Process response curve

Many process response curves have an S-shaped form, as given in Fig. 2.19. 

If the process is first-order and a setpoint change is made, we can drive the output to the setpoint in one sampling period and hold its output right on the setpoint even between sampling periods. This is possible because we can change the slope of a first-order process response curve, as shown in Fig. 20.2b. 

The evaluation involves drawing a tangent to the initial process response curve at the point of maximum slope and noting the point where this tangent intercepts the final steady-state value. In this case, the process time constant is the time between the tangent intercepting the original and... 

It can be observed from the Figure 1 that the sensitivity of I.I. system is quite low at lower thicknesses and improves as the thicknesses increase. Further the sensitivity is low in case of as observed images compared to processed images. This can be attributed to the quantum fluctuations in the number of photons received and also to the electronic and screen noise. Integration of the images reduces this noise by a factor of N where N is the number of frames. Another observation of interest from the experiment was that if the orientation of the wires was horizontal there was a decrease in the observed sensitivity. It can be observed from the contrast response curves that the response for defect detection is better in magnified modes compared to normal mode of the II tube. Further, it can be observed that the vertical resolution is better compared to horizontal which is in line with prediction by the sensitivity curves. 

A critical component of the G-protein effector cascade is the hydrolysis of GTP by the activated a-subunit (GTPase). This provides not only a component of the amplification process of the G-protein cascade (63) but also serves to provide further measures of dmg efficacy. Additionally, the scheme of Figure 10 indicates that the coupling process also depends on the stoichiometry of receptors and G-proteins. A reduction in receptor number should diminish the efficacy of coupling and thus reduce dmg efficacy. This is seen in Figure 11, which indicates that the abiUty of the muscarinic dmg carbachol [51 -83-2] to inhibit cAMP formation and to stimulate inositol triphosphate, IP, formation yields different dose—response curves, and that after receptor removal by irreversible alkylation, carbachol becomes a partial agonist (68). 

Figure 4.34 shows the response to a unit step, or the process reaction curve. 

Describe and illustrate the process of setting a reference dose (RfD) using a schematic dose response curve. Correctly label the axis and all other important information. 

The operational model, as presented, shows dose-response curves with slopes of unity. This pertains specifically only to stimulus-response cascades where there is no cooperativity and the relationship between stimulus ([AR] complex) and overall response is controlled by a hyperbolic function with slope = 1. In practice, it is known that there are experimental dose-response curves with slopes that are not equal to unity and there is no a priori reason for there not to be cooperativity in the stimulus-response process. To accommodate the fitting of real data (with slopes not equal to unity) and the occurrence of stimulus-response cooperativity, a form of the operational model equation can be used with a variable slope (see Section 3.13.4) ... 

A potential pitfall with stop-time experiments comes with temporal instability of responses. When a steady-state sustained response is observed with time, then a linear portion of the production of reporter can be found (see Figure 5.15b). However, if there is desensitization or any other process that makes the temporal responsiveness of the system change the area under the curve will not assume the linear character seen with sustained equilibrium reactions. For example, Figure 5.16 shows a case where the production of cyclic AMP with time is transient. Under these circumstances, the area under the curve does not assume linearity. Moreover, if the desensitization is linked to the strength of signal (i.e., becomes more prominent at higher stimulations) the dose-response relationship may be lost. Figure 5.16 shows a stop-time reaction dose-response curve to a temporally stable system and a temporally unstable system where the desensitization is linked to the... 

The receptor occupancy curve can be converted to concentration-response curves by processing occupancy through the operational model for agonism (see Section 3.6). Under these circumstances, Equation 6.6 becomes... 

The shape of the so called master curve, however, depends strongly on the compound formulation and the type of contact surface in the friction process. Its detailed study gives an insight into the processes responsible for the frictional behavior. 

Dose-response assessment is the process of obtaining quantitative information about the probability of human illness following exposure to a hazard it is the translation of exposure into harm. Dose-response curves have been determined for some hazards. The curves show the relationship of dose exposure and the probabihty of a response. Since vahdated dose-response relationships are scarce, various other inputs are used to underpin the hazard characterization phase of risk assessment. 

The forms of actual tracer response curves may be used to formulate models of the actual mixing processes in the reactor. One has, however, to be careful since the tracer response curve does not give a unique solution. It does, for example, not allow one to distinguish between early and late mixing, which may be important when used in the estimation of conversion in a particular reactor-reaction system. 

As shown below, the influence of three quite distinct dynamic processes play a role in the overall measured oxygen concentration response curve. These are the processes of the dilution of nitrogen gas with air, the gas-liquid transfer, and the electrode response characteristic, respectively. Whether all of these processes need to be taken into account when calculating KLa can be seen by examining the mathematical model and making simulations. 

The processes of both seed formation and fibril extension are dependent on temperature and on peptide concentration, with 37°C being required for establishing equilibrium within 24 h with 30 pM Pi 4o- A full description of the assay system may be found elsewhere [97,117], A 4 h reaction time is typically within the linear portion of the time course. This nucleus-dependent assay detects mainly inhibitors that are substoichiometric with the monomeric peptide, which is present at high concentration. It is relatively insensitive to inhibitors that target the monomeric peptide. Whether the inhibitors interact with the growing end of a seed or with a low abundance conformational form of the p peptide that is competent to add to the seed is difficult to determine at this time. Similar dose-response curves are obtained for Congo Red as an inhibitor with either thioflavin T (ThT) fluorescence or filtration of radioiodinated peptide readouts (Fig. 4) Caveats in the interpretation of both the ThT and radiometric filtration assays for the evaluation of putative inhibitors are discussed elsewhere [97]. 

FIGURE 1.20 Hypothetical concentration-response curves to illustrate how the uptake) process can influence the study of the antagonism of noradrenaline by phentolamine. The two full lines show the response to noradrenaline, first in the absence and then in the presence of phentolamine. If the experiment is repeated, but with the uptake process blocked, the dotted lines would be obtained. Noradrenaline has become more active, and phentolamine now causes a greater shift (compare the lengths of the two horizontal arrows), as explained in the text. 

To make use of empirical tuning relations, one approach is to obtain the so-called process reaction curve. We disable the controller and introduce a step change to the actuator. We then measure the open-loop step response. This practice can simply be called an open-loop step test. Although we disconnect the controller in the schematic diagram (Fig. 6.1), we usually only need to turn the controller to the manual mode in reality. As shown in the block diagram, what we measure is a lumped response, representing the dynamics of the blocks Ga,... 

Empirical tuning with open-loop step test Measure open-loop step response, the so-called process reaction curve. Fit data to first order with dead-time function. 

Zimmerman and Briggs explain their dosage response curves on the basis of three independent pigment systems. However, for several reasons it appears more reasonable to ascribe their complicated patterns to different secondary rather than to distinct primary processes. First, the first and second positive curvatures show essentially the same action spectra (Fig. 3 4 and 5). Second, the Bunsen-Roscoe law holds only for the first 100 s of irradiation. After that time factors other than photochemical ones clearly govern phototropism. Third, the dosage response curves are not real kinetics, i.e. they do not represent continuous traces of bending in time, as the authors assume for their calculations. However, curvature was allowed to develop for 100 min in darkness, measured and plotted as a function of dosage. 

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