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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 The retracted article will remain online to maintain the scholarly record, but it will be digitally watermarked on each page as 'Retracted'.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]

Due to nonlinear friction and uncertainty effects of linear permanent magnet synchronous motor (LPMSM), the existing linear controllers cannot achieve good control performance. In order to increase the robustness of system under some uncertainties disturbances, the proposed adaptive amended Elman neural network backstepping (AAENNB) control system with error compensation controller is adopted for controlling the LPMSM drive system. Firstly, the field-oriented control (FOC) is applied to formulate the dynamic equation of the LPMSM drive system. Secondly, a backstepping approach is proposed for controlling the motion of LPMSM drive system. The proposed backstepping control system and the mover position of the LPMSM drive system possess good transient control performance under the uncertainties action for the tracking of periodic references. Because of the LPMSM with nonlinear and time-varying dynamic characteristics, an adaptive amended Elman neural network uncertainty observer (AAENNUO) with the adaptive law is proposed to estimate the required lumped uncertainty. Moreover, the error compensation controller with the error estimation law is proposed to compensate the minimum reconstructed error according to Lyapunov stability theorem. Furthermore, to improve convergent speed and to obtain better learning performance, the varied learning rate of the weight in the AENN is regulated by use of the corrected particle swarm optimization (CPSO) algorithm with segment regulation mechanics, that is, the innovativeness for using the CPSO algorithm. At last, the usefulness of the proposed control system is confirmed by experimental results. [ABSTRACT FROM AUTHOR]

A linear permanent magnet synchronous motor drive system is existed in many nonlinear effects such as the external load force, the flux saturation, the cogging force, the column friction and Stribeck force, and the parameters variations. Due to the uncertainty effects, the linear permanent magnet synchronous motor drive system is hard to achieve the good control performance by using linear controller. To raise robustness under occurrence of uncertainty, the integral backstepping control system with hitting function is first proposed for controlling the linear permanent magnet synchronous motor drive system. The used integrator can ameliorate the system's robustness under the parameters uncertainties and external force disturbances. To reduce vibration of control strength, the integral backstepping control system by means of the revised recurrent fuzzy neural network with mended particle swarm optimization is next proposed to operate the linear permanent magnet synchronous motor drive system to raise robustness of system. Furthermore, four variable learning rates in the weights of the revised recurrent fuzzy neural network are adopted by using mended particle swarm optimization to speed up parameter's convergence. Finally, comparative performances through some experimental upshots are verified that the integral backstepping control system by means of revised recurrent fuzzy neural network with mended particle swarm optimization has better control performances than those of the proposed methods for the linear permanent magnet synchronous motor drive system. [ABSTRACT FROM AUTHOR]

Because of the uncertainty's action in a linear permanent magnet synchronous motor drive system such as the external load force, the cogging force, the column friction force and the Stribeck effect force and the parameters variations, it is difficult to reach specific control performances by using the existing linear controller. To raise robustness under occurrence of parameters uncertainties and external force disturbances, the smart backstepping control system with three adaptive laws is proposed for controlling the linear permanent magnet synchronous motor drive system. In accordance with the Lyapunov function, three adaptive laws are derived to ameliorate the system's robustness. Furthermore, the smart backstepping control system using revised recurrent fuzzy neural network and revised ant colony optimization with the compensated controller is proposed to improve the control performance. The revised recurrent fuzzy neural network acts as the estimator of the uncertainty's disturbances. In addition, the compensated controller with error estimation law is proposed to compensate the minimum rebuilt error. Moreover, two learning rates of the weights in the revised recurrent fuzzy neural network are derived according to the discrete-type Lyapunov stability to assure convergence of the output tracking error and are adopted by using the revised ant colony optimization to speed-up parameter's convergence. Finally, some comparative performances are verified through some tentative upshots that the smart backstepping control system by virtue of revised recurrent fuzzy neural network and revised ant colony optimization with the compensated controller results in better control performances for the linear permanent magnet synchronous motor drive system. [ABSTRACT FROM AUTHOR]

