[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82714-en":3,"doc-seo-82714-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82714,4810365810221,"Aurora","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Sparse State Feedback Control for Industrial Applications","An optimization-based method designs sparse state-feedback controllers for industrial linear control and demonstrates it through a level controller for an industrial rougher flotation bank at the Aitik mine. Compared with the existing dense linear-quadratic (LQ) design, the approach enforces a sparsity structure aligned with flotation bank interactions and incorporates worst-case expected inflow disturbances during tuning. Controller performance is optimized using the Integral Absolute Error (IAE) index, yielding improved load disturbance rejection in simulations while producing easier-to-adjust, interpretable gain matrices suitable for deployment.","arXiv :2607 .03159v1 [ ee ss . SY] 3 Jul 2026  \nSparse State Feedback Control for Industrial Applications ⋆  \nA. Gurpegui Ram´on ∗ F. Norlund ∗ ,∗∗ K. Soltesz ∗ A. Rantzer ∗  \n∗ Lund University, Dept. Automatic Control, Lund, Sweden (email:  \n{alba.gurpegui ramon, frida.norlund, kristian.soltesz, [anders.rantzer](anders.rantzer}@control.lth.se)[}](anders.rantzer}@control.lth.se)[@control.lth.se](anders.rantzer}@control.lth.se))  \n∗∗ Boliden AB, Boliden, Sweden  \nAbstract: 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.  \nKeywords: Sparse state-feedback control, Numerical Optimization, Integral Absolute Error (IAE), Disturbance Rejection, Flotation, Level Control  \n1. INTRODUCTION  \nClassical optimal regulators such as linear-quadratic (LQ) controllers produce dense gain matrices in which every actuator depends on almost every measurement, but in many industrial systems, this level of interconnection is neither necessary nor practical.  \nSparse control formulations address this by enforcing zeroentries in the feedback matrices, restricting interactions to those that are physically motivated or practically feasible. A substantial body of research demonstrates that introducing sparsity into the feedback gain structure can preserve most of the closed-loop performance while simplifying the communication structure (Lin et al. (2013)), yielding controllers that are easier to interpret and tune. Although sparse controller synthesis has been extensively studied in the control literature, typically via H2 formulations (O’Donoghue et al. (2013); Fardad et al. (2009)), other performance metrics, such as the integral absolute error (IAE) are standard objectives for controller tuning and benchmarking in process control (Guzman and H¨agglund (2024)) .  \n⋆ This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation. Authors from the department of automatic control, Lund university, are members of the ELLIIT Strategic Research Area.  \nThe present work bridges this gap by addressing sparse controller synthesis in a process-control setting. The nonzero entries of the sparse feedback matrix are tuned through numerical optimization to minimize the IAE and the sparsity pattern is chosen to be consistent with the dynamics of the process to enhance interpretability. This renders implementation-ready sparse state-feedback matrices tailored to the process at hand.  \nTo demonstrate the methodology, we design a sparse statefeedback level controller for a flotation bank in the mining industry. Flotation is a commonly used process to separate valuable minerals from waste rock. In tank cells filled with a s","cbCaioKwcUArt61X","https://ap.wps.com/l/cbCaioKwcUArt61X","pdf",4045095,1,6,"English","en",105,"# Introduction\n## Motivation for Sparse vs Dense Controllers\n## Flotation Process and Level Control Context\n## Industry Use of MIMO Controllers and Prior LQ Results","[{\"question\":\"What problem does the document address in industrial controller design?\",\"answer\":\"It addresses the drawback of dense LQ state-feedback gains, which create excessive coupling between actuators and measurements in industrial systems where such full interconnection is neither necessary nor practical.\"},{\"question\":\"How does the proposed method construct sparse controllers?\",\"answer\":\"It selects a sparsity pattern consistent with the flotation bank’s interaction structure and then tunes the non-zero gain entries via numerical optimization to minimize the Integral Absolute Error (IAE), while preserving closed-loop stability under constraints.\"},{\"question\":\"What performance improvements are reported compared to the dense LQ controller?\",\"answer\":\"The sparse controller shows improved load disturbance rejection in the flotation cells, consistently observed across both linear and nonlinear simulations, and its structured gains are easier to adjust and interpret for industrial 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problem does the document address in industrial controller design?","Question",{"text":74,"@type":75},"It addresses the drawback of dense LQ state-feedback gains, which create excessive coupling between actuators and measurements in industrial systems where such full interconnection is neither necessary nor practical.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does the proposed method construct sparse controllers?",{"text":79,"@type":75},"It selects a sparsity pattern consistent with the flotation bank’s interaction structure and then tunes the non-zero gain entries via numerical optimization to minimize the Integral Absolute Error (IAE), while preserving closed-loop stability under constraints.",{"name":81,"@type":72,"acceptedAnswer":82},"What performance improvements are reported compared to the dense LQ controller?",{"text":83,"@type":75},"The sparse controller shows improved load disturbance rejection in the flotation cells, consistently observed across both linear 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