912 lines
37 KiB
TeX
912 lines
37 KiB
TeX
\documentclass[10pt,a4paper]{article}
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\input{|"/home/zamofing_t/Documents/doc-git/git2texInfo.sh"}%works only with PDFLaTeX-argument -shell-escape
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\usepackage{hyperref}
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\usepackage{amsmath}
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\renewcommand{\deg}{$^\circ$}
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\usepackage[section]{placeins} %place images in section
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\usepackage{tcolorbox}
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\title{Tuning/modeling fast stages of ESB-MX}
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\author{Thierry Zamofing}
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\usepackage{datetime}
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\date{\today, \currenttime\\
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\texttt{git:\gitAbrHash, ver:\gitVerNo{ }\gitStatus}}
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\begin{document}
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\maketitle
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\tableofcontents
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\section{Introduction}
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This document describes the tuning and modeling process of the ESB-MX fast stages.
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\section{Measurements}
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The tool used to record data of the fast stages is the bode plots is MXTuning.py, a script specially developed to record system responses. The main call to collect all data was:\\
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\verb|./MXTuning.py --dir MXTuning/19_01_29 --mode 64|\\
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The used frequencies are: 20 kHz phase loop, 5 kHz servo loop, 6.25MHz AdcAmp. This results in 50us phase time and 0.2ms servo time.\\
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According to the amplifier specs \cite[19]{PMAClv} a DAC Value of $32737=2^{15}$ corresponds to 33.85A current. So 1 \verb|curr_bit| is $33.85/32737A =1.034mA$.\\
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\cite[245-259]{PMACusr} Shows how the PwmSf works and is explained with some calculation examples.\\
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This is set in the gpasciiCommander templates:
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\begin{verbatim}
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PwmSf=15134.8909 # =.95*16384. PMAC3-style DSPGATE3 ASIC is being used for the output,
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the counter moves between +/- 16384. PwmSf is typically set to 95% of 16384
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\end{verbatim}
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Nerverless the documentation is confusing. Therefore PwmSf will be measured to convert idCmd bits values to idVolts bits in section \ref{sec:measCurStep}
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The Parker stages are configured to contCur=800mA ,peakCur=2400mA. Specs of the D11 stage are 0.8Amp RMS (producing 4N force) and 2.4Amp RMS peak.\\
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It should be save to use the higher DC value of 0.92Amp and 2.8Amp instead of the RMS value.
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\subsection{Measure Current Step}\label{sec:measCurStep}
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\verb|MXTuning.py –mode 1| $\rightarrow$ \verb|identifyFxFyStage.m|\\
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\includegraphics[scale=.5]{../matlab/figures/currstep_1.eps}
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\includegraphics[scale=.5]{/home/zamofing_t/Documents/doc-ext/DeltaTau/UsrMan257.png}
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The current step looks similar for both motors.
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The transfer function is: $k \cdot {w_0}^2/({w_0}^2+2 \cdot damp \cdot w_0 \cdot s+s^2)$\\
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rise time $(0\rightarrow 100\%)$ ca. 0.4ms\\
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rise time: \url{https://nptel.ac.in/courses/101108056/module7/lecture20.pdf}\\
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$\rightarrow$ \verb|1/(w0*np.sqrt(1-0.75**2))*(np.pi/2+np.arcsin(0.75))|\\
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The loop parameters are:\\
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IiGain=5, IpfGain=8, IpbGain=8
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In steady state an idCmd=idMeas=406. results in aprox. idVolts=7400\\
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This has been measured precisly from gathered data \verb|chirp_all_1a.npz|
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at frequencies from 10 to 220 Hz.
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The images have been generated with
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\verb|./MXTuning.py --dir MXTuning/19_01_29 --mode 128|.\\
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The overall aplification $iqCmd \rightarrow iqVolts$ is approx. 18.2.
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\begin{figure}[h!]
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/iqCmd_TF0.eps}
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/iqCmd_TF1.eps}
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\caption{IqCmd->IqMeas of motor 1 (bode same for both motors)}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/iqCmd_TF2.eps}
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/iqCmd_TF3.eps}
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\caption{IqCmd->IqVolts of motor 1 (bode same for both motors)}
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\end{figure}
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\FloatBarrier
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\subsection{Measure Open Loop}
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The frequency response has been measured with chirps at different amplitudes and frequency regions. The yellow line is averaged measurement data. The black line is the approximated model. The diagram shows \verb|curr_bits| (ca.1mA) to \verb|ActPos| (in um) transfer function.\\
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The images have been generated with
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\verb|./MXTuning.py --dir MXTuning/19_01_29 --mode 32|.\\
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\begin{figure}[h]
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/bode_model_plot0.eps}
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/bode_model_plot2.eps}
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\caption{open loop of motor 1 and 2}
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\label{fig:mot_open}
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\end{figure}
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\emph{Motor 1 (fy) has as expected a better response than Motor 2 (fx), because it has less mass to move.}\\
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\hbox{
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\parbox[t]{5cm}{
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Motor 1:\\
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0dB at 20.28Hz\\
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10 Hz: 9.63 dB -134\deg \\
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100Hz: -28.5dB -191.7\deg\\
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resonances 198 Hz \\
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}
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\parbox[t]{6cm}{
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Motor 2\\
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0dB at 12.39Hz\\
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10 Hz: 4.68 dB -162\deg\\
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100 Hz: -38.15 dB -187.5\deg\\
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resonances 60Hz,142Hz,414Hz,231Hz\\
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}
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}
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The bode plot drops as expected at approx. 40dB/dec. (due to $F=m\ddot{x}$)
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Here a example to roughly calculate at which frequency the motor moves 1um at 2A current:\\
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1curr\_bits is approx. 1mA. At 0dB 1mA moves a sine of 1um.\\
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10dB=factor 10, 20dB=factor 100, 30dB=factor 1000, 3dB $\approx$ factor 2\\
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A factor 2000 is $1000 \cdot 2 =30dB+3dB=33dB$.
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Out of the bode plot we can read approx.:\\
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Motor 1: -33dB at 130Hz\\
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Motor 2: -33dB at 84Hz\\
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The chirp parameters for low frequencies bode measurements (yellow) are: \verb|minFrq=1, maxFrq=15, amp=1000|.\\
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In this regime of 0 to 10Hz the bode amplitude is flat, which is mainly the result of the friction:\\
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Motor 1 has 9.63dB($\approx$ factor 10) at 10 Hz. This means that an amplitude of 1000um needs roughly 100 \verb|curr_bits|.