A six phase copper rotor induction motor (SPCRIM) drive system still exists in lots of nonlinear characteristics such as the added load torque, the Stribeck effect torque, the the cogging torque, the coulomb friction torque and the parameters variations. Due to some uncertainties effects, the using linear controller can not achieve better control performance for the SPCRIM drive system. To obtain better performance, a clever backstepping control system using two adaptive laws and a hitting function is proposed for controlling the SPCRIM drive system. To improve larger chattering phenomenon under uncertainties affects for aforementioned control system, the clever backstepping control system using two adaptive laws, a revised recurrent fuzzy neural network (RRFNN) and a compensated controller is proposed to estimate the required lumped uncertainty and to compensate the minimum reconstructed error of the estimated law. Furthermore, the corrected particle swarm optimization (CPSO) algorithm by using variable dynamic inertia weight and variable dynamic constriction factor with segment regulation mechanics that is the innovativeness for using the CPSO algorithm is adopted to regulate four variable learning rates of the weights in the RRFNN to speed-up parameter's convergence. Finally, comparative performances through some experimental results are verified that the clever backstepping control system using two adaptive laws, a RRFNN and a compensated controller has better control performances than those of the proposed methods for the SPCRIM drive system. [ABSTRACT FROM AUTHOR]

Compared with the classical linear controller, the nonlinear controller can result better control performance for the nonlinear uncertainties of the continuously variable transmission (CVT) system which is driven by the synchronous reluctance motor (SynRM). The better control performance can be shown in the nonlinear uncertainties behavior of CVT system by using the proposed novel admixed improved recurrent Hermite polynomial neural network (AIRHPNN) control system. The novel AIRRHPNN control system can carry out overlooker control, improved recurrent Hermite polynomial neural network control (IRHPNN) with an adaptive law, and reimbursed control with an appraised law. Additionally, according to the Lyapunov stability theorem, the adaptive law in the IRHPNN and the appraised law of the eimbursed controller are established. Furthermore, two weights with two varied learning rates according to increment Lyapunov function are derived to help improving convergence. Finally, comparative examples are illustrated by the experimental results to confirm that the proposed control system could be obtained better control performance. [ABSTRACT FROM AUTHOR]

To cut down influence of nonlinear time-varying uncertainty action in a synchronous reluctance motor driving continuously variable transmission system, an admixed recurrent Gegenbauer polynomials neural network with mended particle swarm optimization control system is posed for improving control performance. The admixed recurrent Gegenbauer polynomials neural network with mended particle swarm optimization control system involves an observer control, a recurrent Gegenbauer polynomial neural network control and a remunerated control. The weights of recurrent Gegenbauer polynomials neural network controller are regulated by using the adaptive law and the gradient descent technology. The remunerated control with a reckoned law is derived and computed by means of the Lyapunov stability theorem so as to pledge stability of the control system. Likewise, to speedup convergence of weights in the recurrent Gegenbauer polynomial neural network, the mended particle swarm optimization algorithm is used for regulating two kinds of learning rates. At last, three kinds of experimental results are demonstrated to confirm the usefulness of the put forward control system with comparative studies. [ABSTRACT FROM AUTHOR]

A switched reluctance motor (SRM) drive system has highly nonlinear uncertainties owing to a convex construction. It is hard for the linear control methods to achieve good performance for the SRM drive system. An adaptive nonlinear backstepping control system using the mended recurrent Romanovski polynomials neural network and mended PSO with an adaptive law and an error estimated law is proposed to estimate the lumped uncertainty and to compensate the estimated error in order to enhance the robustness of the SRM drive system. Additionally, in accordance with the Lyapunov stability theorem, the adaptive law in the mended recurrent Romanovski polynomials neural network and the error estimated law are established. Furthermore, to help improve convergence and to obtain better learning performance, the mended particle swarm optimization (PSO) algorithm is utilized for adjusting the two varied learning rates of the two parameters in the mended recurrent Romanovski polynomials neural network. Finally, some experimental results and a comparative analysis are verified that the proposed control scheme has better control performances for controlling the SRM drive system. [ABSTRACT FROM AUTHOR]

