Model identification

Model identification is the process of quantifying process dynamics. The techniques available fall into one of two approaches - open loop and closed loop testing. Open loop tests are performed with either no controller in place or, if existing, with the controller in manual mode. A disturbance is injected into the process by directly changing the MV. Closed loop tests may be used if a controller exists and already provides some level of stable control. Under these circumstances the MV is changed indirectly by making a change to the SP of the controller. 

Such plant testing should be well organised. While it is clear that the process operator must agree to the test there needs to be discussion about the size and duration of the steps. It is in the engineer s interest to make these as large as possible. The operator of course would prefer that no disturbance be made The operator also needs to appreciate that other changes to the process should not be made during the test. While it is possible to determine 

It seems too obvious to state that the process instrumentation should be fully operational. 

Many data historians included a compression algorithm to reduce the storage requirement. When later used to recover the original data some distortion will occur. While this is not noticeable in most applications, such as process performance monitoring and accounting, it can affect the apparent process dynamics. Any compression should therefore be disabled prior to the plant tests. 

It is advisable to collect more than just the PV and MV. If the testing is to be done closed loop then the SP should also be recorded. Any other process parameter which can cause changes in the PV should also be collected. This is primarily to ensure that they have not changed during the testing, or to help diagnose a poor model lit. While such disturbances usually invalidate the test, it may be possible to account for them and so still identify an accurate model. 

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Implementation Issues A critical factor in the successful application of any model-based technique is the availability of a suitaole dynamic model. In typical MPC applications, an empirical model is identified from data acquired during extensive plant tests. The experiments generally consist of a series of bump tests in the manipulated variables. Typically, the manipulated variables are adjusted one at a time and the plant tests require a period of one to three weeks. The step or impulse response coefficients are then calculated using linear-regression techniques such as least-sqiiares methods. However, details concerning the procedures utihzed in the plant tests and subsequent model identification are considered to be proprietary information. The scaling and conditioning of plant data for use in model identification and control calculations can be key factors in the success of the apphcation. 

Mathews, H.B., Miller, S.J. and Rawlings, J.B., 1996. Model identification for crystallization theory and experimental verification. Powder Technology, 88, 221-235. 

Monnier, O., Fevotte, G., Hoff, C. and Klein, J.P., 1997. Model identification of batch cooling crystallizations through calorimetry and image analysis. Chemical Engineering Science, 52, 1125-1139. 

Rawlings, J.B., Miller, S.M. and Witkowski, W.R., 1993. Model identification and control of solution crystallization processes A review. Industrial and Engineering Chemistry Research, 32, 1275-1296. 

Hjertager, B. H. 1985. Computer simulation of turbulent reactive gas dynamics. Modeling, Identification and Control. 5(4) 211-236. 

Model development is intimately linked to correctly assigning model parameters to avoid problems of identifiability and model misspecification [27-29], A full understanding of the objectives of the modeling exercise, combined with carefully planned study protocols, will limit errors in model identification. Compartmental models, as much as any other modeling technique, have been associated with overzealous interpretation of the model and parameters. 

Skogestad, S. Dynamic and Control of Distillation Columns—A Critical Survey. Modeling Identification Control 18 177-217 (1997). 

Akaike, H., A new look at the statistical model identification, IEEE Trans. Automat. Contr., 19, 716-723,1974. 

Thus, to estimate the variogram, the drift must be known and to estimate the drift, the variogram must be known. This leads to difficulties in model identification which will be discussed later. 

Batch crystallizers are often used in situations in which production quantities are small or special handling of the chemicals is required. In the manufacture of speciality chemicals, for example, it is economically beneficial to perform the crystallization stage in some optimal manner. In order to design an optimal control strategy to maximize crystallizer performance, a dynamic model that can accurately simulate crystallizer behavior is required. Unfortunately, the precise details of crystallization growth and nucleation rates are unknown. This lack of fundamental knowledge suggests that a reliable method of model identification is needed. 

Therefore, a flexible method to evaluate physical and chemical system parameters is still needed (2, 3). The model identification technique presented in this study allows flexibility in model formulation and inclusion of the available experimental measurements to identify the model. The parameter estimation scheme finds the optimal set of parameters by minimizing the sum of the differences between model predictions and experimental observations. Since some experimental data are more reliable than others, it is advantageous to assign higher weights to the dependable data. 

H. Akaike, A new look at statistical model identification, IEEE Trans. 

For each policy specification, the technology matrix of the integrated industry model is transformed from the productive structure existing before the policy change to the productive structure existing after the policy change. This structural transformation is the master key to identifying the economic demands and supplies of the industries modeled. Identification is necessary to soundly estimate (1) the economic demands for crude oil, natural gas, coal, water, and capital (2) the economic costs of pollution control for major water and air pollutants and (3) the economic supplies of the endproducts in the model. 

In this model [i = ea is the dipole moment of each bond along the chain. Eqs. (2.3) are equivalent to the formulae of Zimm (3) for the free draining case provided that the identifications I, II and III of the RB model are made. For the DTO model identifications IV, V and VI are applicable. 

The advantage of such an expansion is that the model is linear in the unknown parameters a so that many of the linear model identification techniques can also be applied to the above non-linear model. Iterative methods of obtaining the parameter estimates for a given model structure have been developed [Billings and Voon, 1986], A number of other non-linear signal models are discussed by Priestley [Priestley, 1988] and Tong [Tong, 1990],... 

J.B. Balchen, B. Lie, and I. Solberg. Internal decoupling in nonlinear process control. Modeling Identification and Control, 9 137-148, 1988. 

This book is aimed at tackling the above problems from a joint academic and industrial perspective. Namely, advanced solutions (i.e., based on recent research results) to the four fundamental problems of modeling, identification, control, and fault diagnosis are developed in detail in seven chapters. 

Larsson, T. and Skogestad, S. (2000). Plantwide control - a review and a new design procedure. Modeling, Identification Contr., 21, 209-240. 

Shah, S. L., Fisher, D. G. and Karim, N. M., "Hyperstability Adaptive Control-A Direct Input-Output Approach without Explicit Model Identification," Proc. Joint Automatic Control Conference, 1979, 481. 

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. 

From a knowledge of the results of stoichiometric, thermochemical and kinetic analyses and on the basis of the general concepts and models of chemical kinetics, a reaction model (or several conceivable models) is built up and compared with the experimental and literature data. This model identification provides both the best reaction model and its associated thermodynamic and kinetic parameters. 

The problems of parametric estimation and model identification are among the most frequently encountered in experimental sciences and, thus, in chemical kinetics. Considerations about the statistical analysis of experimental results may be found in books on chemical kinetics and chemical reaction engineering [1—31], numerical methods [129—131, 133, 138], and pure and applied statistics [32, 33, 90, 91, 195—202]. The books by Kendall and Stuart [197] constitute a comprehensive treatise. A series of papers by Anderson [203] is of interest as an introductory survey to statistical methods in chemical engineering. Himmelblau et al. [204] have reviewed the methods for estimating the coefficients of ordinary differential equations which are linear in the... 

Brue, E.. Moore, J., and Brown, R. C. Process Model Identification of Circulating Fluid Bed Hydrodynamics, in Circulating Fluidized Bed Technology IV (Amos A. Avidan, ed.), pp. 535-540. Somerset, Pennsylvania (1993). 

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