Optimizing control continuous

It may be useful to point out a few topics that go beyond a first course in control. With certain processes, we cannot take data continuously, but rather in certain selected slow intervals (c.f. titration in freshmen chemistry). These are called sampled-data systems. With computers, the analysis evolves into a new area of its own—discrete-time or digital control systems. Here, differential equations and Laplace transform do not work anymore. The mathematical techniques to handle discrete-time systems are difference equations and z-transform. Furthermore, there are multivariable and state space control, which we will encounter a brief introduction. Beyond the introductory level are optimal control, nonlinear control, adaptive control, stochastic control, and fuzzy logic control. Do not lose the perspective that control is an immense field. Classical control appears insignificant, but we have to start some where and onward we crawl. 

Marlin, T. E. and A. N. Hrymak. Real-Time Operations Optimization of Continuous Processes. In Chemical Process Control V. AIChE Symp Ser 316, 93 156-164 (1997). 

Several trials have been performed with antidepressants in the prevention of recurrence of major depression. In an exemplary trial of this kind, Reimherr et al. (1998) explored the optimal length of therapy in a long-term, placebo-controlled continuation study of patients who had responded to 12 14 weeks of open-label fluoxetine treatment (20mg/day) for major depression. Different maintenance schedules were represented by four treatment arms ... 

The present modeling approach to circadian cancer chronotherapy is based on an automaton model for the cell cycle. Continuous approaches to cell cycle progression have also been used to study the link between cell proliferation and circadian rhythms [44] and to determine, in conjunction with optimal control theory, the most efficient circadian schedules of anticancer drug administration [45]. Including more molecular details of the cell cycle in continuous models for cell populations represents a promising line for future research. Hybrid models incorporating molecular details into the automaton approach presented here will also likely be developed. 

Batch distillation is inherently a dynamic process and thus results to optimal control or dynamic optimisation problems (unless batch distillation task is carried out in a continuous distillation column). 

To pose the optimal control problem as a nonlinear programming (NLP) problem the controls u t) are approximated by a finite dimensional representation. The time interval [t0, r r] is divided into a finite number of subintervals (Ns), each with a set of basis functions involving a finite number of parameters u(t) = t, zj), te[( tj.i, tj), j = 1,2,. . J ], where tj = tF. The functions switching time tpj = 1,2,..., J. The control constraints now become ... 

Also note that if Ns is chosen sufficiently large, the piecewise constant optimal control policy will be sufficiently close to the continuous optimal control policy. 

Column process design specifies the separation, and sets column pressure, reflux, stages, and feed point. These in turn yield internal flows and reboiler and condenser duties. This chapter addresses the main column process design considerations. The column is optimized during the process design, and many times later during operation. Computer control continuously optimizes the column on-line. Both design and on-line optimization are also addressed in this chapter. 

Marlin, T. E., and Hrymak, A. N., Real-time operations optimization of continuous processes, in Fifth International Conference on Chemical Process Control , (Kantor, J. C., Garcta, C. E., and Carnahan B., Eds.), AIChE Symposium Series, Vol. 93, pp. 156-164 (1997). 

MacGregor and Tidwell (1979) illustrate some of the steps involved in running plant experimentation, building these process and disturbance models, and implementing simple optimal controllers on some continuous condensation polymerization processes. A number of similar applications to continuous emulsion polymerization processes have also been made. 

Gas-liquid contacting operations, which transfer one or more components between a gas phase and a liquid phase, are important to numerous industrial chemical processes. Their significance is reflected in the abundance of different contactor designs and review articles. The importance of these operations to the chemical industry is affirmed by their global prevalence and involvement in annually producing hundreds of millions of tons of basic chemicals. The various gas-liquid contactor designs attempt to optimize controlling parameters or such specific domains as the gas-liquid interface or continuous-phase residence time. 

Marlin, T.E. Hrymak, A.N. Real-time optimization of continuous processes. Fifth International Conference on Chemical Process Control, Lake Tahoe, NV, Jan, 1996, Kantor, J.C., Garcia, C.E. Carnahan B. Eds. AIChE New York, 1997, 156-164. 

Miettinen, K., Makela, M. M. and Mannikkb, T. (1998). Optimal control of continuous casting by nondifferentiable multiobjective optimization. Computational Optimization and Applications 11, 2, pp. 177-194. 

Concerning the preanalytics that have to be used, two main concepts are available for the application of enzyme electrodes to different fields of analysis. Clinical chemists nowadays are interested in autoanalyzers characterized by high measuring frequency as well as in portable bedside-type analytical systems with extremely short lag time between sample withdrawal and analysis result. On the other hand the optimal control of food production as well as bioprocesses requires the analysis of the substances of interest in a continuous or quasicontinuous way. Therefore, enzyme-electrode-based analytical systems for the application of highly diluted as well as undiluted media have been developed and commercialized. 

Additional process information could be derived from continuous online redox reaction monitoring. Reaction data such as the amount of sodium bisulfite used from batch to batch would indicate varying amounts of unreacted bromine that provided an indication of incomplete reaction or the prevalence of other undesired side reactions. The amount and quality of the data derived from the online redox provided an excellent opportunity for process optimization, control, and real validation. 

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