complete lab coursework

.gitignore

@@ -1,2 +1,3 @@
-.vscode
-build/
+*.md.pdf
+out
+Lab1CourseworkAAR.pdf

Makefile

@@ -1,11 +1,19 @@
 CFLAGS=-lm
+OUTDIR=out
 
 
-build:
-	zip Lab1PrepAAR.zip *.c *.ino *.pdf *.png
+build: out Lab1CourseworkAAR.pdf
+	zip $(OUTDIR)/Lab1PrepAAR.zip *.c *.ino *.pdf *.png
+	zip $(OUTDIR)/Lab1AAR.zip *AAR* Lab1Coursework.pdf
+
+$(OUTDIR):
+	mkdir -p $(OUTDIR)
+
+Lab1CourseworkAAR.pdf:
+	pandoc report.md -o $@ --template=template.tex
 
 %.c:
 	$(CC) $(CFLAGS) -c $< -o $*
 
 clean:
-	rm -f Lab1PrepAAR.zip TestEncoderAAR TwoSensorsAAR
+	rm -rf TestEncoderAAR TwoSensorsAAR Lab1CourseworkAAR.pdf $(OUTDIR)

readme.md

@@ -0,0 +1,9 @@
+# MMME3085 Lab 1
+
+## Prep
+
+### Feedback
+
+Marks: 100%
+
+[Feedback sheet](./res/prep-feedback.pdf)

report.md

@@ -0,0 +1,84 @@
+---
+author: Akbar Rahman (20386125)
+date: \today
+title: MMME3085---Lab 1 Coursework
+tags: [ mmme3085 ]
+uuid: 864e5249-a02c-4896-b274-a0a76789955c
+---
+
+\maketitle
+\newpage
+
+# Questions
+
+## Question 1
+
+- $V_{ref} = 5$ V when converting the ADC-converted value because the ADC in the Arduino can read
+  from 0 V to 5 V, therefore $n_{ADC} = 0$ means the voltage to the pin is 0 V, and $n_{ADC} = 1023$
+  means the voltage to the pin is 5 V
+- This is not the optimum use of the ADC pin as it means the resolution of the voltage measurement
+  is less precise than it could be (roughly a resolution of 5 mV instead of 3 mV)
+- The resolution could be increased by using an op-amp amplification circuit or a 3.3 V to 5 V level
+  converter circuit
+
+\newpage
+
+## Question 2
+
+- 100 % duty cycle PWM is different from all the others as it is not a wave, but just a DC voltage
+- Voltage is not zero in the OFF region because the rotational inertia is still spinning the motor,
+  which creates a back EMF, and that is the voltage being read in the OFF region.
+  Back EMF is proportional to the speed of the motor, which is why the voltage in the off region is
+  higher when the PWM duty cycle, and therefore speed of the motor, is higher.
+
+![PWM waveform at various duty cycles, labelled where the signal is on (green line) and off (red line)](./images/pwm_on_off.png)
+
+\newpage
+
+## Question 3
+
+- The difference between the ON+ and ON- is that the current will go in opposite directions,
+  resulting in the motor spinning in opposite directions
+- The default PWM frequency of pin 13 on the Arduino Mega 2560 is 976.5625 Hz [^1]
+- The audible frequency we hear is a ~1000 Hz square wave, which can be seen by the fact the period of
+  the wave in figure below is roughly 1 millisecond
+
+  ![PWM waveform at 977 Hz](./images/pwm_frequency.jpg)
+
+\newpage
+
+## Question 4
+
+![Oscilloscope trace of quadrature signal in clockwise (positive) direction. The 0 V datum point is marked by the triangles on the left hand side of the screen.](./images/q4+.jpg){ height=2in }
+
+![Oscilloscope trace of quadrature signal in anti-clockwise (negative) direction. The 0 V datum point is marked by the triangles on the left hand side of the screen.](./images/q4-.jpg){ height=2in }
+
+\newpage
+
+
+## Question 5
+
+- Since the internal timer only looks at one edge of one pulse, it cannot be used to determine the
+  direction of the rotation, which is one of the reasons to use a quadrature in the first place
+- Therefore it is a viable alternative if you only care about the speed of rotation and direction
+  is not important to the application
+
+
+## Question 6
+
+- The main shortcoming observed is that the Arduino appeared to freeze/crash when entering a PWM
+  duty cycle above ~20%
+- When this issues occurs, the Arduino is too busy running the function called by interrupts
+  to be able to print to serial, hence appearing to have frozen/crashed
+- This is due to the fact that at higher speeds, the `updateEncoderStateMachine()` function in
+  triggered by the digital pin interrupts (which take higher priority) so frequently that
+  the `loop()` function is not able to run, due to a lack of free CPU cycles, and therefore serial
+  outputs are not printed and inputs not read
+- This effectively makes the counter useless as it cannot be read from as the Arduino is not able
+  to handle any other processing tasks
+- Additionally, there is a good chance that the Arduino is not able to run all the calls to
+  `updateEncoderStateMachine` in real time, and so the value of `count` would be incorrect (of course
+  this does not matter since we do not have the CPU cycles to do anything with `count` anyway)
+
+
+[^1]: `MotorEncoderAAR.ino` defines that pin 13 is used for PWM output. Pin 13 is connected to timer 0 which defaults to 976.5625 Hz (<https://playground.arduino.cc/Main/TimerPWMCheatsheet/>)

