?trivially

trivially發(fā)音

英：['tr?v??l?]　　美：['tr?v?rl?]

英：　　美：

trivially中文意思翻譯

adv. 瑣細地；無(wú)能地；平凡地

trivially常見(jiàn)例句

1 、He works himself up about the most trivial things.───他會(huì )因一些雞毛蒜皮的事而情緒激動(dòng)。

2 、Stop pestering me with your trivial problems.───別再拿你那些雞毛蒜皮的問(wèn)題來(lái)煩擾我。

3 、He gets tied up to trivial affairs.───他被一些無(wú)關(guān)緊要的小事束縛住了。

4 、They warred over trivial matters.───他們因小事而爭吵。

5 、He knew that a nation's honor is not a trivial matter.───他懂得國家的榮譽(yù)絕不是無(wú)足掛齒的。

6 、It would be foolish and impetuous to resign over such a trivial matter.───為這樣的小事辭職未免愚蠢而輕率。

7 、Please don't omit any details, no matter how trivial they may seem.───不管事情有多么瑣碎,不要忽略掉任何細節。

8 、He doesn't want to burden you with trivialities.─── 他不想讓你為這些瑣事煩心

9 、They bickered over trivial things.───他們?yōu)橹ヂ樾∈聽(tīng)幊场?/p>

10 、You have grossly magnified a trivial situation.───你過(guò)分地夸大了一件雞毛蒜皮的小事。

11 、What particular body you currently occupy is trivial.─── 你現在所占據的軀體并不重要

12 、Overparticular about trivial details; fastidious.───吹毛求疵的過(guò)分注意瑣碎細節的；愛(ài)挑剔的

13 、We identify with the most *all and trivial aspects of ourselves.─── 我們總會(huì )與自己細小和次要的一面產(chǎn)生共鳴

14 、Keeping a good bank of ideas is trivially easy.───保持一個(gè)好的“創(chuàng )意銀行”是很容易的。

15 、Don't waste your time on trivial things.───不要把你的時(shí)間浪費在瑣事上。

16 、Let me begin by sketching some that are minor though not trivial.───下面讓我從一些細小的但并不是微不足道的事實(shí)開(kāi)始。

17 、I was worried it might be about something trivial.─── 我還擔心是件毫不重要的事呢

18 、He could remember every trivial incident in great detail.───他能把每件小事的細節都記得很清楚。

19 、Doesn't it get to you that your colleague complains about trivial things?───你不知道你同事抱怨瑣碎的事嗎??

20 、Loaning someone money is not a trivial matter.───借給 別人 錢(qián) 不 是 一 件 雞毛蒜皮 的 小事。

21 、Why do you fritter your time and thought away on trivial things?───你為何將時(shí)間和心思都耗費在瑣碎的小事上。

22 、The only movement he could achieve was a trivial flutter of the left eyelid.───他能做出的惟一的·動(dòng)作只是左眼瞼微微的一顫。

23 、Once again, the trivial necessary condition is, in fact, sufficient.───事實(shí)上，這個(gè)平凡的必要條件也是充分的。

24 、You really shouldn't prattle on about something so trivial.───別為了一點(diǎn)小事就叨嘮。

25 、Do not waste your time on these trivial things.───不要把你的時(shí)間浪費在這些瑣事上。

26 、To talk rapidly, incessantly, and on trivial subjects;jabber.───不停地談急快地、不停地談?wù)摤嵤拢?/p>

27 、The servlet code is quite trivial.───servlet代碼相當簡(jiǎn)單。

28 、They often argue over trivial matters.───他們經(jīng)常為小事?tīng)幊场?/p>

29 、Don't be angry over such trivial matters.───別為這些瑣事生氣。

30 、It is useless to fire away with such trivial details.───喋喋不休地談這些瑣碎細節是沒(méi)有用的。

31 、A trivial name differs from a systematic name in that ti tells little or nothing about structure.───化學(xué)物質(zhì)的俗名與分類(lèi)名稱(chēng)的不同之處在于俗名對其結構幾乎沒(méi)有或根本沒(méi)有提示。

32 、It's useless to fire away with such trivial details.───喋喋不休地談這些瑣碎的細節是無(wú)用的。

33 、Let's stop discussing the trivial details and get to the point.───咱們別再談瑣碎細節了,說(shuō)正事吧。

34 、Viewed in perspective, the quarrel seemed to have been very trivial.───從長(cháng)遠的觀(guān)點(diǎn)來(lái)看，這次爭吵似乎是小事一樁。

35 、Why do you always make a fuss over a trivial things?───只是點(diǎn)風(fēng)吹草動(dòng)，你怎么就大做文章?

