{%
pole/.style{%
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zero/.style{%
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damper/.default={12}{3}
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\tikzset{%
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ground/.default={2.5}{0.3}
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\tikzset{%
forcesensor/.style n args={2}{%
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\newcommand{\AxisRotator}[1][rotate=0]{%
\tikz [x=0.1cm,y=0.30cm,-stealth,#1] \draw (0,0) arc (-150:150:1 and 1);%
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}
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piezo/.default={2}{4}{10}
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\def\voicecoil#1#2#3{
% ======================
% Parameters
% ======================
\def\voicecoilw{#1} % Total Width
\def\voicecoilh{#2} % Total Height
\def\magnetw{\voicecoilw} % Width of the magnet
\def\magneth{\voicecoilh/1.4} % Height of the magnet
\def\magnetwb{0.15*\magnetw} % Width of the borders of the magnet
\def\magnetmw{0.15*\magnetw} % Width of the middle part of the magnet
\def\magnetwg{0.5*\magnetw} % Width of the gap of the magnet
\def\magnethl{\magnetwb} % Height of the low part of the magnet
\def\magnetmh{0.15*\magneth} % Height of the middle part of the magnet
\def\magnethg{0.2*\magneth} % Height of the gap of the magnet
% ======================
\begin{scope}[shift={(0.5*\voicecoilw, 0.5*\voicecoilh)}, rotate=#3, shift={(0, -0.5*\voicecoilh)}]
% ======================
% Magnet
% ======================
\draw[fill=white] (0, 0) -| ++(0.5*\magnetw, \magneth) -| ++(-0.5*\magnetw+0.5*\magnetwg, -\magnethg) -| (0.5*\magnetw-\magnetwb, \magnethl) -| (-0.5*\magnetw+\magnetwb, \magneth-\magnethg) -| (-0.5*\magnetwg, \magneth) -| (-0.5*\magnetw, 0) -- (cycle);
\begin{scope}[shift={(0, \magnethl)}]
\draw[fill=red] (-0.5*\magnetmw, 0) rectangle (0.5*\magnetmw, \magnetmh);
\draw[fill=blue] (-0.5*\magnetmw, \magnetmh) rectangle (0.5*\magnetmw, 2*\magnetmh);
% Top conductive Magnet
\draw[fill=white] (-0.5*\magnetmw, 2*\magnetmh) -| (0.5*\magnetmw, -\magnethl+\magneth-\magnethg) -| ++(0.1, \magnethg) -| ++(-0.2-\magnetmw, -\magnethg) -| (-0.5*\magnetmw, \magnetmh);
\end{scope}
% ======================
% ======================
% Coil
% ======================
\pgfmathsetmacro{\coilwidth}{0.5*0.5*\magnetmw+0.5*0.1+0.25*\magnetwg}%
\draw[] ( \coilwidth, 0.5*\magneth) -- ++(0, 0.7*\magneth);
\draw[] (-\coilwidth, 0.5*\magneth) -- ++(0, 0.7*\magneth);
% Point on the coil
\foreach \x in {0,1,...,9}
{
\node[circle,inner sep=0.6pt,fill] at ( \coilwidth, \x*0.7*\magneth/10+0.5*\magneth);
\node[circle,inner sep=0.6pt,fill] at (-\coilwidth, \x*0.7*\magneth/10+0.5*\magneth);
}
\draw[fill=white] (-0.5*\magnetw, 1.2*\magneth) rectangle ++(\magnetw, \magnethg);
% ======================
% ======================
% Coordinates
% ======================
% Force
\coordinate[] (vc_force) at (0, \magneth-0.5*\magnethg);
% Coil
\coordinate[] (vc_coil) at (0, \voicecoilh);
% Magnet
\coordinate[] (vc_magnet) at (0, 0);
% Coil Wires
\coordinate[] (vc_wire_one) at ( \coilwidth, 1.2*\magneth);
\coordinate[] (vc_wire_two) at (-\coilwidth, 1.2*\magneth);
% ======================
\end{scope}
}
\tikzset{%
->-/.style={
decoration={
markings,
mark = at position #1 with {\arrow{>}
}
},
postaction={decorate}
}
}
\tikzset{%
-<-/.style={
decoration={
markings,
mark = at position #1 with {\arrow{<}
}
},
postaction={decorate}
}
}
\tikzset{%
labelc/.style= {%
draw,
fill=white,
shape=circle,
inner sep=2pt,
outer sep=6pt,
}
}
tikz/figs
-1
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@@ -1 +0,0 @@
../paper/figs
tikz/index.html
-321
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@@ -1,321 +0,0 @@
<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-11-12 jeu. 10:40 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Active Damping of Rotating Platforms using Integral Force Feedback - Tikz Figures</title>
<meta name="generator" content="Org mode" />
<meta name="author" content="Thomas Dehaeze" />
<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
</head>
<body>
<div id="org-div-home-and-up">
<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
</div><div id="content">
<h1 class="title">Active Damping of Rotating Platforms using Integral Force Feedback - Tikz Figures</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgd15976a">1. X-Y Rotating Positioning Platform</a></li>
<li><a href="#orgfba88c8">2. X-Y Rotating Positioning Platform</a></li>
<li><a href="#org732f401">3. Decentralized Integral Force Feedback</a></li>
<li><a href="#org1dd642f">4. Springs in parallel</a></li>
</ul>
</div>
</div>
<p>
Configuration file is accessible <a href="config.html">here</a>.