template.tex

@@ -0,0 +1,557 @@
+% Options for packages loaded elsewhere
+\PassOptionsToPackage{unicode$for(hyperrefoptions)$,$hyperrefoptions$$endfor$}{hyperref}
+\PassOptionsToPackage{hyphens}{url}
+$if(colorlinks)$
+\PassOptionsToPackage{dvipsnames,svgnames,x11names}{xcolor}
+$endif$
+$if(CJKmainfont)$
+\PassOptionsToPackage{space}{xeCJK}
+$endif$
+%
+\documentclass[
+$if(fontsize)$
+  $fontsize$,
+$endif$
+$if(papersize)$
+  $papersize$paper,
+$endif$
+$if(beamer)$
+  ignorenonframetext,
+$if(handout)$
+  handout,
+$endif$
+$if(aspectratio)$
+  aspectratio=$aspectratio$,
+$endif$
+$endif$
+$for(classoption)$
+  $classoption$$sep$,
+$endfor$
+]{$documentclass$}
+$if(beamer)$
+$if(background-image)$
+\usebackgroundtemplate{%
+  \includegraphics[width=\paperwidth]{$background-image$}%
+}
+$endif$
+\usepackage{pgfpages}
+\setbeamertemplate{caption}[numbered]
+\setbeamertemplate{caption label separator}{: }
+\setbeamercolor{caption name}{fg=normal text.fg}
+\beamertemplatenavigationsymbols$if(navigation)$$navigation$$else$empty$endif$
+$for(beameroption)$
+\setbeameroption{$beameroption$}
+$endfor$
+% Prevent slide breaks in the middle of a paragraph
+\widowpenalties 1 10000
+\raggedbottom
+$if(section-titles)$
+\setbeamertemplate{part page}{
+  \centering
+  \begin{beamercolorbox}[sep=16pt,center]{part title}
+    \usebeamerfont{part title}\insertpart\par
+  \end{beamercolorbox}
+}
+\setbeamertemplate{section page}{
+  \centering
+  \begin{beamercolorbox}[sep=12pt,center]{part title}
+    \usebeamerfont{section title}\insertsection\par
+  \end{beamercolorbox}
+}
+\setbeamertemplate{subsection page}{
+  \centering
+  \begin{beamercolorbox}[sep=8pt,center]{part title}
+    \usebeamerfont{subsection title}\insertsubsection\par
+  \end{beamercolorbox}
+}
+\AtBeginPart{
+  \frame{\partpage}
+}
+\AtBeginSection{
+  \ifbibliography
+  \else
+    \frame{\sectionpage}
+  \fi
+}
+\AtBeginSubsection{
+  \frame{\subsectionpage}
+}
+$endif$
+$endif$
+$if(beamerarticle)$
+\usepackage{beamerarticle} % needs to be loaded first
+$endif$
+\usepackage{amsmath,amssymb}
+$if(linestretch)$
+\usepackage{setspace}
+$endif$
+\usepackage{iftex}
+\ifPDFTeX
+  \usepackage[$if(fontenc)$$fontenc$$else$T1$endif$]{fontenc}
+  \usepackage[utf8]{inputenc}
+  \usepackage{textcomp} % provide euro and other symbols
+\else % if luatex or xetex
+$if(mathspec)$
+  \ifXeTeX
+    \usepackage{mathspec} % this also loads fontspec
+  \else
+    \usepackage{unicode-math} % this also loads fontspec
+  \fi
+$else$
+  \usepackage{unicode-math} % this also loads fontspec
+$endif$
+  \defaultfontfeatures{Scale=MatchLowercase}$-- must come before Beamer theme
+  \defaultfontfeatures[\rmfamily]{Ligatures=TeX,Scale=1}
+\fi
+$if(fontfamily)$
+$else$
+$-- Set default font before Beamer theme so the theme can override it
+\usepackage{lmodern}
+$endif$
+$-- Set Beamer theme before user font settings so they can override theme
