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252) + defining Unicode char U+00FD (decimal 253) + defining Unicode char U+00FE (decimal 254) + defining Unicode char U+00FF (decimal 255) + defining Unicode char U+0100 (decimal 256) + defining Unicode char U+0101 (decimal 257) + defining Unicode char U+0102 (decimal 258) + defining Unicode char U+0103 (decimal 259) + defining Unicode char U+0104 (decimal 260) + defining Unicode char U+0105 (decimal 261) + defining Unicode char U+0106 (decimal 262) + defining Unicode char U+0107 (decimal 263) + defining Unicode char U+0108 (decimal 264) + defining Unicode char U+0109 (decimal 265) + defining Unicode char U+010A (decimal 266) + defining Unicode char U+010B (decimal 267) + defining Unicode char U+010C (decimal 268) + defining Unicode char U+010D (decimal 269) + defining Unicode char U+010E (decimal 270) + defining Unicode char U+010F (decimal 271) + defining Unicode char U+0110 (decimal 272) + defining Unicode char U+0111 (decimal 273) + defining Unicode char U+0112 (decimal 274) + defining Unicode char U+0113 (decimal 275) + defining Unicode char U+0114 (decimal 276) + defining Unicode char U+0115 (decimal 277) + defining Unicode char U+0116 (decimal 278) + defining Unicode char U+0117 (decimal 279) + defining Unicode char U+0118 (decimal 280) + defining Unicode char U+0119 (decimal 281) + defining Unicode char U+011A (decimal 282) + defining Unicode char U+011B (decimal 283) + defining Unicode char U+011C (decimal 284) + defining Unicode char U+011D (decimal 285) + defining Unicode char U+011E (decimal 286) + defining Unicode char U+011F (decimal 287) + defining Unicode char U+0120 (decimal 288) + defining Unicode char U+0121 (decimal 289) + defining Unicode char U+0122 (decimal 290) + defining Unicode char U+0123 (decimal 291) + defining Unicode char U+0124 (decimal 292) + defining Unicode char U+0125 (decimal 293) + defining Unicode char U+0128 (decimal 296) + defining Unicode char U+0129 (decimal 297) + defining Unicode char U+012A (decimal 298) + defining Unicode char U+012B (decimal 299) + defining Unicode char U+012C (decimal 300) + defining Unicode char U+012D (decimal 301) + defining Unicode char U+012E (decimal 302) + defining Unicode char U+012F (decimal 303) + defining Unicode char U+0130 (decimal 304) + defining Unicode char U+0131 (decimal 305) + defining Unicode char U+0132 (decimal 306) + defining Unicode char U+0133 (decimal 307) + defining Unicode char U+0134 (decimal 308) + defining Unicode char U+0135 (decimal 309) + defining Unicode char U+0136 (decimal 310) + defining Unicode char U+0137 (decimal 311) + defining Unicode char U+0139 (decimal 313) + defining Unicode char U+013A (decimal 314) + defining Unicode char U+013B (decimal 315) + defining Unicode char U+013C (decimal 316) + defining Unicode char U+013D (decimal 317) + defining Unicode char U+013E (decimal 318) + defining Unicode char U+0141 (decimal 321) + defining Unicode char U+0142 (decimal 322) + defining