</p>
<div id="outline-container-orgd15976a" class="outline-2">
<h2 id="orgd15976a"><span class="section-number-2">1</span> X-Y Rotating Positioning Platform</h2>
<div class="outline-text-2" id="text-1">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-comment">% Angle</span>
<span class="org-font-latex-sedate">\def\thetau</span>{25}
<span class="org-comment">% Rotational Stage</span>
<span class="org-font-latex-sedate">\draw</span>[fill=black!60!white] (0, 0) circle (4.3);
<span class="org-font-latex-sedate">\draw</span>[fill=black!40!white] (0, 0) circle (3.8);
<span class="org-comment">% Label</span>
<span class="org-font-latex-sedate">\node</span>[anchor=north west, rotate=<span class="org-font-latex-sedate">\thetau</span>] at (-2.5, 2.5) {<span class="org-font-latex-sedate"><span class="org-keyword">\small</span></span><span class="org-type"> Rotating Stage</span>};
<span class="org-comment">% Rotating Scope</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[rotate=<span class="org-font-latex-sedate">\thetau</span>]
<span class="org-comment">% Rotating Frame</span>
<span class="org-font-latex-sedate">\draw</span>[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
<span class="org-comment">% Label</span>
<span class="org-font-latex-sedate">\node</span>[anchor=north west, rotate=<span class="org-font-latex-sedate">\thetau</span>] at (-2.6, 2.6) {<span class="org-font-latex-sedate"><span class="org-keyword">\small</span></span><span class="org-type"> Suspended Platform</span>};
<span class="org-comment">% Mass</span>
<span class="org-font-latex-sedate">\draw</span>[fill=white] (-1, -1) rectangle (1, 1);
<span class="org-comment">% Label</span>
<span class="org-font-latex-sedate">\node</span>[anchor=south west, rotate=<span class="org-font-latex-sedate">\thetau</span>] at (-1, -1) {<span class="org-font-latex-sedate"><span class="org-keyword">\small</span></span><span class="org-type"> Payload</span>};
<span class="org-comment">% Attached Points</span>
<span class="org-font-latex-sedate">\node</span>[] at (-1, 0){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\bullet</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[] (-1, 0) -- ++(-0.2, 0) coordinate(cu);
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(cu) + (0, -0.8)$</span>) coordinate(actu) -- (<span class="org-font-latex-math">$(cu) + (0, 0.8)$</span>) coordinate(ku);
<span class="org-font-latex-sedate">\node</span>[] at (0, -1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\bullet</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[] (0, -1) -- ++(0, -0.2) coordinate(cv);
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(cv) + (-0.8, 0)$</span>)coordinate(kv) -- (<span class="org-font-latex-math">$(cv) + (0.8, 0)$</span>) coordinate(actv);
<span class="org-comment">% Spring and Actuator for U</span>
<span class="org-font-latex-sedate">\draw</span>[actuator={0.6}{0.2}] (actu) -- node[above=0.1, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$F</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">u$</span>} (actu-|-2.6,0);
<span class="org-font-latex-sedate">\draw</span>[spring=0.2] (ku) -- node[above=0.1, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$k$</span>} (ku-|-2.6,0);
<span class="org-font-latex-sedate">\draw</span>[damper={8}{8}] (cu) -- node[above left=0.2 and -0.1, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$c$</span>} (cu-|-2.6,0);
<span class="org-font-latex-sedate">\draw</span>[actuator={0.6}{0.2}] (actv) -- node[left, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$F</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">v$</span>} (actv|-0,-2.6);
<span class="org-font-latex-sedate">\draw</span>[spring=0.2] (kv) -- node[left, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$k$</span>} (kv|-0,-2.6);
<span class="org-font-latex-sedate">\draw</span>[damper={8}{8}] (cv) -- node[left=0.1, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$c$</span>} (cv|-0,-2.6);
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-comment">% Inertial Frame</span>
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (-4, -4) -- ++(2, 0) node[below]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">x$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (-4, -4) -- ++(0, 2) node[left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">y$</span>};
<span class="org-font-latex-sedate">\draw</span>[fill, color=black] (-4, -4) circle (0.06);
<span class="org-font-latex-sedate">\node</span>[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">z$</span>] at (-4, -4){};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (0, 0) node[above left, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">w$</span>} -- ++(<span class="org-font-latex-sedate">\thetau</span>:2) node[above, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">u$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (0, 0) -- ++(<span class="org-font-latex-sedate">\thetau</span>+90:2) node[left, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">v$</span>};
<span class="org-font-latex-sedate">\draw</span>[fill, color=black] (0,0) circle (0.06);
