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File: images/logo.png Graphic file (type png) Package luatex.def Info: images/logo.png used on input line 13. +(luatex.def) Requested size: 56.9055pt x 22.63397pt. + [31 + +] +File: images/back.jpg Graphic file (type jpg) + +Package luatex.def Info: images/back.jpg used on input line 13. +(luatex.def) Requested size: 780.44925pt x 341.43306pt. +File: images/logo.png Graphic file (type png) + +Package luatex.def Info: images/logo.png used on input line 13. +(luatex.def) Requested size: 56.9055pt x 22.63397pt. + [32 + +] +File: images/back.jpg Graphic file (type jpg) + +Package luatex.def Info: images/back.jpg used on input line 13. +(luatex.def) Requested size: 780.44925pt x 341.43306pt. +File: images/logo.png Graphic file (type png) + +Package luatex.def Info: images/logo.png used on input line 13. (luatex.def) Requested size: 56.9055pt x 22.63397pt. [33 @@ -2836,34 +2609,40 @@ Package luatex.def Info: images/logo.png used on input line 13. 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(luatex.def) Requested size: 56.9055pt x 22.63397pt. +Overfull \vbox (73.8187pt too high) detected at line 38 + [] + +File: images/back.jpg Graphic file (type jpg) + +Package luatex.def Info: images/back.jpg used on input line 38. +(luatex.def) Requested size: 780.44925pt x 341.43306pt. +File: images/logo.png Graphic file (type png) + +Package luatex.def Info: images/logo.png used on input line 38. +(luatex.def) Requested size: 56.9055pt x 22.63397pt. +[35 + +] +Overfull \vbox (73.8187pt too high) detected at line 38 + [] + +File: images/back.jpg Graphic file (type jpg) + +Package luatex.def Info: images/back.jpg used on input line 38. +(luatex.def) Requested size: 780.44925pt x 341.43306pt. +File: images/logo.png Graphic file (type png) + +Package luatex.def Info: images/logo.png used on input line 38. +(luatex.def) Requested size: 56.9055pt x 22.63397pt. +[36 + +] Overfull \vbox (73.8187pt too high) detected at line 38 [] @@ -2877,34 +2656,6 @@ Package luatex.def Info: images/logo.png used on input line 38. 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[37 -] -Overfull \vbox (73.8187pt too high) detected at line 38 - [] - -File: images/back.jpg Graphic file (type jpg) - -Package luatex.def Info: images/back.jpg used on input line 38. -(luatex.def) Requested size: 780.44925pt x 341.43306pt. -File: images/logo.png Graphic file (type png) - -Package luatex.def Info: images/logo.png used on input line 38. -(luatex.def) Requested size: 56.9055pt x 22.63397pt. -[38 - -] -Overfull \vbox (73.8187pt too high) detected at line 38 - [] - -File: images/back.jpg Graphic file (type jpg) - -Package luatex.def Info: images/back.jpg used on input line 38. -(luatex.def) Requested size: 780.44925pt x 341.43306pt. -File: images/logo.png Graphic file (type png) - -Package luatex.def Info: images/logo.png used on input line 38. -(luatex.def) Requested size: 56.9055pt x 22.63397pt. -[39 - ] File: images/logo.png Graphic file (type png) @@ -2918,14 +2669,14 @@ File: images/logo.png Graphic file (type png) Package luatex.def Info: images/logo.png used on input line 75. 