Summary: Due to air‐gap field harmonic, cogging torque, stator's current time harmonic, and the influence of flux saturation, a six‐phase copper rotor induction motor (SCRIM) drive system has highly nonlinear uncertainties. Thus, the linear control method for the SCRIM drive system is difficult to achieved good performance under the nonlinear uncertainty action. To obtain better control performance, the adaptive backstepping control system using switching function is firstly proposed for controlling the SCRIM drive system to overcome the uncertainty influence. With the proposed control system, the SCRIM drive system holds in robustness to these uncertainties for the tracking of periodic reference trajectories. To enhance the robustness of the SCRIM drive system, the adaptive backstepping control system using adaptive law is proposed for estimating the required lumped uncertainty to reduce chattering phenomenon. When the inertia of the counterweight is varying, this proposed method can perform well in general situations but cannot get a satisfactory performance. The adaptive backstepping control system using mended recurrent Romanovski polynomials neural network with reformed particle swarm optimization (PSO) is thus proposed to estimate the lumped uncertainty and to compensate estimated error for obtaining better control performance. Furthermore, two variable learning rates of the weights in the mended recurrent Romanovski polynomials neural network are adopted by using reformed PSO to speed up parameter's convergence. Finally, some experimental results with comparative control performances are demonstrated, and then, the effectiveness of proposed control system with better control performance is verified for the position tracking of periodic reference inputs. [ABSTRACT FROM AUTHOR]

A six-phase copper rotor induction motor (SCRIM) drive system causes a lot of nonlinear effects such as nonlinear uncertainties. To obtain better performance, the backstepping control system using switching function is firstly proposed for controlling the SCRIM drive system. To reduce chattering in control effort, the backstepping control system using revamped recurrent fuzzy neural network (RFNN) with mended ant colony optimization (ACO) is secondly proposed for controlling the SCRIM drive system to raise robustness of system. Furthermore, four variable learning rates of the weights in the revamped RFNN are adopted by using mended ACO to speed-up parameter's convergence. Finally, comparative performances through some experimental results are verified that the proposed backstepping control system by means of revamped RFNN with mended ACO has better control performances than the other methods for the SCRIM drive system. [ABSTRACT FROM AUTHOR]

Owing to air-gap field harmonic, cogging torque, stator's current time harmonic and the influence of flux saturation, a synchronous reluctance motor (SynRM) drive system has highly nonlinear uncertainties. Thus the linear control method for the SynRM drive system is difficult to achieved good performance under the nonlinear uncertainty action. To obtain better control performance the novel nonlinear backstepping control system using upper bound with switching function is firstly proposed for controlling the SynRM drive system to prevail the lumped uncertainty. With the proposed control system, the SynRM servo-drive system holds in robustness to uncertainties for the tracking of periodic reference trajectories. To enhance the robustness of the SynRM drive system, the novel nonlinear backstepping control system using adaptive law is proposed for estimating the required lumped uncertainty to reduce chattering phenomenon. When the inertia of the counterweight is varying, this proposed method can perform well in general situations, but cannot get a satisfactory performance. The novel nonlinear backstepping control system using reformed recurrent Hermite polynomial neural network with adaptive law and error estimated law is thus proposed to estimate the lumped uncertainty and compensate estimated error for obtaining better control performance. Furthermore, two varied learning rates of the reformed recurrent Hermite polynomial neural network is derived according to increment type Lyapunov function to speed-up parameter's convergence. Finally, some experimental results with comparative control performances are demonstrated, and then the effectiveness of the proposed control system with better control performance is verified for the position tracking of periodic reference inputs with torque ripple consideration. [ABSTRACT FROM AUTHOR]

Because the non-linear and time-varying characteristics of the continuously variable transmission (CVT) system driven by using a six-phase copper rotor induction motor (IM) are unknown, improving the control performance of the linear control design is time consuming. To overcome difficulties in the design of a linear controller for the six-phase copper rotor IM servo-driven CVT system with lumped non-linear load disturbances, a blend modified recurrent Gegenbauer orthogonal polynomial neural network (NN) control system, which has the online learning capability to return to the non-linear time-varying system, was developed. The blend modified recurrent Gegenbauer orthogonal polynomial NN control system can perform overseer control, modified recurrent Gegenbauer orthogonal polynomial NN control and recompensed control. Moreover, the adaptation law of online parameters in the modified recurrent Gegenbauer orthogonal polynomial NN is based on the Lyapunov stability theorem. The use of amended artificial bee colony optimization (ABCO) yielded two optimal learning rates for the parameters, which helped improve convergence. Finally, comparison of the experimental results of the present study with those of previous studies demonstrated the high control performance of the proposed control scheme. [ABSTRACT FROM AUTHOR]