<span class="org-font-latex-sedate">\node</span>[draw, circle, inner sep=0pt, minimum size=0.3cm] at (0, 0){};
<span class="org-font-latex-sedate">\draw</span>[dashed] (0, 0) -- ++(2, 0);
<span class="org-font-latex-sedate">\draw</span>[] (1.5, 0) arc (0:<span class="org-font-latex-sedate">\thetau</span>:1.5) node[midway, right]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\theta</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (3.5, 0) arc (0:40:3.5) node[midway, left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Omega</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="orge4c1dec" class="figure">
<p><img src="figs/system.png" alt="system.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-orgfba88c8" class="outline-2">
<h2 id="orgfba88c8"><span class="section-number-2">2</span> X-Y Rotating Positioning Platform</h2>
<div class="outline-text-2" id="text-2">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{block/.default={0.8cm}{0.8cm}}
<span class="org-font-latex-sedate">\tikzset</span>{addb/.append style={scale=0.7}}
<span class="org-font-latex-sedate">\tikzset</span>{node distance=0.6}
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-font-latex-sedate">\node</span>[block={1.8cm}{2.2cm}] (G) {<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\bm</span></span><span class="org-font-latex-math">{G}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">f$</span>};
<span class="org-comment">% Inputs of the controllers</span>
<span class="org-font-latex-sedate">\coordinate</span>[] (output1) at (<span class="org-font-latex-math">$(G.south east)!0.75!(G.north east)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (output2) at (<span class="org-font-latex-math">$(G.south east)!0.25!(G.north east)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (input1) at (<span class="org-font-latex-math">$(G.south west)!0.75!(G.north west)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (input2) at (<span class="org-font-latex-math">$(G.south west)!0.25!(G.north west)$</span>);
<span class="org-font-latex-sedate">\node</span>[block, left=1.8 of input1] (K1) {<span class="org-font-latex-math">$K</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">F$</span>};
<span class="org-font-latex-sedate">\node</span>[block] (K2) at (<span class="org-font-latex-math">$(K1.east|-input2)+(0.6, 0)$</span>) {<span class="org-font-latex-math">$K</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">F$</span>};
<span class="org-comment">% Connections and labels</span>
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (K1.east) -- (input1)node[above left]{<span class="org-font-latex-math">$F</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">u$</span>}node[below left]{<span class="org-font-latex-math">$-$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (K2.east) -- (input2)node[above left]{<span class="org-font-latex-math">$F</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">v$</span>}node[below left]{<span class="org-font-latex-math">$-$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (output1) -- ++(0.8, 0) node[above left]{<span class="org-font-latex-math">$f</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">u$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (output2) -- ++(0.8, 0) node[above left]{<span class="org-font-latex-math">$f</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">v$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(output1)+(0.2, 0)$</span>)node[branch]{} -- ++(0, 1.2) -| (<span class="org-font-latex-math">$(K1.west) + (-0.8, 0)$</span>)coordinate(start) -- (K1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(output2)+(0.2, 0)$</span>)node[branch]{} -- ++(0, -1.2) -| (start|-K2) -- (K2.west);
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[on background layer]
<span class="org-font-latex-sedate">\node</span>[fit={(K1.north west) (K2.south east)}, inner sep=6pt, draw, dashed, fill=black!20!white] (K) {};
<span class="org-font-latex-sedate">\node</span>[below left] at (K.north east) {<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\bm</span></span><span class="org-font-latex-math">{K}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">F$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="orgd28fad3" class="figure">
<p><img src="figs/control_diagram_iff.png" alt="control_diagram_iff.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-org732f401" class="outline-2">
<h2 id="org732f401"><span class="section-number-2">3</span> Decentralized Integral Force Feedback</h2>
<div class="outline-text-2" id="text-3">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-comment">% Angle</span>
<span class="org-font-latex-sedate">\def\thetau</span>{25}
<span class="org-comment">% Rotational Stage</span>
<span class="org-font-latex-sedate">\draw</span>[fill=black!60!white] (0, 0) circle (4.3);
<span class="org-font-latex-sedate">\draw</span>[fill=black!40!white] (0, 0) circle (3.8);
<span class="org-comment">% Label</span>
