From cd0ec8fa69f8c770d1ef992be43b34ffb09bca61 Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Wed, 25 Sep 2013 12:12:33 +0100 Subject: [PATCH] arrrggghhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh --- mybib.bib | 7 + submission_thesis/CH2_FMEA/copy.tex | 24 ++- submission_thesis/CH3_FMEA_criticism/copy.tex | 36 ++-- submission_thesis/CH4_FMMD/copy.tex | 24 +-- submission_thesis/CH5_Examples/copy.tex | 200 +++++++++--------- .../CH5_Examples/sigma_delta_block.dia | Bin 2160 -> 2282 bytes .../CH6_Software_Examples/software.tex | 72 ++++--- submission_thesis/CH7_Evaluation/copy.tex | 121 ++++++----- .../appendixes/detailed_analysis.tex | 2 +- submission_thesis/style.tex | 2 +- 10 files changed, 262 insertions(+), 226 deletions(-) diff --git a/mybib.bib b/mybib.bib index be0a707..ee0b4d1 100644 --- a/mybib.bib +++ b/mybib.bib @@ -1136,6 +1136,13 @@ ISSN={0098-5589},} year = "1994" } +@MISC{tisallenkey, + author="Texas Instruments", + title = "Analysis of the Sallen Key architecture: Application report", + howpublished = "Available from http://www.ti.com/lit/an/sloa024b/sloa024b.pdf", + year="2002" +} + @MISC{challenger, author = "U.S. Presidential Commission", title = "Report of the SpaceShuttle Challanger Accident", diff --git a/submission_thesis/CH2_FMEA/copy.tex b/submission_thesis/CH2_FMEA/copy.tex index 9c2e7f8..7a627a3 100644 --- a/submission_thesis/CH2_FMEA/copy.tex +++ b/submission_thesis/CH2_FMEA/copy.tex @@ -72,7 +72,7 @@ and in a given environment. An `O' ring for instance can fail by leaking but if fitted to a water seal on a garden hose, the system level failure %is a would be a slight leak at the tap. % outside the house. % -Applied to the rocket engine on a space shuttle that same 'O' ring failure mode +Applied to the rocket engine on a space shuttle an 'O' ring failure could cause a catastrophic fire and destruction of the spacecraft and occupants~\cite{challenger}. % At a lower level, consider a resistor and capacitor forming a potential divider to ground. @@ -113,7 +113,7 @@ is shown in figure~\ref{fig:component_fm_rel}. The next stage is analysis, that is reasoning applied to the system in the event of a given failure mode. % -To perform how a failure +To analyse how a failure mode, after considering its effect on other components in the system, will translate to a system level symptom/failure. % @@ -251,7 +251,7 @@ their relationship to particular standards is presented below. Two common electrical components are used as examples, and examined against two sources of {\fm} information. % define their failure mode behaviour. % -These definitions for a given generic component may not always agree. +Failure mode definitions for a given generic component may not always agree. % The reasons why, some {\fms} can be found in one source, but not in the others and vice versa, are discussed. @@ -429,9 +429,9 @@ investigations. \fmmdglossOPAMP The symptom for this is given as a low slew rate. % -Slew rate for a circuit/component is the rate at which it changes an output voltage level (i.e. $\frac{\delta V}{\delta t} $). +Slew rate for a circuit/component is the maximum rate at which it can change an output voltage level (i.e. $\frac{\delta V}{\delta t} $). % -This means that the op-amp will not react quickly to changes on its input terminals. +A low slew rate will mean that the op-amp will not react quickly to changes on its input terminals. % % This is a failure symptom that may not be of concern in a slow responding system like an @@ -441,7 +441,7 @@ This failure cause can be mapped to a symptomatic {\fm} called $LOW\_SLEW$. \paragraph{No Operation - over stress.} Here the OP-Amp has been damaged, and the output may be held HIGH or LOW, or may be -effectively tri-stated, i.e. not able to drive circuitry in along the next stages of +effectively tri-stated, i.e. not able to drive circuitry along the next stages of the signal path: this {\fm} is termed NOOP (no Operation). % This failure cause thus maps to three {\fms}, $LOW$, $HIGH$, $NOOP$. @@ -494,7 +494,7 @@ $LOW\_SLEW$. \caption{LM358: EN298 Open and shorted pin failure symptom determination technique} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{Amplifier Effect} & & \textbf{Symptom(s)} \\ - \textbf{Failure} & & \textbf{Amplifier Effect} & & \textbf{Derived Component} \\ + \textbf{Failure} & & \textbf{Amplifier Effect} & & \textbf{FMEA component} \\ \textbf{cause} & & \textbf{ } & & \textbf{Failure Mode} \\ \hline @@ -734,7 +734,8 @@ the circuit behaviour is measured in finer granularity, % With this style of fault finding, because it is based on experiment, hopping from module to module eliminating working