Process 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... 

The process transfer curve indicates the power-temperature characteristic of the actuai system, i.e., the extruder and its surroundings. This curve indicates how much power is required to maintain a certain temperature level on the machine. The higher the temperature ievei that needs to be maintained, the more power will be required. For most machines, the reiationship between temperature and power requirement wiii be approximateiy iinear. The power requirement is determined by the heat iosses in the system by conduction, convection, and radiation. By improving the thermai insuiation of the extruder, the heat losses can be reduced. This will directly affect the process transfer curve adding insulation will reduce the power requirements at a certain temperature, resulting in a reduced slope of the process transfer curve. Obviously, this will also improve the energy efficiency of the entire process. 

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. 

Process reaction curve This can be obtained from the forward-path transfer function... 

From Problem 7.17, the open-loop transfer function for generation of the process reaction curve is given by ... 

These data can be converted into frequency-response curves, basically by difTerentiating both input and output curves in the frequency domain. The process transfer function G(jj is... 

Figure 4. Schematic of the potential energy curves of the relevant electronic states The pump pulse prepares a coherent superposition of vibrational states in the electronic A 1 EJ state at the inner turning point. Around v = 13 this state is spin-orbit coupled with the dark b 3n state, causing perturbations. A two-photon probe process transfers the wavepacket motion into the ionization continuum via the (2) llg state [7].

The increase in the rate of recombination upon illumination in the CC14 absorption band is due to the CCl photoionization with an electron being transferred to a continuous spectrum and subsequently captured by an arbitrary MP+ particle. As seen from Fig. 16, in this case the process kinetics (curve 1) is described by the second-order equation... 

Several novel techniques for mass transfer enhancement reported in the literature have been discussed in detail. The present study is focused on the mass transfer enhancement in the rate-controlled separation processes using flow instabilities. There are a large number of examples about the success of flow instabilities produced by Dean vortices in improving the performance by increasing flux and reducing fouling in membrane separation processes. Several curved modules... 

A given process has unknown detailed dynamics that is, it exhibits overdamped open-loop behavior but its exact order and parameter values are poorly known. From the process reaction curve (see Section 16.5) we have approximated its transfer function by the following first-order system with dead time ... 

How can we identify the four process transfer functions In Example 4.13 we saw that a rigorous approach leads to an overwhelming mathematical model. The process reaction curve method, which was discussed in Section 16.5, is a simpler approach and yields the transfer functions between... 

Astrom and Hagglund s work (1984) has prompted research in several different directions. One of these directions, and the focus of Chapter 8, is in the area of process identification, where the objective is to obtain a more complete and accurate model of the process firom data generated under relay feedback. Fitting a more complete process model (i.e. a transfer function model) normally requires knowledge of several points on the process Nyquist curve. Given that the standard relay experiment combined with the DFA identification technique is able to identify only a single point, fitting such a model either requires the availability of some prior process information (e.g. Luyben, 1987) or requires the user to conduct a series of relay experiments in... 

Figure 6.6 illustrates what happens to the cost of the system as the relative position of the composite curves is changed over a range of values of AT ir,. When the curves just touch, there is no driving force for heat transfer at one point in the process, which would require an... 

The shaded areas in Fig. 6.24, known as pockets, represent areas of additional process-to-process heat transfer. Remember that the profile of the grand composite curve represents residual heating and cooling demands after recovering heat within the shifted temperature intervals in the problem table algorithm. In these pockets in Fig. 6.24, a local surplus of heat in the process is used at temperature differences in excess of AT ,in to satisfy a local deficit. ... 

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