The nonlinear and time-varying characteristics of the V-belt continuously variable transmission system driven by a permanent magnet synchronous motor (PMSM) are unknown, therefore, improving the control performance of the linear control design is time-consuming. To overcome difficulties in the design of a linear controller for the PMSM servo-driven V-belt continuously variable transmission system with the lumped nonlinear load disturbances, a composite recurrent Laguerre orthogonal polynomial neural network (NN) control system which has online learning capability to respond the nonlinear time-varying system, was developed. The composite recurrent Laguerre orthogonal polynomial NN control system can perform inspector control, recurrent Laguerre orthogonal polynomial NN control which involves an adaptation law, and recouped control which involves an estimation law. Moreover, the adaptation law of online weight parameters in the recurrent Laguerre orthogonal polynomial NN is based on Lyapunov stability theorem. The use of modified particle swarm optimization yielded two optimal learning rates for the weight parameters which helped improve convergence. Finally, comparison of the experimental results of the present study with those of previous studies demonstrated the high control performance of the proposed control scheme. [ABSTRACT FROM AUTHOR]

A multi-objective optimization design technique for a six-phase copper rotor induction motor is proposed. The amended particle swarm optimization (PSO) and Taguchi methods combined with finite element analysis are used in this design technique. The objectives in the first-stage optimization are the minimization of manufacturing cost and starting current. In the second-stage optimization, the objectives are the maximization of efficiency, power factor and output torque. The Taguchi method can optimize the machine parameters of performance characteristics in electrical discharge machining. The experimental results are further transformed into the signal-to-noise ratios and amended PSO coefficients based on amended PSO analysis with regard to multiple performance characteristics index values. The results of the optimizations showed significant reduction in terms of the use of magnets as well as improvement in the machine performance. Finally, the experimental results confirm the validity of the proposed optimization design approach. [ABSTRACT FROM AUTHOR]

The good control performance of the permanent magnet linear synchronous motor (LSM) drive system is very difficult to achieve using linear controller because of uncertainty effects, such as ending-fictitious force. A backstepping approach is proposed to control the motion of the LSM drive system. With the proposed backstepping control system, the mover position of the LSM drive achieves good transient control performance and robustness. Although favorable tracking responses can be obtained by the backstepping control system, the chattering in the control effort is critical because of the large control gain. Because there are many nonlinear and time-varying uncertainties in the LSM drive systems, the nonlinear backsteping control system, which an adaptive modified recurrent Laguerre orthogonal polynomial neural network (NN) is used to estimate uncertainty, is thus proposed to reduce the chattering in the control effort and thereby enhance the robustness of the LSM drive system. In addition, the on-line parameter training methodology of the modified recurrent Laguerre orthogonal polynomial NN is based on the Lyapunov stability theorem. Furthermore, two optimal learning rates of the modified recurrent Laguerre orthogonal polynomial NN are derived to accelerate parameter convergence. Finally, comparison of the experimental results of the present study demonstrates the high control performance of the proposed control scheme. [ABSTRACT FROM AUTHOR]

A V-belt continuously variable transmission system driven by a permanent magnet synchronous motor has much unknown nonlinear and time-varying characteristics. In order to capture the system's nonlinear and dynamic behavior, a hybrid recurrent Laguerre-orthogonal-polynomials neural network (NN) control system with modified particle swarm optimization (PSO) is proposed for achieving online better learning capacity and faster convergence to enhance system robustness. The hybrid recurrent Laguerre-orthogonal-polynomials NN control system can perform inspected control, recurrent Laguerre-orthogonal-polynomials NN control, which involves an adaptive law, and recouped control, which involves an estimated law. Moreover, the adaptive law of online parameters in the recurrent Laguerre-orthogonal-polynomials NN is derived by means of Lyapunov stability theorem. Furthermore, two optimal learning rates of the online parameters in the recurrent Laguerre-orthogonal-polynomials NN by means of modified PSO are applied to achieve online better learning capacity and faster convergence. Finally, to show the effectiveness of the proposed control scheme, comparative studies are demonstrated by experimental results. [ABSTRACT FROM AUTHOR]