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The friction as measured in figure \ref{fig:mot1_frict} is around 100 \verb|curr_bits|. At lower frequencies than 10 Hz with an amplitude of 1000um, the friction free motion consumes much less current (-40dB) than the friction.
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Therefore the whole current is used to overcome the friction and the bode amplitude remains constant.
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%n times higher mass $\rightarrow$ n times lower frequency for same amplitude response\\
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%n times higher frequency $\rightarrow$ n times higher velocity $\rightarrow$ $n^2$ times more acceleration==current
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%1um at 12Hz with 1 mA $\rightarrow$ with 2000mA $\rightarrow$ sqrt(2000)*12Hz=540Hz
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%
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%A very simplified transfer function of the system is $G(s)=k/s^2$
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\subsection{Closed Loop}
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\subsubsection{Deltatau schematics}
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\includegraphics[scale=.7]{/home/zamofing_t/Documents/doc-ext/DeltaTau/UsrMan290.png}
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\\
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Closed loops have been measured with the following control loop settings.
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\begin{verbatim}
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motor_servo(mot=1,Kp=25,Kvfb=400,Ki=0.02,Kvff=350,Kaff=5000,MaxInt=1000)
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motor_servo(mot=2,Kp=22,Kvfb=350,Ki=0.02,Kvff=240,Kaff=1500,MaxInt=1000)
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\end{verbatim}
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\subsubsection{chirp sine closed loop}
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Figures \ref{fig:mot1_chirp} to \ref{fig:mot2_chirp_cmd}
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shows chirp plot with the input(blue) and the output(green) and its bode plots.
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The parameters for that chirp is:\\
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\verb| amp: 5, minFrq: 10, maxFrq: 220, ts: 0.0002, tSec: 20|
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\begin{figure}[h!]
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/chirp_all_1b0.eps}
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/chirp_all_1b1.eps}
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\caption{DesPos->ActPos of motor 1}
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\label{fig:mot1_chirp}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/chirp_all_2b0.eps}
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/chirp_all_2b1.eps}
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\caption{DesPos->ActPos of motor 2}
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\label{fig:mot2_chirp}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/chirp_all_1b2.eps}
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/chirp_all_1b3.eps}
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\caption{DesPos->IqCmd of motor 1}
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\label{fig:mot1_chirp_cmd}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/chirp_all_2b2.eps}
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/chirp_all_2b3.eps}
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\caption{DesPos->IqCmd of motor 2}
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\label{fig:mot2_chirp_cmd}
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\end{figure}
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Moving 5um with frequencies from 10 to 220Hz\\
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$\rightarrow$ at frequencies above 200 Hz, the current increses up to 2 amps, and the the following error kicks in\\
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$\rightarrow$ The closed loop response becomes bad above 20Hz (motor 1 ca. -10\%, motor 2 +5\% )\\
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\FloatBarrier
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\subsubsection{Friction} \label{sec:friction}
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To measure the friction, the stage is moved at slow speed from
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+lim to -lim. The current is proportional to the force.
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Additionally the friction is measured depending on the stage positions and motion directions. This is measured at different speed to see if at these velocities the viscose friction is visible.
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\begin{figure}[h!]
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/friction10.eps}
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/friction11.eps}
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\caption{position dependant friction of motor 1}
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\label{fig:mot1_frict}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/friction20.eps}
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\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/friction21.eps}
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\caption{position dependant friction of motor 2}
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\label{fig:mot2_frict}
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\end{figure}
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Data recording is done with: \verb|./MXTuning.py --dir MXTuning/19_01_29 --mode 16|.\\
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The function parameters are: \verb|pMin=-10000, pMax=10000, speed=(5,10,20,30,60), cnt=2, period=10|.
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The recorded data moves from -10000um to 10000um at speed of 5 to 60 mm/s.\\
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Avg current forward: 111.7 Avg current backward: -105.3\\
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Avg current forward: 95.3 Avg current backward: -130.7\\
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These values should be used for the $K_{fff}$ parameter of the Servo loop:\\
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Motor 1,2: $K_{fff}\approx100$\\
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\FloatBarrier
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\subsubsection{using advanced Deltatau Servo Loop}
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For now only following settings of the servo loop are used:Kp, Kvfb, Ki, Kvff, Kaff, MaxInt.\\
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The standard PID servo loop (figure\ref{fig:deltatau_std_ctrl}) has some additional features, that were not yet used, especially the polynomial filters.
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\begin{figure}[h!]
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\center
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\includegraphics[scale=.2]{/home/zamofing_t/Documents/doc-ext/DeltaTau/ServoBlockDiag.png}
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\caption{position dependant friction of motor 2}
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\label{fig:deltatau_std_ctrl}
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\end{figure}
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\cite[293]{PMACusr} shows details about the standard servo loop but unfortunately there are errors in documentation and the explanations are not really helpful. Hopefully the implementation is correct.\\
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\textbf{Polynomial Filters:}
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\begin{description}
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\item[A:] $Ka_0+Ka_1z^{-1}+\ldots+Ka_1z^{-7}$
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\item[B:] $Kb_0+Kb_1z^{-1}+\ldots+Kb_1z^{-7}$
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\item[C/D:] $\frac{Kc_0+Kc_1z^{-1}+\ldots+Kc_1z^{-7}}
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{Kd_0+Kd_1z^{-1}+\ldots+Kd_1z^{-7}}$
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\item[E:] $\frac{1}{Ke_0+Ke_1z^{-1}+Ke_1z^{-2}}$
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\item[F:] $\frac{1}{Kf_0+Kf_1z^{-1}+Kf_1z^{-2}}$
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\end{description}
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Filters A, B, C, and D are 7th-order polynomials.
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if \texttt{Motor[x].Servo.SwPoly7} is set to its default value of 0, these only execute as 2nd-order polynomials, saving computation time.
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If this element is set to 1, these execute as full 7th-order polynomials.
