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32
submission_thesis/CH5_Examples/copy.tex
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@ -569,7 +569,7 @@ Both analysis strategies obtained the same failure modes for the
inverting amplifier (i.e. the same failure modes for the {\dc} INVAMP). inverting amplifier (i.e. the same failure modes for the {\dc} INVAMP).
\subsection{Conclusion} \subsection{Conclusion}
All FMEA is performed in the context of the environment and functionality of the enitity All FMEA is performed in the context of the environment and functionality of the entity
under analysis. under analysis.
This example shows that for the condition where the input voltage This example shows that for the condition where the input voltage
is constrained to being positive, we can apply two levels of decomposition. is constrained to being positive, we can apply two levels of decomposition.
@ -914,7 +914,7 @@ to periodically switch in test signals in place of the input signal.
\subsection{Conclusion} \subsection{Conclusion}
This example shows a three stages hierarchy, and a graph tracing the base~component failure modes to the This example shows three stages of hierarchy, and a graph tracing the base~component failure modes to the
top level event. It also re-visits the decisions about membership of {\fgs}, due to the context top level event. It also re-visits the decisions about membership of {\fgs}, due to the context
of the circuit raised in section~\ref{subsec:invamp2}. of the circuit raised in section~\ref{subsec:invamp2}.
% %
@ -1543,7 +1543,7 @@ A finer grained approach produces more potentially re-usable {\dcs} and
involves several stages with lower reasoning distances. involves several stages with lower reasoning distances.
The lower reasoning distances, or complexity comparision figures are given in the metrics chapter~\ref{sec:chap7} The lower reasoning distances, or complexity comparision figures are given in the metrics chapter~\ref{sec:chap7}
at section~\ref{sec:bubbaCC}. at section~\ref{sec:bubbaCC}.
This show that the finer grained models also benefit from lower reasoning distances for the failure mode model. These show that the finer grained models also benefit from lower reasoning distances for the failure mode model.
\clearpage \clearpage
@ -1874,8 +1874,8 @@ We now show the final {\dc} hierarchy in figure~\ref{fig:eulersdfinal}.
% The output from the DQ is sent to the digital comparator formed by R3,R4 % The output from the DQ is sent to the digital comparator formed by R3,R4
% and IC3. % and IC3.
% The output from this is sent to the summing integrator as the signal summed with the input. % The output from this is sent to the summing integrator as the signal summed with the input.
\subsection{conclusion} \subsection{Conclusion}
The \sd example, shows that FMMD can be applied to mixed digital and analogue circuitry. The {\sd} example, shows that FMMD can be applied to mixed digital and analogue circuitry.
%\clearpage %\clearpage
@ -1897,7 +1897,11 @@ The \sd example, shows that FMMD can be applied to mixed digital and analogue ci
%% STATS MOVED TO FUTURE WORK %% STATS MOVED TO FUTURE WORK
%% %%
For this example we look at an industry standard temperature measurement circuit, For this example we look at an industry standard temperature measurement circuit,
the Pt100. The four wire Pt100 configuration is a commonly used and well known safety critical circuit. the `four~wire~Pt100'.
%
The four wire Pt100 configuration is a commonly used
and is a well known safety critical circuit.
%
Applying FMMD lets us look at this circuit in a fresh light. Applying FMMD lets us look at this circuit in a fresh light.
We analyse this for both single and double failures, We analyse this for both single and double failures,
in addition it demonstrates FMMD coping with component parameter tolerances. in addition it demonstrates FMMD coping with component parameter tolerances.
@ -1964,9 +1968,9 @@ look-up tables or a suitable polynomial expression.
\end{figure} \end{figure}
% %
% %
The voltage ranges we expect from this three stage potential divider\footnote{ The voltage ranges we expect from this three stage potential divider\footnote{Two stages are required
two stages are required for validation, a third stage is used to measure the current flowing for validation, a third stage is used to measure the current flowing
through the circuit to obtain accurate temperature readings} through the circuit to obtain accurate temperature readings.}
are shown in figure \ref{fig:Pt100vrange}. Note that there is are shown in figure \ref{fig:Pt100vrange}. Note that there is
an expected range for each reading, for a given temperature span. an expected range for each reading, for a given temperature span.
Note that the low reading goes down as temperature increases, and the higher reading goes up. Note that the low reading goes down as temperature increases, and the higher reading goes up.