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{\beamer@documentpages {39}} \headcommand {\gdef \inserttotalframenumber {15}} diff --git a/Presentations/ERLM/main.pdf b/Presentations/ERLM/main.pdf new file mode 100644 index 000000000..84ff506c6 Binary files /dev/null and b/Presentations/ERLM/main.pdf differ diff --git a/Presentations/ERLM/main.synctex.gz b/Presentations/ERLM/main.synctex.gz index 46a78019a..6481ac5b5 100644 Binary files a/Presentations/ERLM/main.synctex.gz and b/Presentations/ERLM/main.synctex.gz differ diff --git a/Presentations/ERLM/main.tex b/Presentations/ERLM/main.tex index a7fc79b7d..3e3421e6c 100644 --- a/Presentations/ERLM/main.tex +++ b/Presentations/ERLM/main.tex @@ -55,14 +55,14 @@ \titlepage \end{frame} -\input{slides/1_Hook} -\input{slides/2_State_of_the_Art} -\input{slides/3_Limitations} -\input{slides/4_Research_Approach} -\input{slides/5_Metrics_of_Success} -\input{slides/6_Risks_and_Contingencies} -\input{slides/7_Broader_Impacts} -\input{slides/8_Money_Slide} +\input{slides/1_Hook_v2} +\input{slides/2_State_of_the_Art_v2} +\input{slides/3_Limitations_v2} +\input{slides/4_Research_Approach_v2} +\input{slides/5_Metrics_of_Success_v2} +\input{slides/6_Risks_and_Contingencies_v2} +\input{slides/7_Broader_Impacts_v2} +\input{slides/8_Money_Slide_v2} \end{document} diff --git a/Presentations/ERLM/slides/1_Hook_v2.tex b/Presentations/ERLM/slides/1_Hook_v2.tex new file mode 100644 index 000000000..4af478d8c --- /dev/null +++ b/Presentations/ERLM/slides/1_Hook_v2.tex @@ -0,0 +1,57 @@ +\begin{frame}{The United States stands on the precipice of a severe + energy crisis} + + \begin{columns} + \begin{column}{0.5\textwidth} + \centering{ + + \begin{figure} + \begin{center} + \includegraphics[height=0.50\textheight]{images/1_hook/energy-demand-graph-small.png} + \end{center} + \caption*{Source: Pew Research Center, Data from IEA} + \end{figure} + + % \scriptsize{ + % \begin{tabular}{lcc} + % \textbf{Source} (30yr LCOE) & \textbf{Total (\$/MWh)} & \textbf{O\&M (\$/MWh)} \\ + % \midrule Adv. Nuclear & 88.24 & \cellcolor{red!30!primary}\textbf{16.15} \\ + % Natural Gas & 39.94 & 1.68 \\ + % \bottomrule + % \end{tabular} + % } + % + % \scriptsize Source: EIA Annual Energy Outlook 2022 + % + } + \end{column} + + \begin{column}{0.5\textwidth} + \center + + \textbf<1>{How much baseload power increase is this?} + + \only<2>{% TikZ grid of nuclear plants + \begin{tikzpicture} + % Adjustable parameters + \def\iconsize{0.44cm} % Size of each icon + \def\xspacing{0.6cm} % Horizontal spacing between icons + \def\yspacing{0.6cm} % Vertical spacing between icons + + % Draw grid of icons + \foreach \row in {0,...,9} { + \foreach \col in {0,...,9} { + \node at (\col*\xspacing, -\row*\yspacing) + {\includegraphics[width=\iconsize]{images/1_hook/nuclear-plant.png}}; + } + } + \end{tikzpicture} + + + \textbf<2>{30 gigawatts!} + } + + \end{column} + \end{columns} + +\end{frame} diff --git a/Presentations/ERLM/slides/2_State_of_the_Art_v2.tex b/Presentations/ERLM/slides/2_State_of_the_Art_v2.tex new file mode 100644 index 000000000..9368f754a --- /dev/null +++ b/Presentations/ERLM/slides/2_State_of_the_Art_v2.tex @@ -0,0 +1,82 @@ +\begin{frame}{Nuclear reactors are operated with prescriptive handbooks and + legacy control technologies} + \centering + \includegraphics[width=\textwidth,height=0.75\textheight,keepaspectratio]{images/2_state_of_the_art/control_room.jpg} +\end{frame} + +\begin{frame}{Building a fleet of new reactors with current requirements + will be an incredible staffing challenge + } + \centering + \underline{How many reactor operators are required to staff this new fleet?} + + \vspace{0.3cm} + + \begin{columns}[c] + \begin{column}{0.3\textwidth} + + \begin{figure} + \includegraphics[width=0.3\textwidth]{images/2_state_of_the_art/nuclear-plant.png} + \caption*{For one Small Modular Reactor (SMR)...