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Filters E and F are always 2nd-order polynomials.\\
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The flat amplitude in figure \ref{fig:mot_open} at low frequencies is mostly the result of the static and viscose friction and not of a linear mechanical spring and element as one could suggest out of the bode plot.\\
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The Value of $K_{fff}$ is used to compensate the non linear static friction. It can be estimated out of the bode plot at low frequencies. It is a non linear element, because it only depends on the sign if the velocity.\\
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$K_{vff}$ is used to compensate the linear viscose friction.\\
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\begin{tcolorbox}[colback=red!5!white,colframe=red!75!black,colbacktitle=red!50,coltitle=black,title=TODO]
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Make simulations in MATLAB. Set C/D filter to compensate resonance and the current loop.\\
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This sshould be mostly the inverse of the figures: \ref{fig:mot1_chirp} and \ref{fig:mot2_chirp}.\\
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Use $K_{fff}$
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\end{tcolorbox}
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\newpage
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\section{Modeling the system}
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\subsection{Electrical model}
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\label{sec:mdlElec}
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\begin{figure}[h!]
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\centering
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\includegraphics[scale=.45]{model1.eps}
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\includegraphics[scale=.6]{model2.eps}
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\caption{electrical model}
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\end{figure}
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Basic formulas: $U=R \cdot I$ \hspace{.5cm}
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$U=L \cdot \frac{di}{dt}$\\
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Solving in Laplace space:\\
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$iqVolts=(R+Ls)\cdot iqMeas$\\
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$s \cdot iqMeas =\frac{1}{L}iqVolts - \frac{R}{L}iqMeas$\\
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Transferfunction open loop of $G_1(s)=iqVolts \rightarrow iqCmd$
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\\
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using Masons rule:
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\url{https://en.wikipedia.org/wiki/Mason's_gain_formula}:
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\[
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G_1(s)=\frac{y_{out}}{y_{in}}=\frac{iqCmd}{iqVolts}=
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\frac{\frac{1}{Ls}}{1+ \frac{R}{Ls}} = \frac{1}{Ls+R} = \frac{k}{1+Ts} = \frac{\frac{1}{R}}{1+\frac{L}{R}s}
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\]
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\vspace{1pc}
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Transferfunction closed loop of $G_2(s)=iqCmd \rightarrow iqMeas$:
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\[
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\begin{aligned}
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&\text{with}\quad
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a=Ipf+\frac{Li}{s} \quad
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b=PwmSF \cdot G(s) \quad
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c=Ipb \quad
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d=1\\
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&\text{using Masons rule:} \quad G_2(s)=\frac{ab}{1+bc+abd}\\
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\\
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&\text{extending:} \quad =\frac{(Ipf+\frac{Ii}{s}) \cdot PwmSF \cdot G_1(s)}
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{1+PwmSF \cdot G_1(s) \cdot Ipb +(Ipf+\frac{Ii}{s})
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\cdot PwmSF \cdot G_1(s)}\\
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\\
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&=\left.\frac{(Ipf+\frac{Ii}{s}) \cdot PwmSF \cdot \frac{1}{Ls+R}}
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{1+PwmSF \cdot \frac{1}{Ls+R} \cdot Ipb +(Ipf+\frac{Ii}{s}) \cdot PwmSF \cdot \frac{1}{Ls+R}} \right| \cdot (Ls+R) \cdot s\\
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\\
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&=\frac{(Ipf \cdot s+Ii) \cdot PwmSF }
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{(Ls+R)s+PwmSF \cdot Ipb \cdot s +(Ipf \cdot s+Ii) \cdot PwmSF }\\
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\\
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&=\frac{Ipf \cdot s+Ii }
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{\frac{L}{PwmSF}s^2 +(\frac{R}{PwmSF}+ Ipb+Ipf)s +Ii}\\
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\\
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\end{aligned}
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\]
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To use real values we have to consider: The values
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$IiGain=5, IpfGain=8, IpbGain=8$ for the Deltatau are in z-domain.\\
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Therefore for the continous domain they have to be scaled:
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$Ii=IiGain/ts \quad Ipf=IpfGain \quad Ipb=IpbGain$ with $ts=50\mu s$ (20kHz)\\
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The overall aplification $iqCmd \rightarrow iqVolts$ measured in section \ref{sec:measCurStep} is approx. 18.2.
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The resistance of the stage is 8.8 $\Omega$\\
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The inductance of the stage is 2.4 mH.\\
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Nevertheless simulations with \verb|current_loop.slx| showed, that the current loop only works in the discrete domain. In continous domain neither the amplification nor the shape mached.\\
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Therefore the only approach is to use the second order transfer function as approximated in section \ref{sec:measCurStep}.\\
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A further test is to 'turn of' the current loop. This can be done by setting:$IiGain=0, IpfGain=1, IpbGain=-1$.
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The resulting transfer function is:
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\[
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\frac{Ipf}
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{\frac{L}{PwmSF}s +\frac{R}{PwmSF}} =\\
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\frac{Ipf \cdot PwmSF}
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{L s +R} =\\
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\frac{\frac{Ipf \cdot PwmSF}{R}}
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{\frac{L}{R} s +1}\\
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\\
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\]
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This is a $PT_1$ element with a time constant of $\frac{L}{R}=\frac{2.4mH}{8.8\Omega}=0.27ms$. Figures \ref{fig:curr_ol} shows a current step of 3000 \verb|curr_bit| resulting in a current of about 150 \verb|curr_bit|. The rise time matches roughly. So the cable resistance has not a major impact.
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\begin{figure}[h!]
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\centering
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\includegraphics[scale=.25]{../python/MXTuning/19_01_29/img/curr_step_ol_10.eps}
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\includegraphics[scale=.25]{../python/MXTuning/19_01_29/img/curr_step_ol_20.eps}
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\caption{voltage step (current open loop)}
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\label{fig:curr_ol}
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\end{figure}
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\subsection{Mechanical model}
|
||
|
||
\begin{figure}[h!]
