Real-Time Systems. Design Principles for Distributed Embedded Applications. Herman Kopetz. Second Edition (811374), страница 36
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1.9 are measured by the two controller nodes and sent to the man–machine interface (MMI) node for verifying the following alarm condition:whenðp1 <p2 Þthen everything okelse raise pressure alarm;The rolling mill is characterized by the following parameters: maximumpressure between the rolls of a stand ¼ 1,000 kp cm2 [kp is kilopond],absolute pressure measurement error in the value domain ¼ 5 kp cm2, maximum rate of change of the pressure ¼ 200 kp cm2 s1. It is required that theerror due to the imprecision of the points in time when the pressures aremeasured at the different rolls should be of the same order of magnitude as the1104 Real-Time Modelmeasurement error in the value domain, i.e., 0.5% of the full range. Thepressures must be continuously monitored, and the first alarm must be raisedby the alarm monitor within 200 ms (at the latest) after a process has possiblyleft the normal operating range.
A second alarm must be raised within 200 msafter the process has definitely entered the alarm zone.1. Assume an event-triggered architecture. Each node contains a local realtime clock, but no global time is available. The minimum time dmin for thetransport of a single message by the communication system is 1 ms. Derivethe temporal control signals for the three tasks.2. Assume a time-triggered architecture. The clocks are synchronized with aprecision of 10 ms. The time-triggered communication system is characterized by a TDMA round of 10 ms. The time for the transport of a singlemessage by the communication system is 1 ms. Derive the temporalcontrol signals for the three time-triggered tasks.3.
Compare the solutions of 4.16.(a) and 4.16.(b) with respect to the generated computational load and the load on the communication system. Howsensitive are the solutions if the parameters, e.g., the jitter of the communication system or the duration of the TDMA round, are changed?Chapter 5Temporal RelationsOverview The behavior of a real-time cluster must be based on timely informationabout the state of its physical environment and the state of other cooperatingclusters. Real-time data is temporally accurate for a limited real-time intervalonly.
If real-time data is used outside this application specific time interval, thesystem will fail. It is the objective of this chapter to investigate the temporalrelations among state variables in the different parts of a cyber-physical system.In this chapter, the notions of a real-time (RT) entity, a real-time (RT) image, anda real-time (RT) object are introduced and the concept of temporal validity of an RTimage is established. The temporal validity of the RT image can be extended bystate estimation. A real-time clock is associated with every RT object. The object’sclock provides periodic temporal control signals for the execution of the objectprocedures, particularly for state estimation purposes.
The granularity of the RTobject’s clock is aligned with the dynamics of the RT entity in the controlled objectthat is associated with the RT object. The notions of parametric and phase-sensitiveobservations of RT entities are introduced, and the concept of permanence of anobservation is discussed. The duration of the action delay, which is the time intervalbetween the transmission of a message and the instant when this message becomespermanent, is estimated.The final section of this chapter is devoted to an elaboration of the concept ofdeterminism. Determinism is a desired property of a computation that is needed iffault-tolerance is to be achieved by the replication of components. Determinism isalso helpful for testing and for understanding the operation of a system. A set ofreplicated RT objects is replica determinate if the objects visit the same state atapproximately the same future point in time.
The main causes for a loss ofdeterminism are failures that the fault-tolerance mechanisms are intended to maskand non-deterministic design constructs which must be avoided in the design ofdeterministic systems.H. Kopetz, Real-Time Systems: Design Principles for Distributed Embedded Applications,Real-Time Systems Series, DOI 10.1007/978-1-4419-8237-7_5,# Springer Science+Business Media, LLC 20111111125.15 Temporal RelationsReal-Time EntitiesA real-time (RT ) entity is a state variable of relevance for the given purpose. It islocated either in the environment of the computer system or in the computer systemitself. Examples of RT entities are the flow of a liquid in a pipe, the setpoint of a controlloop that is selected by the operator, or the intended position of a control valve.