+$if(beamer)$
+$if(theme)$
+\usetheme[$for(themeoptions)$$themeoptions$$sep$,$endfor$]{$theme$}
+$endif$
+$if(colortheme)$
+\usecolortheme{$colortheme$}
+$endif$
+$if(fonttheme)$
+\usefonttheme{$fonttheme$}
+$endif$
+$if(mainfont)$
+\usefonttheme{serif} % use mainfont rather than sansfont for slide text
+$endif$
+$if(innertheme)$
+\useinnertheme{$innertheme$}
+$endif$
+$if(outertheme)$
+\useoutertheme{$outertheme$}
+$endif$
+$endif$
+$-- User font settings (must come after default font and Beamer theme)
+$if(fontfamily)$
+\usepackage[$for(fontfamilyoptions)$$fontfamilyoptions$$sep$,$endfor$]{$fontfamily$}
+$endif$
+\ifPDFTeX\else
+  % xetex/luatex font selection
+$if(mainfont)$
+  \setmainfont[$for(mainfontoptions)$$mainfontoptions$$sep$,$endfor$]{$mainfont$}
+$endif$
+$if(sansfont)$
+  \setsansfont[$for(sansfontoptions)$$sansfontoptions$$sep$,$endfor$]{$sansfont$}
+$endif$
+$if(monofont)$
+  \setmonofont[$for(monofontoptions)$$monofontoptions$$sep$,$endfor$]{$monofont$}
+$endif$
+$for(fontfamilies)$
+  \newfontfamily{$fontfamilies.name$}[$for(fontfamilies.options)$$fontfamilies.options$$sep$,$endfor$]{$fontfamilies.font$}
+$endfor$
+$if(mathfont)$
+$if(mathspec)$
+  \ifXeTeX
+    \setmathfont(Digits,Latin,Greek)[$for(mathfontoptions)$$mathfontoptions$$sep$,$endfor$]{$mathfont$}
+  \else
+    \setmathfont[$for(mathfontoptions)$$mathfontoptions$$sep$,$endfor$]{$mathfont$}
+  \fi
+$else$
+  \setmathfont[$for(mathfontoptions)$$mathfontoptions$$sep$,$endfor$]{$mathfont$}
+$endif$
+$endif$
+$if(CJKmainfont)$
+  \ifXeTeX
+    \usepackage{xeCJK}
+    \setCJKmainfont[$for(CJKoptions)$$CJKoptions$$sep$,$endfor$]{$CJKmainfont$}
+  \fi
+$endif$
+$if(luatexjapresetoptions)$
+  \ifLuaTeX
+    \usepackage[$for(luatexjapresetoptions)$$luatexjapresetoptions$$sep$,$endfor$]{luatexja-preset}
+  \fi
+$endif$
+$if(CJKmainfont)$
+  \ifLuaTeX
+    \usepackage[$for(luatexjafontspecoptions)$$luatexjafontspecoptions$$sep$,$endfor$]{luatexja-fontspec}
+    \setmainjfont[$for(CJKoptions)$$CJKoptions$$sep$,$endfor$]{$CJKmainfont$}
+  \fi
+$endif$
+\fi
+$if(zero-width-non-joiner)$
+%% Support for zero-width non-joiner characters.
+\makeatletter
+\def\zerowidthnonjoiner{%
+  % Prevent ligatures and adjust kerning, but still support hyphenating.
+  \texorpdfstring{%
+    \TextOrMath{\nobreak\discretionary{-}{}{\kern.03em}%
+      \ifvmode\else\nobreak\hskip\z@skip\fi}{}%
+  }{}%
+}
+\makeatother
+\ifPDFTeX
+  \DeclareUnicodeCharacter{200C}{\zerowidthnonjoiner}
+\else
+  \catcode`^^^^200c=\active
+  \protected\def ^^^^200c{\zerowidthnonjoiner}
+\fi
+%% End of ZWNJ support
+$endif$
+% Use upquote if available, for straight quotes in verbatim environments
+\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
+\IfFileExists{microtype.sty}{% use microtype if available
+  \usepackage[$for(microtypeoptions)$$microtypeoptions$$sep$,$endfor$]{microtype}