Because the nonlinear uncertainty of the continuously variable transmission system operated by the synchronous reluctance motor is unknown, control performance obtained for classical linear controller is poor, with comparison to more complex, nonlinear control methods. Due to good learning skill online, a blend amended recurrent Gegenbauer-functional-expansions neural network (NN) control system was developed to return to the nonlinear uncertainties behavior. The blend amended recurrent Gegenbauer-functional-expansions NN control system can fulfill overseer control, amended recurrent Gegenbauer-functional-expansions NN control with an adaptive dharma and recompensed control with a reckoned dharma. In addition, according to the Lyapunov stability theorem, the adaptive dharma in the amended recurrent Gegenbauer-functional-expansions NN and the reckoned dharma of the recompensed controller are established. Furthermore, an altered artificial bee colony optimization yields two varied learning rates for two parameters to find two optimal values, which helped improving convergence. Finally, various comparisons of the experimental results are demonstrated to confirm that the proposed control system can result better control performance. [ABSTRACT FROM AUTHOR]

Because the nonlinear and time-varying characteristics of the continuously variable transmission system operated using a six-phase copper rotor induction motor are unknown, improving the control performance of the linear control design is time-consuming. To capture the nonlinear and dynamic behaviour of the six-phase copper rotor induction motor servo-driven continuously variable transmission system, a blend modified recurrent Gegenbauer orthogonal polynomial neural network (NN) control system, which has the online learning capability to return to the nonlinear time-varying system, was developed. The blend modified recurrent Gegenbauer orthogonal polynomial NN control system can perform overseer control, modified recurrent Gegenbauer orthogonal polynomial NN control, and recompensed control. Moreover, the adaptation law of online parameters in the modified recurrent Gegenbauer orthogonal polynomial NN is based on the Lyapunov stability theorem. The use of amended artificial bee colony optimization yielded two optimal learning rates for the parameters, which helped improve convergence. Finally, comparison of the experimental results of the present study with those of previous studies demonstrated the high control performance of the proposed control scheme. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In order to capture nonlinear and dynamic behaviors of the V-belt continuously variable transmission system with lots of unknown nonlinear and time-varying characteristics, an intelligent dynamic control system using modified particle swarm optimization is proposed for controlling a permanent magnet synchronous motor servo-drive V-belt continuously variable transmission system to raise robustness. The intelligent dynamic control system comprised an inspector control system, a recurrent Laguerre-orthogonal-polynomials neural network controller with adaptive law and a recouped controller with estimation law. The adaptive law of parameters in the recurrent Laguerre-orthogonal-polynomials neural network is derived according to Lyapunov stability theorem. To achieve better learning performance and faster convergence, the modified particle swarm optimization is employed to regulate two varied learning rates of the parameters in the recurrent Laguerre-orthogonal-polynomials neural network. At last, comparative studies shown by experimental results are illustrated to demonstrate the control performance of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper describes a multiobjective optimization design technique for a six-phase copper rotor induction motor mounted with a scroll compressor to achieve minimum manufacturing cost and starting current, and maximum efficiency and power factor. The proposed algorithm uses the modified particle swarm optimization and the Taguchi method with finite-element analysis. The experimental results confirm the validity of the proposed method. [ABSTRACT FROM PUBLISHER]

Because of the unknown nonlinearity and time-varying characteristics of a V-belt continuously variable transmission (CVT) driven electric scooter system using a permanent magnet synchronous motor (PMSM) servo drive, its accurate dynamic model is difficult to establish for the design of the linear controller in the whole system. In order to conquer this difficulty and increase robustness, a novel adaptive modified recurrent Legendre neural network (NN) control system is proposed for controlling a PMSM servo-driven electric scooter with a V-belt CVT system. The novel adaptive modified recurrent Legendre NN control system consists of a modified recurrent Legendre NN control with adaptation law and a compensated control with estimation law. Additionally, the online parameter tuning methodology of the modified recurrent Legendre NN control and the estimation law of the compensated control can be derived by using the Lyapunov stability theorem. Furthermore, two optimal learning rates of the modified recurrent Legendre NN are proposed according to a discrete-type Lyapunov function in order to raise the speed of convergence. Finally, comparative studies are provided by experimental results in order to show the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Because a V-belt continuously variable transmission system driven by Permanent magnet synchronous motor (PMSM) has many nonlinear and time-varying characteristics, the linear control design with better control performance has to execute a complex and time consuming procedure. To reduce this difficulty and raise robustness of system under the occurrence of the uncertainties, a hybrid recurrent Laguerre-orthogonal-polynomial Neural network (NN) control system which has online learning ability to respond to the system's nonlinear and time-varying behavior is proposed in this study. This control system consists of an inspector control system, a recurrent Laguerre- orthogonal-polynomial NN control with adaptive law and a recouped control with estimated law. Moreover, the adaptive law of online parameter in the recurrent Laguerre-orthogonal-polynomial NN is derived using Lyapunov stability theorem. Two optimal learning rates of the parameters based on modified Particle swarm optimization (PSO) are proposed to achieve fast convergence. Finally, to verify the effectiveness of the proposed control scheme, comparative studies are demonstrated by experimental results. [ABSTRACT FROM AUTHOR]

