Transient errors

The total response of the system is always the sum of the transient and steady-state eomponents. Figure 3.1 shows the transient and steady-state periods of time response. Differenees between the input funetion X[ t) (in this ease a ramp funetion) and system response Xo t) are ealled transient errors during the transient period, and steady-state errors during the steady-state period. One of the major objeetives of eontrol system design is to minimize these errors. 

In practice, there will always be transient errors, but the transient period should be kept as small as possible. It is usually possible to design the controller so that steady-state errors are minimized, or ideally, eliminated. 

In discrete analyzers, a batch sample is taken at selected intervals and then analyzed, with the information being fed to the controller and operator in the usual fashion. Obviously, the samphng and analytical dead times are increased over continuous analyzers, and the manipulated variable is held at a fixed value between measurements. If a transient error occurs between measurements, it may not be detected and corrected for. On the other hand, a short transient error may be detected during the measurement interval and a correction for this applied during the entire interval between measurements. 

The literature also presents other approaches, such as the one proposed in Nieu-wland (2006), where the critical path of combinational circuits is hardened through the duplication of gates and transient errors are masked due to the extra capacitance available in the node. It is also very common to find processors partially hardened, where only the most critical registers are replicated, such as the PC and the SP. 

CHEYNET, R NICOLESCU, B. VELAZCO, R. REBAUDENGO, M. REORDA, S. VIOLANTE, M. Experimentally evaluating an automatic approach for generating safety-critical software with respect to transient errors. IEEE Transactions On Nuclear Science, [S.l.] IEEE Nuclear and Plasma Sciences Society, 2000, v. 47, n. 6 (part 3X pp. 2231-2236. 

As more fresh water is added, more fresh MEA is added due to the ratio. The MF.A concentration of the stripper bottoms (xB) drops slightly, but the MEA concentration controller adjusts the ratio of fresh MEA to fresh water and drives the concentration close to its specification of 15.2 mol% MEA. Stripper vapor product and reflux both increase as expected with increasing feed. The stripper temperature controller shows a peak transient error of about 3 K. 

Changes in the absolute pressure of the system alter not only the boiling point of the liquor, but the flashing temperature of the condensate in the condensing chamber as well. Unfortunately, the latter effect occurs much more rapidly than the former, resulting in transient errors which may take a long time to resolve. It is therefore critical that absolute pressure be closely controlled if temperature difference is to be a successful measure of product concentration. 

If 4> is calculated at a high frequency, for example by the use of on-stream analyser measurements, then care must be taken to ensure that the process is at steady state. Because the dynamics of the analyser will be longer than those of the inferential, any change in the inferential will be reflected some time later in the analyser measurement. There will therefore appear to be a transient error, even if both the inferential and analyser are accurate. Alternatively, dynamic compensation can be applied. We cover this later in this chapter. 

Memik, G., Kandemir, M.T., Ozturk, O. Increasing register file immunity to transient errors. In Design, Automation and Test in Europe (DATE), pp. 586 591 (2005)... 

Even very stiff torsion bars must twist slightly to record the torque. With high viscosity polymer melts, this small twist can lead to significant errors in the strain or transient strain rate imposed on a sample (Gottlieb and Macosko, 1982). For example, consider stress relaxation after a step strain of 100% on a polymer melt with Go = 10 Pa (see Figure 3.3.6). Using a 0.1 rad, 25 mm diameter cone, to achieve a strain of 100% requires an initial torque of 0.4 N-m. However, if the transducer stiffness is 10 N-m/rad then it will twist 0.04 rad, and the true strain in the sample will only be 60%. There are also transient errors, For very viscous samples, the parameter C in eq. 8.2.1 dominates the damping of the transducer, and it can be used to estimate the time constant of the error ... 

Where there is no diverent operation to realize, the process is always performed twice to detect transient errors and code violations during each cycle. 

Software-implemented fault tolerance is the most common TMR technique in use. This method involves three processors that nm asynchronously. This guards against transient errors. Each processor waits for the other two to cast their vote at certain points in the program cycle (at least once per input/output scan). The processors vote about ... 

A kinetics text with a strong theoreticai bent that overviews transient kinetic methods and discusses data anaiysis issues such as error propagation and sensitivity anaiysis. 

