Dane Sabo
2497bb4aa5
M .task/backlog.data M .task/completed.data M .task/pending.data M .task/undo.data A PLAN_OF_STUDY_111225.pdf R Writing/202510270-Emerson-Pres/SaboOneSlide.pdf -> Presentations/202510270-Emerson-Pres/SaboOneSlide.pdf R Writing/202510270-Emerson-Pres/beamerthemedane.sty -> Presentations/202510270-Emerson-Pres/beamerthemedane.sty R Writing/202510270-Emerson-Pres/beamerthemedane_native.sty -> Presentations/202510270-Emerson-Pres/beamerthemedane_native.sty
36 lines
1.5 KiB
TeX
36 lines
1.5 KiB
TeX
% Hybrid Systems
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\begin{frame}{Hybrid systems combine continuous dynamics with discrete mode switching}
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\begin{center}
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\begin{tikzpicture}
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\draw[thick, fill=gray!20] (0,0) rectangle (12,7);
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\node[align=center, text width=10cm] at (6,3.5) {
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\textbf{FIGURE: Hybrid System Visualization}\\[0.3cm]
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Top: Split diagram\\
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LEFT: Continuous (temp, flux, pressure curves)\\
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Equation: $\dot{x}(t) = f(x(t), q(t), u(t))$\\[0.2cm]
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RIGHT: Discrete (state machine diagram)\\
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Equation: $q(k+1) = \nu(x(k), q(k), u(k))$\\[0.3cm]
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Bottom: Reactor startup state machine\\
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Cold $\xrightarrow{T>400°F}$ Heatup $\xrightarrow{\text{near crit}}$ Crit $\rightarrow$ Power\\
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Each box shows continuous dynamics within
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};
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\end{tikzpicture}
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\end{center}
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%SPEAKER NOTES: See comments below
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%
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\textbf{Nuclear plants are inherently hybrid systems}
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\textbf{Continuous Dynamics:} Reactor temperature, neutron flux, pressure, flow rates, heat transfer.
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Governed by differential equations: $\dot{x}(t) = f(x(t), q(t), u(t))$
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\textbf{Discrete Decisions:} Mode transitions, control strategy changes, safety system actuation, procedure steps.
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Governed by logic: $q(k+1) = \nu(x(k), q(k), u(k))$
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\textbf{Example:} Reactor startup: Cold Shutdown → Heatup → Approach Criticality → Low Power
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Each mode has continuous dynamics; transitions are discrete strategic decisions.
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This is exactly what human operators do today.
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% (End of speaker notes)
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\end{frame}
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