ones, until -failure is found~\cite{maikowski}, is effective. +failure is found~\cite{maikowski}, it is efficient in terms of +concentrating effort. % The rationale and work-culture of those tasked to perform FMEA are generally personnel who have performed fault finding~\cite{cbds}[p.97]. @@ -812,7 +813,7 @@ From a large system perspective, it may be found that {\bc} {\fms} may have more than one possible system event associated with them. % Often there will be a clear one to one mapping, but -probabilities to failure (as used in FMECA) +probabilities to failure (as used in FMECA, see section~\ref{sec:FMECA}) could mean one ({\fm}) too many (system level symptoms). % mapping. % \paragraph{Use of Markov chains to model failure modes.} @@ -1094,7 +1095,7 @@ Where $RD_{double}$ is the reasoning~distance for double failure scenarios: \end{equation} % For a theoretical system with 100 components and a fixed 3 failure modes each, this gives reasoning distance of -$100*99*98*3=2,910,600$. % failure mode scenarios. +$100 \times 99 \times 98 \times 3 = 2,910,600$. % failure mode scenarios. % In practise there is an additional complication here, that of the circuit topology changes that {\fms} can cause. @@ -1177,7 +1178,8 @@ An example PFMEA report is presented in table~\ref{tbl:pfmeareport}. \section{FMECA - Failure Modes Effects and Criticality Analysis} - \fmmdglossFMECA +\fmmdglossFMECA +\label{sec:FMECA} \paragraph{ FMECA - Failure Modes Effects and Criticality Analysis.} % \begin{figure} % \centering diff --git a/submission_thesis/CH3_FMEA_criticism/copy.tex b/submission_thesis/CH3_FMEA_criticism/copy.tex index 86cbb1c..da672dd 100644 --- a/submission_thesis/CH3_FMEA_criticism/copy.tex +++ b/submission_thesis/CH3_FMEA_criticism/copy.tex @@ -91,7 +91,7 @@ This means that the reasoning involved in determining the system level failure/s Ideally supporting documentation would give the reasoning and calculations behind each analysis case, but the structure of current FMEA reports does not encourage this. % -\paragraph{Re-use of FMEA analysis} +\paragraph{Re-use of FMEA analysis.} % Given the {\bc} {\fm} to system level failure mode paradigm it is difficult to re-use FMEA analysis. @@ -207,8 +207,8 @@ A small group of components performing a well defined function is termed a `{\fg}'. % Potentially, using {\fgs}, is a way of de-composing -the problem and reducing the $O(N^2)$ state explosion effect -associated with XFMEA. +the problem and reducing the $O(N^2)$---see equation~\ref{eqn:fmea_single}---state explosion effect associated with XFMEA. +% \fmmdglossSTATEEX % That is if the analysis problem can be broken into smaller steps, involving @@ -234,11 +234,12 @@ It is therefore desirable to reduce this order further. \section{Software and FMEA} Traditional FMEA deals only with electrical and mechanical components, i.e. it does not have provision for software. +% Modern control systems nearly always have a significant software/firmware element, and not being able to model software with current FMEA methodologies is a cause for criticism~\cite{safeware}[Ch.12]. % -Some techniques apply blanket estimates for a given software implementation, based +Some techniques apply blanket estimates for a given software implementation~\cite{safeware}[pp.156-9], based on the verification techniques applied in its testing, to aid calculation of system level reliability statistics~\cite{5492693}. %Even the traditionally conservative nuclear industry is now @@ -339,24 +340,29 @@ a master controller. % Most modern cars follow this information technology pattern and use CANbus~\cite{canspec,can}. % -For instance, in a modern car there will be no mechanical linkage from the pedal to the engine, instead the throttle pedal -will be linked to a sensor to determine how -far the pedal is pressed. +For instance, in a modern car there will be no mechanical linkage from the throttle pedal to the engine, instead the pedal +will be linked to a sensor to determine how far down it is pressed. % -This sensor will be read by a micro-controller, and passed, via CANbus, to the Engine Control Unit (ECU) +This sensor will be read by a micro-controller, and values passed via CANbus, to the Engine Control Unit (ECU) which will use that information (along with information from other sensors) to adjust the power required from the engine. % This adjustment could be direct, or could be another CANbus message passed to a micro-controller regulating engine function. % In terms of FMEA, see figure~\ref{fig:distcon}, our reasoning path spans (at least) four interface layers of electronics to software. % -Traditional FMEA does not cater for the software hardware interface, and this leads to the additional complications -%with the additional complications -of the communications protocol used to transmit data and the failure mode characteristics -of the communications physical layer. +Traditional FMEA does not cater for the software hardware interface and using +a distributed system means the signal path will +cross several hardware/software interfaces\footnote{The complications of introducing a +communications protocol and the failure mode characteristics of the communications +physical~layer must also be considered in a distributed system.