updates on slides

slides/main.md

@@ -61,9 +61,9 @@ header-includes:
 
   - Crazy software stacks on crazy hardware
     
-  - $\rightsquigarrow$ unpredictable
+  - Many sources of unpredictability
 
-  - but want to guarantee a behavior, a Quality-of-Service
+  - $\rightsquigarrow$ need for dynamic management
   
 - Usual approaches:
 
@@ -125,7 +125,7 @@ Use the knowledge about the current state of the system to respond
 
 # Some Examples
 
-- Regulate the heat of a processor based on its frequency
+- Regulate the **heat of a processor** based on its frequency
 
   - Sensor: CPU thermometer
   
@@ -133,7 +133,7 @@ Use the knowledge about the current state of the system to respond
   
   - Reference: Desired CPU temperature
   
-- Regulate the waiting time of users based on the number of available servers
+- Regulate the **waiting time of users** based on the number of available servers
 
   - Sensor: Waiting time of a request
   
@@ -141,7 +141,7 @@ Use the knowledge about the current state of the system to respond
   
   - Reference: Mean waiting time for the requests
   
-- Regulate the FPS of an online video rendering based on the quality
+- Regulate the **FPS of an online video rendering** based on the quality
 
   - Sensor: FPS
   
@@ -184,37 +184,14 @@ Act on dynamic system to reach desired behavior with guarantees
 :::
 ::::::::::::::
 
-# Controllers
-
-## Goal
-
-\begin{center}
-Map the error to the next input to reach desired system state with guarantees
-\end{center}
-
-## Many (many) types of Controllers
-
-- Feedback (PID, MFC, RST, etc.)
-
-- Feedforward (proactive reaction to disturbances)
-
-- Adaptive (change behavior at runtime)
-
-- Model Predictive
-
-- Event Based
-
-- Optimal
-
-- and more!
-
-
 # Methodology
 
 
 ![Control Theory Methodology](figs/methodo.pdf){width=90% height=50%}
 
 
+
+
 # The (famous) PID Controller (discretized)
 
 \begin{block}{First, \textbf{a Model ...} (i.e., how does the system behave (Open-Loop))}
@@ -229,7 +206,7 @@ Map the error to the next input to reach desired system state with guarantees
 \begin{block}{... then \textbf{a PID Controller} (i.e., the Closed-Loop behavior)}
 \begin{center}
 \scalebox{0.8}{
-$\displaystyle Output = \textbf{K}_p \times Error + \textbf{K}_i \times \sum_k Error_k + \textbf{K}_d \times \left(Error_k - Error_{k-1}\right)$
+$\displaystyle {\color{blue}\textbf{u}}_k = \textbf{K}_p \times Error_k + \textbf{K}_i \times \sum_k Error_k + \textbf{K}_d \times \left(Error_k - Error_{k-1}\right)$
 }
 \end{center}
 \end{block}
@@ -248,7 +225,7 @@ $\displaystyle Output = \textbf{K}_p \times Error + \textbf{K}_i \times \sum_k E
 
 \begin{block}{Method}
     \begin{enumerate}
-\item Open-Loop expe (fixed ${\color{blue}\textbf{u}}$)
+\item Open-Loop expe (predefined ${\color{blue}\textbf{u}}$)
 \item Model parameters ($a_i, b_j$)
 \item Choice controller behavior ($\textbf{K}_{*}$)
     \end{enumerate}
@@ -267,6 +244,31 @@ $\displaystyle Output = \textbf{K}_p \times Error + \textbf{K}_i \times \sum_k E
 The controller gains define this behavior!
 \end{center}
 
+# Controllers
+
+## Goal
+
+\begin{center}
+Map the error to the next action to reach desired system state with guarantees
+\end{center}
+
+## Many (many) types of Controllers
+
+- Feedback (PID, MFC, RST, etc.)
+
+- Feedforward (proactive reaction to disturbances)
+
+- Adaptive (change behavior at runtime)
+
+- Model Predictive
+
+- Event Based
+
+- Optimal
+
+- and more!
+
+
 # Your turn! 
 
 ## What you will do now