@ -2094,17 +2098,17 @@ The Pt100 element is a precision part and will be chosen for a specified accurac
One or other of the load resistors (the one we measure current over) should also One or other of the load resistors (the one we measure current over) should also
be of this accuracy. be of this accuracy.
The \ohms{2k2} loading resistors may be ordinary, in that they would have a good temperature co-effecient The \ohms{2k2} loading resistors may be ordinary, in that they would have a good temperature co-efficient
(typically $\leq \; 50(ppm)\Delta R \propto \Delta \oc $), and should be subjected to (typically $\leq \; 50(ppm)\Delta R \propto \Delta \oc $), and should be subjected to
a narrow temperature range anyway, being mounted on a PCB. a narrow temperature range anyway, being mounted on a PCB.
%\glossary{{PCB}{Printed Circuit Board}} %\glossary{{PCB}{Printed Circuit Board}}
To calculate the resistance of the Pt100 element % (and thus derive its temperature), To calculate the resistance of the Pt100 element % (and thus derive its temperature),
having the voltage over it, we now need the current. having the voltage over it, we now need the current.
Lets use, for the sake of example $R_2$ to measure the current flowing in the temperature sensor loop. Lets use, for the sake of example, $R_2$ to measure the current flowing in the temperature sensor loop.
As the voltage over $R_3$ is relative (a design feature to eliminate resistance effects of the cables). As the voltage over $R_3$ is relative (a design feature to eliminate resistance effects of the cables),
We can calculate the current by reading we can calculate the current by reading
the voltage over the known resistor $R2$.\footnote{To calculate the resistance of the Pt100 we need the current flowing though it. the voltage over the known resistor $R2$.\footnote{To calculate the resistance of the Pt100 we need the current flowing though it.
We can determine this via ohms law applied to $R_2$, $V=IR$, $I=\frac{V}{R_2}$, We can determine this via Ohms law applied to $R_2$, $V=IR$, $I=\frac{V}{R_2}$,
and then using $I$, we can calculate $R_{3} = \frac{V_{R3}}{I}$.} and then using $I$, we can calculate $R_{3} = \frac{V_{R3}}{I}$.}
As these calculations are performed by ohms law, which is linear, the accuracy of the reading As these calculations are performed by ohms law, which is linear, the accuracy of the reading
will be determined by the accuracy of $R_2$ and $R_{3}$. will be determined by the accuracy of $R_2$ and $R_{3}$.

18
submission_thesis/CH6_Software_Examples/software.tex
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@ -254,8 +254,9 @@ a per~mil representation of the {\ft} input current.
% %
For the purpose of example the `C' programming language~\cite{DBLP:books/ph/KernighanR88} is used. For the purpose of example the `C' programming language~\cite{DBLP:books/ph/KernighanR88} is used.
% %
A 'C' function function is declared with parenthesis to A 'C' function is declared with parenthesis to
differentiate from other type of variables (data types or pointers). differentiate from other type of variables (data types or pointers).
%
In this document we borrow that format, hence the C~language In this document we borrow that format, hence the C~language
function called `main' will be presented as \cf{main}. function called `main' will be presented as \cf{main}.
% %
@ -895,7 +896,7 @@ We list these, and begin, from the bottom-up, to apply FMMD analysis.
\subsection{FMMD Analysis of PID temperature Controller} \subsection{FMMD Analysis of PID temperature Controller}
To summarise from the design stage, To summarise from the design stage,
Identified electronic components: the electronic components identified thus far:
\begin{itemize} \begin{itemize}
\item ADCMUX --- Electronics, analysed in previous example. \item ADCMUX --- Electronics, analysed in previous example.
\item TIMER --- Internal micro controller timer \item TIMER --- Internal micro controller timer
@ -955,8 +956,9 @@ $$ fm(PWM) = \{ HIGH, LOW \}.$$
The Micro controller is a complex piece of highly integrated electronics. The Micro controller is a complex piece of highly integrated electronics.
At a minimum it would include a micro-processor with PROM and RAM At a minimum it would include a micro-processor with PROM and RAM
general I/O lines ane external interupt lines. general I/O and external interrupt lines.
Typically therer are many other I/O module incorporated (e.g. TIMERS, UARTS, PWM, ADC, ADCMUX, CAN). %
Typically there are many other I/O modules incorporated (e.g. TIMERS, UARTS, PWM, ADC, ADCMUX, CAN).