} + \end{figure} + + \end{column} + + \begin{column}{0.7\textwidth} + \centering + \only<2->{ + \vspace{0.3cm} + \textbf{24/7 operations require \(\sim\)6 shifts:} + + \vspace{0.1cm} + + \begin{tikzpicture} + % Adjustable parameters + \def\iconsize{0.6cm} + \def\xspacing{0.8cm} + \def\yspacing{0.9cm} + + % 12 Senior Operators (2 per shift � 6 shifts) + \foreach \row in {0,1} { + \foreach \col in {0,...,5} { + \node at (\col*\xspacing, -\row*\yspacing) + {\includegraphics[width=\iconsize]{images/2_state_of_the_art/foreman.png}}; + } + } + + % 12 Reactor Operators (2 per shift � 6 shifts) + \foreach \row in {2,3} { + \foreach \col in {0,...,5} { + \node at (\col*\xspacing, -\row*\yspacing) + {\includegraphics[width=\iconsize]{images/2_state_of_the_art/worker.png}}; + } + } + + % Labels + \node[right] at (6*\xspacing, -0.5*\yspacing) {\small 12 SROs}; + \node[right] at (6*\xspacing, -2.5*\yspacing) {\small 12 ROs}; + \end{tikzpicture} + + \vspace{0.1cm} + \textbf{24 licensed operators per reactor} + } + + \end{column} + + \end{columns} + + \onslide<2->{\vspace{0.2cm} + \large{ + \textbf{To meet demand we require 2,400 new licensed operators!} + } +} + + +\onslide<3>{ + \alert{ + \textit{We currently have only 3,600 licensed operators total...} + } +} + +\end{frame} + diff --git a/Presentations/ERLM/slides/3_Limitations_v2.tex b/Presentations/ERLM/slides/3_Limitations_v2.tex new file mode 100644 index 000000000..7c3e155a5 --- /dev/null +++ b/Presentations/ERLM/slides/3_Limitations_v2.tex @@ -0,0 +1,59 @@ +\begin{frame}{Human reactor operators have key limitations that limit nuclear + buildout} + + \begin{columns}[t] + \begin{column}{0.33\textwidth} + \only<1>{ + \begin{alertblock}{Humans cannot meet labor demand} + + \centering + + \includegraphics[width=2cm]{images/3_limitations/foreman.png} + \includegraphics[width=2cm]{images/3_limitations/worker.png} + + \end{alertblock} + } + \only<2->{ + \begin{block}{Humans cannot meet labor demand} + + \centering + + \includegraphics[width=2cm]{images/3_limitations/foreman.png} + \includegraphics[width=2cm]{images/3_limitations/worker.png} + \end{block} + } +\end{column} + + \pause + + \begin{column}{0.33\textwidth} + \only<2>{ + \begin{alertblock}{Procedures are not formally verified} + \centering + \includegraphics[width=2cm]{images/3_limitations/computer.png} + \end{alertblock} + } + + \only<3->{ + \begin{block}{Procedures are not formally verified} + \centering + \includegraphics[width=2cm]{images/3_limitations/computer.png} + \end{block} + + } + \end{column} + + \pause + + \begin{column}{0.33\textwidth} + \only<3>{ + \begin{alertblock}{Human factors cannot be trained away} + \centering + \includegraphics[width=2cm]{images/3_limitations/test.png} + \end{alertblock} + } + + \end{column} + \end{columns} + +\end{frame} diff --git a/Presentations/ERLM/slides/4_Research_Approach_v2.tex b/Presentations/ERLM/slides/4_Research_Approach_v2.tex new file mode 100644 index 000000000..86178ab20 --- /dev/null +++ b/Presentations/ERLM/slides/4_Research_Approach_v2.tex @@ -0,0 +1,189 @@ +\begin{frame}{The goal of this research is to create verified autonomous control + systems} + + \textbf{\underline{ + If this research is successful, we will be able to do the following: + }} + \pause + + \begin{enumerate} + + \item \alert<2>{Translate written procedures into discrete control logic} + \pause + + \item \alert<3>{Verify continuous control behavior across discrete mode + transitions} + \pause + + \item \alert<4>{Demonstrate autonomous reactor startup with verifiable safety + guarantees} + + \end{enumerate} +\end{frame} + +\begin{frame}{First, we will