|
||
\centering
|
||
\includegraphics[scale=.45]{model3.eps}
|
||
\caption{mechanical model}
|
||
\end{figure}
|
||
|
||
Input: Force $u(t)=F$\\
|
||
Output: Position $y(t)=x_1(t)$\\
|
||
mass $m=m_1+m_2+\ldots+m_n$\\
|
||
damping: $d=d_1+d_2+\ldots+d_n$\\
|
||
springs: $k=k_1+k_2+\ldots+k_n$\\
|
||
|
||
\eqref{mech1} shows the mechanical differential equations:
|
||
|
||
\begin{equation}
|
||
\begin{aligned}
|
||
m_1\ddot{x}_1 = & u(t) -k_1x_1-d_1\dot{x}_1\\
|
||
& + k_2(x_2-x_1)+d_2(\dot{x}_2-\dot{x}_1)
|
||
+ k_3(x_3-x_1)+d_3(\dot{x}_3-\dot{x}_1)
|
||
+ k_4(x_4-x_1)+d_4(\dot{x}_4-\dot{x}_1)\\
|
||
m_2\ddot{x}_2= & k_2(x_2-x_1)+d_2(\dot{x}_2-\dot{x}_1)\\
|
||
m_3\ddot{x}_3= & k_3(x_3-x_1)+d_3(\dot{x}_3-\dot{x}_1)\\
|
||
m_4\ddot{x}_4= & k_4(x_4-x_1)+d_4(\dot{x}_4-\dot{x}_1)\\
|
||
\end{aligned}\label{eq:mech1}
|
||
\end{equation}
|
||
|
||
\begin{equation}
|
||
\begin{aligned}
|
||
\mathbf{\dot{x} = Ax + Bu}\\
|
||
\mathbf{y = Cx + Du}
|
||
\end{aligned}\label{eq:mech2}
|
||
\end{equation}
|
||
|
||
\eqref{eq:mech2} are the general input output equations in matrix form with x and A defines as \eqref{eq:mech3}:
|
||
|
||
\begin{equation}
|
||
\mathbf{x}=
|
||
\begin{bmatrix}
|
||
x_1\\
|
||
\dot{x}_1\\
|
||
x_2\\
|
||
\dot{x}_2\\
|
||
x_3\\
|
||
\dot{x}_3\\
|
||
x_4\\
|
||
\dot{x}_4\\
|
||
\end{bmatrix},\quad
|
||
\mathbf{\dot{x}}=
|
||
\begin{bmatrix}
|
||
\dot{x}_1\\
|
||
\ddot{x}_1\\
|
||
\dot{x}_2\\
|
||
\ddot{x}_2\\
|
||
\dot{x}_3\\
|
||
\ddot{x}_3\\
|
||
\dot{x}_4\\
|
||
\ddot{x}_4\\
|
||
\end{bmatrix},\quad
|
||
\mathbf{A}=
|
||
\begin{bmatrix}
|
||
0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\
|
||
-\frac{k}{m_1} & -\frac{d}{m_1} & \frac{k_2}{m_1} & \frac{d_2}{m_1} & \frac{k_3}{m_1} & \frac{d_3}{m_1} & \frac{k_4}{m_1} & \frac{d_4}{m_1}\\
|
||
|
||
0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\
|
||
-\frac{k_1}{m_2} & -\frac{d_1}{m_2} & \frac{k_2}{m_2} & \frac{d_2}{m_2} & 0 & 0 & 0 & 0 \\
|
||
|
||
0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\
|
||
-\frac{k_1}{m_3} & -\frac{d_1}{m_3} & 0 & 0 & \frac{k_3}{m_1} & \frac{d_3}{m_3} & 0 & 0 \\
|
||
|
||
0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\
|
||
-\frac{k_1}{m_4} & -\frac{d_1}{m_4} & 0 & 0 & 0 & 0 & \frac{k_4}{m_1} & \frac{d_4}{m_4} \\
|
||
\end{bmatrix},\quad
|
||
B=\begin{bmatrix}
|
||
\frac{1}{m_1} \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0\\
|
||
\end{bmatrix}
|
||
%,\quad
|
||
%C=\begin{bmatrix}
|
||
%\1 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0\\
|
||
%\end{bmatrix},\quad
|
||
%D=0
|
||
\label{eq:mech3}
|
||
\end{equation}
|
||
|
||
\begin{tcolorbox}[colback=red!5!white,colframe=red!75!black,colbacktitle=red!50,coltitle=black,title=TODO]
|
||
$k_1=0$ The non linear friction has to be compensate outside of the control loop.\\
|
||
$d_1$ seems to be negligable (section \ref{sec:stageData}).\\
|
||
But the system is not observable. $\rightarrow$ Perhaps the integrators of the system can be removed. having only $\mathbf{x}=[ \dot{x}_1 \dot{x}_2 \dot{x}_3 \dot{x}_4]$ as the state vector
|
||
\end{tcolorbox}
|
||
|
||
\subsection{Stage data}
|
||
\label{sec:stageData}
|
||
|
||
This data comes from datasheets and construction information \cite{DynParker}.
|
||
|
||
\begin{tabular}{|r|l|}
|
||
\hline
|
||
Stage Y mass& 340g \\
|
||
Stage X mass& 950g \\
|
||
Interferometer mirrors & 51g (additional)\\
|
||
Aluminun (instead ABS) & 42g (additional)\\
|
||
\hline
|
||
\end{tabular}
|
||
|
||
\vspace{1pc}
|
||
|
||
\begin{tabular}{|r|c|l|}
|
||
\hline
|
||
Continous force && 5.51N \\
|
||
Peak force && 12N \\
|
||
Static friction && 1N\\
|
||
Viscose damping && 0.5N$\cdot$s/m\\
|
||
Motor constant &Km& 1.46N/$\sqrt{watt}$\\
|
||
Resistance &R&8.8$\Omega$\\
|
||
Inductance &L& 2.4mH\\
|
||
\hline
|
||
\end{tabular}
|
||
|
||
\vspace{1pc}
|
||
|
||
The data sheet for the current are quite confusing (sine, trap, rms). But lets check the motor Konstant Km.\\
|
||
The data sheet says:\\
|
||
Stall Current Continous 0.92A (trap, DC), Stall force Continous 4N
|
||
\[
|
||
U=R\cdot I \qquad P=U \cdot I \quad \rightarrow \quad P=R \cdot I^2\\
|
||
\]
|
||
at a constant current of 0.92A we have $ 8.8 \cdot 0.92^2 = 7.44 $W the resulting force will be:\\
|
||
$1.46N \cdot \sqrt{7.44} = 3.98 N$\\
|
||
|
||
Lets have a look at the viscose damping:\\
|
||
our speed is roughly 50$\mu$m/10ms. this is 5mm/s. The damping force at that speed is: $0.5\frac{Ns}{m}\cdot 5\frac{mm}{s}=2\cdot10^{-3}N$.
