Optimal Tracking Control of Blast Furnace Molten Iron Quality Based on Krotov's Method and Nonlinear Subspace Identification

In order to address the high-performance control problem of multivariate molten iron quality (MIQ) in the blast furnace (BF) ironmaking process, specifically molten iron silicon content ([Si]) and molten iron temperature, this article proposes a novel optimal tracking control algorithm based on Krotov's method and nonlinear subspace identification. To begin with, a nonlinear Hammerstein model for MIQ is established to represent the relationship between the key process variables and MIQ indexes using nonlinear subspace identification technology. Then, to reduce the computational burden, an augmented system is established such that the optimal tracking control problem of MIQ is transformed into an optimal regulation problem. Furthermore, the candidate optimal controller for the augmented system is derived by utilizing the iterative optimization characteristic of Krotov's method and designing an improving function. Finally, the numerical solution of the optimal controller is obtained by solving nonlinear equations through the quasi-Newton method, resulting in the optimal output trajectory of MIQ. Theoretical analysis and experiments based on actual BF production data verify the effectiveness and advancement of the proposed method.