+  \UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts
+}{}
+$if(indent)$
+$else$
+\makeatletter
+\@ifundefined{KOMAClassName}{% if non-KOMA class
+  \IfFileExists{parskip.sty}{%
+    \usepackage{parskip}
+  }{% else
+    \setlength{\parindent}{0pt}
+    \setlength{\parskip}{6pt plus 2pt minus 1pt}}
+}{% if KOMA class
+  \KOMAoptions{parskip=half}}
+\makeatother
+$endif$
+$if(verbatim-in-note)$
+\usepackage{fancyvrb}
+$endif$
+\usepackage{xcolor}
+$if(geometry)$
+$if(beamer)$
+\geometry{$for(geometry)$$geometry$$sep$,$endfor$}
+$else$
+\usepackage[$for(geometry)$$geometry$$sep$,$endfor$]{geometry}
+$endif$
+$endif$
+$if(beamer)$
+\newif\ifbibliography
+$endif$
+$if(listings)$
+\usepackage{listings}
+\newcommand{\passthrough}[1]{#1}
+\lstset{defaultdialect=[5.3]Lua}
+\lstset{defaultdialect=[x86masm]Assembler}
+$endif$
+$if(lhs)$
+\lstnewenvironment{code}{\lstset{language=Haskell,basicstyle=\small\ttfamily}}{}
+$endif$
+$if(highlighting-macros)$
+$highlighting-macros$
+$endif$
+$if(tables)$
+\usepackage{longtable,booktabs,array}
+$if(multirow)$
+\usepackage{multirow}
+$endif$
+\usepackage{calc} % for calculating minipage widths
+$if(beamer)$
+\usepackage{caption}
+% Make caption package work with longtable
+\makeatletter
+\def\fnum@table{\tablename~\thetable}
+\makeatother
+$else$
+% Correct order of tables after \paragraph or \subparagraph
+\usepackage{etoolbox}
+\makeatletter
+\patchcmd\longtable{\par}{\if@noskipsec\mbox{}\fi\par}{}{}
+\makeatother
+% Allow footnotes in longtable head/foot
+\IfFileExists{footnotehyper.sty}{\usepackage{footnotehyper}}{\usepackage{footnote}}
+\makesavenoteenv{longtable}
+$endif$
+$endif$
+$if(graphics)$
+\usepackage{graphicx}
+\makeatletter
+\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth\else\Gin@nat@width\fi}
+\def\maxheight{\ifdim\Gin@nat@height>\textheight\textheight\else\Gin@nat@height\fi}
+\makeatother
+% Scale images if necessary, so that they will not overflow the page
+% margins by default, and it is still possible to overwrite the defaults
+% using explicit options in \includegraphics[width, height, ...]{}
+\setkeys{Gin}{width=\maxwidth,height=\maxheight,keepaspectratio}
+% Set default figure placement to htbp
+\makeatletter
+\def\fps@figure{htbp}
+\makeatother
+$endif$
+$if(svg)$
+\usepackage{svg}
+$endif$
+$if(strikeout)$
+$-- also used for underline
+\usepackage{soul}
+$endif$
+\setlength{\emergencystretch}{3em} % prevent overfull lines
+\providecommand{\tightlist}{%
+  \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
+$if(numbersections)$
+\setcounter{secnumdepth}{$if(secnumdepth)$$secnumdepth$$else$5$endif$}
+$else$
+\setcounter{secnumdepth}{-\maxdimen} % remove section numbering
+$endif$
+$if(subfigure)$
+\usepackage{subcaption}
+$endif$
+$if(beamer)$
+$else$
+$if(block-headings)$
+% Make \paragraph and \subparagraph free-standing
+\ifx\paragraph\undefined\else
