Controller transfer curve

To understand the mechanism by which offset occurs with a proportional controller, one should look at the controller transfer curve and the process transfer curve at the same time, as in Fig. 4.28. 

Controller transfer curve and process transfer curve... 

Figure 4.28 shows the controller transfer curve (power input curve) superimposed on the process transfer curve (power loss curve). The point where the two curves intersect is the temperature where the input power to the heaters is in equilibrium with the power losses. If the point of intersection occurs above the setpoint, there will be a positive droop if it occurs below the setpoint, the droop will be negative. From Fig. 4.28 it is now clear how the offset can be eliminated without changing the width of the proportional band. This is done by shifting the entire proportional band to a higher or lower temperature. Figure 4.29 illustrates the effect of resetting the proportional band. 

Notice in Fig. 13.20 that the curve for the P controller does not approach 0 dB at low frequencies. This shows that there is a steadystate offset with a proportional controller. The curve for the PI controller does go to 0 dB at low frequencies because the integrator drives the closedloop servo transfer function to unity (i.e., no offset). 

Curve b in Figure 1 shows the uptake curve for the same kg as in curve a but with only the external film resistance controlling the heat transfer. Curve c shows the corresponding isothermal uptake. These curves clearly... 

X 10" cm s" at 323 K). The solid lines are the theoretical curves for isothermal diffusion from Eq. (6.4) with the appropriate value of D fr, The uptake curves for the small (7.3-/im) crystals show considerable deviation from the isothermal curves but conform well to the theoretical nonisothermal curves calculated from Eqs. (6.67) and (6.68) with the value of D estimated from the data for the large crystals, the value of p calculated from the equilibrium data, and the value of a iestimated using heat transfer parameters estimated from uptake rate measurements with a similar system under conditions of complete heal transfer control. The curve marked Eq. (6.6) is the limiting isothermal curve. (From ref. 20, with permission.)... 

Current potential diagram for a cathodic reaction under diffusion control, and with superimposed charge transfer control (dashed curve). 

FIG. 16-14 Constant separation factor batch adsorption curves for external mass-transfer control with an infinite fluid volume and n j = 0. 

Reactive control can alter the line length ( f LC) to the level at which the system will have the least possible swings. It is evident from these curves that an uncompensated line of a much shorter length may not be able, to transfer even its natural load (Pq) successfully. This is due to the steeply drooping characteristics of the voltage profile at about this load point, which may subject the... 

Engineering factors include (a) contaminant characteristics such as physical and chemical properties - concentration, particulate shape, size distribution, chemical reactivity, corrosivity, abrasiveness, and toxicity (b) gas stream characteristics such as volume flow rate, dust loading, temperature, pressure, humidity, composition, viscosity, density, reactivity, combustibility, corrosivity, and toxicity and (c) design and performance characteristics of the control system such as pressure drop, reliability, dependability, compliance with utility and maintenance requirements, and temperature limitations, as well as size, weight, and fractional efficiency curves for particulates and mass transfer or contaminant destruction capability for gases or vapors. 

As described above, metallic CNTs are of great interest because they possess molecular orbitals which are highly delocalised. However, metallic CNTs are very difficult to use in actual devices because they require very low temperatures to control their carrier transfer. On the contrary, even at room temperature, the nonlinear /-V jas curve and the effective gate voltage dependence have been presented by using individual semiconducting SWCNTs [29]. 

The region of immunity [Fig. 1.15 (bottom)] illustrates how corrosion may be controlled by lowering the potential of the metal, and this zone provides the thermodynamic explanation of the important practical method of cathodic protection (Section 11.1). In the case of iron in near-neutral solutions the potential E = —0-62 V for immunity corresponds approximately with the practical criterion adopted for cathodically protecting the metal in most environments, i.e. —0-52 to —0-62V (vs. S.H.E.). It should be observed, however, that the diagram provides no information on the rate of charge transfer (the current) required to depress the potential into the region of immunity, which is the same (< —0-62 V) at all values of pH below 9-8. Consideration of curve//for the Hj/HjO equilibrium shows that as the pH... 

Fig. 1.25 I) w. log / curves for a cathodic reaction (a) when the rate is solely controlled by transport and (b) when both transport and activated charge transfer are rate determining. (Derivations of the relationships are provided in Section 9.1)...

Over the years the original Evans diagrams have been modified by various workers who have replaced the linear E-I curves by curves that provide a more fundamental representation of the electrode kinetics of the anodic and cathodic processes constituting a corrosion reaction (see Fig. 1.26). This has been possible partly by the application of electrochemical theory and partly by the development of newer experimental techniques. Thus the cathodic curve is plotted so that it shows whether activation-controlled charge transfer (equation 1.70) or mass transfer (equation 1.74) is rate determining. In addition, the potentiostat (see Section 20.2) has provided... 

The simplest and most thoroughly studied solutions are those based on phosphoric acid at low temperatures (<35°C) which alone can fulfil all three requirements of acid solvent, film former (as metal phosphate) and diffusion agent by virtue of its viscosity. Thus copper and its main alloys of brasses and bronzes can be very effectively electropolished in 60-70% orthophos-phoric acid with the temperature maintained below 35°C under other conditions copper passivates or dissolves freely under mass transfer controlled conditions, but by varying the conditions appropriately polishing can be continued under mild agitation. An annotated polarisation curve is given in Fig. 11.7 readers are referred to recent studies for more detailed 2ispects " . 

Stern and Geary on the basis of a detailed analysis of the polarisation curves of the anodic and cathodic reactions involved in the corrosion of a metal, and on the assumption that both reactions were charge-transfer controlled (transport overpotential negligible) and that the /R drop involved in determining the potential was negligible, derived the expression... 

Where large samples of reactant are used and/or where C02 withdrawal is not rapid or complete, the rates of calcite decomposition can be controlled by the rate of heat transfer [748] or C02 removal [749], Draper [748] has shown that the shapes of a—time curves can be altered by varying the reactant geometry and supply of heat to the reactant mass. Under the conditions used, heat flow, rather than product escape, was identified as rate-limiting. Using large ( 100 g) samples, Hills [749] concluded that the reaction rate was controlled by both the diffusion of heat to the interface and C02 from it. The proposed models were consistent with independently measured values of the transport parameters [750—752] whether these results are transfenable to small samples is questionable. 

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