Process model identification, empirical

For continuous process systems, empirical models are used most often for control system development and implementation. Model predictive control strategies often make use of linear input-output models, developed through empirical identification steps conducted on the actual plant. Linear input-output models are obtained from a fit to input-output data from this plant. For batch processes such as autoclave curing, however, the time-dependent nature of these processes—and the extreme state variations that occur during them—prevent use of these models. Hence, one must use a nonlinear process model, obtained through a nonlinear regression technique for fitting data from many batch runs. 

Empirical Model Identification. In this section we consider linear difference equation models for characterizing both the process dynamics and the stochastic disturbances inherent in the process. We shall discuss how to specify the model structure, how to estimate its parameters, and how to check its adequacy. Although discussion will be limited to single-input, single-output processes, the ideas are directly extendable to multiple-input, multiple-output processes. 

Most work on the development of dynamic process models has been empirical this work is usually referred to as process identification. As mentioned earlier, two classes of empirical identification techniques are available one uses deterministic (step, pulse, etc.) functions, the other stochastic (random) identification functions. With either technique, the process is perturbed and the resulting variations of the response are measured. The relationship between the perturbing variable and the response is expressed as a transfer function. This function is the process model. Empirical identification of process models by the deterministic method has been reported by various workers [55-58]. A drawback of this method is the difficulty in obtaining a measurable response while restricting the process to a linear response (small perturbation). If the perturbation is large, the process response will be nonlinear and the representations of the process with a linear process model will be inaccurate. 

Intermediate in complexity and accuracy between true mechanisms and abstract models are empirical rate law models. Here, the modeler eschews the identification of elementary steps and, instead, works with experimentally established rate laws for the component overall stoichiometric processes that make up a particular reaction. Each process may consist of several elementary steps and involve many reaction intermediates, but it enters the model only as a single empirical rate equation, and only those species that appear in the rate equation need be included in the model. Assuming that the empirical rate laws have been accurately determined, this approach will give results for the species contained in the rate laws that are identical to the results from the full mechanism, so long as no intermediate builds up to a significant concentration and so long as the component processes are independent of one another. This last requirement implies that no intermediate that is omitted from the model is involved in more than one process, and that there are no cross-reactions between intermediates involved in different processes. 

Fitting Dynamic Models to E erimental Data In developing empirical transfer functions, it is necessary to identify model parameters from experimental data. There are a number of approaches to process identification that have been pubhshed. The simplest approach involves introducing a step test into the process and recording the response of the process, as illustrated in Fig. 8-21. The i s in the figure represent the recorded data. For purposes of illustration, the process under study will be assumed to be first order with deadtime and have the transfer func tion ... 

Empirical grey models based on non-isothermal experiments and tendency modelling will be discussed in more detail below. Identification of gross kinetics from non-isothermal data started in the 1940-ties and was mainly applied to fast gas-phase catalytic reactions with large heat effects. Reactor models for such reactions are mathematically isomorphical with those for batch reactors commonly used in fine chemicals manufacture. Hopefully, this technique can be successfully applied for fine chemistry processes. Tendency modelling is a modern technique developed at the end of 1980-ties. It has been designed for processing the data from (semi)batch reactors, also those run under non-isothermal conditions. 

First of all are determined physicochemical processes enabling the solution of the set problem and are selected those laws of thermodynamics and kinetics or known empiric correlations, which formalize them and set sought for final data in correlation with available initial data in the studied system. Chemical processes in the geological medium are mutually associated by strict restrictions of charge neutrality, mass and energy conservation. Structurization of models in these conditions boils down to identification of cause and effect associations between various physicochemical processes and in the selection or derivation of equations describing them. Such structurization is intended for the creation of a system of interrelated equations, which characterize the physicochemical state of groimd water and may be considered as an independent physicochemical submodel. 

Usually, chemical reaction models are composed from individual reactions steps, ether elementary or global. Each reaction step has a prescribed rate law, which is characterized by a set of parameters. The parameter values are collected from literature, evaluated using theoretical machinery, estimated by empirical rules, or simply guessed. The predictive power of a reaction model is thus determined by two factors, the authenticity of the reaction steps and the correctness of the rate parameters. For the purpose of the present discussion, we assume that the complete set of reaction steps (i.e., the reaction mechanism) is known and our focus is entirely on the identification of the correct parameter values. It is pertinent to mention, though, that the process of reaching conclusions on the authenticity of the reaction mechanism is often based on and is coupled to the parameter identification. The assumption of the known mechanism should not be viewed as a simplification of the problem but rather a pedagogical device for presenting the material. 

The diversity and lifetime of the products formed as a result of ionizing radiations add to the complexity in their detection and identification. Over the past several years, theoretical calculations on DNA model systems have significantly contributed to further determination of the chemical properties of many of the unstable species formed, [6] and hence to better our understanding of the processes involved. Ab initio and semi empirical methods were first employed in this field by Pullman s laboratory in the 1960s to investigate the electron affinities and ionization potentials of the DNA bases. Since then, rapid development of hardware and software at the end of the eighties has allowed additional and more complete theoretical studies to be performed and hence contributed to the understanding of free radical processes in irradiated components. 

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