36 、Check it out! It's called trivial pursuit.─── 快看 這個(gè)叫做"追根究底"

37 、You must not sing small about such a trivial thing.───你不必為了這一點(diǎn)小事而垂頭喪氣。

38 、Minute, trivial, unnecessary, and unjustified criticism or faultfinding.───吹毛求疵瑣碎的微不足道的，不必要的且不公平的指責或挑剔

39 、For what does it profit us to dwell on trivial matters?───因為心煩瑣碎小事于我們有何益處呢?

40 、It is a trivial matter and not worth fighting about .───區區小事不值得爭吵。

41 、Marked by a disposition to find and point out trivial faults.───吹毛求疵的傾向于找出并指出細小錯誤的

42 、He jogged on about trivial issues during the meeting.───會(huì )議期間，他漫談了那些瑣碎的事件。

43 、One who does menial or trivial work; a drudge.───作粗重工作的人一個(gè)做體力勞動(dòng)或不重要工作的人；干重活的人

44 、To find fault constantly and trivially; carp.───吹毛求疵，找碴常在細枝末節處找錯誤

45 、The others came back; the bare, familiar, trivial opera began again.───其他的人回來(lái)了，那索然無(wú)味，司空見(jiàn)慣，輕浮庸俗的歌劇重新開(kāi)始了。

46 、It's not trivial. It's a triumph of will.─── 不是微不足道 那是意志的勝利

47 、The logic becomes trivial when you put regular expressions into action.───使用正則表達式,邏輯就變得簡(jiǎn)單了。

48 、A trivial issue was brought to their attention.───一個(gè)不重要的問(wèn)題引起了他們的注意。

49 、Let's stop discussing trivial details and come/get to the point.───咱們別再談瑣碎細節了, 說(shuō)正事吧.

50 、They often fall out over trivial matters.───他們常因小事?tīng)幊场?/p>

51 、May be sulking or other trivial things were the triggers.───也許只是賭氣，也許只是因為小小的事。

52 、Why do you get angry over such trivial matters?───你何必為這種瑣事生氣?

53 、The distractions are trivial in comparison to your work.─── 這些干擾和你們的工作相比不值一提

54 、Is it worthwhile committing suicide due to such a trivial setback?───為這點(diǎn)挫折，犯得上尋死嗎?

55 、Too small or unimportant to merit attention or consideration; trivial.───不值得考慮的因太小或不重要而不值得重視或考慮的；瑣碎的

56 、His article is loaded down with trivial details.───他的文章寫(xiě)得很煩瑣。

57 、He became interested in the idea he terned(termed )"vital few and trivial many.───他開(kāi)始對他稱(chēng)為“重要的少數與瑣碎的多數原理”感興趣。

58 、She'd never leave me over anything that trivial.─── 她不會(huì )因為這么無(wú)聊的事離開(kāi)我的

59 、He often dissipated his energies in trivial matters.───他常在無(wú)關(guān)緊要的小事上浪費精力。

60 、To engage in a disagreeable argument, usually over a trivial matter; wrangle.───爭吵卷入一場(chǎng)不愉快的爭吵,通常由瑣事引起;口角。

61 、Only this trivial thing discouraged me from an entire victory.───只是這件小事使我不能取得完全勝利。

62 、Even trivial things can set Arthur and his wife at loggerheads.───即使是雞毛蒜皮的小事也能使阿瑟和他妻子吵起來(lái)。

63 、To see or make trivial distinctions; quibble.───發(fā)現或找出細微的差距

64 、Don't get impatient about trivial thing like that.───不要為那種瑣事煩躁。

65 、Don't get bogged down in trivial matters.───不要只顧鼻子底下的小事。

66 、His boss will jump on every little mistake he makes, no matter how trivial.───哪怕是出了再小的差錯，老板也會(huì )對他橫加斥責。