|
||
The used current for that force is negligable, and theerefore the viscose damopling is negligable.
|
||
|
||
|
||
|
||
\subsection{identification of stages}
|
||
|
||
The goal is to build an optimal state space model of the plant with following input and output taps:
|
||
|
||
\begin{figure}[h!]
|
||
\center
|
||
\includegraphics[scale=.7]{model4.eps}
|
||
\caption{model taps}
|
||
\end{figure}
|
||
|
||
|
||
\verb|full_bode_mot[1|2].mat| is generated from \verb|MXTuning.py| in function \verb|bode_model_plot()|. It contains the bode data of real measurements and approximated transfer functions.
|
||
|
||
\verb|identifyFxFyStage.m| reads the python data \verb|full_bode_mot[1|2].mat| and build motor objects with transfer functions and state space models.
|
||
|
||
The approximated transfer functions can be tweaked and edited with: e.g. \verb|controlSystemDesigner('bode',1,mot1.tf_xx)| to enhance the model.
|
||
The full transfer function is then split in individual parts that are put back into \verb|MXTuning.py|.\\
|
||
|
||
the transfer functions for each two motors are separated atomic transfer function as stated in table \ref{tab:trfFunc1}\\
|
||
tfc = transfer function current, tfp = transfer function position. Consecutive letters are simplified transfer functions. tf[1-9]=transfer function resonance.
|
||
|
||
\begin{table}[h!]
|
||
\center
|
||
\begin{tabular}{|l|l|l|l|}
|
||
\hline
|
||
key & description & motor1 (fy) & motor2 (fx) \\
|
||
\hline
|
||
tfc & current loop tf & f=694 ? 1389 , d=0.75 & same \\
|
||
tfd & simplified cur.loop tf $PT_1$ & f-3dB, 45\deg at 400Hz & same \\
|
||
\hline
|
||
tfp & \vtop{\hbox{\strut main mechanical tf} \hbox{\strut with -40dB/dec }}
|
||
& mag=6dB f=7.96Hz d=0.6 & mag=12dB f=3.34 d=0.4 \\
|
||
tfq & \vtop{\hbox{\strut simplified mechanical tf} \hbox{\strut 2 integrators with -40dB/dec }}
|
||
& 0dB at 19.8Hz & 0dB at 11.84Hz\\
|
||
\hline
|
||
tf1 & mechanical resonance tf & f=[197,199] d=[0.02,0.02] & f=[55|61] d=[0.2|0.2] \\
|
||
tf2 & mechanical resonance tf & & f=[128|137] d=[0.05|0.05] \\
|
||
tf3 & mechanical resonance tf & & f=[410|417] d=[0.015|0.015] \\
|
||
tf4 & mechanical resonance tf & & f=[230|233] d=[0.04|0.04] \\
|
||
\hline
|
||
\end{tabular}
|
||
\caption{plant partial transfer functions}
|
||
\label{tab:trfFunc1}
|
||
\end{table}
|
||
%\vspace{1pc}
|
||
|
||
The black line on figure \ref{fig:mot_open} shows the concatenate transfer function $tfc \cdot tfp \cdot tf1 \cdot tf2 \cdot tf3 \cdot tf4$.\\
|
||
\vspace{1pc}
|
||
|
||
\fbox{\parbox[t]{15cm}{The current loop frequency from the MATLAB identification looks different than the used one. Matlab identifies $w_0=8727rad/sec = f0=1389Hz$ but to match the bode plot a value of half frequency need to be taken:$f_0=694$. The reason could be discretization and time delay because the servo loop is processed after the phase loop.}}
|
||
\vspace{1pc}
|
||
|
||
\section{Simulink/MATLAB simulations}
|
||
|
||
It has to be checked if the model matches the real stage. Therefore simulations in MATLAB have been done to validate the identification process of the stages.
|
||
|
||
\subsection{chirp sine closed loop with simulink model}
|
||
|
||
To compare the measurements with the model following lines were executed in MATLAB
|
||
\begin{verbatim}
|
||
clear;clear global;close all;
|
||
mot=identifyFxFyStage(7);
|
||
for k =1:2
|
||
[pb]=simFxFyStage(mot{k});sim('stage_closed_loop');
|
||
f=figure(); h=plot(desPos_actPos.Time,desPos_actPos.Data,'g');
|
||
set(h(1),'color','b'); set(h(2),'color',[0 0.5 0]);
|
||
print(f,sprintf('figures/sim_cl_DTGz_%d',mot{k}.id),'-depsc');
|
||
end
|
||
\end{verbatim}
|
||
|
||
The Simulink model \verb|stage_closed_loop| contains various controller blocks. as \verb|PID G(s)|, \verb|PID G(z)|, \verb|ServoDeltaTau_z G(s)| and \verb|ServoDeltaTau_z G(z)|.
|
||
|
||
With the controller block \verb|ServoDeltaTau_z G(z)| the real measurements can be compared with the simulated model.
|
||
Figures \ref{fig:mot_chirp_sim} showed similar response as the real stages (Figures \ref{fig:mot1_chirp}, \ref{fig:mot2_chirp}). Therefore the model matches the real stage well.
|
||
|
||
|
||
\begin{figure}[h!]
|
||
\center
|
||
|
||
\includegraphics[scale=.45]{../matlab/figures/sim_cl_DTGz.png}\\
|
||
\includegraphics[scale=.45]{../matlab/figures/sim_cl_DTGz_1.eps}
|
||
\includegraphics[scale=.45]{../matlab/figures/sim_cl_DTGz_bode1.eps}\\
|
||
\includegraphics[scale=.45]{../matlab/figures/sim_cl_DTGz_2.eps}
|
||
\includegraphics[scale=.45]{../matlab/figures/sim_cl_DTGz_bode2.eps}
|
||
\caption{Motor 1 sim Motor 2 sim}
|
||
\label{fig:mot_chirp_sim}
|
||
\end{figure}
|
||
|
||
|
||
The model can be used to imrove the controller in MATLAB/simulink.
|
||
|
||
Improvement of the regulation with a simple PID loop and with prefilters did not improve the regulation quality.\\
|
||
Therefore for better regulation quality more sophisticated controllers as state controllers will be tested.