In this project we are using the ADCMUX, TIMER, PWM and general purpose computing facilities. In this project we are using the ADCMUX, TIMER, PWM and general purpose computing facilities.
We have to therefore consider the general~computing, CLOCK, PROM and RAM failure modes. We have to therefore consider the general~computing, CLOCK, PROM and RAM failure modes.
$$fm (micro-controller) =\{ PROM\_FAULT, RAM\_FAULT, CPU\_FAULT, ALU\_FAULT, CLOCK\_STOPPED \}.$$ $$fm (micro-controller) =\{ PROM\_FAULT, RAM\_FAULT, CPU\_FAULT, ALU\_FAULT, CLOCK\_STOPPED \}.$$
@ -965,7 +967,7 @@ $$fm (micro-controller) =\{ PROM\_FAULT, RAM\_FAULT, CPU\_FAULT, ALU\_FAULT, CLO
Identified Software Components: Identified Software Components:
\begin{itemize} \begin{itemize}
\item --- \cf{Monitor} (which calls PID algorithm and sets status LEDS) \item --- \cf{Monitor} (which calls PID algorithm and sets status LEDS)
\item --- \cf{PID} (which calls cf{determine\_set\_point\_error} and \cf{output\_control}) \item --- \cf{PID} (which calls \cf{determine\_set\_point\_error} and \cf{output\_control})
\item --- \cf{determine\_set\_point\_error} (which calls convert\_ADC\_to\_T) \item --- \cf{determine\_set\_point\_error} (which calls convert\_ADC\_to\_T)
\item --- \cf{convert\_ADC\_to\_T} (which calls read\_ADC which we can re-use from the last example) \item --- \cf{convert\_ADC\_to\_T} (which calls read\_ADC which we can re-use from the last example)
\item --- \cf{read\_ADC} \item --- \cf{read\_ADC}
@ -1027,7 +1029,7 @@ and the function \cf{determine\_set\_point\_error}.
The pre-condition for \cf{determine\_set\_point\_error} is that the temperature read by it The pre-condition for \cf{determine\_set\_point\_error} is that the temperature read by it
is accurate, and its post condition is to return the correct control error value. is accurate, and its post condition is to return the correct control error value.
Most failure modes from a Pt100 are observable. Most failure modes from a Pt100 are observable.
we can divide the post condition into two variants, a known incorrect error value, KnownIncorrectErrorValue We can divide the post condition into two variants, a known incorrect error value, KnownIncorrectErrorValue
where we can detect the Pt100 value is suspect, and IncorrectErrorValue where we simply have where we can detect the Pt100 value is suspect, and IncorrectErrorValue where we simply have
an incorrect error value. This analysis is presented in table~\ref{tbl:geterror}. an incorrect error value. This analysis is presented in table~\ref{tbl:geterror}.
@ -1122,7 +1124,7 @@ $$fm(HeaterOutput) = \{ HeaterOnFull, HeaterOff, HeaterOutputIncorrect \}$$
The status LEDS will be controlled by general purpose (GPIO) I/O pins. The status LEDS will be controlled by general purpose (GPIO) I/O pins.
% %
We could have say, three LEDS one flashing with a human readable mark We could have, three LEDS, one flashing with a human readable mark
space ratio representing the heater output, one flashing at a regular interval to space ratio representing the heater output, one flashing at a regular interval to
indicate the processor is alive and another flashing at an interval related to the temperature, indicate the processor is alive and another flashing at an interval related to the temperature,
(to indicate if the temperature readings are within expected ranges). (to indicate if the temperature readings are within expected ranges).
@ -1147,7 +1149,7 @@ We apply FMMD analysis to this {\fg} in table~\ref{tbl:ledoutput}.
\centering \centering
\includegraphics[width=300pt]{./CH5_Examples/euler_led_output.png} \includegraphics[width=300pt]{./CH5_Examples/euler_led_output.png}
% euler_heater_output.png: 392x141 pixel, 72dpi, 13.83x4.97 cm, bb=0 0 392 141 % euler_heater_output.png: 392x141 pixel, 72dpi, 13.83x4.97 cm, bb=0 0 392 141
\caption{Euler diagram showing LEDOutput with its three LEDs and GPIO hardware elements, and its \caption{Euler diagram showing LEDOutput with its three LEDs and GPIO hardware elements,
and its software component setLEDS.} and its software component setLEDS.}
\label{fig:eulerheateroutput} \label{fig:eulerheateroutput}
\end{figure} \end{figure}