[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84382-en":3,"doc-seo-84382-105":30,"detail-sidebar-cat-0-en-105":92},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},84382,13056703020460,"Valentina","https://ap-avatar.wpscdn.com/avatar/be000253dac470eee5d?_k=1778207105932848923",8,"Research & Report","Decoupled Online Feedforward Generation of Optimal References for Saturated Synchronous Machine Drives","Presents a modular method for generating reference signals online for saturable synchronous machine drives. The approach dynamically computes optimal references without precomputed lookup tables, following the maximum-torque-per-ampere trajectory while enforcing maximum-torque-per-volt, current, and voltage constraints. Exact, decoupled first-order error dynamics are derived for predictable tracking and simplified tuning. The algorithm uses only the forward flux map, avoiding current-map inversion. Feedforward operation yields noise-free references structurally separated from feedback, with simulations and experiments matching lookup-table performance while eliminating precomputed reference tables.","Decoupled Online Feedforward Generation of Optimal References for Saturated Synchronous Machine Drives  \nMikko Sarn, Hannu Hartikainen, Antti Piippo, and Marko Hinkkanen, Fellow, IEEE  \narXiv :2607 .08528v1 [ ee ss . SY] 9 Jul 2026  \nAbstract—This paper presents a modular method for generating reference signals online for saturable synchronous machine drives. The method dynamically generates optimal references without precomputed lookup tables, following the maximum-torque-per-ampere (MTPA) trajectory while respecting maximum-torque-per-volt (MTPV), current, and voltage limits. The proposed tracking laws are formulated to yield exact, decoupled first-order error dynamics, ensuring predictable tracking responses and simplifying system tuning. The algorithm requires only the forward flux map, thereby eliminating the need for current-map inversion. By operating in a feedforward manner, the method ensures noise-free reference signals and structural separation from the feedback control. Both simulation and experimental results are presented, demonstrating that the proposed method achieves dynamic and steady-state performance on par with conventional lookup-table-based approaches, while avoiding the need for precomputed reference tables.  \nIndex Terms—Feedforward system, magnetic saturation, motor drives, optimal control, permanent magnet, synchronous machines.  \nI. Introduction  \nPERMANENT-MAGNET (PM)  \nchronous machines are utilized  \nand reluctance synin demanding applica-  \ntions ranging from electric vehicles to industrial servo drives. Achieving maximum efficiency and full utilization of inverter capacity in these drives requires precise reference generation strategies that minimize resistive losses while rigorously respecting system constraints. In particular, reference signals must satisfy the maximum-torque-per-ampere (MTPA) condition and, during high-speed operation, comply with maximumtorque-per-volt (MTPV), current, and voltage limits. However, magnetic saturation introduces significant nonlinearities in the flux-current relationship, complicating accurate real-time tracking of these optimal conditions.  \nThis work has been submitted to the IEEE for possible publication. This arXiv version includes minor bug fixes and language improvements compared with the version submitted to the journal. Copyright may be transferred without notice, after which this version may no longer be accessible.  \nThis work was supported by ABB Oy as well as by the Research Council of Finland through the Center of Excellence in High-Speed Electromechanical Energy Conversion Systems. The authors acknowledge the use of EPE infrastructure of Aalto School of Electrical Engineering.  \nMikko Sarn, Hannu Hartikainen, and Marko Hinkkanen are with Aalto University, Espoo, Finland ([e-mail: mikko.saren@aalto.fi](e-mail: mikko.saren@aalto.fi), hannu.1. hartikainen@aalto.fi, marko.hinkkanen@aalto.fi) .  \nAntti Piippo is with ABB Oy, Drives, 00380 Helsinki, Finland (e-mail: [antti.piippo@fi.abb.com](antti.piippo@fi.abb.com)).  \nTraditionally, optimal reference signals are generated using precomputed lookup tables [1]–[4] . While straightforward to execute, creating and implementing these lookup tables is cumbersome and potentially error-prone. Furthermore, static lookup tables cannot seamlessly accommodate dynamic changes in the machine. If the magnetic model or PM-flux linkage is updated online—for example, due to thermal variations—the precomputed reference tables become immediately inconsistent with the active control algorithm, leading to sub-optimal performance.  \nTo avoid the rigid nature of lookup tables, explicit analytical solutions have been developed to calculate optimal current references in closed form. For example, by assuming a linear magnetic model, the MTPA problem can be formulated as a fourth-order polynomial and solved in real time using algebraic root-finding algorithms, such as Ferrari’s method [5] . Other mathematical formulations mode","cbCaikSeRRP9ybpw","https://ap.wps.com/l/cbCaikSeRRP9ybpw","pdf",5508452,5,1,10,"English","en",105,"# Introduction\n## Problem context: optimal references under saturation and constraints\n## Limitations of lookup-table reference generation\n## Analytical closed-form approaches and their saturation limits\n## Search-based and injection-based strategies\n## Numerical optimization and feedback-based reference generation approaches","[{\"question\":\"What core idea does the paper introduce for reference generation in saturated synchronous machine drives?\",\"answer\":\"It introduces a decoupled, modular online feedforward method that generates optimal reference signals dynamically, without precomputed lookup tables, while tracking the MTPA trajectory under MTPV, current, and voltage limits.\"},{\"question\":\"Which constraints does the method enforce during reference tracking?\",\"answer\":\"The method respects maximum-torque-per-volt (MTPV) limits as well as maximum current and maximum voltage constraints while following the MTPA condition.\"},{\"question\":\"How does the proposed approach avoid needing current-map inversion and reduce reference-table dependence?\",\"answer\":\"It relies only on the forward flux map, eliminating current-map inversion, and it does not require precomputed reference tables because references are computed 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core idea does the paper introduce for reference generation in saturated synchronous machine drives?","Question",{"text":76,"@type":77},"It introduces a decoupled, modular online feedforward method that generates optimal reference signals dynamically, without precomputed lookup tables, while tracking the MTPA trajectory under MTPV, current, and voltage limits.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"Which constraints does the method enforce during reference tracking?",{"text":81,"@type":77},"The method respects maximum-torque-per-volt (MTPV) limits as well as maximum current and maximum voltage constraints while following the MTPA condition.",{"name":83,"@type":74,"acceptedAnswer":84},"How does the proposed approach avoid needing current-map inversion and reduce reference-table dependence?",{"text":85,"@type":77},"It relies only on the forward flux map, eliminating current-map inversion, and it does not require precomputed reference tables because references are computed 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