CHAPTER S CONCLUSIONS

The motivation for obtaining improved control of the batch production of steel in the electric arc furnace has been highlighted. A survey of the literature has exposed that, to date, progress made towards obtaining computer control of the steelmaking process has been confined primarily to the problems of scrap selection for the initial charge and power allocation between furnaces. A study of conventional furnace operating practice has demonstrated the complexity of the process and the considerable skill required from the operator for its control. Justified by the common chemical principles and similarity in engineering environment of all steel- making processes a review of modelling of the Basic Oxygen Process has been presented. In this review both analytical and statistical techniques for model development have been considered. The former technique has been found to give non-linear models of large dimension which are unlikely to be practical for on-line applications. The latter technique, however, has been found to encounter difficulties due to the poor accuracy of the available furnace instrumentation.

The objectives of the present investigation have been shown to dictate that the analytical modelling technique be employed to develop a model of the steelmaking process in the electric arc furnace. Based on a study of the metallurgical theory of the steelmaking process and the range of variation of the constituent chemical species a set of chemical reactions

describing the process has been determined. The evaluation of the equilibrium state for the chemical system has been shown to require the solution of a constrained non-linear programming problem. Although techniques for solving such problems are available the shortcomings in both the range and the accuracy of the necessary thermo-chemical data have been shown to make this approach unpractical.

A study of tha sequence cf steps contributory to the bulk reaction rates has been conducted and the rates of the. major reactions have been shown

to be determined by the effects of mass transport. A lumped parameter representation of kick’s first diffusion law has been employed to describe mathematically these mass transport effects. This approach has been based on the accepted assumption that the driving forces for diffusion may be approximated by the differences between the average chemical potentials in the various phases. The rates of mass transfer have been given as the product of these driving forces and system

conductances. These conductances have been shown to be functions of a number of the process states and that an exact formulation of the rates of reaction gives a set of highly non-linear differential equations.

Subsequent to this study of the metallurgical theory of the proce.ss a set of system variables, necessary to describe the process, has been determined. The structure cf a set of equations describing the dynamics of these variables has been developed. This development has made use of the results of the many recent studies on the chemistry of steelmaking. That the structure of some of the equations is determined wholly h y regression techniques has been shown to be an inevitable consequence of the fact that much of the information on the process, available from the literature, is presented in graphical form. The validity of these statistically derived components of the model has been assessed h y comparison with the results from independent studies.

To determine the accuracy with which this model described the dynamics of the major process phenomena, simulation studies have been conducted. Initial conditions for the process states and control strategies typical of tha industrial process have been employed in these studies. The results obtained have demonstrated good agreeement between the simulated and observed behaviour of the carbon, iron oxide and temperature state

trajectories. In the absence of adequate plant data little could be concluded about the accuracy with which the model simulated the dynamics of the manganese oxidation reaction. The oxygen efficiency of the process, as predicted by the model, has been compared with published data. The results obtained from the model have been shown to be in close proximity to these data indicating the validity of the structure of the model. A comparison of the total decarburisation time as estimated by the model with that observed in practice exposes a discrepancy which has been assumed to be due to the losses inherent in the normal practice of stopping and starting the process. It has been concluded from these simulation studies that the techniques employed to develop the model have proved successful but that a significant amount of plant data would be required to facilitate the tuning of the model necessary to make it suitable for use in a practical control system.

A further study cf plant operating practice has been reported and the difficulties encountered when monitoring the process for the collection of data have been described. The variety of modes of furnace operation have been considered and the collected data have been employed to extend the model to include the effects of the power input from the electrodes. However, because of the large and often abrupt perturbations in the trajectories of the process states that can result from either additions made to the furnace or de-slagging, only the simple operating modes have been considered. A proposal to employ a numerical technique for parameter estimation has been rejected because of the difficulties attendant to obtaining sufficient process data for statistically meaningful studies to be conducted. Instead minor manual adjustments made to a number of parameters when simulating the monitored casts have been shown to be sufficient to ensure that the model is accurate for a limited class of operating practice.

The inherent complexity of the mathematical models evolved from theoretical considerations, has been examined. A reduction in the dimension of the model state vector has been effected by the introduction of stochastic parameters to account for the non**raeasureable states associated with the slag phase and the hypotheses on which the model has been developed. Techniques recently developed for obtaining noise corrupted measurements of the carbon content and temperature of the process have been investi­ gated and the statistics of the uncertainty on these measurements has been determined. The implementation of the extended Kalman filter for on-line state estimation has been considered. Divergence of the

estimation procedure has been shown to result from partial noise

decoupling, when only the carbon state was measured. A simple scheme for ensuring that the filter does not diverge, due to modelling errorss has been incorporated in the filter and the performance of the state estimation procedure under varied conditions of uncertainty has been studied. It has been shown that even under extreme conditions the filter is capable of estimating the chemical and temperature states with the accuracy required for control of the industrial process.

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