formalize written procedures into logical + statements} + + \begin{columns}[c] + \begin{column}{0.7\textwidth} + \includegraphics[ + width=1.0\textwidth, + trim={1cm 22cm 1cm 0cm}, + clip + ] + {images/4_research_approach/procedure.png} + \scriptsize{ + Westinghouse Technology Systems Manual, Section 19.0 - Plant Operations + } + \end{column} + + \begin{column}{0.3\textwidth} + \only<2>{ + \begin{alertblock}{FRET Specification} + \scriptsize + \texttt{INITIAL\_CONDITIONS shall satisfy:} + \begin{itemize} + \item[] \texttt{mode = MODE\_5} + \item[] \texttt{k\_eff < 0.99} + \item[] \texttt{power = 0} + \item[] \texttt{t\_avg < 200} + \item[] \texttt{...} + \end{itemize} + \end{alertblock} + } + + \only<3->{ + \begin{block}{FRET Specification} + \scriptsize + \texttt{INITIAL\_CONDITIONS shall satisfy:} + \begin{itemize} + \item[] \texttt{mode = MODE\_5} + \item[] \texttt{k\_eff < 0.99} + \item[] \texttt{power = 0} + \item[] \texttt{t\_avg < 200} + \item[] \texttt{...} + \end{itemize} + \end{block} + } + + \only<3>{ + \begin{alertblock}{LTL Formula} + \scriptsize + \texttt{$\Box$ (initial $\rightarrow$ (} + \begin{itemize} + \item[] \texttt{mode\_5\_active $\land$} + \item[] \texttt{k\_eff\_subcritical $\land$} + \item[] \texttt{zero\_power $\land$} + \item[] \texttt{temp\_safe $\land$} + \item[] \texttt{...))} + \end{itemize} + \end{alertblock} + } + \end{column} + + \end{columns} + +\end{frame} + +\begin{frame}{Second, we will use reactive synthesis to convert the logical formulae to generate discrete + automata} + + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{tikzpicture} + \node (chess) at (0cm,0cm){\includegraphics[width=0.4\textwidth]{images/4_research_approach/strategy.png}}; + \node[draw=textcolor, fill=secondary, left=0.1cm of chess, yshift=-0.8cm] {Plant}; + \node[draw=textcolor, fill=primary!30!red, right=0.1cm of chess, yshift=0.4cm] {Controller}; + \end{tikzpicture} + \end{column} + \begin{column}{0.5\textwidth} + \pause + \begin{tikzpicture}[ + state/.style={circle, draw=textcolor, fill=secondary, minimum size=1.2cm}, + transition/.style={->, >=stealth, thick} + ] + + % States arranged vertically + \coordinate (start) at (0,1.5); + \node[state] (s0) at (0,0) {\scriptsize MODE 5}; + \node[state] (s1) at (0,-2) {\scriptsize MODE 4}; + \node[state] (s2) at (1,-4) {\scriptsize MODE 3}; + \node[state] (s3) at (3,-5.) {\scriptsize MODE 2}; + \node[state] (s4) at (5,-6) {\scriptsize MODE 1}; + \node[state] (s5) at (3,-1.5) {\scriptsize SCRAM}; + + % Transitions + \draw[transition] (start) -- node[midway, right] {\scriptsize Start} (s0); + \draw[transition] (s0) -- (s1); + \draw[transition] (s1) -- (s2); + \draw[transition] (s2) -- (s3); + \draw[transition] (s3) -- (s4); + \draw[transition] (s2) to[bend right] (s5); + \draw[transition] (s1) to[bend right] (s5); + \draw[transition] (s3) to[bend right] (s5); + \draw[transition] (s4) to[bend right] (s5); + + \draw[transition] (s0) to[loop left] (s0); + \draw[transition] (s1) to[loop left] (s1); + \draw[transition] (s2) to[loop left] (s2); + \draw[transition] (s3) to[loop below] (s3); + \draw[transition] (s4) to[loop below] (s4); + + \end{tikzpicture} + \end{column} + \end{columns} + +\end{frame} + +\begin{frame}{Finally, we will build continuous controllers to move between + discrete states} + + \begin{columns} + \begin{column}{0.5\textwidth} + \includegraphics[height=0.7\textheight]{bouncing_ball_hybrid.png} + + \end{column} + + \begin{column}{0.5\textwidth} + \only<2>{ + \begin{alertblock}{Key Challenge} + \small + Verify continuous