Variations in a produet s material properties, serviee loads, environment and use typieally lead to random failures over the most protraeted period of the produet s expeeted life-eyele. During the eonditions of use, environmental and serviee variations give rise to temporary overloads or transients eausing failures, although some failures are also eaused by human related events sueh as installation and operation errors rather than by any intrinsie property of the produet s eomponents (Klit et al., 1993). Variability, therefore, is also the souree of unreliability in a produet (Carter, 1997). However, it is evident that if produet reliability is determined during the design proeess, subsequent manufaeturing, assembly and delivery of the system will eertainly not improve upon this inherent reliability level (Kapur and Lamberson, 1977). 

Transient torques Gears with indexing or positioning errors. 

The first term in equation (3.39) represents the input quantity, the seeond is the steady-state error and the third is the transient eomponent. When time t is expressed as a ratio of time eonstant T, then Table 3.3 and Figure 3.15 ean be eonstrueted. In Figure 3.15 the distanee along the time axis between the input and output, in the steady-state, is the time eonstant. 

Thus, when r t) and f2(f) are unehanging, or have step ehanges, there are no steady-state errors as ean be seen in Figure 4.25. The seeond-order dynamies of the elosed-loop system depend upon the values of T[, T, K and K. Again, a high value of K will provide a fast transient response sinee it inereases the undamped natural frequeney, but with higher order plant transfer funetions ean give rise to instability. 

The root locus method provides a very powerful tool for control system design. The objective is to shape the loci so that closed-loop poles can be placed in the. v-plane at positions that produce a transient response that meets a given performance specification. It should be noted that a root locus diagram does not provide information relating to steady-state response, so that steady-state errors may go undetected, unless checked by other means, i.e. time response. 

Compatibility with Personnel Expectations Compatibility refers to the degree of similarity between the direction of physical movement of a control or an instrument indicator and the worker s expectations. Many errors are due to the fact that the operation of the controls or the layout of the displays is incompatible with population stereotypes. For instance, on a control panel it is customary to increase the value of a parameter by turning the appropriate switch clockwise and reduce its value by turning it coimterclockwise. (Note that this stereotype is the opposite for controls which control flow directly, e.g., valves.) If such a stereotype is violated, errors may occur. Although such errors may be recoverable in the short run, under the stress of a process transient they may lead to serious consequences. 

Process transients and equipment failures may require workers to develop a new strategy to control the process. Detection, diagnosis, and fault-compensation are tasks in which workers may have little experience and the information needs may be different from those of familiar tasks. Again, methods of task and error analyses, particularly those concerned with human cognitive functions, may be useful in deciding what information should be displayed to help workers detect process transients, diagnose their causes and develop new strategies. 

In April 1982, a data workshop was held to evaluate, discuss, and critique data in order to establish a consensus generic data set for the USNRC-RES National Reliability Evaluation Program (NREP). The data set contains component failure rates and probability estimates for loss of coolant accidents, transients, loss of offsite power events, and human errors that could be applied consistently across the nuclear power industry as screening values for initial identification of dominant accident sequences in PRAs. This data set was used in the development of guidance documents for the performance of PRAs. 

FIGURE 11.2 Paired experimental data. Values of constitutive calcitonin receptor activity [1 -(Tr/Tj) units] in transiently transfected melanophores. Five separate experiments are shown. Points to the left indicate the basal level of constitutive activity before (filled circles) and after (open circles) addition of 100 nM AC512 (calcitonin receptor inverse agonist). Lines join values for each individual experiment. Points to the right are the mean values for constitutive activity in control (filled circles) and after AC512 (open circles) for all five experiments (bars represent standard errors of the mean). Data shown in Table 11.3. 

FIGURE 11.3 One-way ANOVA (analysis of variance). One-way analysis of variance of basal rates of metabolism in melanophores (as measured by spontaneous dispersion of pigment due to G,.-protein activation) for four experiments. Cells were transiently transfected with cDNA for human calcitonin receptor (8 j-ig/ml) on four separate occasions to induce constitutive receptor activity. The means of the four basal readings for the cells for each experiment (see Table 11.4) are shown in the histogram (with standard errors). The one-way analysis of variance is used to determine whether there is a significant effect of test occasion (any one of the four experiments is different with respect to level of constitutive activity). 

Plotting the errors for all individual data points (Figure 56) for the different calibration runs it is clear that largest errors are associated with periods of transient heat flux. Moreover, errors during the period with heat extraction (1—40 h and 1-80 h), increase with time. 

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