67 、They are locked together in a fierce quarrel over a trivial matter.───他們?yōu)榱艘稽c(diǎn)小事而吵得難分難解。

68 、He will jump on every little mistake you make, no matter how trivial.───他對你的每一點(diǎn)差錯都要斥責一番, 不管是什么雞毛蒜皮的事。

69 、Something unsubstantial or trivial.───不重要或無(wú)價(jià)值的事

70 、Don't work yourself up/get worked up about something so trivial.───不要為這點(diǎn)小事大動(dòng)肝火。

71 、Cool off, okay? Stop quarreling over the trivial matter.───冷靜好嗎?停止在瑣碎的事情上爭吵。

72 、He is liable to flare up at trivial things.───他愛(ài)為小事發(fā)作。

73 、I don't care about such trivial things.─── 我可不在乎這些不重要的東西

74 、Don't allow trivial things to crowd out the important things.───不要讓瑣碎的事情擠掉重要的事。

75 、He is a very trivial person.───他是個(gè)非常淺薄輕浮的人。

76 、To talk rapidly, incessantly, and on trivial subjects; jabber.───不停地談急快地、不停地談?wù)摤嵤?；急促含糊地說(shuō)

77 、Of little importance;trivial.───不重要的;微不足道的

78 、Of little importance; trivial.───不重要的；微不足道的

79 、Don't spend your time on these trivial things.───不要把妳的時(shí)間浪費在這些瑣事上。

80 、Don't waste your time exchanging words with him over such trivial matters.───不要為了這種小事情浪費時(shí)間跟他爭論。

81 、for something as trivial as this trade dispute.─── 對解決貿易糾紛的談判不太相干

82 、Don't pester me with your trivial matters.───別拿你那些雞毛蒜皮的事同我糾纏。

83 、It' s a trivial matter and not worth fighting about.───區區小事不值得爭吵.

84 、There were only a few trivial details that needed to be reviewed.───只有一些次要的細節還需審查一下。

85 、A trivial thing may sometimes bring about undesirable consequences.───一個(gè)微不足道的事物有時(shí)也會(huì )引起人們不愿意見(jiàn)到的后果。

86 、They always spar over trivial matters.───他們總是為一些小事而爭吵。

87 、Only small and fairly trivial adjustments to code would be required.───只需要對代碼進(jìn)行微不足道的更改。

88 、Don't take such trivial matters to heart.───別把這些稀松的事放在心里。

89 、He often comes to loggerheads with his wife about the most trivial matters.───他經(jīng)常為一些雞毛蒜皮的事和他妻子吵架。

90 、Cool down; there's no need to lose your temper over such a trivial matter.───冷靜些，沒(méi)有必要為如此區區小事而大動(dòng)肝火。

PLC 故障 英文文獻

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PLC 故障 英文文獻

PLC-based Implementation of Process Observation and Fault Detection for

Discrete Event Systems

Tord Alenljung, Markus Sköldstam, Bengt Lennartson and Knut Åkesson

Automation Group

Department of Signals and Systems

Chalmers University of Technology

torda@chalmers.se, markus.skoldstam@chalmers.se, bengt.lennartson@chalmers.se, knut@chalmers.se

Abstract—This paper demonstrates how PLC-code for process

observation can be automatically generated from a discrete

event process model expressed as either PLC-code or as

extended finite automata (EFA). The generated code will also

detect faults due to unexplainable sensor signal changes.

Extended finite automata are automata augmented with

variables and transition conditions. These features make EFA

suitable for modeling systems that interact with a PLC through

binary signals. In order for the generated observer code to

work, the EFA model must fulfill some requirements concerning

determinism and observability. These requirements are here

formalized.

Using the PLC-languages of the IEC 61131 standard for

process modeling narrows the gap between the pragmatic

industry and the formal academia. The cyclic execution model

of a PLC is here replaced by execution at stochastic intervals.

Index Terms—fault detection, process observation, programmable

logic controllers, PLC, discrete event systems,

modeling, automata, extended finite automata

I. INTRODUCTION

There is a need for an improved development process

for Programmable Logic Controller (PLC) programs within

industry, both considering the quality and efficiency of the

resulting control programs as well as the efficiency of the

development process. PLC programs are typically written

using one of the languages in the IEC 61131 standard [1].

