Kinetic adaptive control

Platt EJ, Dumin IP, Rabat D (2005) Kinetic factors control efficiencies of cell entry, efficacies of entry inhibitors, and mechanisms of adaptation of human immunodeficiency virus, J Virol 79 4347 356... 

An adaptive control of the batch reactor-I Identification of kinetics (with H.H.-Y. Chien). Automatica 2,41-58 (1964). 

Figure 5.15. Plot of log air saturation concentration = p°/RT versus water solubility C°ater for selected chemicals (25 °C). Chemicals of equal H lie on the same 45° diagonal. Water phase control and air phase control refer to the transfer kinetics (rate-controlling steps) in the two-film theory. (Adapted from Mackay, 1991.)...

The present paper steps into this gap. In order to emphasize ideas rather than technicalities, the more complicated PDE situation is replaced here, for the time being, by the much simpler ODE situation. In Section 2 below, the splitting technique of Maas and Pope is revisited in mathematical terms of ODEs and associated DAEs. As implementation the linearly-implicit Euler discretization [4] is exemplified. In Section 3, a cheap estimation technique for the introduced QSSA error is analytically derived and its implementation discussed. This estimation technique permits the desired adaptive control of the QSSA error also dynamically. Finally, in Section 4, the thus developed dynamic dimension reduction method for ODE models is illustrated by three moderate size, but nevertheless quite challenging examples from chemical reaction kinetics. The positive effect of the new dimension monitor on the robustness and efficiency of the numerical simulation is well documented. The transfer of the herein presented techniques to the PDE situation will be published in a forthcoming paper. 

Figure 7 - Various kinetic regimes controlling a gas-phase reaction around and inside a porous solid catalyst, D step corresponds to AE a AE% activation energies cited in the text, C to AE eUnd AE p B to AE d and A to AE c (adapted from Ref. 52)...

Large-scale crude oil exploitation began in the late nineteenth century. Internal combustion engines, which make use of the heat and kinetic energy of controlled explosions in a combustion chamber, were developed at approximately the same time. The pioneers in this field were Nikolaus Otto and Gottleib Daimler. These devices were rapidly adapted to military purposes. Small internal-combustion motors were used to drive dynamos to provide electric power to fortifications in Europe and the United States before the outbreak of World War I. Several armies experimented vith automobile transportation before 1914. The growing demand for fossil fuels in the early decades of the twentieth centuiy was exacerbated by the modernizing armies that slowly introduced mechanization into their orders of battle. The traditional companions of the soldier, the horse and mule, were slowly replaced by the armored car and the truck in the early twentieth century. 

Throughout the book I have tried to constrain the wonders of imagination inspired by the subject by using simple calculations. Can all of the water on the Earth have been delivered by comets if so, how many comets How do I use molecular spectroscopy to work out what is happening in a giant molecular cloud Calculations form part of the big hard-sell for astrochemistry and they provide a powerful control against myth. I have aimed the book at second-year undergraduates who have had some exposure to quantum mechanics, kinetics, thermodynamics and mathematics but the book could easily be adapted as an introduction to all of these areas for a minor course in chemistry to stand alone. 

FIGURE 5.10. Kinetic control by the enzymatic reaction. Normalized catalytic waves. From right to left log [feC l/fc.z + l/fci,2 + 1/fciCj)] = — oo,0,1,2,3. Adapted from Figure 2 of reference 20a, with permission from Elsevier. 

FIGURE 5.11. Kinetic control by the enzymatic reaction. Substrate calibration curve. Adapted from Figure 1 of reference 20a, with permission from Elsevier. 

FIGURE 5.12. Cyclic voltammetry. Passage from kinetic control by enzymatic reaction (1) to control by substrate diffusion. From left to right log(I%k /yfDsFv/TIT) =6,5,4,3, 2,1,0, — 1. Adapted from Figure 4 of reference 20a, with permission from Elsevier. 

Although, in practice, ion exchange kinetics are unlikely to limit the rate, the solutions proposed by Thomas may be adapted to represent other controlling mechanisms, as discussed later. 

It seems that the simulation of diffusion controlled reactions of groups on polymer chains developed by Muthukumar et al. ( ) that takes into account the bond formation by determined conformational rearrangement, can be adapted for the equilibrium situation, i.e. for systems controlled by pure chemical kinetics. 

The branching theories In their present state can treat a number of complex branching reactions of Industrial importance. It is to be stressed, however, that there does not exist any universal approach to all systems. The understanding of the reaction mechanism and kinetics is a necessary prerequisite for adaptation of the proper theory to give relations for structural parameters. Further progress in the network formation theory seems highly desirable particularly in the field of cycllzatlon and diffusion control and in understanding the network structure-properties relations. 

Figure 9.17 Green fluorescent protein (GFP) synthesis in water-in-oil emulsion as visualized by fluorescence microscopy. (Adapted from Pietrini and Luisi, 2004). Shown are the compartments in which GFP has been expressed (green in the original), (a) Typical micrographs of the cell-free GFP synthesis in Span 80 (0.45% v/v)/Tween 80 (0.05% v/v)/aqueous solution (0.5% v/v) in mineral oil emulsion droplets, preparation at 4 °C incubation at 37°C (i) 0 min, (ii) 11 min, (iii) 23 min, (iv) 32 min, (v) 44 min, (vi) 57 min, (vii) 21 h. Negative control (viii) 0 min, (ix) 21 h. The bar represents 50 p.m. (b) Kinetics of the cell-free GFP synthesis in emulsion droplets, on average 10 droplets with diameters of 30-60 um are evaluated per time point, cell-free enhanced GFP synthesis in emulsion droplets (i, ii and iii are three independent experiments) and negative controi (iv and v are two independent experiments).

The model reduction procedure must be adapted to the use of the simplified models and to the availability of experimental data needed to evaluate the unknown parameters, as discussed in Chap. 3. In general, more complex models are used for the design of the reactor and for the simulation of the entire process, whereas more simplified models are best fit for feedback control. In the following chapters it is shown that fairly accurate results are obtained when a strongly simplified kinetic model is used for control and fault diagnosis purposes. 

After performing the kinetic analysis of the reacting system, the researchers possess suitable kinetic models of different complexity to be used to design and control the entire process. The more complex model should be used to design the reactor this subject is outside the purpose of this book and is only briefly considered in Sect. 7.4. On the contrary, in Chaps. 5 and 6 the kinetic model is used to design adaptive model-based control and fault diagnosis schemes for a class of reactions taking place in batch reactors. 

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