The composite recurrent Laguerre orthogonal polynomials neural network (NN) control system using altered particle swarm optimization (PSO) is developed for controlling the V-belt continuously variable transmission (CVT) system driven by permanent magnet synchronous motor to obtain better control performance. The simplified dynamic and kinematic models of a V-belt CVT system are derived by law of conservation. The control system consists of an inspector control, a recurrent Laguerre orthogonal polynomials NN control with adaptation law, and a recouped control with estimation law. Moreover, the adaptation law of online parameters in the recurrent Laguerre orthogonal polynomials NN is originated from Lyapunov stability theorem. Additionally, two optimal learning rates of the parameters by means of altered PSO are posed in order to achieve better convergence. At last, comparative studies shown by experimental results are illustrated to demonstrate the control performance of the proposed control scheme. [ABSTRACT FROM AUTHOR]

The range-extended electric vehicle is proposed to improve the range anxiety drivers have of electric vehicles. Conventionally, a gasoline/diesel generator increases the range of an electric vehicle. Due to the zero-CO2 emission stipulations, utilizing fuel cells as generators raises concerns in society. This paper presents a novel charging strategy for fuel cell/battery electric vehicles. In comparison to the conventional switch control, a fuzzy control approach is employed to enhance the battery’s state of charge (SOC). This approach improves the quick loss problem of the system’s SOC and thus can achieve an extended driving range. Smooth steering experience and range extension are the main indexes for development of fuzzy rules, which are mainly based on the energy management in the urban driving model. Evaluation of the entire control system is performed by simulation, which demonstrates its effectiveness and feasibility. [ABSTRACT FROM AUTHOR]

Because of unknown nonlinearity and time-varying characteristics of electric scooter with V-belt continuously variable transmission (CVT) driven by permanent magnet synchronous motor (PMSM), its accurate dynamic model is difficult to establish for the design of the linear controller in whole system. In order to conquer this difficulty and raise robustness, an adaptive recurrent Chebyshev neural network (NN) control system is proposed to control for PMSM servo-drive electric scooter with V-belt CVT under lumped nonlinear external disturbances in this study. The adaptive recurrent Chebyshev NN control system consists of a recurrent Chebyshev NN control and a compensated control with estimation law. In addition, the online parameters tuning methodology of the recurrent Chebyshev NN and the estimation law of the compensated controller can be derived by using the Lyapunov stability theorem. Moreover, the two optimal learning rates of the recurrent Chebyshev NN based on a discrete-type Lyapunov function are proposed to guarantee the convergence of tracking error. Finally, comparative studies are demonstrated by experimental results in order to show the effectiveness of the proposed control scheme. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Because of unknown nonlinear and time-varying characteristics of V-belt continuously variable transmission (CVT)-driven electric scooter by using permanent magnet synchronous motor (PMSM) servo drive system, all gains tuning process for linear controller is a very time-consuming task. A hybrid modified recurrent Legendre neural network (NN) control system, which consists of an inspector control, a hybrid modified recurrent Legendre NN control and a recouped control with estimation law, is proposed for controlling the V-belt CVT-driven electric scooter under the occurrence of the nonlinear load disturbances and the variation of parameters to acquire better control performance. Moreover, the online parameters tuning method of the modified recurrent Legendre NN is based on Lyapunov stability theorem and gradient descent method. Furthermore, the two optimal learning rates of the hybrid modified recurrent Legendre NN control system are derived according to discrete Lyapunov function to enhance convergence speed. The proposed control scheme is capable of responding to system's nonlinear and time-varying behaviors due to online learning ability. Finally, some experimental results are verified to show that the effectiveness of the proposed hybrid modified recurrent Legendre NN control system controlled the V-belt CVT-driven electric scooter by using PMSM servo drive system. [ABSTRACT FROM AUTHOR]