<span class="org-font-latex-sedate">\node</span>[anchor=north west, rotate=<span class="org-font-latex-sedate">\thetau</span>] at (-2.5, 2.5) {<span class="org-font-latex-sedate"><span class="org-keyword">\small</span></span><span class="org-type"> Rotating Stage</span>};
<span class="org-comment">% Rotating Scope</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[rotate=<span class="org-font-latex-sedate">\thetau</span>]
<span class="org-comment">% Rotating Frame</span>
<span class="org-font-latex-sedate">\draw</span>[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
<span class="org-comment">% Label</span>
<span class="org-font-latex-sedate">\node</span>[anchor=north west, rotate=<span class="org-font-latex-sedate">\thetau</span>] at (-2.6, 2.6) {<span class="org-font-latex-sedate"><span class="org-keyword">\small</span></span><span class="org-type"> Suspended Platform</span>};
<span class="org-comment">% Mass</span>
<span class="org-font-latex-sedate">\draw</span>[fill=white] (-1, -1) rectangle (1, 1);
<span class="org-comment">% Label</span>
<span class="org-font-latex-sedate">\node</span>[anchor=south west, rotate=<span class="org-font-latex-sedate">\thetau</span>] at (-1, -1) {<span class="org-font-latex-sedate"><span class="org-keyword">\small</span></span><span class="org-type"> Payload</span>};
<span class="org-comment">% Attached Points</span>
<span class="org-font-latex-sedate">\node</span>[] at (-1, 0){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\bullet</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
<span class="org-font-latex-sedate">\node</span>[] at (0, -1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\bullet</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[] (0, -1) -- ++(0, -0.2) coordinate(av);
<span class="org-comment">% Force Sensors</span>
<span class="org-font-latex-sedate">\draw</span>[fill=white] (<span class="org-font-latex-math">$(au) + (-0.2, -0.5)$</span>) rectangle (<span class="org-font-latex-math">$(au) + (0, 0.5)$</span>);
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(au) + (-0.2, -0.5)$</span>)coordinate(actu) -- (<span class="org-font-latex-math">$(au) + (0, 0.5)$</span>);
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(au) + (-0.2, 0.5)$</span>)coordinate(ku) -- (<span class="org-font-latex-math">$(au) + (0, -0.5)$</span>);
<span class="org-font-latex-sedate">\draw</span>[fill=white] (<span class="org-font-latex-math">$(av) + (-0.5, -0.2)$</span>) rectangle (<span class="org-font-latex-math">$(av) + (0.5, 0)$</span>);
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(av) + ( 0.5, -0.2)$</span>)coordinate(actv) -- (<span class="org-font-latex-math">$(av) + (-0.5, 0)$</span>);
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(av) + (-0.5, -0.2)$</span>)coordinate(kv) -- (<span class="org-font-latex-math">$(av) + ( 0.5, 0)$</span>);
<span class="org-comment">% Spring and Actuator for U</span>
<span class="org-font-latex-sedate">\draw</span>[actuator={0.6}{0.2}] (actu) -- coordinate[midway](actumid) (actu-|-2.6,0);
<span class="org-font-latex-sedate">\draw</span>[spring=0.2] (ku) -- node[above=0.1, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$k$</span>} (ku-|-2.6,0);
<span class="org-comment">% </span><span class="org-font-latex-sedate"><span class="org-comment">\draw</span></span><span class="org-comment">[actuator={0.6}{0.2}] (actv) -- node[right, rotate=</span><span class="org-font-latex-sedate"><span class="org-comment">\thetau</span></span><span class="org-comment">]{$F_v$} (actv|-0,-2.6);</span>
<span class="org-font-latex-sedate">\draw</span>[actuator={0.6}{0.2}] (actv) -- coordinate[midway](actvmid) (actv|-0,-2.6);
<span class="org-font-latex-sedate">\draw</span>[spring=0.2] (kv) -- node[left, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$k$</span>} (kv|-0,-2.6);
<span class="org-font-latex-sedate">\node</span>[block={0.8cm}{0.6cm}, rotate=<span class="org-font-latex-sedate">\thetau</span>] (Ku) at (<span class="org-font-latex-math">$(actumid) + (0, -1.2)$</span>) {<span class="org-font-latex-math">$K_{F}$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(au) + (-0.1, -0.5)$</span>) |- (Ku.east) node[below right, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$f_{u}$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (Ku.north) -- (<span class="org-font-latex-math">$(actumid) + (0, -0.1)$</span>) node[below left, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$F_u$</span>} node[below right, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$-$</span>};
<span class="org-font-latex-sedate">\node</span>[block={0.8cm}{0.6cm}, rotate=<span class="org-font-latex-sedate">\thetau</span>] (Kv) at (<span class="org-font-latex-math">$(actvmid) + (1.2, 0)$</span>) {<span class="org-font-latex-math">$K_{F}$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(av) + (0.5, -0.1)$</span>) -| (Kv.north) node[above right, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$f_{v}$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (Kv.west) -- (<span class="org-font-latex-math">$(actvmid) + (0.1, 0)$</span>) node[below right, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$F_v$</span>} node[above right, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$-$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-comment">% Inertial Frame</span>