Unicode char U+0143 (decimal 323) + defining Unicode char U+0144 (decimal 324) + defining Unicode char U+0145 (decimal 325) + defining Unicode char U+0146 (decimal 326) + defining Unicode char U+0147 (decimal 327) + defining Unicode char U+0148 (decimal 328) + defining Unicode char U+014A (decimal 330) + defining Unicode char U+014B (decimal 331) + defining Unicode char U+014C (decimal 332) + defining Unicode char U+014D (decimal 333) + defining Unicode char U+014E (decimal 334) + defining Unicode char U+014F (decimal 335) + defining Unicode char U+0150 (decimal 336) + defining Unicode char U+0151 (decimal 337) + defining Unicode char U+0152 (decimal 338) + defining Unicode char U+0153 (decimal 339) + defining Unicode char U+0154 (decimal 340) + defining Unicode char U+0155 (decimal 341) + defining Unicode char U+0156 (decimal 342) + defining Unicode char U+0157 (decimal 343) + defining Unicode char U+0158 (decimal 344) + defining Unicode char U+0159 (decimal 345) + defining Unicode char U+015A (decimal 346) + defining Unicode char 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486) + defining Unicode char U+01E7 (decimal 487) + defining Unicode char U+01E8 (decimal 488) + defining Unicode char U+01E9 (decimal 489) + defining Unicode char U+01EA (decimal 490) + defining Unicode char U+01EB (decimal 491) + defining Unicode char U+01F0 (decimal 496) + defining Unicode char U+01F4 (decimal 500) + defining Unicode char U+01F5 (decimal 501) + defining Unicode char U+0218 (decimal 536) + defining Unicode char U+0219 (decimal 537) + defining Unicode char U+021A (decimal 538) + defining Unicode char U+021B (decimal 539) + defining Unicode char U+1E02 (decimal 7682) + defining Unicode char U+1E03 (decimal 7683) + defining Unicode char U+200C (decimal 8204) + defining Unicode char U+2010 (decimal 8208) + defining Unicode char U+2011 (decimal 8209) + defining Unicode char U+2012 (decimal 8210) + defining Unicode char U+2013 (decimal 8211) + defining Unicode char U+2014 (decimal 8212) + defining Unicode char U+2015 (decimal 8213) + defining Unicode char U+2018 (decimal 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b/documents/Protokoll/Protokoll.tex @@ -1,9 +1,14 @@ \documentclass[10pt,a4paper,twoside]{article} \usepackage[a4paper, left=2cm, right=3cm]{geometry} -%\usepackage[latin1]{inputenc} +\usepackage[utf8]{inputenc} \usepackage[ngerman]{babel} -\usepackage[T1]{fontenc} + + +\usepackage{pdfpages} +\usepackage{pdflscape} +\usepackage{hyperref} +\usepackage{blindtext} \usepackage{amsmath} \usepackage{amsthm} @@ -59,6 +64,120 @@ \begin{document} -\todo + +\section{Aufgabenstellung} +Es soll ein Doppelpendel gebaut werden, welches sich wenig bis vernachlässigbar chaotisch verhält. +Dazu muss die Masse des unteren Pendels vielfach größer als die des oberen Pendels sein. +Das obere Pendel besitzt keine weitere Masse und ist 50cm bis 1m lang. +Es dient grundsätzlich nur der Aufhängung des unteren Pendels, welches aus einem 50cm