Sparse State Feedback Control for Industrial Applications

Alba Gurpegui Ramón, Frida Norlund, Kristian Soltesz, Anders Rantzer

We present an optimization-based methodology for designing sparse state-feedback controllers for industrial applications that are suited for linear control, and demonstrate the framework by designing a level controller for an industrial rougher flotation bank at the Aitik mine. In contrast to the dense linear-quadratic (LQ) controller gains currently operating at the concentrator, our approach enforces a sparsity pattern that is consistent with the interaction structure of the flotation bank and accounts for the worst-case expected inflow disturbances during tuning, while optimizing controller performance through the Integral Absolute Error (IAE) index. The non-zero elements of the sparse gain matrices are optimized using a coordinate search algorithm that handles bound constraints and preserves closed-loop stability. The resulting sparse controller achieves improved load disturbance rejection in the flotation cells compared to the LQ controller. These improvements are consistently observed in both linear and nonlinear simulations. In addition, the imposed structure, results in gain matrices that are easier to adjust and interpret. Importantly, the sparse controllers generated for the Aitik mine are directly suitable for industrial deployment and offer an effective alternative to the existing dense LQ design.