Dynamic Controllability

Additional details of the economic and sizing calculations can be found in Luyben (1993). Notice that the flowsheet with the smallest annual cost has four CSTRs. Now let s compare this system with a process that has one CSTR and a column whose overhead product is recycled back to the reactor. Economic studies of this system have shown that a simple stripping column is cheaper than a full column. Table 2.3 gives size and cost data over a range of reactor sizes. 

This simplistic economic evaluation shows that the reactor/stripper process is more economical than the reactors-in-series process. A 2500 ft1 reactor followed by a stripping column can achieve the same result that would require four 1435 ft3 reactors in series with no recycle. 

In the simple binary process considered above, the 2500 ft3 reactor with a 17-tray stripper gives the process with the smallest total annual cost 936,000/yr versus 1,550,000,Nr for the best of the CSTR-in-series flowsheets. Thus this process with recycle is more economical, from the viewpoint of steady state, than the alternative process consisting of reactors in series. This is the point we made in Sec. 2.2 about the economic advantage for recycle. 

Dynamic simulations of two alternative processes provide a quantitative comparison of their dynamic controllabilities. To strike a balance between simplicity and the economic optimum, we selected the three-CSTR process to compare with the reactor/stripper process. The scheme 

The scheme for the reactor/stripper process uses a PI controller to hold product composition (xB) by manipulating vapor boilup in the stripper. The same analyzer deadtime is used. Proportional level controllers are used for the stripper base (manipulating bottoms flow ), the overhead receiver (manipulating recycle flow), and the reactor (manipulating reactor effluent flow) with gains of 2. 

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FIGURE 10 8 Energy dia gram showing relationship of kinetic control to thermo dynamic control in addition of hydrogen bromide to 1 3 butadiene... 

It is imphcit that increasing the value of Ly will raise the supersaturation and growth rate to levels at which mass homogeneous nucleation can occur, thereby leading to periodic upsets of the system or cycling [Randolph, Beer, and Keener, Am. In.st. Chem. Eng. J., 19, 1140 (1973)]. That this could actually happen was demonstrated experimentally by Randolph, Beckman, and Kraljevich [Am. In.st. Chem. Eng. J., 23, 500 (1977)], and that it could be controlled dynamically by regulating the fines-destruction system was shown by Beckman and Randolph [ibid., (1977)]. Dynamic control of a ciystaUizer with a fines-destruction baffle and fine-particle-detection equipment... 

Although dynamic responses of microbial systems are poorly understood, models with some basic features and some empirical features have been found to correlate with actual data fairly well. Real fermentations take days to run, but many variables can be tried in a few minutes using computer simulation. Optimization of fermentation with models and reaf-time dynamic control is in its early infancy however, bases for such work are advancing steadily. The foundations for all such studies are accurate material Balances. 

Pawson T (2007) Dynamic control of signaling by modular adaptor proteins. Curr Opin Cell Biol 19 112-116... 

It is now widely accepted that the compositions of the atmosphere and world ocean are dynamically controlled. The atmosphere and the ocean are nearly homogeneous with respect to most major chemical constituents. Each can be viewed as a reservoir for which processes add material, remove material, and alter the compositions of substances internally. The history of the relative rates of these processes determines the concentrations of substances within a reservoir and the rate at which concentrations change. Commonly, only a few processes predominate in determining the flux of a substance between reservoirs. In turn, particular features of a predominant process are often critical in controlling the flux of a phase through that process. These are rate-controlling steps. 

Saxena AM, Udgaonkar JB, Krishnamoorthy G (2005) Protein dynamics control proton transfer from bulk solvent to protein interior a case study with a green fluorescent protein. Protein Sci 14 1787-1799... 

Nijland, R., Veening, J.W. and Kuipers, O.P. (2007) A derepression system based on the Bacillus subtilis sporulation pathway offers dynamic control of heterologous gene expression. Applied and Environmental Microbiology, 73 (7), 2390-2393. 