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (-4, -4) -- ++(2, 0) node[below]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}_x$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (-4, -4) -- ++(0, 2) node[left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}_y$</span>};
<span class="org-font-latex-sedate">\draw</span>[fill, color=black] (-4, -4) circle (0.06);
<span class="org-font-latex-sedate">\node</span>[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}_z$</span>] at (-4, -4){};
<span class="org-font-latex-sedate">\node</span>[draw, circle, inner sep=0pt, minimum size=0.3cm] at (0, 0){};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (0, 0) node[above left, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}_w$</span>} -- ++(<span class="org-font-latex-sedate">\thetau</span>:2) node[above, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}_u$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (0, 0) -- ++(<span class="org-font-latex-sedate">\thetau</span>+90:2) node[left, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}_v$</span>};
<span class="org-font-latex-sedate">\draw</span>[dashed] (0, 0) -- ++(2, 0);
<span class="org-font-latex-sedate">\draw</span>[] (1.5, 0) arc (0:<span class="org-font-latex-sedate">\thetau</span>:1.5) node[midway, right]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\theta</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[] at (0,0) {<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\bullet</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (3.5, 0) arc (0:40:3.5) node[midway, left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Omega</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="orgfc98ac7" class="figure">
<p><img src="figs/system_iff.png" alt="system_iff.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-org1dd642f" class="outline-2">
<h2 id="org1dd642f"><span class="section-number-2">4</span> Springs in parallel</h2>
<div class="outline-text-2" id="text-4">
<div class="org-src-container">
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-comment">% Angle</span>
<span class="org-font-latex-sedate">\def\thetau</span>{25}
<span class="org-comment">% Rotational Stage</span>
<span class="org-font-latex-sedate">\draw</span>[fill=black!60!white] (0, 0) circle (4.3);
<span class="org-font-latex-sedate">\draw</span>[fill=black!40!white] (0, 0) circle (3.8);
<span class="org-comment">% Label</span>
<span class="org-font-latex-sedate">\node</span>[anchor=north west, rotate=<span class="org-font-latex-sedate">\thetau</span>] at (-2.5, 2.5) {<span class="org-font-latex-sedate"><span class="org-keyword">\small</span></span><span class="org-type"> Rotating Stage</span>};
<span class="org-comment">% Rotating Scope</span>
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[rotate=<span class="org-font-latex-sedate">\thetau</span>]
<span class="org-comment">% Rotating Frame</span>
<span class="org-font-latex-sedate">\draw</span>[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
<span class="org-comment">% Label</span>
<span class="org-font-latex-sedate">\node</span>[anchor=north west, rotate=<span class="org-font-latex-sedate">\thetau</span>] at (-2.6, 2.6) {<span class="org-font-latex-sedate"><span class="org-keyword">\small</span></span><span class="org-type"> Suspended Platform</span>};
<span class="org-comment">% Mass</span>
<span class="org-font-latex-sedate">\draw</span>[fill=white] (-1, -1) rectangle (1, 1);
<span class="org-comment">% Label</span>
<span class="org-font-latex-sedate">\node</span>[anchor=south west, rotate=<span class="org-font-latex-sedate">\thetau</span>] at (-1, -1) {<span class="org-font-latex-sedate"><span class="org-keyword">\small</span></span><span class="org-type"> Payload</span>};
<span class="org-comment">% Attached Points</span>
<span class="org-font-latex-sedate">\draw</span>[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
<span class="org-font-latex-sedate">\draw</span>[] (0, -1) -- ++(0, -0.2) coordinate(av);
<span class="org-comment">% Force Sensors</span>
<span class="org-font-latex-sedate">\draw</span>[fill=white] (<span class="org-font-latex-math">$(au) + (-0.2, -0.5)$</span>) rectangle (<span class="org-font-latex-math">$(au) + (0, 0.5)$</span>);
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(au) + (-0.2, -0.5)$</span>)coordinate(actu) -- (<span class="org-font-latex-math">$(au) + (0, 0.5)$</span>);
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(au) + (-0.2, 0.5)$</span>)coordinate(ku) -- (<span class="org-font-latex-math">$(au) + (0, -0.5)$</span>);
<span class="org-font-latex-sedate">\node</span>[below=0.1, rotate=<span class="org-font-latex-sedate">\thetau</span>] at (<span class="org-font-latex-math">$(au) + (-0.1, -0.5)$</span>) {<span class="org-font-latex-math">$f</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">{u}$</span>}