}. +%of the communications physical layer.. % -This means the signal path will -cross several hardware/software interfaces. +%, and this leads on to the additional complications +%with the additional complications +%of the communications protocol used to transmit data and the failure mode characteristics +%of the communications physical layer. +% + % \fmmdglossSIGPATH %(figure~\ref{fig:distcon} @@ -402,7 +408,7 @@ A summary of deficiencies in current FMEA methodologies is listed below: Traditional forms of FMEA are no longer % fit for purpose! of meaningful use for complex modern systems especially those incorporating programmatic elements. They were designed to analyse simple electro-mechanical systems -and even common place large analogue circuits (that are usually physically small), are +and even common place high component count analogue circuits (that are usually surface mount and therefore physically small), are getting too complicated for meaningful analysis using FMEA. % % diff --git a/submission_thesis/CH4_FMMD/copy.tex b/submission_thesis/CH4_FMMD/copy.tex index c9b0db3..3688577 100644 --- a/submission_thesis/CH4_FMMD/copy.tex +++ b/submission_thesis/CH4_FMMD/copy.tex @@ -98,7 +98,7 @@ at the top of the hierarchy. The failure modes of the final or top {\dc} are the failure modes of the system under investigation. % -That is, the traditional FMEA process has be taken and modularised from the bottom-up. +That is, the traditional FMEA process has been taken and modularised from the bottom-up. %piss break down each stage of reasoning %into small manageable groups, and use the failure mode behaviour from them to create {\dcs} %to build higher level groups. @@ -107,8 +107,8 @@ In this way FMEA is applied incrementally to an entire system. %, with document \fmmdgloss % This has advantages of concentrating -effort in where modules interact (interfaces), of -being able to re-use work and savings in the complexity of performing +effort where modules interact (interfaces), +of being able to re-use work and savings in the complexity of performing FMEA (because the analysis is typically performed in several small stages thus avoiding state explosion). %A notation is then described to index and classify objects created in FMMD hierarchical models. @@ -117,10 +117,8 @@ thus avoiding state explosion). \section{Worked Example: Non-Inverting Amplifier} \label{sec:noninvamp} -%% here bring in sys safety paper from 2011 -%% -%% GARK BEGIN - +% +% The principles of FMMD are demonstrated, by using it to analyse a common circuit, the non-inverting amplifier built from an op amp~\cite{aoe}[p.234] and two resistors; a circuit schematic for this is shown in figure \ref{fig:noninvamp}. @@ -960,11 +958,11 @@ starting where possible with known base~component failure~modes. % % An advantage of working from the bottom up is that it can be ensured that -all component failure modes must be considered. +all component failure modes have been considered. % A top down approach (such as FTA) can miss~\cite{faa}[Ch.~9] individual failure modes of components, -especially where there are non-obvious top-level faults. +especially where there are non-obvious or unexpected top-level failures. % \fmmdglossFTA % @@ -979,7 +977,7 @@ and collecting symptoms of failure, is termed `symptom abstraction'. % \fmmdglossSA % -This is dealt with in detail using an algorithmic description, in appendix \ref{sec:algorithmfmmd}. +This is examined using an algorithmic description, in appendix \ref{sec:algorithmfmmd}. \fmmdglossFG \fmmdglossDC % % define difference between a \fg and a \dc @@ -1025,7 +1023,7 @@ A {\fg} will only be associated with one {\dc} and is given a one to one relatio % Each {\fg} will have one analysis report associated with it. % -The UML representation (in figure \ref{fig:cfg}) shows a `{\fg}' having a one to one relationship with a derived~component. +The UML representation is shown in figure \ref{fig:cfg}. %) shows a `{\fg}' having a one to one relationship with a derived~component. % % %%% FORMAL DEF SLIGHTLY OUT OF PLACE HERE ---- J.HOWSE @@ -1128,7 +1126,7 @@ Also a detailed cause and effect model is useful for creating diagnostic schema -\paragraph{Keeping track of the derived components position in the hierarchy} +\paragraph{Keeping track of the derived components position in the hierarchy.