(721b) Economic Model Predictive Control of the Electric Arc Furnace Using Data-Driven Models

Electric arc furnaces (EAF) are widely used in the steel industry to produce molten steel from scrap metal. The EAF is used for approximately one-third of the total steel produced in the world and its use is expected to increase. Although the technology for recycling steel is more economical and flexible than large blast furnaces that consume vast amounts of iron ore and coal, steel manufacturing is generally an energy intensive process with harsh operating conditions that is prone to dramatic shifts in demand and price due to the cyclical nature of the industry. In addition, steel production is a complicated process with complex physical and chemical phenomena that are not well understood. Therefore, the EAF involves relatively low levels of automation and relies heavily on operator involvement [1]. Nevertheless, the continual rapid growth in the power of silicon chips, digital sensors and high-bandwidth communications can potentially improve steelmaking and make the control and optimization of the EAF a crucial component of modern steel mills.

The development of optimal operating policies for the electric arc furnace aimed at improving the corporate profitability, energy efficiency and environmental sustainability of steelmaking is essential for successful control and optimization. One of the main challenges in the EAF operation is that the measurements related to the steel quality are often unavailable during the batch and only made through off-line laboratory analysis. Moreover, the EAF exhibits strong nonlinear, transient operating behavior and is characterized by stages with varying dynamics that makes conventional system identification approaches, where a single linear model is identified, ill-suited for developing an accurate temporal model that is capable of characterizing the time-varying nonlinear dynamics [2].

Recent efforts have recognized the importance of including the economic objective function in standard model predictive control (MPC) formulations, and analyzed the stability properties of economic MPC formulations [3, 4]. In the context of batch processes, standard MPC regulation is equivalent to tracking predefined process set-point trajectories. It has been recognized that for batch processes, where the end-point quality is the variable of importance, it remains meaningful to penalize only the final quality variable deviation in the objective function, while incorporating input restriction as constraints in the optimization problem [5]. One way to optimally compute the inputs is to solve another problem where the final quality (obtained as a solution of the first problem) is imposed as a constraint with the objective function only containing other terms of economic relevance [6].

Motivated by the above considerations, an economic model predictive control (EMPC) framework for the EAF is developed in this work. The design utilizes the multi-model approach to identify local linear models and an appropriate weighting scheme to capture the nonlinear nature of the EAF using only limited process measurements [5], and notions of economic MPC to compute the best input profile that meets the desired quality specifications. To this end, a database of historical process measurements is initially clustered into a number of operating regions and a weighting scheme is devised for the training data to appropriately weight the local models. Subsequently, local linear models are estimated simultaneously using an appropriate latent variable regression method, namely the partial least squares (PLS) regression technique. The resulting model is used to design a two-level predictive controller that enables minimization of an economic objective function subject to end-point and path constraints. The proposed economic MPC is benchmarked against existing trajectory tracking approaches and the simulation results demonstrate the superior performance of the economic MPC over the traditional trajectory tracking approaches.

References

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[5] S. Aumi, B. Corbett, T. Clarke-Pringle, and P. Mhaskar. Data-driven model predictive quality control of batch processes. AIChE J., 59:2852-2861, 2013.

[6] Z. Chong and C.L.E. Swartz. Optimal operation of process plants under partial shut-down conditions. AIChE J., 59:4151-4168, 2013.