+  \let\oldparagraph\paragraph
+  \renewcommand{\paragraph}[1]{\oldparagraph{#1}\mbox{}}
+\fi
+\ifx\subparagraph\undefined\else
+  \let\oldsubparagraph\subparagraph
+  \renewcommand{\subparagraph}[1]{\oldsubparagraph{#1}\mbox{}}
+\fi
+$endif$
+$endif$
+$if(pagestyle)$
+\pagestyle{$pagestyle$}
+$endif$
+$if(csl-refs)$
+\newlength{\cslhangindent}
+\setlength{\cslhangindent}{1.5em}
+\newlength{\csllabelwidth}
+\setlength{\csllabelwidth}{3em}
+\newlength{\cslentryspacingunit} % times entry-spacing
+\setlength{\cslentryspacingunit}{\parskip}
+\newenvironment{CSLReferences}[2] % #1 hanging-ident, #2 entry spacing
+ {% don't indent paragraphs
+  \setlength{\parindent}{0pt}
+  % turn on hanging indent if param 1 is 1
+  \ifodd #1
+  \let\oldpar\par
+  \def\par{\hangindent=\cslhangindent\oldpar}
+  \fi
+  % set entry spacing
+  \setlength{\parskip}{#2\cslentryspacingunit}
+ }%
+ {}
+\usepackage{calc}
+\newcommand{\CSLBlock}[1]{#1\hfill\break}
+\newcommand{\CSLLeftMargin}[1]{\parbox[t]{\csllabelwidth}{#1}}
+\newcommand{\CSLRightInline}[1]{\parbox[t]{\linewidth - \csllabelwidth}{#1}\break}
+\newcommand{\CSLIndent}[1]{\hspace{\cslhangindent}#1}
+$endif$
+$if(lang)$
+\ifLuaTeX
+\usepackage[bidi=basic]{babel}
+\else
+\usepackage[bidi=default]{babel}
+\fi
+$if(babel-lang)$
+\babelprovide[main,import]{$babel-lang$}
+$if(mainfont)$
+\ifPDFTeX
+\else
+\babelfont[$babel-lang$]{rm}{$mainfont$}
+\fi
+$endif$
+$endif$
+$for(babel-otherlangs)$
+\babelprovide[import]{$babel-otherlangs$}
+$endfor$
+% get rid of language-specific shorthands (see #6817):
+\let\LanguageShortHands\languageshorthands
+\def\languageshorthands#1{}
+$endif$
+$for(header-includes)$
+$header-includes$
+$endfor$
+\ifLuaTeX
+  \usepackage{selnolig}  % disable illegal ligatures
+\fi
+$if(dir)$
+\ifPDFTeX
+  \TeXXeTstate=1
+  \newcommand{\RL}[1]{\beginR #1\endR}
+  \newcommand{\LR}[1]{\beginL #1\endL}
+  \newenvironment{RTL}{\beginR}{\endR}
+  \newenvironment{LTR}{\beginL}{\endL}
+\fi
+$endif$
+$if(natbib)$
+\usepackage[$natbiboptions$]{natbib}
+\bibliographystyle{$if(biblio-style)$$biblio-style$$else$plainnat$endif$}
+$endif$
+$if(biblatex)$
+\usepackage[$if(biblio-style)$style=$biblio-style$,$endif$$for(biblatexoptions)$$biblatexoptions$$sep$,$endfor$]{biblatex}
+$for(bibliography)$
+\addbibresource{$bibliography$}
+$endfor$
+$endif$
+$if(nocite-ids)$
+\nocite{$for(nocite-ids)$$it$$sep$, $endfor$}
+$endif$
+$if(csquotes)$
+\usepackage{csquotes}
+$endif$
+\IfFileExists{bookmark.sty}{\usepackage{bookmark}}{\usepackage{hyperref}}
+\IfFileExists{xurl.sty}{\usepackage{xurl}}{} % add URL line breaks if available
+\urlstyle{$if(urlstyle)$$urlstyle$$else$same$endif$}
+$if(links-as-notes)$
+% Make links footnotes instead of hotlinks:
+\DeclareRobustCommand{\href}[2]{#2\footnote{\url{#1}}}
+$endif$
+$if(verbatim-in-note)$
+\VerbatimFootnotes % allow verbatim text in footnotes
+$endif$
+\hypersetup{
+$if(title-meta)$