} \label{sec:alpha} The UML meta model in figure \ref{fig:cfg}, shows the relationships between the entities used in FMMD. @@ -1146,7 +1144,7 @@ derivation %`$\derivec$' have led to the current derived component) we can add an attribute to the component data type. % -This can be a natural number called the level variable $\abslev \in \mathbb{N}$. +This can be a natural number called the level variable $\abslev \in \mathbb{N}_{0}$. % J. Howse says zero is a given in comp sci. This can be a natural number called the level variable $\alpha \in \mathbb{N}_0$. The $\abslev$ level variable in each component, indicates the position in the hierarchy. Base components diff --git a/submission_thesis/CH5_Examples/copy.tex b/submission_thesis/CH5_Examples/copy.tex index 2d653dc..4b6d4f2 100644 --- a/submission_thesis/CH5_Examples/copy.tex +++ b/submission_thesis/CH5_Examples/copy.tex @@ -91,6 +91,7 @@ and then combining it with the OPAMP failure mode model. The second is to place all three components in one {\fg}. Both approaches are followed in the next two sub-sections. % +\clearpage \subsection{First Approach: Inverting OPAMP using a Potential Divider {\dc}} % Ideally the {\dcs} from the $PD$ from section~\ref{subsec:potdiv} would be re-used; on initial inspection it %at first glance, @@ -205,7 +206,7 @@ by forming a {\fg} with the OpAmp and the new {\dc} $IPD$. \end{table} % % -\clearpage +%\clearpage %%This gives the same results as the analysis from figure~\ref{fig:invampanalysis}. % % @@ -345,6 +346,7 @@ This concern is re-visited in the differencing amplifier example in the next sec % maybe do an ac amplifier later at some stage. % \begin{table}[h+] +\centering \caption{Inverting Amplifier: Single failure analysis: 3 components} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{Inverted Amp Effect} & & \textbf{Symptom} \\ \hline @@ -635,7 +637,7 @@ for the second stage \end{figure} -\paragraph{First Order Low Pass Filter.} +\subsection{First Order Low Pass Filter} \label{sec:lp} % WEEEE ECUNT Starting with the first order low pass filter formed by $R10$ and $C10$. @@ -691,7 +693,7 @@ called $FirstOrderLP$. % Applying the $fm$ function yields: $$ fm(FirstOrderLP) = \{ LPnofilter,LPnosignal \}.$$ % -\paragraph{Addition of Buffer Amplifier: First stage.} +\subsection{Addition of Buffer Amplifier: First stage} % The op-amp IC1 is being used simply as a buffer. \fmmdglossOPAMP @@ -744,7 +746,7 @@ In terms of the circuit, the {\fgs} $FirstOrderLP$, and $LP1$ have been modelled. % These can be represented on the circuit diagram by drawing contours around the components -on the schematic as in figure~\ref{fig:circuit2002_LP1}. +on the schematic in figure~\ref{fig:circuit2002_LP1}. \begin{figure}[h] \centering @@ -756,8 +758,12 @@ on the schematic as in figure~\ref{fig:circuit2002_LP1}. \end{figure} -\paragraph{Second order Sallen Key Low Pass Filter.} -The next two filters in the signal path are R1,R2,C2,C1,IC2 and R3,R4,C4,C3,IC3. +\subsection{Second order Sallen Key Low Pass Filter} +% +The next two filters in the signal path are the component groups R1,R2,C2,C1,IC2 and R3,R4,C4,C3,IC3. +% +These are Sallen Key low pass filters~\cite{tisallenkey}. +% From a failure mode perspective these are identical. % The first one can be analysed (see table~\ref{tbl:sallenkeylp}) and then these @@ -801,7 +807,7 @@ A derived component is created to represent the Sallen Key low pass filter, call $$ fm ( SKLP ) = \{ SKLPHigh, SKLPLow, SKLPIncorrect, SKLPnosignal . \} $$ % % -\paragraph{A failure mode model of Op-Amp Circuit 2.} +\subsection{A failure mode model of Op-Amp Circuit 2} % A {\dcs} representing the three stages of this filter is created following the signal flow in the filter circuit (see figure~\ref{fig:blockdiagramcircuit2}). @@ -895,6 +901,7 @@ The FMMD hierarchy is shown in figure~\ref{fig:circuit2h}. \label{tbl:fivepole} \end{table} % +\clearpage % A {\dc} is created to represent the circuit in figure~\ref{fig:circuit2}, called $FivePoleLP$: applying the $fm$ function (see table~\ref{tbl:fivepole}) @@ -917,10 +924,14 @@ It is not surprising therefore that they have very similar failure modes. From a safety point of view, the failure modes $LOW$, $HIGH$ and $NO\_SIGNAL$ could be easily detected; the failure symptom $FilterIncorrect$ is not detectable. % +%\clearpage \subsection{Conclusion} This example shows the analysis of a