<span class="org-font-latex-sedate">\draw</span>[fill=white] (<span class="org-font-latex-math">$(av) + (-0.5, -0.2)$</span>) rectangle (<span class="org-font-latex-math">$(av) + (0.5, 0)$</span>);
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(av) + ( 0.5, -0.2)$</span>)coordinate(actv) -- (<span class="org-font-latex-math">$(av) + (-0.5, 0)$</span>);
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(av) + (-0.5, -0.2)$</span>)coordinate(kv) -- (<span class="org-font-latex-math">$(av) + ( 0.5, 0)$</span>) ;
<span class="org-font-latex-sedate">\node</span>[right=0.1, rotate=<span class="org-font-latex-sedate">\thetau</span>] at (<span class="org-font-latex-math">$(av) + (0.5, -0.1)$</span>) {<span class="org-font-latex-math">$f</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">{v}$</span>}
<span class="org-comment">% Spring and Actuator for U</span>
<span class="org-font-latex-sedate">\draw</span>[actuator={0.6}{0.2}] (actu) -- node[below=0.1, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$F</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">u$</span>} (actu-|-2.6,0);
<span class="org-font-latex-sedate">\draw</span>[spring=0.2] (ku) -- node[below=0.1, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$k</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">a$</span>} (ku-|-2.6,0);
<span class="org-font-latex-sedate">\draw</span>[spring=0.2] (-1, 0.8) -- node[above=0.1, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$k</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">p$</span>} (-1, 0.8-|-2.6,0);
<span class="org-font-latex-sedate">\draw</span>[actuator={0.6}{0.2}] (actv) -- node[right=0.1, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$F</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">v$</span>} (actv|-0,-2.6);
<span class="org-font-latex-sedate">\draw</span>[spring=0.2] (kv) -- node[right=0.1, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$k</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">a$</span>} (kv|-0,-2.6);
<span class="org-font-latex-sedate">\draw</span>[spring=0.2] (-0.8, -1) -- node[left=0.1, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$k</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">p$</span>} (-0.8, -1|-0,-2.6);
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
<span class="org-comment">% Inertial Frame</span>
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (-4, -4) -- ++(2, 0) node[below]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">x$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (-4, -4) -- ++(0, 2) node[left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">y$</span>};
<span class="org-font-latex-sedate">\draw</span>[fill, color=black] (-4, -4) circle (0.06);
<span class="org-font-latex-sedate">\node</span>[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">z$</span>] at (-4, -4){};
<span class="org-font-latex-sedate">\node</span>[draw, circle, inner sep=0pt, minimum size=0.3cm] at (0, 0){};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (0, 0) node[above left, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">w$</span>} -- ++(<span class="org-font-latex-sedate">\thetau</span>:2) node[above, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">u$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (0, 0) -- ++(<span class="org-font-latex-sedate">\thetau</span>+90:2) node[left, rotate=<span class="org-font-latex-sedate">\thetau</span>]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\vec</span></span><span class="org-font-latex-math">{i}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">v$</span>};
<span class="org-font-latex-sedate">\draw</span>[dashed] (0, 0) -- ++(2, 0);
<span class="org-font-latex-sedate">\draw</span>[] (1.5, 0) arc (0:<span class="org-font-latex-sedate">\thetau</span>:1.5) node[midway, right]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\theta</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\node</span>[] at (0,0) {<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\bullet</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (3.5, 0) arc (0:40:3.5) node[midway, left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Omega</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="orgc785e50" class="figure">
<p><img src="figs/system_parallel_springs.png" alt="system_parallel_springs.png" />
</p>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2020-11-12 jeu. 10:40</p>
</div>
</body>
</html>
tikz/index.org
-270
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@@ -1,270 +0,0 @@
#+TITLE: Active Damping of Rotating Platforms using Integral Force Feedback - Tikz Figures
:DRAWER:
#+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP: ../index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{/home/thomas/Cloud/thesis/papers/dehaeze20_contr_stewa_platf/tikz/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results file raw replace
#+PROPERTY: header-args:latex+ :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports both
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END:
Configuration file is accessible [[file:config.org][here]].