control behavior across discrete mode transitions + \end{alertblock} + } + \only<3->{ + \begin{block}{Key Challenge} + \small + Verify continuous control behavior across discrete mode transitions + \end{block} + } + + \vspace{0.3cm} + + \only<3>{ + \begin{alertblock}{Reachable Set} + \small + $\mathcal{R}(t) = \{x(t) \mid x(0) \in X_0, \dot{x} = f(x)\}$ + \end{alertblock} + } + \only<4->{ + \begin{block}{Reachable Set} + \small + $\mathcal{R}(t) = \{x(t) \mid x(0) \in X_0, \dot{x} = f(x)\}$ + \end{block} + } + + \vspace{0.3cm} + + \only<4>{ + \begin{alertblock}{Barrier Certificate} + \small + $B(x) > 0 \land \nabla B \cdot f(x) \leq 0 \implies x \in \text{Safe}$ + \end{alertblock} + } + \end{column} + \end{columns} + +\end{frame} + + diff --git a/Presentations/ERLM/slides/5_Metrics_of_Success_v2.tex b/Presentations/ERLM/slides/5_Metrics_of_Success_v2.tex new file mode 100644 index 000000000..7a635b4ca --- /dev/null +++ b/Presentations/ERLM/slides/5_Metrics_of_Success_v2.tex @@ -0,0 +1,53 @@ +\begin{frame}{Success will be measured through Technology Readiness Level advancement} + + \begin{columns} + \begin{column}{0.3\textwidth} + \begin{block}{Why TRLs?} + \small + Bridge gap between proof-of-concept and deployment + \begin{itemize} + \item[] Measure both rigor and feasibility + \end{itemize} + \end{block} + + \vspace{0.5cm} + + \textbf{Current:} TRL 2-3\\ + \textbf{Target:} TRL 5 + \end{column} + + \begin{column}{0.7\textwidth} + \begin{columns} + \begin{column}{0.33\textwidth} + \centering + \only<1->{\only<1>{\alert{\textbf{TRL 3}}}% + \only<2->{\textbf{TRL 3}}\\ + \small Components\\ + \vspace{0.2cm} + \includegraphics[width=0.8\textwidth]{images/5_metrics_of_success/puzzle.png}} + \end{column} + + \begin{column}{0.33\textwidth} + \centering + \only<2->{\only<2>{\alert{\textbf{TRL 4}}}% + \only<3->{\textbf{TRL 4}}\\ + \small Integration\\ + \vspace{0.2cm} + \includegraphics[width=0.8\textwidth]{images/5_metrics_of_success/puzzle_complete.png}} + \end{column} + + \begin{column}{0.33\textwidth} + \centering + \only<3->{\alert<3>{\textbf{TRL 5}}\\ + \small Hardware\\ + \vspace{0.2cm} + \begin{tikzpicture} + \node[anchor=south west,inner sep=0] (controller) at (0,0) {\includegraphics[width=0.8\columnwidth]{images/5_metrics_of_success/controller.png}}; + \node[anchor=center,inner sep=2pt] at (2.48,1.88) {\includegraphics[width=0.3\columnwidth]{images/5_metrics_of_success/emerson_logo_only.png}}; + \end{tikzpicture}} + \end{column} + \end{columns} + \end{column} + \end{columns} + +\end{frame} diff --git a/Presentations/ERLM/slides/6_Risks_and_Contingencies_v2.tex b/Presentations/ERLM/slides/6_Risks_and_Contingencies_v2.tex new file mode 100644 index 000000000..8a51499bd --- /dev/null +++ b/Presentations/ERLM/slides/6_Risks_and_Contingencies_v2.tex @@ -0,0 +1,13 @@ +\begin{frame}{Four primary risks are identified with clear mitigation and contingency plans} + + \begin{enumerate} + \item<1-> \alert<1>{Computational Tractability of Synthesis} + + \item<2-> \alert<2>{Discrete-Continuous Interface Complexity} + + \item<3-> \alert<3>{Procedure Formalization Completeness} + + \item<4-> \alert<4>{Hardware-in-the-Loop Integration} + \end{enumerate} + +\end{frame} diff --git a/Presentations/ERLM/slides/7_Broader_Impacts_v2.tex b/Presentations/ERLM/slides/7_Broader_Impacts_v2.tex new file mode 100644 index 000000000..228a2b684 --- /dev/null +++ b/Presentations/ERLM/slides/7_Broader_Impacts_v2.tex @@ -0,0 +1,75 @@ +\begin{frame}{Broader Impact: Multi-billion dollar O\&M cost reduction} + + \begin{block}{The