linear signal path circuit with three easily identifiable {\fgs} and re-use of the Sallen-Key {\dc}. % +% +% +% \clearpage % \section{Quad Op-Amp Oscillator} @@ -1042,7 +1053,7 @@ the {\fg} for this analysis can be expressed thus: % %$$ G^1_0 = \{ PHS45^1_1, NIBUFF^0_1, PHS45^1_2, NIBUFF^0_2, PHS45^1_3, NIBUFF^0_3 PHS45^1_4, INVAMP^1_0 \} ,$$ $$ G = \{ PHS45_1, NIBUFF_1, PHS45_2, NIBUFF_2, PHS45_3, NIBUFF_3, PHS45_4, INVAMP \} ,$$ -or in Euler diagram format as in figure~\ref{fig:bubbaeuler1}. +or in Euler diagram format in figure~\ref{fig:bubbaeuler1}. % HTR 23SEP2012 \begin{figure}[h+] % HTR 23SEP2012 \centering % HTR 23SEP2012 \includegraphics[width=300pt,keepaspectratio=true]{CH5_Examples/poss1finalbubba.png} @@ -1114,7 +1125,7 @@ It should be possible to determine smaller {\fgs} and refine the model further. \paragraph{Outline of finer grained FMMD analysis of the Bubba oscillator.} % The pre-analysed $NIBUFF$ and $PHS45$ -{\dcs} are used to form a {\fg}, analysed in table~\ref{tbl:buff45}, giving the +{\dcs} are used to form a {\fg}, analysed in appendix~\ref{tbl:buff45}, giving the {\dc} $BUFF45$. % %Thus, @@ -1129,7 +1140,7 @@ Together these apply a $135^{\circ}$ phase shift to the signal. This property is used to model a higher level {\dc}, that of a $135^{\circ}$ phase shifter. % The three $BUFF45$ {\dcs} form a -{\fg} which is analysed in table~\ref{tbl:phs135buffered}. +{\fg} which is analysed in appendix~\ref{tbl:phs135buffered}. % The result of this analysis is the {\dc} $PHS135BUFFERED$ which represents an actively buffered $135^{\circ}$ phase shifter. @@ -1140,7 +1151,7 @@ $PHS135BUFFERED$ which represents an actively buffered $135^{\circ}$ phase shift A PHS45 {\dc} and an inverting amplifier\footnote{Inverting amplifiers apply a $180^{\circ}$ phase shift to a signal regardless of its frequency.}, form a {\fg} -providing an amplified $225^{\circ}$ phase shift, analysed in table~\ref{tbl:phs225amp} +providing an amplified $225^{\circ}$ phase shift, analysed in appendix~\ref{tbl:phs225amp} resulting in the {\dc} $PHS225AMP$. % Applying FMMD the {\dc} $PHS225AMP$ is created with the following failure modes: @@ -1198,7 +1209,8 @@ $$ % This has meant a drastic reduction in the number of failure-modes to check against components. %It has %also This more decomposed approach has -given us five {\dcs}, building blocks, which could % +given us five {\dcs}, %building blocks, +which could % potentially be re-used in other projects. %potentially be re-used for similar circuitry %to analyse in the future. @@ -1291,7 +1303,9 @@ and fed to the D type flip flop. % % The output of the flip flop is routed to the digital output and to the feedback loop. -It must be level converted, i.e. from digital logic voltage levels to analogue levels, before being fed to the analogue feedback. +% +It must be level converted, i.e. from digital logic voltage levels to analogue levels, before being fed to the analogue feedback/integrator. +% It is level converted to an analogue signal by IC3---i.e. a digital 0 becomes a -ve voltage and a digital 1 becomes a +ve voltage--- and fed into the summing integrator completing the negative feedback loop. % @@ -1333,7 +1347,7 @@ A CLOCK signal is required for the \sd. % For the purpose of example one failure mode is assigned to this, that it might stop. -The failure modes of the CLOCK, is stated thus: +The failure mode of the CLOCK, is stated thus: % $$ fm ( CLOCK ) = \{ STOPPED \}. $$ @@ -1536,7 +1550,7 @@ $$ FG = \{ FFB , BISJ \} .$$ The buffered {\sd} circuit is analysed using FMMD (see appendix~\ref{detail:SDADC}) giving a {\dc} $SDADC$ which provides a failure mode model for the \sd: -$$fm(SSDADC) = \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\} . $$ +$$fm(SDADC) = \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\} . $$ The {\dc} hierarchy is shown in figure~\ref{fig:eulersdfinal}. % \begin{figure}[h] @@ -1581,7 +1595,7 @@ This leads onto interfacing to software and digital~systems in the next chapter. % % -%\clearpage +\clearpage \section{Pt100 Analysis: FMMD and Double Failure Mode Analysis} \label{sec:Pt100} { @@ -1611,38 +1625,13 @@ It is analysed for both single and double failures, in addition it demonstrates FMMD coping with component parameter tolerances. % The circuit is described from a conventional safety perspective and then analysed using the FMMD methodology. - - -%A derived component, representing this circuit is then presented. - - +% +%A derived component, representing this circuit is then present The Pt100, or platinum wire \ohms{100} sensor is a widely used industrial temperature sensor that is slowly replacing the use of