Multicapacity process

In this example, the steady state gain is unity, which is intuitively obvious. If we change the color of the inlet with a food dye, all the mixed tanks will have the same color eventually. In addition, the more tanks we have in a series, the longer we have to wait until the -th tank "sees" the changes that we have made in the first one. We say that the more tanks in the series, the more sluggish is the response of the overall process. Processes that are products of first order functions are also called multicapacity processes. 

It is frequently required to examine the combined performance of two or more processes in series, e.g. two systems or capacities, each described by a transfer function in the form of equations 7.19 or 7.26. Such multicapacity processes do not necessarily have to consist of more than one physical unit. Examples of the latter are a protected thermocouple junction where the time constant for heat transfer across the sheath material surrounding the junction is significant, or a distillation column in which each tray can be assumed to act as a separate capacity with respect to liquid flow and thermal energy. 

Let us now see how multicapacity processes result in second-order systems. We start with noninteracting capacities. 

How do you understand the interaction or noninteraction of several capacities in multicapacity processes Give the general set of two differential equations describing (a) two noninteracting capacities, and (b) two interacting capacities. 

N first-order processes in series (multicapacity processes)... 

Why do most of the opened loops have a sigmoidal response like that of Figure 16.8a The answer is rather clear using the analysis of Chapters 10 through 12. There we noticed that almost all physical processes encountered in a chemical plant are simple first-order or multicapacity processes whose response has the general overdamped shape of Figures 11.1a and 11.6. The oscillatory underdamped behavior is produced mainly by the presence of... 

Disks, for digital computer, 555-56 Distillation batch binary, 108 degrees of freedom, 87-88 difficulties in modeling, 77 ideal binary, 70-74 modeling, 70-74 as a multicapacity process, 214 nonideal binary, 109 thermally coupled columns, 536 Distillation control adaptive, 442-43... 

Modified z-transform, 606-7 Modulus of complex numbers, 319 MOS memory, 555 Multicapacity process, 187, 193-94, 212-14... 

Multicapacity processes, processes that consist of two or more capacities (first-order systems) in series, through which material or energy must flow. In Section 11.3 we discuss the characertistics of such systems. 

The very large majority of the second- or higher-order systems encountered in a chemical plant come from multicapacity processes or the effect of process control systems. Very rarely we will find systems with appreciable inherent second- or higher-order dynamics. 

Overdamped are the responses of multicapacity processes, which result from the combination of first-order systems in series, as we will see in Section 11.3. 

Multicapacity processes do not have to involve more than one physical processing unit. It is quite possible that all capacities are associated... 

Use a PID controller to increase the speed of the closed-loop response and retain robustness. The PI eliminates the offset but reduces the speed of the closed-loop response. For a multicapacity process whose response is very sluggish, the addition of a PI controller makes it even more sluggish. In such cases the addition of the derivative control action with its stabilizing effect allows... 

Multicapacity processes These constitute the large majority of real processes. Consider two first-order systems in series with... 

Figure 16.10 Closed-loop responses of multicapacity process in Example 16.4 for (a) set-point and (b) load unit step changes.

Consider the multicapacity process of case 2 in Example 16.4, We have 1 1... 

Postulate a model. In Example 12.1 we observed that a jacketed cooler is a multicapacity process. For our problem we can identify the following three interacting capacities in series (1) heat capacity of tank s content, (2) heat capacity of the coolant in the jacket, and (3) heat capacity of the tank s wall. Therefore, our first suggestion is to use a third-order overdamped model without significant dead time. A closer examination of the physical system reveals that the tank s wall does not possess significant capacity for heat storage and could be omitted. Consequently, we suggest a second-order model without dead time of the form... 

Between the most and least difficult elements lies a broad spectrum of moderately difficult processes. Although most of these processes are dynamically complex, their behavior can be modeled, to a large extent, by a combination of dead time plus single capacity. The proportional band required to critically damp a single-capacity process is zero. For a dead-time process. It Is Infinite. It would appear, then, that the proportional band requirement Is related to the dead time in a process, divided by Its time constant. Any proportional band, hence any process, would fit somewhere In this spectrum of processes. A discussion of multicapacity processes In Chap. 2 will reaffirm this point. 

From Fig. 2.2 it can be seen that the interacting multicapacity process differs from the dead time plus single-capacity process in the smooth upturn at the beginning of the step response. This curvature indicates that the dead time is not pure, but instead is the result of many small lags, and therefore the process will be somewhat easier to control. By the same token, derivative action will be of more value than it was in the case of dead time and a single capacity. Nonetheless, if we choose to estimate the necessary controller settings on the basis of a single-capacity plus dead-time representation we will err on the safe side. 

FIG 2.3. The step response of a multicapacity process can be reduced to dead time plus a single capacity. 

The dynamic response of composition to a change in distillate flow exhibits considerable dead time, as is expected in a multicapacity process. But the presence of an additional feature is indicated by step-response tests. Figure 11.13 illustrates results which are typically encountered. The response is the sort which would be seen in a transmission line with... 

Multicapacity Processes 38 Gain and Its Dependence 44 Testing the Plant 55... 

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