New sparse control method beats dense LQ controllers in mining flotation

Engineers at Lund University have developed an optimization-based methodology for designing sparse state-feedback controllers that outperform traditional dense linear-quadratic (LQ) regulators in industrial applications. The work, accepted for the 23rd IFAC World Congress, focuses on a level controller for an industrial rougher flotation bank at Boliden's Aitik mine in Sweden. The key innovation is enforcing a sparsity pattern on the gain matrix that mirrors the physical interaction structure of the flotation cells — only the most relevant feedback connections are kept, while others are set to zero. This not only simplifies the controller but also improves performance. The authors use a coordinate search algorithm that respects bound constraints and guarantees closed-loop stability during tuning, optimizing the Integral Absolute Error (IAE) index for worst-case inflow disturbances.

Compared to the existing dense LQ controller, the sparse design achieves measurably better load disturbance rejection in both linear and nonlinear simulations. The resulting gain matrices are sparser and therefore easier for plant operators to adjust and interpret — a critical advantage in real-world industrial settings where control engineers need to understand and modify controller behavior without extensive re-tuning. The authors validated their approach using detailed simulations of the Aitik flotation bank, and emphasize that the sparse controllers are directly suitable for industrial deployment. This work demonstrates that sparsity can be both a design constraint and a performance enabler, offering a practical alternative to the dense optimal control solutions that dominate industrial practice today.