thermocouples in many industrial applications below 600\oc, due to high accuracy\cite{aoe}. % -%This section looks at the most common configuration, the -%four wire circuit, and analyses it from an FMEA perspective twice. -%FMMD is performed twice on this circuit -%firstly considering single faults only -%(cardinality constrained powerset of 1) -%and secondly, considering the -%possibility of double faults. % (cardinality constrained powerset of 2). -% -% \ifthenelse {\boolean{pld}} -% { -% The section is performed using Propositional Logic -% diagrams to assist the reasoning process. -% } -% { -% } -% -% This chapter describes taking -% the failure modes of the components, analysing the circuit using FMEA -% and producing a failure mode model for the circuit as a whole. -% Thus after the analysis the $Pt100$ temperature sensing circuit, may be viewed -% from an FMEA perspective as a component itself, with a set of known failure modes. -% } % \begin{figure}[h] \centering @@ -1662,9 +1651,9 @@ By measuring voltages from sections of this circuit forming potential dividers, the resistance of the platinum wire sensor can be determined. % -The resistance -of this is directly related to temperature, and may be determined by -look-up tables~\cite{eurothermtables} or a suitable polynomial expression. +%The resistance +%of this is directly related to temperature, and may be determined by +%look-up tables~\cite{eurothermtables} or a suitable polynomial expression. % % \begin{figure}[h] @@ -1677,7 +1666,7 @@ look-up tables~\cite{eurothermtables} or a suitable polynomial expression. % % The voltage ranges expected from this three stage potential divider\footnote{Two stages are required -for validation, a third stage is used to measure the current flowing +for validation, a third stage is necessary to measure the current flowing through the circuit to obtain accurate temperature readings.} are shown in figure \ref{fig:Pt100vrange}. % @@ -1691,8 +1680,8 @@ and the higher as {\em sense+}. \paragraph{Accuracy despite variable resistance in cables.} -For electronic and accuracy reasons, a four wire circuit is preferred -because of resistance in the cables. +%For electronic and accuracy reasons, a four wire circuit is preferred +%because of resistance in the cables. % Resistance from the supply causes a slight voltage @@ -1713,8 +1702,8 @@ through the circuit and knowing the voltage drop over the $Pt100$, its resistance is calculated by Ohms law $V=I.R$, $R=\frac{V}{I}$. % -Thus a little loss of supply voltage due to resistance in the cables -does not impinge on accuracy. +%Thus a little loss of supply voltage due to resistance in the cables +%does not impinge on accuracy. % The resistance to temperature conversion is achieved through the published $Pt100$ tables\cite{eurothermtables}. @@ -1785,11 +1774,11 @@ in the diagram, it will be considered a fault. Should the reading be above its expected range, this is a `High Fault' and if below a `Low Fault'. % -Table \ref{ptfmea} plays through the scenarios of each of the resistors failing +Table~\ref{ptfmea} plays through the scenarios of each of the resistors failing in both SHORT and OPEN failure modes, and hypothesises an error condition in the readings. % -The range {0\oc} to {300\oc} will be analysed using potential divider equations to -determine out of range voltage limits in section~\ref{sec:ptbounds}. +The temperature range {0\oc} to {300\oc} will be used to determine potential divider voltage outputs (see section~\ref{sec:ptbounds}), +and these used to validate the FMEA in table~\ref{ptfmea}. \begin{table}[ht] \caption{Pt100 FMEA Single Faults} % title of Table @@ -1817,15 +1806,15 @@ $R_2$ SHORT & - & Low Fault & Value Out of Range Value \\ From table \ref{ptfmea} it can be seen that any component failure in the circuit should cause a common symptom, that of one or more of the values being `out of range'. % -Temperature range calculations and detailed calculations -on the effects of each test case are found in section \ref{Pt100range} -and \ref{Pt100temp}. +%Temperature range calculations and detailed calculations +%on the effects of each test case are found in section \ref{Pt100range} +%and \ref{Pt100temp}. \paragraph{Consideration of Resistor Tolerance} \label{sec:resistortolerance} % -The separate sense lines ensure the voltage read over the Pt100 thermistor are not -altered due to having to pass any significant current. +%The separate sense lines ensure the voltage read over the Pt100 thermistor are not +%altered due to having to pass any significant current. % The Pt100 element is a precision part and will be chosen for a specified accuracy/tolerance range. % @@ -1833,27 +1822,30 @@ One or other of the load resistors (the one that current is measured over) shoul be of this accuracy. 