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Merge branch 'master' of dev:/home/robin/git/thesis

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Robin P. Clark 2012-11-27 14:18:41 +00:00
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submission_thesis/CH5_Examples/software.tex
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@ -1031,12 +1031,58 @@ $$fm(GetError) = \{ KnownIncorrectErrorValue, IncorrectErrorValue \}.$$
We now follow the afferent path to the PID algorithm. 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}
\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} \\
OK STOP AT PID and follow the other data flows until we are ready to bring them to the top: i.e. \hline
FC1: $ KnownIncorrectErrorValue $ & pre-condition violated & KnownControlValueErrorV \\
& observable/detectable & \\
& failure mode & \\ \hline
the monitor program....... FC2: $, IncorrectErrorValue $ & pre-condition violated & IncorrectControlErrorV \\
& unobservable & \\
& undetectable failure mode & \\ \hline
\end{tabular}
\end{table}
}
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.......