AnRT entity has static attributes that do not change during the lifetime of the RT entity,and dynamic attributes that change with the progression of real-time. Examples ofstatic attributes are the name, the type, the value domain, and the maximum rate ofchange. The value set at a particular instant is the most important dynamic attribute.Another example of a dynamic attribute is the rate of change at a chosen instant.5.1.1Sphere of ControlEvery RT entity is in the sphere of control (SOC) of a subsystem that has theauthority to set the value of the RT entity [Dav79].
Outside its SOC, the RT entitycan only be observed, but the semantic content of the RT entity cannot be modified.At the chosen level of abstraction, syntactic transformations of the representation ofthe value of an RT entity that do not change its semantic content (see Sect. 2.2.4) aredisregarded.Example: Figure 5.1 shows another view of Fig. 1.8 and represents the small controlsystem that controls the flow of a liquid in a pipe according to a setpoint selected by theoperator.
In this example, there are three RT entities involved: the flow in the pipe is inthe SOC of the controlled object, the setpoint for the flow is in the SOC of the operator, andthe intended position of the control valve is in the SOC of the computer system.5.1.2Discrete and Continuous Real-Time EntitiesAn RT entity can have a discrete value set (discrete RT entity) or a continuousvalue set (continuous RT entity). If the timeline proceeds from left to right, then theBdistributed computerRT LANoperatorRT entityRT imageRT objectFig. 5.1 RT entities, RT images, and RT objectscontrolled objectACA: measured value of flowB: setpoint for flowC: intended valve position5.2 Observations113Fig.
5.2 Discrete RT entitystate10LLRRreal-timeobservationsvalue set of a discrete RT entity is constant during an interval that starts with a leftevent (L_event) and ends with a right event (R_event) – see Fig. 5.2.In the interval between an R_event and the next L_event, the set of values of adiscrete RT entity is undefined. In contrast, the set of values of a continuous RTentity is always defined.Example: Consider a garage door. Between the defined states specified by door closed anddoor open, there are many intermediate states that can be classified neither as door open noras door closed.5.2ObservationsThe information about the state of an RT entity at a particular instant is captured bythe notion of an observation. An observation is an atomic data structureObservation ¼ <Name; tobs ; Value>consisting of the name of the RT entity, the instant when the observation was made(tobs), and the observed value of the RT entity.
A continuous RT entity can be observedat any instant while the observation of a discrete RT entity gives a meaningful valueonly in the interval between a L_event and an R_event (see Fig. 5.2).We assume that an intelligent sensor node is associated with a physical sensor tocapture the physical signal, to generate the timestamp, and to transform the physicalsignal to meaningful digital technical units. An observation should be transported ina single message from this sensor node to the rest of the system because themessage concept provides for the needed atomicity of an observation message.5.2.1Untimed ObservationIn a distributed system without global time, a timestamp can only be interpretedwithin the scope of the node that created the timestamp. The timestamp of a senderthat made an observation is thus meaningless at the receiver of the observationmessage if no global time is available.
Instead, the time of arrival of an untimedobservation message at the receiver node is often taken to be the time of observationtobs. This timestamp is imprecise because of the delay and the jitter between the1145 Temporal Relationsinstant of observation and the arrival instant of the message at its destination. In asystem with a significant jitter of the execution time of the communication protocol(in comparison to the median execution time) and without access to a global timebase it is not possible to determine the instant of observation of an RT entityprecisely.
This imprecision of time measurement can reduce the quality of theobservation (see Fig. 1.6).5.2.2Indirect ObservationIn some situations, it is not possible to observe the value of an RT entity directly.Consider, for example, the measurement of the internal temperature within a slab ofsteel. This internal temperature (the value of the RT entity) must be measuredindirectly.The three temperature sensors T1, T2, and T3 measure the change of temperatureof the surface (Fig. 5.3) over a period of time. The value of the temperature T withinthe slab and the instant of its relevance must be inferred from these surfacemeasurements by using a mathematical model of heat transfer.5.2.3State ObservationAn observation is a state observation if the value of the observation contains thestate of the RT entity.
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