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We, the Editors and Publisher of the journal Engineering Optimization, have retracted the following article at the request and agreement of the author: Chih-Hong Lin (2020): Mended grey wolf optimization and Taguchi method with multi-goal optimization for six-phase copper rotor induction motor design, Engineering Optimization, DOI: The content of this article contains a high level of similarity with the published article below: Chih-Hong Lin (2020): Altered Grey Wolf Optimization and Taguchi Method with FEA for Six-Phase Copper Squirrel Cage Rotor Induction Motor Design, Energies, 13, 2282, DOI: We have been informed in our decision-making by our policy on publishing ethics and integrity and the COPE guidelines on retractions. The retracted article will remain online to maintain the scholarly record, but it will be digitally watermarked on each page as 'Retracted'. [ABSTRACT FROM AUTHOR]

A self-constructing fuzzy neural network (SCFNN) is proposed to control the rotor position of a permanent-magnet synchronous motor (PMSM) drive to track periodic step and sinusoidal reference inputs in this study. The structure and the parameter learning phases are preformed concurrently and online in the SCFNN. The structure learning is based on the partition of input space, and the parameter learning is based on the supervised gradient decent method using a delta adaptation law. Several simulation and experimental results are provided to demonstrate the effectiveness of the proposed SCFNN control stratagem under the occurrence of parameter variations and external disturbance. Index Terms--Fuzzy neural network, gradient decent method, self-constructing, synchronous motor.

In this paper, a robust controller design with [H.sub.[infinity]] performance using a recurrent neural network (RNN) is proposed for the position tracking control of a permanent-magnet linear synchronous motor. The proposed robust [H.sub.[infinity]] controller, which comprises a RNN and a compensating control, is developed to reduce the influence of parameter variations and external disturbance on system performance. The RNN is adopted to estimate the dynamics of the lumped plant uncertainty, and the compensating controller is used to eliminate the effect of the higher order terms in Taylor series expansion of the minimum approximation error. The tracking performance is ensured in face of parameter variations, external disturbance and RNN estimation error once a prespecified [H.sub.[infinity]] performance requirement is achieved. The synthesis of the RNN training rules and compensating control are based on the solution of a nonlinear [H.sub.[infinity]] control problem corresponding to the desired [H.sub.[infinity]] performance requirement, which is solved via a choice of quadratic storage function. The proposed control method is able to track both the periodic step and sinusoidal commands with improved performance in face of large parameter perturbations and external disturbance. Index Terms--[H.sub.[infinity]] control, linear synchronous motor, lumped uncertainty, recurrent neural network (RNN).

In this study a particular incremental motion control problem, which is specified by the trapezoidal velocity profile using multisegment sliding mode control (MSSMC), is proposed to control a permanent magnet linear synchronous motor (PMLSM) servo drive system. First, the structure and operating principle of the PMLSM are described in detail. Second, a field-oriented control PMLSM servo drive is introduced. Then, each segment of the multisegment switching surfaces is designed to match the corresponding part of the trapezoidal velocity profile, thus the motor dynamics on the specified-segment switching surface have the desired velocity or acceleration corresponding part of the trapezoidal velocity profile. In addition, the proposed control system is implemented in a PC-based computer control system. Finally, the effectiveness of the proposed PMLSM servo drive system is demonstrated by some simulated and experimental results.