|
||
|
||
\subsection{State Space Controller with Observer}
|
||
|
||
\verb|(s.a. http://ctms.engin.umich.edu/CTMS/index.php?example=Introduction§ion=ControlStateSpace)|
|
||
|
||
A standard PID controller uses feedback to detect errors between the desired position and the actual position and applies corrective commands to compensate for those errors. Although PID control is the most common type of industrial controller, it does have limitations.
|
||
The idea of a state space controller with observer is to have a model of the plant which follows all internal states of the real plant. All these internal states of the model can then be used states to build an optimal controller.
|
||
opposite to the PID cpntroller which is a ‘black-box design’, the state space controller with observer is a ‘white box design’. (Figure \ref{fig:observer1})\\
|
||
|
||
\begin{figure}[h!]
|
||
\centering
|
||
\includegraphics[scale=.75]{observer_statefeedback.png}
|
||
\caption{observer controller}\label{fig:observer1}
|
||
\end{figure}
|
||
|
||
|
||
To implement a state space controller with observer the model has to be observable and controllable. The full model of the tranfer function $tfc \cdot tfp \cdot tf1 \cdot tf2 \cdot tf3 \cdot tf4$ is not controllable due to the various resonance frequencies. Therefore for the observer design the state space model has to be simplified. (see simplified transfer function in table \ref{tab:trfFunc1}\\
|
||
|
||
|
||
Figure \ref{fig:mdl_bode1} shows the bode plots of the best model to the most simplified model:\\
|
||
|
||
\begin{tabular}{ll}
|
||
plant & best model tranfer function: $tfc \cdot tfp \cdot tf1 \cdot tf2 \cdot tf3 \cdot tf4$\\
|
||
mdlcp & main mechanical with second order current loop: $tfc \cdot tfp$\\
|
||
mdldp & main mechanical with $PT_1$ current loop (first order): $tfd \cdot tfp$\\
|
||
mdlp & main mechanical (incl. 'viscose friction'): $tfp$\\
|
||
mdlq & only 2 integrators: $tfq$\\
|
||
\end{tabular}
|
||
\vspace{1pc}
|
||
|
||
\begin{figure}[h!]
|
||
\center
|
||
\includegraphics[scale=.44]{../python/MXTuning/19_01_29/img/bode_model_plot1.eps}
|
||
\includegraphics[scale=.44]{../python/MXTuning/19_01_29/img/bode_model_plot3.eps}
|
||
\caption{bode plots of best and simplified models}
|
||
\label{fig:mdl_bode1}
|
||
\end{figure}
|
||
|
||
\verb|identifyFxFyStage.m| is the code that generates 'state space models' of different complexity out of the these transfer functions. All that information is stored in the 'motor objects'.\\
|
||
|
||
|
||
As first approach the tf function is just converted to the ss space and the ss matrices are glued together.
|
||
|
||
The matlab models are:\\
|
||
|
||
\begin{tabular}{ll}
|
||
\texttt{ss\_plt:} & best approach of the plant with mechanics, resonance, current loop etc.\\
|
||
\texttt{ss\_cp:} & model without resonance (only current and main mechanical)\\
|
||
\texttt{ss\_dp:} & model without resonance (simplified current and main mechanical)\\
|
||
\texttt{ss\_p:} & model without current loop, no resonance (only main mechanical)\\
|
||
\texttt{ss\_q:} & simplified mechanical, no current loop, no resonance\\
|
||
\end{tabular}\\
|
||
\vspace{1pc}
|
||
|
||
The state space controller is calculated by pole placement.\\
|
||
Following code calculates parameters for a observer controller, does a simulation and plots the results:
|
||
\begin{verbatim}
|
||
clear;clear global;close all;
|
||
mot=identifyFxFyStage(7);
|
||
for sscType=0:1
|
||
for k=1:2
|
||
[ssc]=StateSpaceControlDesign(mot{k},sscType);sim('observer');
|
||
f=figure(); h=plot(desPos_actPos.Time,desPos_actPos.Data,'g');grid on;
|
||
set(h(1),'color','b'); set(h(2),'color',[0 0.5 0]);
|
||
print(f,sprintf('figures/sim_cl_obs_%d_%d',sscType,mot{k}.id),'-depsc');
|
||
f=bodeSamples(desPos_actPos);
|
||
print(f,sprintf('figures/sim_cl_obs_bode%d_%d',sscType,mot{k}.id),'-depsc');
|
||
end
|
||
end
|
||
|
||
|
||
\end{verbatim}
|
||
|
||
|
||
\begin{figure}[h!]
|
||
\center
|
||
\includegraphics[scale=.35]{../matlab/figures/sim_cl_observer.png}
|
||
\caption{Observer flow chart}
|
||
\label{fig:mot_observer_sim}
|
||
\end{figure}
|
||
|
||
|
||
\begin{figure}[h!]
|
||
\center
|
||
\includegraphics[scale=.45]{../matlab/figures/sim_cl_obs_0_1.eps}
|
||
\includegraphics[scale=.45]{../matlab/figures/sim_cl_obs_bode0_1.eps}\\
|
||
\includegraphics[scale=.45]{../matlab/figures/sim_cl_obs_0_2.eps}
|
||
\includegraphics[scale=.45]{../matlab/figures/sim_cl_obs_bode0_2.eps}
|
||
\caption{Observer sim: Motor 1 Motor 2}
|
||
\label{fig:mot_observer_sim}
|
||
\end{figure}
|
||
|
||
|
||
|
||
Comparing figures \ref{fig:mot_chirp_sim} and \ref{fig:mot_observer_sim} shows the better behavious of the observer model.
|
||
|
||
With an additional prefilter resonance and reductions can be suppressed a bit.\\
|
||
|
||
\begin{figure}[h!]
|
||
\center
|
||
\includegraphics[scale=.45]{../matlab/figures/sim_cl_obs_1_1.eps}
|
||
\includegraphics[scale=.45]{../matlab/figures/sim_cl_obs_bode1_1.eps}\\
|
||
\includegraphics[scale=.45]{../matlab/figures/sim_cl_obs_1_2.eps}
|
||
\includegraphics[scale=.45]{../matlab/figures/sim_cl_obs_bode1_2.eps}
|
||
\caption{Observer with prefilter sim: Motor 1 Motor 2}
|
||
\label{fig:mot_observer_sim}
|
||
\end{figure}
|
||
|
||
|
||
|
||
The system was simulated with 5kHz servo loop frequency.