B. Roffel and J. E. Rijnsdorp, Process Dynamics, Control, and Protection (Ann Arbor, MI Ann Arbor... 

Wolfe, D. B. Conroy, R. S. Garstecki, P. Mayers, B. T. Fischbach, M. A. Paul, K. E. Prentiss, M. Whitesides, G. M., Dynamic control of liquid core/liquid cladding optical wave... 

NPM Huck, WF Jager, B de Lange, and BL Feringa, Dynamic control and amplification of molecular chirality by circular polarized light, Science, 273 1686-1691, 1996. 

Wang, J., Myers, C.D. and Robertson, G.A. (2000) Dynamic control of deactivation gating by a soluble amino-terminal domaininhERG K+ channels. TheJournal of General Physiology, 115, 749—758. 

Consider here the nonlinear robust regulation problem (NRRP), which consists in finding, if possible, a dynamic controller of the form... 

H. Nijmeijer and A.J. van der Schaft. Nonlinear Dynamical Control Systems. Springer Verlag, 1991. 

Because of the very low concentrations, the detection and quantification of POCs in the water of alpine lakes and streams is very challenging [38] and is therefore rarely attempted. Nevertheless, studies of POCs in lakes in Europe show HCH concentrations in water that rival those of the highest measured in inland waters [46]. Mountain lakes close to populated areas showed PAH profiles which favored the lighter PAHs, including some transformation products, whereas a more remote lake contained relatively higher concentrations of heavier PAHs, a hallmark of LRT because the lighter PAHs are generally the more labile [47]. The concentration of POCs in water and sediments of alpine lakes is dynamically controlled by the rates of input and loss. In order to understand the contamination of the alpine aquatic biota, it is important to understand the processes that deliver POCs to the lakes and that lead to their loss from the lakes (Pig. 2). Two alpine lakes in particular have... 

The reaction selectivity is better under these conditions at steady state, because an equihbrated ratio is observed between the resulting higher and lower homolog alkanes. In addition, dynamic conditions allow us to vary the contact time to obtain information about primary products and then about the mechanism. It appears that, in the case of propane metathesis in a stationary regime, conversion increases Hnearly with contact time, which shows that the reaction is under dynamic control with no diffusion Hmitation. Under these conditions, decreasing contact time results in an increase of the selectivity for hydrogen and olefin whereas that of alkanes decreases. Similarly, the alkanes/olefins ratio tends to zero as the contact... 

The BIPOLato-Ti-TADDOLato catalysts prepared by addition of BIPOL and TADDOL to Ti(0 Pr)4, catalyze methylation with an achiral methyltitanium reagent to give highly enantiomerically pure methylcarbinol. Since the sterically bulky 3,3 -substituents leads to an increase in enantioselectivity, the chirality of BlPOLato-Ti(0 Pr)2 catalyst 30 can be dynamically controlled by the chiral TADDOL moiety (Scheme 8.25). 3,3 -Dimethoxy derivative affords complete enantioselectivity (100% ee), while the moderate enantioselectivity is obtained with the parent BIPOL (73% ee). 

There are many other quantum dynamics control protocols that we have not discussed see Ref. 10 for descriptions and a discussion of those that fall into the shortcuts to adiabaticity category, and Refs 1,2 for descriptions and discussion of other control methodologies. 

FROM COHERENT TO INCOHERENT DYNAMICAL CONTROL OF OPEN QUANTUM... 

Remarkably, when our general ME is applied to either AN or PN in Section 4.4, the resulting dynamically controlled relaxation or decoherence rates obey analogous formulae provided the corresponding density matrix (generalized Bloch) equations are written in the appropriate basis. This underscores the universality of our treatment. It allows us to present a PN treatment that does not describe noise phenomenologically, but rather dynamically, starting from the ubiquitous spin-boson Hamiltonian. 

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