Control implications

The analysis presented in Section 4.4 indicates that, impurity levels notwithstanding, the rate at which the overall process evolves is not significantly different (i.e., faster or slower) than the dynamics of the individual units. On the other hand, we can expect the impurity levels in the process to respond very slowly to changes in the manipulated variables. This suggests that the control of integrated processes in which impurities are present should be approached using two layers of control action. 

It is important to note that, in typical practical situations in which cost constraints play an important role, impurity-concentration measurements are available for only a few units (and, more often than not, just for a single unit). Thus, a model of the evolution of the total impurity inventory (such as those developed in the examples above, i.e., Equations (4.43) and (4.45)) is not well suited for controller design. Rather, an appropriate coordinate change of the type in Equation (4.33) should be used to obtain a model of the evolution of the measured concentration variable in the slow time scale. An example of this approach is presented in the case study following this section. 

Our analysis also provides clues regarding the manipulated inputs that are available for use in each of the control layers. Recall that the flow rates u1 of the material streams not connected with the process impurity input and output are present only in the model of the fast dynamics (4.20). u1 thus represent the 

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Milford, J. B., A. G. Russell, and G. J. McRae, A New Approach to Photochemical Pollution Control Implications of Spatial Patterns in Pollutant Responses to Reductions in Nitrogen Oxides and Reactive Organic Gas Emissions, Environ. Sci. Technol., 23, 1290-1301 (1989). 

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Referring back to the theory introduced in Chapter 2, we can expect that the presence of terms of very different magnitudes (i.e., 0(1) and 0(e)) in the model (4.18) reflects a two-time-scale behavior in the dynamics of typical processes with recycle and purge. In what follows, we will show that this is indeed the case. Also, we will address the derivation of reduced-order models of the fast and slow dynamics, provide a physical interpretation of this dynamic behavior, and highlight its control implications. 

Finally, we analyzed the control implications of the presence of impurities in a process, concluding that the control of impurity levels must be addressed over an extended time horizon using the flow rate of the purge stream as a manipulated input. To close the impurity-levels loop, one should resort either to an appropriately tuned linear controller (e.g., a PI controller with long reset time) or to a (nonlinear) model-based controller that uses (an inverse of) the reduced-order model of the slow dynamics - as developed in this chapter - to compute the necessary control action. 

Subsequently, we considered the control implications of our findings, and showed that control objectives related to the energy dynamics of the individual units (e.g., temperature control) should typically be addressed in the fast time scale. On the other hand, control objectives related to the energy dynamic at the process level (such as managing energy use) should be addressed in the slow time scale. These concepts were illustrated through several examples and a simulation case study. 

Jogwar, S.S. and Daoutidis, P. (2010). Energy flow patterns and control implications for integrated distillation networks. Ind. Eng. Chem. Res., 49, 8048-8061. 

While the individual reaction rates are the variables that, can be affected in a reacting system, we often express the performance of the reactor in terms of measures derived from the rates. Conversion and yield are such quantities. Conversion refers to the fractional consumption of a reactant in the reactor feed, whereas yield refers to the amount of product made relative to the amount of a key reactant fed to the reactor. In recycle systems the per-pass conversion of the various reactants is a relevant measure. It depends upon the rate of reaction for the specific component but also on the reactor feed. The per-pass conversion of an excess reactant is less than that of a limiting reactant. For example, the per-pass conversion of ethylene in a typical vinyl acetate reactor is only 7 percent whereas the per-pass conversion of oxygen is 36 percent. In Chap. 2 we discussed the plantwide control implications of incomplete conversion. 

What are the control implications of this analysis The first conclusion is that autothermal systems (no furnace) have two or more steady states. There is also a good chance that the normal operating point corresponds to the intermediate steady state that is open-loop unstable. This is certainly the case when the reactor is operated at less than 100 percent conversion. 

Equation (A.36) shows that the exergy destruction rate increases with changes in the gradients as well as the fluxes. There are interesting control implications from this relationship. We outline two of them here. Others are mentioned in the main text in connection with the control strategies for specific unit operations. 

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S. J. D. Schwartzstein, statement included in Hearing before the Subcommittee on Arms Control, Oceans, International Operations and Environment of the Committee on Foreign Relations United States Senate, Yellow Rain The Arms Control Implications, 98th Congress, first session (24 February 1983) p. 109. See also Haig report, p. 17. 

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Charging of solids into reactors and transfer of solids between operations are among the most important and widely used operations in the chemical industry. The transfer of solid materials often generates dust. This section reviews safety and control implications related primarily to dust generation and flammable atmospheres in such transfer operations. 

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