+  pdftitle={$title-meta$},
+$endif$
+$if(author-meta)$
+  pdfauthor={$author-meta$},
+$endif$
+$if(lang)$
+  pdflang={$lang$},
+$endif$
+$if(subject)$
+  pdfsubject={$subject$},
+$endif$
+$if(keywords)$
+  pdfkeywords={$for(keywords)$$keywords$$sep$, $endfor$},
+$endif$
+$if(colorlinks)$
+  colorlinks=true,
+  linkcolor={$if(linkcolor)$$linkcolor$$else$Maroon$endif$},
+  filecolor={$if(filecolor)$$filecolor$$else$Maroon$endif$},
+  citecolor={$if(citecolor)$$citecolor$$else$Blue$endif$},
+  urlcolor={$if(urlcolor)$$urlcolor$$else$Blue$endif$},
+$else$
+$if(boxlinks)$
+$else$
+  hidelinks,
+$endif$
+$endif$
+  pdfcreator={LaTeX via pandoc}}
+
+$if(title)$
+\title{$title$$if(thanks)$\thanks{$thanks$}$endif$}
+$endif$
+$if(subtitle)$
+$if(beamer)$
+$else$
+\usepackage{etoolbox}
+\makeatletter
+\providecommand{\subtitle}[1]{% add subtitle to \maketitle
+  \apptocmd{\@title}{\par {\large #1 \par}}{}{}
+}
+\makeatother
+$endif$
+\subtitle{$subtitle$}
+$endif$
+\author{$for(author)$$author$$sep$ \and $endfor$}
+\date{$date$}
+$if(beamer)$
+$if(institute)$
+\institute{$for(institute)$$institute$$sep$ \and $endfor$}
+$endif$
+$if(titlegraphic)$
+\titlegraphic{\includegraphics{$titlegraphic$}}
+$endif$
+$if(logo)$
+\logo{\includegraphics{$logo$}}
+$endif$
+$endif$
+
+\begin{document}
+$if(has-frontmatter)$
+\frontmatter
+$endif$
+$if(title)$
+$if(beamer)$
+\frame{\titlepage}
+$else$
+\maketitle
+$endif$
+$if(abstract)$
+\begin{abstract}
+$abstract$
+\end{abstract}
+$endif$
+$endif$
+
+$for(include-before)$
+$include-before$
+
+$endfor$
+$if(toc)$
+$if(toc-title)$
+\renewcommand*\contentsname{$toc-title$}
+$endif$
+$if(beamer)$
+\begin{frame}[allowframebreaks]
+$if(toc-title)$
+  \frametitle{$toc-title$}
+$endif$
+  \tableofcontents[hideallsubsections]
+\end{frame}
+$else$
+{
+$if(colorlinks)$
+\hypersetup{linkcolor=$if(toccolor)$$toccolor$$else$$endif$}
+$endif$
+\setcounter{tocdepth}{$toc-depth$}
+\tableofcontents
+}
+$endif$
+$endif$
+$if(lof)$
+\listoffigures
+$endif$
+$if(lot)$
+\listoftables
+$endif$
+$if(linestretch)$
+\setstretch{$linestretch$}
+$endif$
+$if(has-frontmatter)$
+\mainmatter
+$endif$
+$body$
+
+$if(has-frontmatter)$
+\backmatter
+$endif$
+$if(natbib)$
+$if(bibliography)$
+$if(biblio-title)$
+$if(has-chapters)$
+\renewcommand\bibname{$biblio-title$}
+$else$
+\renewcommand\refname{$biblio-title$}
+$endif$
+$endif$
+$if(beamer)$
+\begin{frame}[allowframebreaks]{$biblio-title$}
+  \bibliographytrue
+$endif$
+  \bibliography{$for(bibliography)$$bibliography$$sep$,$endfor$}
+$if(beamer)$
+\end{frame}
+$endif$
+
+$endif$
+$endif$
+$if(biblatex)$
+$if(beamer)$
+\begin{frame}[allowframebreaks]{$biblio-title$}
+  \bibliographytrue
+  \printbibliography[heading=none]
+\end{frame}
+$else$
+\printbibliography$if(biblio-title)$[title=$biblio-title$]$endif$
+$endif$
+
+$endif$
+$for(include-after)$
+$include-after$
+
+$endfor$
+\end{document}