From 481031aa4b2ae670d8fb4185e3f401c06f645561 Mon Sep 17 00:00:00 2001
From: Robin Clark <R.P.Clark@brighton.ac.uk>
Date: Mon, 26 Nov 2012 19:47:40 +0000
Subject: [PATCH] Up to PID now..... Tidy other parts of call tree

---
 submission_thesis/CH5_Examples/software.tex | 52 +++++++++++++++++++--
 1 file changed, 49 insertions(+), 3 deletions(-)

diff --git a/submission_thesis/CH5_Examples/software.tex b/submission_thesis/CH5_Examples/software.tex
index aaae1b6..8ee23df 100644
--- a/submission_thesis/CH5_Examples/software.tex
+++ b/submission_thesis/CH5_Examples/software.tex
@@ -1031,12 +1031,58 @@ $$fm(GetError) = \{ KnownIncorrectErrorValue, IncorrectErrorValue \}.$$
 
 
 We now follow the afferent path to the PID algorithm.
-Here we assume that the PID constants are fixed (i.e. are not parameters)
+Here we assume that the PID constants are fixed (i.e. are not parameters).
+We use the $GetError$ {\dc} and the PID function to form a {\fg}.
+The pre-condition for the PID function is that % are that it is called 
+%iat the correct frequency and that 
+it receives the correct error value.
+The post-condition is that it outputs correct control values.
+% RESP FOR TIMEING IS ON CALLING FUNCTION AND IS A SEPARATE ERROR- TGHINK ABOUT JITTER.....
+% and controll values..... Jitter might not matter, wrong int times would
+% controlling function provdes context of use.
+Those familiar with the PID algorithm may here notice raise the point of calling frequency.
+were this function to be called at an incorrect rate its output
+would be wrong (the differential and integral parameters would effectively have been changed).
+However this problem  is a failure mode for the function calling it.
+The calling function sets the context for the PID algorithm (i.e. what it is used for).
+If this PID were to be used, say as some form of low pass filter, we could consider jitter
+for instance. In a control environment with PID jitter would not be a significant factor.
 
+{
+\tiny
+\begin{table}[h+]
+\caption{ PID: Failure Mode Effects Analysis} % title of Table
+\label{tbl:pidfunction}
 
-OK STOP AT PID and follow the other data flows until we are ready to bring them to the top: i.e. 
+\begin{tabular}{|| l   | c |   l ||} \hline
+% \textbf{Failure}   &  \textbf{failure}     & \textbf{Symptom}          \\ 
+% \textbf{Scenario}  &  \textbf{effect}      &     \textbf{RADC }                     \\ \hline 
+ \hline 
+ \textbf{Failure} &  \textbf{Failure }         & \textbf{Derived Component}          \\ 
+ \textbf{cause}   &   \textbf{Effect}                & \textbf{Failure Mode}          \\
+  
+ 
+               \hline
+     FC1: $ KnownIncorrectErrorValue $      &   pre-condition violated        & KnownControlValueErrorV         \\  
+                                         &   observable/detectable        &                 \\ 
+                                         &   failure mode        &    \\ \hline
+                                         
+       FC2: $, IncorrectErrorValue $           &  pre-condition violated          &  IncorrectControlErrorV               \\  
+                                        &  unobservable                    &                 \\ 
+                                        &  undetectable failure mode          &        \\ \hline     
+                                         
+                                         
+     
+\end{tabular}
+\end{table}
+}
 
-the monitor program.......
+We now create a PID {\dc}, with the following failure modes:
+
+$$ fm(PID) = \{  KnownControlValueErrorV, IncorrectControlErrorV \} .$$
+%OK STOP AT PID and follow the other data flows until we are ready to bring them to the top: i.e. 
+%
+%the monitor program.......