* X-Y Rotating Positioning Platform
#+begin_src latex :file system.pdf
\begin{tikzpicture}
% Angle
\def\thetau{25}
% Rotational Stage
\draw[fill=black!60!white] (0, 0) circle (4.3);
\draw[fill=black!40!white] (0, 0) circle (3.8);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};
% Rotating Scope
\begin{scope}[rotate=\thetau]
% Rotating Frame
\draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small Suspended Platform};
% Mass
\draw[fill=white] (-1, -1) rectangle (1, 1);
% Label
\node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};
% Attached Points
\node[] at (-1, 0){$\bullet$};
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(cu);
\draw[] ($(cu) + (0, -0.8)$) coordinate(actu) -- ($(cu) + (0, 0.8)$) coordinate(ku);
\node[] at (0, -1){$\bullet$};
\draw[] (0, -1) -- ++(0, -0.2) coordinate(cv);
\draw[] ($(cv) + (-0.8, 0)$)coordinate(kv) -- ($(cv) + (0.8, 0)$) coordinate(actv);
% Spring and Actuator for U
\draw[actuator={0.6}{0.2}] (actu) -- node[above=0.1, rotate=\thetau]{$F_u$} (actu-|-2.6,0);
\draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0);
\draw[damper={8}{8}] (cu) -- node[above left=0.2 and -0.1, rotate=\thetau]{$c$} (cu-|-2.6,0);
\draw[actuator={0.6}{0.2}] (actv) -- node[left, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
\draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6);
\draw[damper={8}{8}] (cv) -- node[left=0.1, rotate=\thetau]{$c$} (cv|-0,-2.6);
\end{scope}
% Inertial Frame
\draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
\draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
\draw[fill, color=black] (-4, -4) circle (0.06);
\node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};
\draw[->] (0, 0) node[above left, rotate=\thetau]{$\vec{i}_w$} -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
\draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
\draw[fill, color=black] (0,0) circle (0.06);
\node[draw, circle, inner sep=0pt, minimum size=0.3cm] at (0, 0){};
\draw[dashed] (0, 0) -- ++(2, 0);
\draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
\draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
\end{tikzpicture}
#+end_src
#+RESULTS:
[[file:figs/system.png]]
* X-Y Rotating Positioning Platform
#+begin_src latex :file control_diagram_iff.pdf
\tikzset{block/.default={0.8cm}{0.8cm}}
\tikzset{addb/.append style={scale=0.7}}
\tikzset{node distance=0.6}
\begin{tikzpicture}
\node[block={1.8cm}{2.2cm}] (G) {$\bm{G}_f$};
% Inputs of the controllers
\coordinate[] (output1) at ($(G.south east)!0.75!(G.north east)$);
\coordinate[] (output2) at ($(G.south east)!0.25!(G.north east)$);
\coordinate[] (input1) at ($(G.south west)!0.75!(G.north west)$);
\coordinate[] (input2) at ($(G.south west)!0.25!(G.north west)$);
\node[block, left=1.8 of input1] (K1) {$K_F$};
\node[block] (K2) at ($(K1.east|-input2)+(0.6, 0)$) {$K_F$};
% Connections and labels
\draw[->] (K1.east) -- (input1)node[above left]{$F_u$}node[below left]{$-$};
\draw[->] (K2.east) -- (input2)node[above left]{$F_v$}node[below left]{$-$};
\draw[->] (output1) -- ++(0.8, 0) node[above left]{$f_u$};
\draw[->] (output2) -- ++(0.8, 0) node[above left]{$f_v$};
\draw[->] ($(output1)+(0.2, 0)$)node[branch]{} -- ++(0, 1.2) -| ($(K1.west) + (-0.8, 0)$)coordinate(start) -- (K1.west);
\draw[->] ($(output2)+(0.2, 0)$)node[branch]{} -- ++(0, -1.2) -| (start|-K2) -- (K2.west);
\begin{scope}[on background layer]
\node[fit={(K1.north west) (K2.south east)}, inner sep=6pt, draw, dashed, fill=black!20!white] (K) {};
\node[below left] at (K.north east) {$\bm{K}_F$};
\end{scope}
\end{tikzpicture}
#+end_src
#+RESULTS:
[[file:figs/control_diagram_iff.png]]
* Decentralized Integral Force Feedback
#+begin_src latex :file system_iff.pdf
\begin{tikzpicture}
% Angle
\def\thetau{25}
% Rotational Stage
\draw[fill=black!60!white] (0, 0) circle (4.3);
\draw[fill=black!40!white] (0, 0) circle (3.8);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};
% Rotating Scope
\begin{scope}[rotate=\thetau]
% Rotating Frame
\draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small Suspended Platform};
% Mass
\draw[fill=white] (-1, -1) rectangle (1, 1);
% Label
\node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};
% Attached Points
\node[] at (-1, 0){$\bullet$};
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
\node[] at (0, -1){$\bullet$};
\draw[] (0, -1) -- ++(0, -0.2) coordinate(av);
% Force Sensors
\draw[fill=white] ($(au) + (-0.2, -0.5)$) rectangle ($(au) + (0, 0.5)$);
\draw[] ($(au) + (-0.2, -0.5)$)coordinate(actu) -- ($(au) + (0, 0.5)$);
\draw[] ($(au) + (-0.2, 0.5)$)coordinate(ku) -- ($(au) + (0, -0.5)$);
\draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$);
\draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5, 0)$);
\draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv) -- ($(av) + ( 0.5, 0)$);
% Spring and Actuator for U
\draw[actuator={0.6}{0.2}] (actu) -- coordinate[midway](actumid) (actu-|-2.6,0);
\draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0);
% \draw[actuator={0.6}{0.2}] (actv) -- node[right, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
\draw[actuator={0.6}{0.2}] (actv) -- coordinate[midway](actvmid) (actv|-0,-2.6);
\draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6);
\node[block={0.8cm}{0.6cm}, rotate=\thetau] (Ku) at ($(actumid) + (0, -1.2)$) {$K_{F}$};
\draw[->] ($(au) + (-0.1, -0.5)$) |- (Ku.east) node[below right, rotate=\thetau]{$f_{u}$};
\draw[->] (Ku.north) -- ($(actumid) + (0, -0.1)$) node[below left, rotate=\thetau]{$F_u$} node[below right, rotate=\thetau]{$-$};
\node[block={0.8cm}{0.6cm}, rotate=\thetau] (Kv) at ($(actvmid) + (1.2, 0)$) {$K_{F}$};
\draw[->] ($(av) + (0.5, -0.1)$) -| (Kv.north) node[above right, rotate=\thetau]{$f_{v}$};
\draw[->] (Kv.west) -- ($(actvmid) + (0.1, 0)$) node[below right, rotate=\thetau]{$F_v$} node[above right, rotate=\thetau]{$-$};
\end{scope}
% Inertial Frame
\draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
\draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
\draw[fill, color=black] (-4, -4) circle (0.06);
\node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};
\node[draw, circle, inner sep=0pt, minimum size=0.3cm] at (0, 0){};
\draw[->] (0, 0) node[above left, rotate=\thetau]{$\vec{i}_w$} -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
\draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
\draw[dashed] (0, 0) -- ++(2, 0);
\draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
\node[] at (0,0) {$\bullet$};
\draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
\end{tikzpicture}
#+end_src
#+RESULTS:
[[file:figs/system_iff.png]]
* Springs in parallel
#+begin_src latex :file system_parallel_springs.pdf
\begin{tikzpicture}
% Angle
\def\thetau{25}
% Rotational Stage
\draw[fill=black!60!white] (0, 0) circle (4.3);
\draw[fill=black!40!white] (0, 0) circle (3.8);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};
% Rotating Scope
\begin{scope}[rotate=\thetau]
% Rotating Frame
\draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small Suspended Platform};
% Mass
\draw[fill=white] (-1, -1) rectangle (1, 1);
% Label
\node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};
% Attached Points
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
\draw[] (0, -1) -- ++(0, -0.2) coordinate(av);
% Force Sensors
\draw[fill=white] ($(au) + (-0.2, -0.5)$) rectangle ($(au) + (0, 0.5)$);
\draw[] ($(au) + (-0.2, -0.5)$)coordinate(actu) -- ($(au) + (0, 0.5)$);
\draw[] ($(au) + (-0.2, 0.5)$)coordinate(ku) -- ($(au) + (0, -0.5)$);
\node[below=0.1, rotate=\thetau] at ($(au) + (-0.1, -0.5)$) {$f_{u}$}
\draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$);
\draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5, 0)$);
\draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv) -- ($(av) + ( 0.5, 0)$) ;
\node[right=0.1, rotate=\thetau] at ($(av) + (0.5, -0.1)$) {$f_{v}$}
% Spring and Actuator for U
\draw[actuator={0.6}{0.2}] (actu) -- node[below=0.1, rotate=\thetau]{$F_u$} (actu-|-2.6,0);
\draw[spring=0.2] (ku) -- node[below=0.1, rotate=\thetau]{$k_a$} (ku-|-2.6,0);
\draw[spring=0.2] (-1, 0.8) -- node[above=0.1, rotate=\thetau]{$k_p$} (-1, 0.8-|-2.6,0);
\draw[actuator={0.6}{0.2}] (actv) -- node[right=0.1, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
\draw[spring=0.2] (kv) -- node[right=0.1, rotate=\thetau]{$k_a$} (kv|-0,-2.6);
\draw[spring=0.2] (-0.8, -1) -- node[left=0.1, rotate=\thetau]{$k_p$} (-0.8, -1|-0,-2.6);
\end{scope}
% Inertial Frame
\draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
\draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
\draw[fill, color=black] (-4, -4) circle (0.06);
\node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};
\node[draw, circle, inner sep=0pt, minimum size=0.3cm] at (0, 0){};
\draw[->] (0, 0) node[above left, rotate=\thetau]{$\vec{i}_w$} -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
\draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
\draw[dashed] (0, 0) -- ++(2, 0);
\draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
\node[] at (0,0) {$\bullet$};
\draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
\end{tikzpicture}
#+end_src
#+RESULTS:
[[file:figs/system_parallel_springs.png]]