(684f) Multi-Rate Subspace-Based System Identification and Economic Model Predictive Control of the Electric Arc Furnace

The electric arc furnace (EAF) process is widely employed in steelmaking, using electricity to melt post-consumer scrap metal to produce new steel. The process provides significant reductions in the labor, energy and environmental costs of steelmaking over conventional blast furnaces that forge steel out of iron ore, coal and gas. Despite these efficiency gains, the EAF process requires generating tremendous amounts of heat to recycle the scrap steel, while the industrial sector struggles with electricity costs that are exorbitantly high [1]. The energy efficiency and economics of the EAF process can hence be improved by leveraging the proliferation of new technologies in optimization and advanced control systems. The application of mathematical programming problems, such as model predictive control and optimization in general, however, rely heavily on good predictions from process models.

One approach for modeling and control of the EAF process involves the development of first-principles/mechanistic models that can then be used for the purposes of optimization [1]. While numerous variations of these model-based approaches have improved the computational tractability of such problems, the development and implementation of first-principles model-based controllers remains challenging. Compared to first-principles models, recent work has exploited the increased availability of historical process data to develop data-driven models that are simple enough to make model-based control design practical. The data-driven causal dynamic models identified using latent variable [2, 3] or subspace [4] methods can be readily integrated into an on-line optimization framework, where at each sampling instant a finite horizon optimal control problem is solved, yielding an optimal control sequence that achieves desired closed-loop performance. However, most of these data-driven models are ill-suited for the electric arc furnace application where output measurements are scheduled at different sampling rates because of hardware limitations on sensors. Specifically, the harsh environment and high corrosiveness of molten steel mean that on-line measurements of the molten steel temperature and chemical composition are often disrupted with unmeasured process variables and missing data, thus making existing data-driven modeling approaches inapplicable.

Even with the availability of good models, the optimization of the arc furnace, analogous to other batch processes, deals with the effective allocation of a set of limited resources over a finite time duration. When considering competing criteria and from an industrial perspective where the prevailing incentive is of an economic nature, the multi-objective optimization problem for the EAF process is to economically reach the desired product end-point target at the termination of the batch. While recent contributions have demonstrated the advantages of economic model predictive control under the assumption that all batches are of equal durations [5], using a data-driven model that is capable of handling inconsistent batch lengths opens new and beneficial possibilities of optimizing the operation of batches with variable durations.

Motivated by the above considerations, in this work we develop a system identification method and economic model predictive control framework for the EAF process. The system identification method is based on a subspace formulation and uses the reliable singular value decomposition to identify a dynamic model of the process from a finite number of noisy data samples that are disrupted with unmeasured process variables and asynchronous data. Furthermore, the proposed subspace-based system identification approach does not require the use of iterative computational procedures or nonlinear (and possibly non-convex) optimization. The resulting dynamic model is integrated into a tiered economic model predictive control (EMPC) formulation, where solutions to computationally tractable quadratic and linear programming problems achieve the desired final product end-point specification by batch termination while minimizing the operating costs. The multi-rate subspace-based system identification technique and EMPC framework is implemented on the EAF process subject to the limited availability of process measurements, missing data, measurement noise, and constraints.

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