|
||
Higher servo loop frequency does not help, because a continious state space controller behaves not relevantly better than a sampled state space controller at 5kHz.\\
|
||
|
||
Now the controller must be implemented on deltatau to check the performance on the real stage.
|
||
|
||
\FloatBarrier
|
||
\subsection{Implementing state space controller on Deltatau}
|
||
|
||
In MATLAB the function \verb|StateSpaceControlDesign()| produces files \verb%/tmp/ssc[1|2].mat%.\\
|
||
|
||
The servo loop code is generated with: \verb|MXTuning.py –mode 256|.\\
|
||
This python code reads \verb%/tmp/ssc[1|2].mat% and substitutes part of
|
||
\verb%usr_code/usrcode_template.[h|c]% to build the servo loop code \verb%usr_code/usrcode.[h|c]%.\\
|
||
|
||
Finally the real time servo code is compliled and installed on the DeltaTau with:\\
|
||
|
||
\verb|/epics_ioc_modules/ESB_MX/python/usr_code$ make install|\\
|
||
|
||
Following lines in gpasciiCommander will activate the user servo loop code.
|
||
\vspace{1pc}
|
||
|
||
The \verb|make install| process consists of many sub parts:\\
|
||
%\begin{itemize}
|
||
%\setlength\itemsep{-1em}
|
||
%\item asfgd
|
||
%\item asfgd
|
||
%\item asfgd
|
||
%\end{itemize}
|
||
- generate observer date in MATLAB with \verb|StateSpaceControlDesign()|\\
|
||
- generate code in python with \verb|MXTuning.py|\\
|
||
- compile the code with \verb|MXTuning.py| (make all)\\
|
||
- upload the module to Deltatau (make install)\\
|
||
- activate the user servo loop (make install)\\
|
||
|
||
Here the full process:
|
||
|
||
\begin{tcolorbox}[width=15cm,colback=yellow!5!white,colframe=yellow!75!black,colbacktitle=yellow!50,coltitle=black,title=MATLAB]
|
||
\begin{verbatim}
|
||
clear;clear global;close all;
|
||
mot=identifyFxFyStage(7);
|
||
sscType=0;
|
||
for k =1:2
|
||
[ssc]=StateSpaceControlDesign(mot{k},sscType);
|
||
end
|
||
\end{verbatim}
|
||
\end{tcolorbox}
|
||
|
||
\begin{tcolorbox}[width=15cm,colback=yellow!5!white,colframe=yellow!75!black,colbacktitle=yellow!50,coltitle=black,title=Shell]
|
||
\begin{verbatim}
|
||
cd /home/zamofing_t/Documents/prj/SwissFEL/epics_ioc_modules/ESB_MX/python
|
||
./MXTuning.py -m512
|
||
|
||
cd /home/zamofing_t/Documents/prj/SwissFEL/epics_ioc_modules/ESB_MX/python/usr_code
|
||
make
|
||
|
||
cd /home/zamofing_t/Documents/prj/SwissFEL/PBTools/pbtools/usr_servo_phase
|
||
scp userservo_util userphase_util usrServoSample/usralgo.ko root@SAR-CPPM-EXPMX1:/tmp
|
||
|
||
|
||
\end{verbatim}
|
||
\end{tcolorbox}
|
||
|
||
\begin{tcolorbox}[width=15cm,colback=yellow!5!white,colframe=yellow!75!black,colbacktitle=yellow!50,coltitle=black,title=DeltaTau Shell]
|
||
\begin{verbatim}
|
||
root@:/opt/ppmac#
|
||
LD_LIBRARY_PATH=/opt/ppmac/libppmac/ /tmp/userservo_util -d 1
|
||
rmmod usralgo
|
||
insmod /tmp/usralgo.ko
|
||
LD_LIBRARY_PATH=/opt/ppmac/libppmac/ /tmp/userservo_util -l 1 usr_servo_ctrl_2
|
||
LD_LIBRARY_PATH=/opt/ppmac/libppmac/ /tmp/userservo_util -e 1
|
||
|
||
gpascii:
|
||
Motor[1].Ctrl =UserAlgo.ServoCtrlAddr[1]
|
||
\end{verbatim}
|
||
\end{tcolorbox}
|
||
|
||
|
||
\FloatBarrier
|
||
\subsection{The reality of the state space controller}
|
||
|
||
The state space controller assumes that the system is observable and controlable. The bode plot shows a flat amplitude at low frequencies, which makes the feeling, that the system is observable and controlable. But in fact the reason of that flat amplitude is friction (section \ref{sec:friction}). The viscode damping is negligable.\\
|
||
This results to the fact that the stage consists of really 2 integrators and behaves without friction roughly like $F=m \cdot \ddot{x}$. But an integrator $\frac{1}{s}$ is neighter observable nor controlable. Therefore we have to check, how to implement an optimal controller for such a system.\\
|
||
|
||
|
||
A controller consists of a feed forward H(s) and a feed back G(s) path.
|
||
|
||
|
||
\begin{figure}[h!]
|
||
\center
|
||
\includegraphics[scale=.9]{model5.eps}
|
||
\caption{$1/s^2$ plant}
|
||
\end{figure}
|
||
|
||
|
||
Assume a plant consists of a integrator $\frac{1}{s}$ the overall transfer functions are $\frac{y}{u}=\frac{\frac{H}{s}+\frac{G}{s}}{1+\frac{G}{s}}=\frac{H+G}{s+G}$ and $\frac{y}{e}=\frac{\frac{G}{s}}{1+\frac{G}{s}}=\frac{G}{s+G}$. Setting H(s)=s and G(s)=k results in a overall transfer function of $\frac{y}{u}=\frac{s+G}{s+G}=1$ and $\frac{y}{e}=\frac{k}{s+k}$. So the output follows the input and k defines how fast errors will be compensated.\\
|
||
|
||
|
||
Simulating a single integrator plant in MATLAB works. But with 2 integrators the system is unstable because of the two derivate elements. With a discrete differentiator it becomes stable again. In fact a derivate element is a very critical element, because it can create instability and adds a lot of noise. But in this case it is acceptable, because is acts on the trajectory and not on the feedback loop. The only thing that has to be granted is that the trajectory is twice differentiable. This is the case with limited jirk or with the pvt motion. A step response should be avoided and not used to tweak the parameters.\\
|
||
|
||
\includegraphics[scale=.45]{FF_FB_ctrl.png}
|
||
The optimal parameters for a pure feed forward systems are calculated
|
||
in equation \ref{eq:calc_Kaff}.
