Dursun, Mustafa2023-07-262023-07-2620230941-0643https://doi.org/10.1007/s00521-023-08408-0https://hdl.handle.net/20.500.12684/12181In this article, a study has been carried out to further develop the Runge–Kutta (RK) algorithm, which has a current and robust mathematical structure, using the fitness distance balance (FDB) method, and to test it for induction machine control. The RK algorithm was developed to avoid local optimum solutions, speed up convergence, and seek out the best possible solutions globally. Despite offering promising solutions, it is clear that this algorithm has its shortcomings, especially in solving high-dimensional problems like asynchronous motor control. In this study, the FDB method was used to build the guide selection process in the RK algorithm to reach the optimal solution. The developed FDB-based RK algorithm has been tested and verified on the CEC17 benchmark problems for 30-dimensional search spaces. The results of the proposed algorithm have been compared to the performance of the classical RK algorithm, and it shows that the changes in the design of the RK algorithm are successful. The proportional–integral–derivative (PID) parameters employed as a controller in the indirect rotor field-oriented control approach of a three-phase induction motor have then been optimized using the accuracy-proven algorithm. The FDB-RK, RK, genetic algorithm, particle swarm (PSO), differential evolution, artificial bee colony, and weighted average of vectors (INFO) algorithms have been used in this study with three different fitness functions and Wilcoxon and Freidman statistical analyses to find the best values for PID parameters. According to the data, FDB-RK-based PID controller has the best performance among the techniques. © 2023, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.en10.1007/s00521-023-08408-0info:eu-repo/semantics/closedAccessFitness distance balanceIndirect field-oriented controlOptimizationPID controllerRunge–KuttaControllersElectric control equipmentGenetic algorithmsInduction motorsParticle swarm optimization (PSO)Proportional control systemsRobust controlStatistical methodsVector control (Electric machinery)Balance methodsDistance balanceFitness distance balanceIndirect field oriented controlOptimisationsPerformanceProportional-integral-derivatives controllersRunge-Kutta algorithmsRunge–kuttumThree phase induction motorThree term control systemsArticle2-s2.0-85150267240WOS:000952828500002Q1Q2