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 -a narrow temperature range anyway, being mounted on a PCB. +(typically $\leq \; 50(ppm)\Delta R \propto \Delta \oc $), and typically be subjected to +a narrow temperature range, being mounted on a PCB. %\glossary{{PCB}{Printed Circuit Board}} % To calculate the resistance of the Pt100 element % (and thus derive its temperature), -having the voltage over it, the current flowing through it must be measured. +the voltage over it is read +and with the current flowing through it, its resistance can be found. +%must be measured. % -For the sake of example, let be used $R_2$ to measure the current flowing in the temperature sensor loop. +Let $R_2$ be used to measure the current flowing in the temperature sensor loop. +% +%As the voltage over the Pt100 element $R_3$ is relative to % (a design feature to eliminate resistance effects of the cables), +%the current, can be calculated by reading +%the voltage over the known resistor +%$R_2$. % -As the voltage over $R_3$ is relative (a design feature to eliminate resistance effects of the cables), -the current can be calculated by reading -the voltage over the known resistor -$R2$.\footnote{To calculate the resistance of the Pt100 we need the current flowing though it. -This can be determined via Ohms law applied to $R_2$, $V=I R_2$, $I=\frac{V}{R_2}$, -and then using $I$, $R_{3} = \frac{V_{R3}}{I}$.} 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}$\footnote{To calculate the resistance of the Pt100 we need the current flowing though it. +This can be determined via Ohms law applied to $R_2$, $V=I R_2$, $I=\frac{V}{R_2}$, +and then using $I$, $R_{3} = \frac{V_{R3}}{I}$.}. %It is reasonable to %take the mean square error of these accuracy figures. -\paragraph{Range and $Pt100$ Calculations} +\paragraph{Range and $Pt100$ Calculations.} \label{Pt100temp} $Pt100$ resistors are designed to have a resistance of \ohms{100} at {0\oc} \cite{aoe},\cite{eurothermtables}. @@ -1875,8 +1867,8 @@ As the Pt100 forms a potential divider with the \ohms{2k2} load resistors, the upper and lower readings are calculated thus: % % -$$ highreading = 5V.\frac{2k2+Pt100}{2k2+2k2+pt100} $$ -$$ lowreading = 5V.\frac{2k2}{2k2+2k2+Pt100} $$ +$$ highreading = 5V.\frac{2k2+Pt100}{2k2+2k2+pt100} ,$$ +$$ lowreading = 5V.\frac{2k2}{2k2+2k2+Pt100} .$$ % So by defining an acceptable measurement/temperature range, and ensuring the @@ -1888,9 +1880,9 @@ resistors in this circuit have failed. % To convert these to twelve bit ADC (\adctw) counts: % -$$ highreading = 2^{12}.\frac{2k2+Pt100}{2k2+2k2+pt100} $$ +$$ highreading = 2^{12}.\frac{2k2+Pt100}{2k2+2k2+pt100} , $$ % -$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+Pt100} $$ +$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+Pt100} . $$ % % \begin{table}[ht] @@ -1955,7 +1947,7 @@ will detect it. % \ifthenelse{\boolean{pld}} { -\paragraph{Single Fault Modes as PLD} +\paragraph{Single Fault Modes as PLD.} % The component~failure~modes in table \ref{ptfmea} can be represented as contours on a PLD diagram. @@ -1983,7 +1975,7 @@ for the circuit shown in figure \ref{fig:vd}. % % % -\paragraph{Proof of Out of Range Values for Failures} +\paragraph{Proof of Out of Range Values for Failures.} \label{pt110range} % Using the temperature ranges defined above the voltages can be compared; @@ -1996,11 +1988,11 @@ There are six test cases and each will be examined in turn. With Pt100 at 0\oc: $$ highreading = 5V $$ Since the highreading or sense+ is directly connected to the 5V rail, -both temperature readings will be 5V.. -$$ lowreading = 5V.\frac{2k2}{2k2+100\Omega} = 4.78V$$ +both temperature readings will be 5V, +$$ lowreading = 5V.\frac{2k2}{2k2+100\Omega} = 4.78V .$$ With Pt100 at the high end of the temperature range 300\oc. -$$ highreading = 5V $$ -$$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$ +$$ highreading = 5V ,$$ +$$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V .$$ % Thus with $R_1$ shorted both readings are outside the proscribed range in table \ref{ptbounds}. @@ -2015,12 +2007,12 @@ proscribed range in table \ref{ptbounds}. \paragraph{ TC 3 : Voltages $R_2$ SHORT } % With Pt100 at 0\oc: -$$ lowreading = 0V $$ +$$ lowreading = 0V .$$ Since the lowreading or sense- is directly connected to the 0V rail, -both temperature readings will be 0V. -$$ lowreading = 5V.\frac{100\Omega}{2k2+100\Omega} = 0.218V$$ -With Pt100 at the high end of the temperature range 300\oc. -$$ highreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$ +both temperature readings will be 0V, +$$ lowreading = 5V.