Economic Opportunity} + \small + Datacenter electricity demand projected to reach \textbf{1,050 TWh/year by 2030} + \end{block} + + \vspace{0.5cm} + + \textbf{If supplied by nuclear power:} + + \begin{align*} + \text{Total annual cost} &= 1,050 \text{ TWh/yr} \times \$88.24/\text{MWh} \\ + &= \textbf{\$92.7 billion/year} + \end{align*} + + \pause + + \vspace{0.3cm} + + \textbf{O\&M represents 23-30\% of LCOE:} + + \begin{align*} + \text{O\&M costs} &= \$92.7\text{B} \times 0.23\text{-}0.30 \\ + &= \textbf{\$21-28 billion/year} + \end{align*} + + \pause + + \vspace{0.5cm} + + \begin{center} + \large + \textbf{Autonomous control directly addresses\\ + this multi-billion dollar challenge} + \end{center} + +\end{frame} + +\begin{frame}{Beyond nuclear: A generalizable framework for safety-critical autonomy} + + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{block}{Why Nuclear First?} + \small + \begin{itemize} + \item Highest regulatory requirements + \item Most safety-critical domain + \item Procedures already documented + \item Establishes regulatory pathway + \end{itemize} + \end{block} + \end{column} + + \begin{column}{0.5\textwidth} + \begin{block}{Future Applications} + \small + \begin{itemize} + \item Chemical process control + \item Aerospace systems + \item Autonomous transportation + \item Critical infrastructure + \end{itemize} + \end{block} + \end{column} + \end{columns} + + \vspace{1cm} + + \begin{center} + \textbf{Translate procedures $\rightarrow$ Synthesize logic $\rightarrow$ Verify behavior}\\ + \small Applicable to any hybrid system with documented operational requirements + \end{center} + +\end{frame} diff --git a/Presentations/ERLM/slides/8_Money_Slide_v2.tex b/Presentations/ERLM/slides/8_Money_Slide_v2.tex new file mode 100644 index 000000000..4697862ea --- /dev/null +++ b/Presentations/ERLM/slides/8_Money_Slide_v2.tex @@ -0,0 +1,35 @@ +\begin{frame}[plain] + \LARGE\textbf{Formally Verified Autonomous Hybrid Control} + + \vspace{0.2cm} + + \begin{columns}[T] + % Left column: Contact info + \begin{column}{0.35\textwidth} + \normalsize Enabling Economic Viability of Next-Generation Nuclear Power + + \vspace{0.5cm} + + \large\textbf{Dane A. Sabo}\\ + \small dane.sabo@pitt.edu + + \vspace{0.5cm} + + \textbf{Advisor:}\\ + Dr. Daniel G. Cole\\ + \small dgcole@pitt.edu + + \vspace{0.5cm} + + University of Pittsburgh\\ + Department of Mechanical Engineering and Materials Science + \end{column} + + % Right column: Money image + \begin{column}{0.65\textwidth} + \centering + \includegraphics[height=0.7\textheight]{images/money.png} + \end{column} + \end{columns} + +\end{frame} diff --git a/Presentations/ERLM/theme/beamerouterthemedane_native.sty b/Presentations/ERLM/theme/beamerouterthemedane_native.sty index 8a8c2a9be..d794ace89 100644 --- a/Presentations/ERLM/theme/beamerouterthemedane_native.sty +++ b/Presentations/ERLM/theme/beamerouterthemedane_native.sty @@ -42,9 +42,11 @@ \ifx\insertframesubtitle\@empty% %NO SUBTITLE - {\node[anchor=west, headingcolor,font=\large] at (1.05,1.0){\parbox[l]{13cm}{\insertframetitle}};} + {\node[anchor=west, headingcolor,font=\large] at + (1.05,1.0){\parbox[l]{17cm}{\raggedright \insertframetitle}};} \else% INCLUDE SUBTITLE - {\node[anchor= west, headingcolor,font=\normalsize] at (1.05,1.31){\parbox[l]{13cm}{\insertframetitle}};% + {\node[anchor= west, headingcolor,font=\normalsize] at + (1.05,1.31){\parbox[l]{17cm}{\raggedright \insertframetitle}};% \node[anchor= west, headingcolor,font=\footnotesize] at (1.05,0.31){\textit{\insertframesubtitle}}; }%