The code is most often developed and validated manually in

an ad hoc manner.

Given a formal model of the process/plant/environment

that the PLC interacts with, we can apply a number of

methods that might contribute to this improvement that are

not yet widely applied within industry, for example synthesis

of control code based on the methods of Supervisory Control

Theory (SCT) [2], formal verification/model checking [3],

model driven development of code for process observation

and fault detection etc. This paper deals with the latter.

By process observation we mean the tracking and estimation

of the state of the environment. Process observation

is necessary in case the current value of the sensor signals

do not reveal enough about the internal state of the process.

The PLC-code used for process observation is today in most

cases manually written and tightly coupled with the rest of

the control code.

It is beneficial to detect faults as early as possible. Today,

fault detecting code is in most cases manually written and

covers only the most frequent or severe faults. Typical faults

are unexplainable sensor signal changes and unexpectedly

long process response times.

By diagnosis of discrete event systems we mean finding

out what has gone wrong, often based on a possibly

nondeterministic model with explicitly defined (possibly

unobservable) failure states or events. Most work around

observers and diagnosis for discrete event systems is based

on the observability of events and the concept of languages

or finite state automata, for example [4], [5] or [6]. This

event-driven and asynchronous approach stand in contrast to

the synchronous signal-based execution of PLCs. This gap

cannot trivially be bridged, see [7]. A state-based diagnosis

approach built on Moore automata is presented in [8].

An alternative to explicitly defined fault states or events

is to consider deviations from the model as faults, i.e. the

model describes only the normal behavior. In this case,

we are satisfied if faults are detected and let a human do

the diagnosis. Several approaches to this theme have been

published. Timed automata are used in [9] for modeling

systems to be used for fault detection. Holloway and Krogh

[10] presents a component/actor based approach for both

fault detection and diagnosis, while Petri nets are used by

[11].

Common for most work concerning observation and fault

detection/diagnosis is that implementation details are not

discussed. In addition, the process modeling used is targeted

towards fault handling only, and do not consider other uses

of the model, such as verification or synthesis.

This paper presents a process modeling approach that

enables code generation for process observation and fault

detection. The modeling language used, extended finite automata

(EFA) [12] are automata augmented with variables,

transition guards and actions. The synthesis and verification

tool Supremica [13], [14] supports EFA. This way, the same

process model can be used for both code generation as

for dynamic analysis. For verification and synthesis, the

benefits of having a model of the process includes a possible

reduction of the state space and the possibility to specify

requirements on the whole closed loop system instead of

only the open loop controller.

An algorithm for generating PLC-code for process observation

and fault detection is presented. It detects unexpected

sensor signal changes by checking for deviations from the

model. The model must be detailed enough for the generated

code to work. These requirements are formalized. The notion

of observability of EFA variables is introduced.

As an alternative to EFA, this paper also shows how

the PLC-languages of IEC 61131 can be used for process

Proceedings of the 3rd Annual

IEEE Conference on Automation Science and Engineering

Scottsdale, AZ, USA, Sept 22-25, 2007

SuRP-B01.5

1-4244-1154-8/07/$25.00 ©2007 IEEE. 207

Authorized licensed use limited to: IEEE Xplore. Downloaded on March 28, 2009 at 23:36 from IEEE Xplore. Restrictions appl

modeling. This may hopefully speed up the acceptance of

process modeling within industry. A PLC-coded process

model is considered to be executed at stochastic intervals

rather than continuously as a PLC. It is demonstrated how

PLC-code is compiled into a neutral form that can be used

for process observer code generation or dynamic analysis.

II. PRELIMINARIES

A manufacturing system can typically be seen as a closed

loop system where a controller affects the environment

through control signals U and collects information though

sensor signals Y . In this paper the controller is a PLC and

the signals are binary. The process can typically be divided

into a number of subprocesses (active objects), e.g. robot,

workpiece, fixture etc.

The IEC 61131 language Structured Text (ST) is used

throughout this paper, both as the target language as well as

for modeling. Extending the PLC-coded process modeling to

other languages can probably be handled without any greater

effort.

III. EXTENDED FINITE AUTOMATA

An Extended Finite Automaton (EFA) is an augmentation

of the ordinary automaton with guard formulas and action

functions. We associate the guards and actions to the transitions

in the automaton. The guard and the actions forms

the pre- and postconditions of the transition, while the event

label states the synchronization condition.