langem Stab bestehen soll. +Über einen Magneten am Ende des Pendels und einer Spule an bzw. nahe der Ruheposition des Pendels soll mittels eines Mikrocontrollers (ATmega16) sowohl die Schwingungsdauer gemessen als auch auf die Position des Pendels in Echtzeit geschlossen werden. +Je nach Auslenkung sollen auf einem 50cm langem LED-Streifen verschiedene Farben des Regenbogens angezeigt werden. +Beim Erreichen einer Amplitude soll ein Regenbogen entlang des LED-Streifens angezeigt werden, der sich bis zum Erreichen der Ruheposition zu einer einheitlichen Mittelwertfarbe der Extrema wandelt und bis zum Erreichen der anderen Amplitude wieder zu einem Regenbogen, jedoch in umgekehrter Reihenfolge, wandelt. +Bei den LEDs soll es sich um WS2812B oder protokoll-gleichen Alternativen handeln. +Das Protokoll der \textit{Daisy-Chain} soll implementiert werden. +Ebenfalls soll der Mikrocontroller mittels der zur Messung verwendeten Spule das Pendel antreiben, sodass es bei gegebener Energiezufuhr ewig schwingen könnte. +Zur Spannungsversorgung wird ein Netzteil verwendet, welches 12 Volt Gleichstrom mit 6 Watt und hoher Restwelligkeit liefert, die auszugleichen ist und auf konstante 5 Volt Gleichstrom geregelt werden soll. + +\section{Spannungsversorgung} +Zu aller erst wurde die Versorgungsspannung in Angriff genommen. +Ein Netzteil mit den durch die Aufgabenstellung gegeben Anforderungen soll über eine Buchse (\textit{Barrel-Jack}) angeschlossen werden. +Dessen Signal wird über einen Linearregler (LT1084) mit einer Widerstandsrückkopplung von 1 : 3 auf 5 Volt reguliert. +Kondensatoren vor und nach dem Linearregler dienen dem Ausgleich leichter Schwankungen. +Ein Verpolungsschutz wurde zusätzlich vor und eine Zenerdiode, die bei 6.2 Volt in Sperrrichtung leitet, nach dem Linearregler eingebaut. +\\ +Daraus entstand eine eigene Platine, die eigens geplant, entwurfen, bedruckt, geätzt, gebohrt und gelötet wurde. +Dabei wurde auf Wiederverwendbarkeit geachtet und Pins angebracht, um die Platine auf einem handelsüblichen Steckbrett als 5-Volt-Spannungsversorgung nutzen zu können. +Bei einigen Test unter Volllast wurde der Linearregler sehr heiß, Abhilfe schaffte die Montage eines Kühlkörpers und eines kleinen Lüfters (12 Volt, 0.5 Watt). + +Nun folgen der Footprint und der Schaltplan der Platine: + +\includepdf[landscape=true,pages={1}]{../boards/footprints/Spannungsversorgung.pdf} + +\includepdf[landscape=true,pages={1}]{../boards/schematics/Spannungsversorgung.pdf} + +\section{Mikrocontroller und Programmer} +Als Mikrocontroller wurde ein ATmega328P verwendet, da nur ein solcher zur Verfügung stand. +Beim Programmieren wurde stets darauf geachtet, dass jegliche Programme ebenso auf einem ATmega16 ausgeführt werden könnten. +Als Programmer wurde ein Arduino mit modifizierten \textit{ArduinoISP}-Sketch als \textit{In System Programmer} eingesetzt. +Somit wurde dann über die Verbindung mit SClk, MISO, MOSI und RESET der eigentliche Mikrocontroller