\frac{100\Omega}{2k2+100\Omega} = 0.218V .$$ +With Pt100 at the high end of the temperature range 300\oc , +$$ highreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V .$$ % Thus with $R_2$ shorted both readings are outside the proscribed range in table \ref{ptbounds}. @@ -2036,12 +2028,15 @@ Here the potential divider is simply between the two 2k2 load resistors. Thus it will read a nominal; 2.5V. % -Assuming the load resistors are -precision components, and then taking an absolute worst case of 1\% either way. +Because the readings here depend on the values of resistors $R_1$ and $R_2$ +resistor tolerance must be considered. % -$$ 5V.\frac{2k2*0.99}{2k2*1.01+2k2*0.99} = 2.475V $$ +Assuming the load resistors are fairly typical in terms of precision +precision, taking an absolute worst case of 1\% either way: % -$$ 5V.\frac{2k2*1.01}{2k2*1.01+2k2*0.99} = 2.525V $$ +$$ 5V.\frac{2k2*0.99}{2k2*1.01+2k2*0.99} = 2.475V ,$$ +% +$$ 5V.\frac{2k2*1.01}{2k2*1.01+2k2*0.99} = 2.525V .$$ % These readings both lie outside the proscribed range. Also the sense+ and sense- readings would have the same value. @@ -2080,7 +2075,12 @@ resistors in this circuit have failed. % \subsection{Derived Component with one failure mode.} The Pt100 circuit can now be treated as a component in its own right, and has one failure mode, -{\textbf OUT\_OF\_RANGE}. This is a single, detectable failure mode. The detectability of a +{\textbf OUT\_OF\_RANGE} i.e.: + + +$$ fm(Pt100) = \{ {OUT\_OF\_RANGE} \} . $$ + +This is a single, detectable failure mode. The detectability of a fault condition is very good with this circuit. This should not be a surprise, as the four wire $Pt100$ has been developed for safety critical temperature measurement. % @@ -2145,7 +2145,7 @@ faults as FMMD test cases. TC 7: & $R_1$ OPEN $R_2$ OPEN & Floating input Fault & Floating input Fault & Unknown value readings \\ \hline TC 8: & $R_1$ OPEN $R_2$ SHORT & low & low & Both out of range \\ \hline \hline - TC 9: & $R_1$ OPEN $R_3$ OPEN & high & low & Both out of Range \\ \hline + TC 9: & $R_1$ OPEN $R_3$ OPEN & Floating & low & Sense- out of range \\ \hline TC 10: & $R_1$ OPEN $R_3$ SHORT & low & low & Both out of range \\ \hline \hline @@ -2194,8 +2194,8 @@ Thus both values will be out of range. % \paragraph{ TC 9 : Voltages $R_1$ OPEN $R_3$ OPEN.} % -Sense- will be floating. -Sense+ will be tied to Vcc and will thus be out of range. +Sense+ will be floating. +Sense- will be tied to ground and will thus be out of range. % \paragraph{ TC 10 : Voltages $R_1$ OPEN $R_3$ SHORT.} % @@ -2242,8 +2242,8 @@ Both values will be out of range. % \paragraph{ TC 17 : Voltages $R_2$ SHORT $R_3$ OPEN.} % -This shorts the sense- to ground. -The sense- value will be out of range. +This shorts the sense- to ground, and sense+ to Vcc. +Both values will be out of range. % % \paragraph{ TC 18 : Voltages $R_2$ SHORT $R_3$ SHORT.} @@ -2281,7 +2281,7 @@ not that all for a given cardinality constraint have been included. { } % -\paragraph{Symptom Extraction} +\paragraph{Symptom Extraction, forming a {\dc}.} % The results of the test case analysis can now be examined and symptom abstraction applied. % @@ -2312,10 +2312,12 @@ in figure \ref{fig:Pt100_doublef}. } % %\clearpage -\subsection{Derived Component : The Pt100 Circuit} +%\subsection{Derived Component : The Pt100 Circuit for double failures} \label{sec:Pt100floating} The Pt100 circuit again, can now be treated as a component in its own right, and has two failure modes, -{\textbf{OUT\_OF\_RANGE}} and {\textbf{FLOATING}}. +{\textbf{OUT\_OF\_RANGE}} and {\textbf{FLOATING}}, i.e. + +$$ fm(Pt100) = \{ {OUT\_OF\_RANGE}, {FLOATING} \} . $$ % \ifthenelse{\boolean{pld}} { diff --git a/submission_thesis/CH5_Examples/sigma_delta_block.dia b/submission_thesis/CH5_Examples/sigma_delta_block.dia index dbd8992dd73af603720a4c639600b2d189a85de1..9df31b1b6b6e984759d1ab6100e8afba536904df 100644 GIT binary patch literal 2282 zcmV_fZzYRER@ zXe&#GEGNy&{`NhjoF=xVTqHA%1G#7%%QQccJm2BR!$arS-@Y%?=-L+RB+t%=1mR(1 zvspe*vc>uE-(Np})WhE{2EWde_!s!UDB@)VpUBqk)%ozMELXpbMmIM%D7{_BWnQ2( z*`T!@{Vz__cm#z;!;3)_J*;3Jm$AFHy&9KgkxVzGjk0)Y&xg}^_H9w*n`}O;N^Q%{ z@-#1^>o`3hez^3H;b>dUXs4b>>R!bQJ1uPdt+{Fp4`bR?y|TrAwaZn$PM}D6yE-V+ zP>=ihpv<<^8VY5Lix0o^57jMgFWlEvccYCUeUnxlL6N4ELT3o04OU!{ zyFPh2-1K$f($|G6UKcJ|PgZ$R7I9J@LQeBMwQ*LVmc_=l$63$f6in=~W_4)AWm1;; z6Zd}^r|ai5pt}5nZ7*f+qDbbC6L+UXLoGMSyu6xx57b>%?YDtyzfRW4G_`eipJe6H zs=qx>_4}jaz4!gcJ6c0kTjTUF*H&2Z^66o*N#=I_gqiJ@X{hOHTWs`HukV+8ZpT!Y z_9kl&k;b>S*jE4PewvQ91HAP(Q9LV?>$_JE`XrzJ*UrjqW51MfHjj&W^fCIBe;?j! 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