|
||
|
||
\def\ccdot{\negthinspace\cdot\negthinspace}
|
||
|
||
\begin{equation}
|
||
\begin{aligned}
|
||
&DesPosFB=DesVelFF=0,\quad posErrFB=velErrFB=accErrFB=0\\
|
||
&\text{Motor 1: 19.8Hz 0dB, Ts=5kHz=.2ms,}\quad
|
||
k=(19.8 \ccdot 2 \ccdot \pi)^2\\
|
||
&Kaff = 1/(Ts \ccdot Ts \ccdot k) = 1/((19.8 \ccdot 2 \ccdot \pi)^2/5000^2) = 1615.2\\
|
||
&\text{Motor 2:11.84Hz 0dB, Ts=5kHz=.2ms,}\quad
|
||
k=(11.84 \ccdot 2 \ccdot \pi)^2\\
|
||
&Kaff = 1/(Ts \ccdot Ts \ccdot k) = 1/((11.84 \ccdot 2 \ccdot \pi)^2/5000^2) = 4517.28\\
|
||
\end{aligned}\label{eq:calc_Kaff}
|
||
\end{equation}
|
||
|
||
To correct errors, posErrFB is increased. But in a discrete system, the regulation becomes instable, because the actPos always lags the desPos for one sample. To avoid instability, a fiter can attenuate this problem.\\
|
||
|
||
The Standard Delta Tau controller (figure \ref{fig:deltatau_std_ctrl}), shows a very similar feed forward and feedback loop structure with additional filters. So after all the measurements, we can calculate the optimal Kfff and Kaff values.
|
||
Kp and Ki values will attenuate the errors. Kvff=Kvfb makes the system stable at higher Kp values, but setting the filter B seems to be more appropriate.\\
|
||
|
||
MATLAB simulations \verb|(tool: DeltaTauOptimizer.m)| and real test showed similar behaviour and the following error could be reduced roughly by factor 2 with first tests.\\
|
||
|
||
This should be good enough for the beam time in March 2019 but further improvements still should be possible.
|
||
|
||
|
||
|
||
% Motor 2:11.84Hz 0dB
|
||
% Kaff = 1/((11.84*2*np.pi)**2/5000/5000) = 4517.278506241804
|
||
|
||
|
||
% Motor 1: 19.8Hz 0dB
|
||
% K=(19.8*2*np.pi)**2
|
||
% Ts=5kHz=.2ms
|
||
% Kaff = 1/(Ts*Ts*K) = 1/((19.8*2*np.pi)**2/5000/5000) = 1615.2877200403302
|
||
|
||
% Motor 2:11.84Hz 0dB
|
||
% Kaff = 1/((11.84*2*np.pi)**2/5000/5000) = 4517.278506241804
|
||
|
||
\vspace{1pc}
|
||
|
||
\begin{appendix}
|
||
\section{Appendix}
|
||
|
||
\begin{verbatim}
|
||
amp: 5, minFrq: 10, maxFrq: 220, ts: 0.0002, tSec: 20
|
||
|
||
***ORIG***
|
||
Motor[1] Kp=25 Kvfb=400 Ki=0.02 Kvff=350 Kaff=5000 MaxInt=1000 Kfff=0
|
||
Motor[2] Kp=22 Kvfb=350 Ki=0.02 Kvff=240 Kaff=1500 MaxInt=1000 Kfff=0
|
||
(spiral motion 25 Hz)
|
||
motion average error x 1.54099 um, y 1.04259 um, 2.0391 um
|
||
shot average error x 1.68984 um, y 1.42837 um, 2.47304 um
|
||
|
||
**OPTIMIZED***
|
||
Motor[1] Kp=25 Kvfb=350 Ki=0.02 Kvff=350 Kaff=1615. MaxInt=1000 Kfff=10
|
||
Motor[2] Kp=22 Kvfb=450 Ki=0.02 Kvff=450 Kaff=4517. MaxInt=1000 Kfff=10
|
||
motion average error x 0.663518 um, y 0.585719 um, 1.01806 um
|
||
shot average error x 0.865708 um, y 0.965126 um, 1.49323 um
|
||
|
||
\end{verbatim}
|
||
|
||
|
||
\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/chirp_all_1b0.eps}
|
||
\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/chirp_all_1b1.eps}
|
||
|
||
\includegraphics[scale=.45]{../python/MXTuning/opt1/img/chirp_all_1b0.eps}
|
||
\includegraphics[scale=.45]{../python/MXTuning/opt1/img/chirp_all_1b1.eps}
|
||
|
||
\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/chirp_all_2b0.eps}
|
||
\includegraphics[scale=.45]{../python/MXTuning/19_01_29/img/chirp_all_2b1.eps}
|
||
|
||
\includegraphics[scale=.45]{../python/MXTuning/opt1/img/chirp_all_2b0.eps}
|
||
\includegraphics[scale=.45]{../python/MXTuning/opt1/img/chirp_all_2b1.eps}
|
||
|
||
|
||
|
||
|
||
|
||
\textbf{Overview of code:}\\
|
||
|
||
\begin{tabular}{ll}
|
||
\texttt{MXTuning.py} & tuning functions to gather/plot data and to generate c servo loop code\\
|
||
|
||
\texttt{helicalscan.py} & functions for helical scan motion (motion program, coordinate transformation, calibration)\\
|
||
\texttt{shapepath.py} & functions for x,y-scan motion (trajectory planing, motion program)\\
|
||
\texttt{ShapePathAnalyser.py} & interactive analyse tool of recorded x,y-scan motion\\
|
||
\\
|
||
\texttt{identifyFxFyStage.m}& read python data and build motor objects. plot bode\\
|
||
\texttt{simFxFyStage.m}& build a pb structure which contains current (Jan 2019) Powerbrick controller settings\\
|
||
\texttt{StateSpaceControlDesign.m}& design a discrete observer for Fx,Fy stages\\
|
||
\end{tabular}
|
||
|
||
|
||
\bibliographystyle{alpha}
|
||
\bibliography{myBib}
|
||
%\printbibliography
|
||
\end{appendix}
|
||
|
||
\include{Scratch}
|
||
|
||
\end{document}
|
||
|