geflasht. +Der Einfachheit halber wurde sowohl für den Programmer als auch für den Mikrocontroller ein Breakoutboard auf einer Lochrasterplatine hergestellt. +Die physische Verbindung wurde mit Jumperkabeln geschaffen. +Zum Kompilieren und Flashen wurde ein Makefile verwendet. + +\section{LEDs: WS2812B} +Das Daisy-Chain-Protokoll wurde gemäß Datenblatt implementiert (siehe \textit{pendulum}). +\subsection{Timing} +Es wurde ein Oszillator mit 20 MHz als externer Taktgeber für den Mikrocontroller verwendet. +Dies führte zu 50 ns Ausführungszeit pro Befehl. +Um das WS2812B-Protokoll zu implementieren, mussten mit Assembler Routinen implementiert werden, die genau 6, 8, 14 oder 15 Takte andauerten. +Die genauen Zeiten werden als Kommentar in pendulum.c aufgeschlüsselt. +Ein Problem hierbei war die Optimierung des Kompilers, da dieser selbst auf niedrigster Optimierungsstufe mehrere NOP (\textit{no operation}) wegoptimierte. +Abhilfe schaffte zuletzt die Verwendung eines bzw. mehrerer \textit{relativer Sprung + 0}. +\subsection{Colors} +Um die Farben gemäß der Aufgabenstellung regenbogenähnlich darzustellen, wurde die HSV-Farbskala verwendet (siehe color\_hsv.c). +Hier wurde die Minimum- und die Maximum-Farbe gezielt in festen Schritten in Grad zu- bzw. voneinander verschoben. +Anschließend wurde eine lineare Interpolation zwischen diesen beiden Werten durchgeführt, um die einzelnen Farben der LEDs zu ermitteln. +Zuletzt wurden die HSV-Farben und RGB-Farben umgerechnet. +Eine Demonstration einer 1-Grad-Verschiebung wurde in \textit{led-driver} implementiert. + +\section{Pendelaufbau} +Als Pendel wurde zu Beginn ein einfaches Fadenpendel mit einem Gewicht und einem Magneten aufgebaut und für jeglich Test verwendet. +Schnell wurde klar, dass die Anforderung des Anstoßens aufgrund der hohen Masse vernachlässigt werden muss. +Die spätere Umsetzung mittels eines Holzstabs als unteres Pendel führt leider zu keiner wesentlichen Verbesserung des Problems. +Das Pendel muss somit per Hand angestoßen werden und schwingt nicht länger als eine Minute. +Das Gegenmagnetfeld der Messspule bremst das Pendel zusätzlich bei jedem Passieren der Ruheposition. +Im finalen Aufbau wurde auf das elektromagnetische Anstoßen in Gänze verzichtet. +\paragraph{Verbesserungsvorschläge} Das Pendel sollte leichter gebaut werden. Eine \textit{kräftigere} Spule müsste eingesetzt werden. + +\section{Gesamtschaltplan} +\includepdf[landscape=true,pages={1}]{../boards/schematics/Gesamtschaltplan.pdf} +\subsection{Signale} +Beim schwingenden Pendel mit Magnet wird eine Spannung in der Spule induziert, die an bzw. nahe der Ruheposition platziert wurde. +Diese Spannung beträgt 5 bis 20 mV und muss für die Nutzung in Digitalschaltungen verstärkt werden. +Dazu wurde ein Operationsverstärker (LMV824M) verwendet und per Widerstandsverhältnis auf einen Verstärkungsfaktor von rund 190 eingestellt. +Dies reichte aus um das verstärkte Rauschen unter 1 Volt zu halten und bei Erregungen durch