Let us se an example of process modeling with EFAs.

Consider the system in Fig. 1, which consists of a lift that

should be used for sorting balls. When a ball has arrived then

the program should send the ball to the first or the second

floor by setting the control signals qToMiddle or qToUp to 1.

Sensor signal iBallInLift indicates the presence of a ball

in the lift, and qMiddleOut and qUpOut push the balls out

from the lift.

iLiftUp

iLiftMiddle

iLiftDown

qToUp

qToMiddle

iBallInLift

qUpOut

qMiddleOut

Fig. 1. Ball sorting example

The EFA-model of the lift is shown in Fig. 2. Here, each

state represents a discrete position of the lift in Fig. 1.

The guards and actions give the condition under which a

movement occurs.

q0

q1

q2

q3

q4

qToMiddle OR qToUp

iLiftDown := 0

qToMiddle OR qToUp

iLiftMiddle := 1

qToUp AND NOT iLiftMiddle’

qToUp AND iLiftUp’

NOT qToUp AND

NOT iLiftUp’

NOT qToUp AND iLiftMiddle’

NOT (qToMiddle OR qToUp)

iLiftMiddle := 0

NOT (qToMiddle OR qToUp)

iLiftDown := 1

Fig. 2. An extended finite automaton that models the uncontrolled behavior

of the lift in Fig. 1. All transitions are labeled with an unobservable event

"1. The use of actions (lower half) is semantically equivalent to using

postcondition in the guard (upper half). By iLiftUp’ we denote the posttransition

value of iLiftUp

The following EFA-definition differs slightly from the

definition in [12] due to the addition of post-conditions and

observability of variables.

Definition 1 (Extended Automaton):

An extended finite-state automaton E is a tuple E = hQ ×

V,X,,→, (q0, v0)i, where:

(i) Q × V is the extended finite set of states, where Q is

a set of locations (ordinary states) and V is the set of

possible variable value combinations;

(ii) X is the set of variables, each variable x ∈ X having a

domain of definition Vx, which gives the set of possible

value combinations V = Vx1 × . . . × Vxn;

(iii)  is a nonempty finite set of events (the alphabet);

(iv) →⊆ Q××G×A×Q is the state transition relation.

G denotes the set of all possible guard predicates and

A is the set of all possible action functions.

(v) (q0, v0) ∈ Q × V is the initial state. 

A. Variables

By V we denote the domain of definition of the variable

tuple, i.e. V = Vx1 × . . . × Vxn, and by V the domain

of definition including the don’t care value , i.e. V =

(Vx1 ∪ {}) × . . . × (Vxn ∪ {}). A specific variable value

is denoted v = (vx1 , . . . , vxn). Used in conjunction with

a transition, v denotes the pre-transition value, and v′ the

post-transition value, i.e. the value of the variables before

and after the transition respectively.

When including  in the definition domain, we need an

alternative definition of equality between variable values, -

equality:

Definition 2 (-equality): Two values v and w are said to

be -equal, denoted v = w if (v = w)∨(v = )∨(w = ).

Two variable tuples v and w, each with n elements, are -

equal if vi = wi for every i ∈ {1 . . . n}. 

B. Guard

A guard g ∈ G is a predicate over the variables that relate

each pair of pre- and post-transition variable values (v, v′) ∈

V × V, to either 1 (true) or 0 (false). We denote a guard

by g = g(v, v′).

By G = {W | W ∈ 2V × 2V} we denote the set of

all possible guard predicates. 2V denotes the power set of

V and W denotes the characteristic function of a set W,

defined by

W(v) =  1 if v ∈ W

0 if v /∈ W.

C. Action

An action a ∈ A, where A = V → V denotes the

set of all possible action functions, is a convenient way of

expressing a postcondition. It is a function from the pretransition

values to the post-transition values: v′ = a(v).

Since an action is a postcondition, and postconditions

can be expressed as a guard, the action feature is in fact

superfluous. Assume that we have a guard g and actions a.

By replacing g with g∧(v′ = a), the action can be removed.

It might be tempting to interpret the action as being an

effect of the transition, but the causality (cause and effect)

of an EFA is not defined. It depends on the application.

An example of how postconditions can be express