D. Bonvin

Application of Estimation Techniques to Batch Reactors. III. Modelling Refinements which Improve the Quality of State and Parameter Estimation

Abstract This study is concerned with modelling refinements which improve significantly the estimation (using extended Kalman filter) of the rate of heat production in batch chemical reactors. Several ways of modelling heuristic knowledge are illustrated both in simulations and experiments, for example the use of random-ramp models instead of random-walk models for drifting parameters, the use of dynamic variance terms for parameters and states which change at known time instants, the use of a dynamic perturbation collector and the use of simplified kinetic models for higher-order chemical kinetics.

On line procedures for supervising the operation of batch reactors

Abstract Two methods of monitoring the progress of a chemical reaction in a batch reactor are developed. The first uses temperature measurements and reaction kinetics to estimate the reaction time corresponding to a well-documented run done in the laboratory. The second procedure relies on calorimetry, using a model of the reactor, to calculate the heat which evolves in the system. By combining the estimations generated by the two methods, many disturbances that may occur in the reactor/reaction system can be identified, and systems of competing reactions can be investigated. The supervision of the performance of a consecutive reaction system is illustrated through simulation.

Selection of input and output variables as a model reduction problem

The procedure for selecting input and output variables, proposed by Keller and Bonvin [4] is analysed using the principle of internal dominance proposed by Moore [6]. Using that principle, a dominance condition for the subsystem of the selected variables over the subsystem of the neglected variables is derived. It can be shown that the proposed variable selection procedure maximizes the dominance of the subsystem of the selected variables, hence justifying the proposed selection. The investigation further shows that prior model reduction can significantly improve variable selection since it eliminates the negative effects of inappropriate modelling.

Selection of Inputs for the Purpose of Model Reduction and Controller Design

Abstract This study discusses the choice of appropriate sets of inputs for linear multivariable systems. It is shown, for example, that reduced-order models with better directionality properties can be obtained when fewer inputs are considered. Furthermore, the selection of a good set of inputs for control may become important when both strong and weak inputs are available. The transmission of information from the inputs to the outputs is investigated and appropriate scaling procedures to derive a scaled input matrix are proposed. Singular value decomposition methods facilitate the quantification of the system’s excitation stemming from the various inputs, and thus the selection of an appropriately strong and orthogonal set of inputs. The need for and the implementation and benefits of reducing the number of inputs are illustrated by a large-scale model of a real process.

Monitoring Chemical Reaction Systems Using Incremental Target Factor Analysis

Abstract Factor-analysis techniques are used with chemical reaction systems at two levels to (i) analyze absorbance spectra in order to determine the species and the corresponding concentrations, and (ii) to analyze the inferred concentration data in order to uncover the reactions and their corresponding extents. Measurement errors are shown to be detrimental to the approach. The use of targets and of an incremental procedure, labelled here incremental target factor analysis, helps reduce the influence of errors. The approach can then be used to monitor on-line the operation of complex reaction systems on the basis of spectral measurements. The focus of this paper is on the development and use of incremental target factor analysis. The approach is illustrated by simulated examples.

Experimental Estimation of Concentrations From Reactor Temperature Measurement

Abstract Isothermal batch operation of two irreversible, exothermic, first-order reactions in series is investigated in an experimental pilot-scale reactor. Standard nonlinear Kalman filter is used to estimate on-line the concentrations of the limiting reagent and the intermediate product from reactor temperature as the only measured output. The accuracy of these estimates is verified using an on-line electrical-conductivity measurement that essentially measures a known linear combination of the two concentrations that are estimated. It is shown that validation with respect to this linear combination implies validation with respect to each individual concentration. An important aspect of the estimator is that it does not require complete a priori knowledge of the kinetic constants and the heats of reaction. In particular, it requires knowledge of only the ratios of the two kinetic constants and the two heats of reaction, which are readily obtained from off-line data and remain constant for essentially isothermal operation. Thus with only a single readily-measured output, the filter identifies on-line one unknown rate constant and one unknown heat of reaction along with the two concentrations. The identified values of these unknown parameters compare favorably with approximate values obtained from the literature and from off-line data.

On the Dynamics of a Bench-scale Calorimeter

Abstract A dynamic model for a bench-scale heat-flow calorimeter is derived in order to support the accurate reconstruction of the heat evolution in the reactor. The importance of describing the heat transfer between the reactor contents and the heating/cooling medium is described. The degree of discretization of the inner wall is deduced from the comparison of experimental and model-based frequency responses. The nonlinear behavior of the calorimeter is modelled and verified over a large range of operating conditions. Finally a qualitative assessment of the validity of such a dynamic model for both parameter and state estimation is provided.

Rescaling State and Input Variables for the Purpose of Analyzing Process Models

Many techniques which are used for analyzing the structure of large-scale, interactive systems (including structural dominance analysis and the singular value decomposition method) require a careful scaling of input and state variables to yield useful results. A suitable scaling procedure motivated by physical arguments is presented and illustrated through several examples, including linear and nonlinear as well as lumped and distributed parameter models.

Cost Decomposition of Large-Scale Systems and Scaling of Input and Output Variables

Abstract A cost decomposition technique whose range of application goes beyond that of known dominance measures, participation matrices or component cost methods is presented. The approach consists of a four-dimensional array whose elements express the cost of each output-state-mode-input coupling. Such a wealth of information can be combined in many ways to provide either the dominance of various three or two-dimensional couplings or the participation of the individual outputs, states, modes or inputs in the output energy. The method lends itself ideally to model reduction, control structure selection or model structure analysis. Since cost decomposition techniques depend highly on the choice of units for the input and output variables, a scaling of input and output variables based on physical arguments is also presented and tested on simple models.