das vorbeischwingende Pendel auf über 1 Volt zu kommen. +Dies wurde dann in einen Optokoppler (4N35) an dessen Anode eingespeist. +Hinter einem Pullup-Widerstand wurde der Kollektor des Optokopplers an den externen Interrupt-Pins des Mikrocontrollers angeschlossen, welcher auf fallende Flanken reagieren soll. +Dies hat zur Folge, dass Pendel diese fallende Flanke genau in der Ruheposition auslöst. + +Diese Kombination aus Messspule, Operationsverstärker und Optokoppler resultierte in folgenden Signalen: + +\begin{figure}[!htb] + \minipage{0.32\textwidth} + \includegraphics[width=\linewidth]{../Messungen/VorNachOPV.png} + \caption{CH1: Verstärkte Spannung am Ausgang des Operationsverstärkers; CH2: Induzierte Spannung der Spule am Eingang des Operationsverstärkers}\label{fig:f1} + \endminipage\hfill + \minipage{0.32\textwidth} + \includegraphics[width=\linewidth]{../Messungen/VorOPTONachOPTOGrosseAuslenkung.png} + \caption{CH1: Verstärkte Spannung am Ausgang des Operationsverstärkers bei noch \textit{großer Auslenkung} des Pendels; CH2: Ausgang des Optokopplers/Signal für externen Interrupt}\label{fig:f2} + \endminipage\hfill + \minipage{0.32\textwidth}% + \includegraphics[width=\linewidth]{../Messungen/VorOPTONachOPTOKleineAuslenkung.png} + \caption{CH1: Verstärkte Spannung am Ausgang des Operationsverstärkers bei nur noch \textit{kleiner Auslenkung} des Pendels; CH2: Ausgang des Optokopplers/Signal für externen Interrupt}\label{fig:f3} + \endminipage +\end{figure} +\subsection{Timer Interrupts} +Interne Timer 0 und 1 wurden in timer.c so konfiguriert, dass die in 32-bit bis über 200s und in 64-bit rund 30000 Jahre genau Zählen können. +Somit kann die Periodendauer auf 50ns genau berechnet werden. +Außerdem wurde eine Echtzeitberechnung der Pendelposition und der zugehörigen Farbwerte ermöglicht. +\\ + +Da der Operationsverstärker nur als SMD-Bauteil zu Verfügung stand, wurde eine weitere Breakout-Platine erstellt. Nun folgend der Footprint und der Schaltplan der Platine des Operationsverstärkers: + +\includepdf[landscape=true,pages={1}]{../boards/footprints/OPV.pdf} + +\includepdf[landscape=true,pages={1}]{../boards/schematics/OPV.pdf} + +\section{Fazit} +Es wurde eine für das gegebene Netzteil und zu der Gesamtschaltung passende Spannungsversogung geschaffen. Das Daisy-Chain-Protokoll der WS2812B-LEDs wurde erfolgreich implementiert, sowie eine HSV-zu-RGB-Umrechnung samt einer linearen Interpolation der Regenbogenfarben. Induzierte Spannungen an der Messspule wurden geglättet, verstärkt und schließlich genutzt, um einen externen Interrupt am Mikrocontroller auszulösen. Der Mikrocontroller selbst wurde über einen Arduino als In-System-Programmer mit Assembler-/C-Programmen geflasht. Es wurde ein 20 MHz Oszillator als externer Taktgeber verwendet und u.a. mittels Timer-Interrupts eine Echtzeitberechnung der Farben und deren Ausgabe realisiert. Zusätzlich sind einige Platinen/Breakoutboards entwurfen und gefertigt wurden.\\ +\\ +Auf das Aufbringen des LED-Streifens auf den Stab des 2. Pendels wurde verzichtet, ebenso wie auf das elektromagnetische Anstoßen aufgrund des Masseproblems.\\ +\\ +Die Anforderungen der Aufgabenstellung wurden somit mehrheitlich umgesetzt. +\\ +\hrule + +\paragraph{Hinweis 1} Datenblätter aller verwendeten Bauteile, sowie Quellcodedateien, Schaltpläne, Messungen, etc. sind ebenfalls in einem Repository\footnote{\url{https://git.tiband.de/ht/mca-pendel}} zu finden. +\paragraph{Hinweis 2} Beim Planen und Umsetzen des Projekts wurde stets versucht, vorhandene Bauteile zu verwenden oder zu recyclen. Dies reduzierte zwar die Materialkosten, minderte jedoch auch drastisch die Auswahl der zu verwendenden Bauteile. Ein weiteres Ziel war es die Umsetzung sehr modular zu gestalten, sodass eine Wiederverwendbarkeit der Bauteile und Platinen ermöglicht wird. So können diese auch in zukünftigen Projekten zum Einsatz kommen. \end{document} \ No newline at end of file diff --git a/documents/boards/footprints/OPV.pdf b/documents/boards/footprints/OPV.pdf new file mode 100644 index 0000000000000000000000000000000000000000..76c66481dd48b3e75fa17a45ba9e659161393703 GIT binary patch literal 6829 zcmb_h2{=^k+kf9e42q(RB_k|`s+PD=JABWu>k7Q)yQ z*_StaDY9f~$ahBG_j{M``+xuMy8h>ybDrP%o%=q&=Xvh?IoDkGBcO9dO-$kf93*hp zKOhhUgNQ@$mUbX{c?k3d+7aVo3y}gSJqT0{i*rE}fEI^xL0>^z;jPgS1qBe%g@8sm zfZRvEn3)yjztpOmthcs z`}971Y4HAmMeEA+(1Yok(w5qb$epfmzn)fTk#yy*+1_%`*38CQ>O#}yy$>fxGz5=2 z?orz0t5y6rV(dS4?)d~Nyxzh@NL}7>^c(5X(`Xpa&}KJZ)tRC6ysZCD+1pwz+S`!c z`yXU2!X8CzOkvMEaAJOKZ~Vs;6rZ~1O&h>zBfM^W+i<8;;T=Y8hj zV4}d0UE+M`Y_oQuDy!))K3Uzf_JiAxbZH*D@%YUXzC44R(xo{yQZ4fiG#Zns*&!}- zh1IlpgQR>ugTC-)ui+71T^i(tcEg8fDzB@VI8;MJf6J|kd^7I^&>FT0Uyda$~N}WNA{(4&ri6!u{ z+K5MwXRKh@REp!S0;X{J&RqTOxEa2%Juz=(&aS3P7+=_O067m}ZcWusxJoqu;ak83 zULQu{V1A>EpUlZB;itu9g(fZIM=6-?>gv+5eo<*yM^`67zjUng0KyKSW*6Zngi{Tw z_sxD@GK2gxM`-L`O1!%cGFNb8%OmKiB`5JTQ+6lNnIi78CZ0VtqCf}cJU)y zIoLJ4-{wu(M9epvH|6G>pSrHD=Y|;I)o|;Yy@{-;i2_D=wN}ph3HYQ>*0wHQO)7F? zD_gqmV>sS(I?;Ul0L~`3-b_ej;-i zhDn=a>P+%afa(01biz=dk0rpwiF9`|ZM zT~lL0wCJQ`JfqppXcrv6`lxKhaAp^`27O3l4Be;Z9aD$4juS*wQ4V*X~VoU$;8V!G9NR1u!!_yzm3)Mn(a9Q1W7$Tya zF!oIInj_!q4bh>H)1~5PvtmqaHJrbkoFz>Z<*xaWa@PDdRFn7Q4$fn|Gt5`L%kk1MmG{eo%k zfRo@PB>2iPPrrf>o1TGYq}#6;jj~PR7zFNK1lLFSy7RIOUFnu>XybYHQ5?#ED`mJD zJye_P<}RtAAwB`8tr*Vdd_9bdAHYMQ)rPN z;_#^R?)Axa)%NGb?*z!*Ib?NS=b){$0;og9^vxe#ZwzF3SF0|J&ky-+e>j5GEQuWz zX)cMCiyr=(-ywEaV%f0G`&sOKT&Yz`+ee0ki<|iZDVuf|iu?L1_7qTGLfmjB0__uo zJ4NV^0*?zA7HQlEXx>E>La_-(X<2>yp$`)24>gQR|w^{KvSz7&` z#eFrm0ikS;Ut!5v za;JVOvU7X8100zmFcJB2dv>E$``Bc7)%_QsAOk)e6H1?+OXU`AqcDqM@C!+R%4b5c z(=Xm8g1=x$E4!zrba3ysA*z6up4J;#?@*LOnP z)@uUz*FmV;^nuD89Li7@Pye?fK`DIepmYpVJvFmd`ICB85w)J=MR6%Lw42n$`X zxHv#DF`-!Kn<%U{ztJNZ;a#s;H^xKxI#c+8pJ~C3B<>GO(z;PMlq*{^G2DEEYbw;Y zu{XZ{>23~LKa`H7zofFjuG~Y_^yA>84@zV4ytl7TArG;{igAB0mgfC z%G1|+4oO#He4Nh)tikmlD#atkKR;ga7JFm+!CXV~dDU*wG-j|E-g_Y&^oURN5Q>%l zq4F&bfI4~a1$_{2+ZmJR?EF%PYcIbN+A2*BySQ)@kSZ04q0@!! 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