Because of unknown nonlinearity and time-varying characteristic of electric scooter with V-belt continuously variable transmission system driven by using permanent magnet synchronous motor, its accurate dynamic model is difficult to establish for the design of the linear controller in whole system. In order to conquer this difficulty and raise robustness, an adaptive recurrent Chebyshev neural network control system is proposed to control for permanent magnet synchronous motor servo-drive electric scooter with V-belt continuously variable transmission under lumped nonlinear external disturbances in this study. The adaptive recurrent Chebyshev neural network control system consists of a recurrent Chebyshev neural network control and a compensated control with estimation law. In addition, the online parameter tuning methodology of the recurrent Chebyshev neural network and the estimation law of the compensated controller can be derived by using the Lyapunov stability theorem. Moreover, the two optimal learning rates of the recurrent Chebyshev neural network based on the discrete-type Lyapunov function are proposed to guarantee the convergence of tracking error. Finally, comparative studies are demonstrated by experimental results in order to show the effectiveness of the proposed control scheme. [ABSTRACT FROM PUBLISHER]

Because permanent magnet synchronous generator (PMSG) system driven by permanent magnet synchronous motor (PMSM) based on wind turbine emulator (WTE) is a nonlinear and time-varying system with high complication, an accurate dynamic model of the PMSG system directly driven by WTE is difficult to establish for the linear controller design. In order to conquer this difficulty and improve the robustness of dynamic system, the PMSG system controlled by the online-tuned parameters of the novel modified recurrent wavelet neural network (NN)-controlled system is proposed to control output voltages and powers of controllable rectifier and inverter in this study. First, a closed-loop PMSM-driven system based on WTE is designed for driving the PMSG system to generate output power. Second, the rotor speeds of the PMSG, the voltages, and currents of the two power converters are detected simultaneously to yield maximum power output. In addition, two sets of the online-tuned parameters of the modified recurrent wavelet NN controllers in the controllable rectifier and inverter are developed for the voltage-regulating controllers in order to improve output performance. Finally, some experimental results are verified to show the effectiveness of the proposed novel modified recurrent wavelet NN controller for the power output of the PMSG system driven by WTE. [ABSTRACT FROM AUTHOR]

Due to nonlinear uncertainties of the electric scooter such as nonlinear friction force of the transmission belt and clutch, these will lead to degenerate tracking responses in command current and speed of the permanent magnet synchronous motor (PMSM) servo-driven electric scooter. In this study a novel hybrid recurrent wavelet neural network (HRWNN) control system is proposed to raise robustness of the PMSM servo-driven electric scooter under the occurrence of the variation of rotor inertia and load torque disturbance. First, the field-oriented mechanism is applied to formulate the dynamic equation of the PMSM servo drive. Then, a novel HRWNN control system is proposed to control motion for a PMSM servo-driven electric scooter. The HRWNN control system composed of a supervisor control, a RWNN and a compensated control with adaptive law. The online parameter training methodology with adaptive law in the RWNN is derived based on the Lyapunov stability theorem. Then adaptive law of the parameter in the RWNN can be updated by using the gradient descent method and the backpropagation algorithm. Finally, the effectiveness of the proposed control scheme is verified by experimental results. [ABSTRACT FROM AUTHOR]

The two recurrent modified Elman neural networks (NNs) controlled permanent magnet (PM) synchronous generator system based on wind turbine emulator is proposed to regulate output voltages of rectifier and inverter in this study. First, the wind turbine emulator, which adopts a closed-loop PM synchronous servo motor drive system to act as prime machine, is designed to drive the PM synchronous generator system to yield the maximum power at different wind speeds. Then, the rotor speed of the PM synchronous generator, the DC bus voltage, and current of the rectifier are detected simultaneously to yield maximum DC power of the rectifier through DC bus power control. Moreover, one online training recurrent modified Elman NN controller is developed to regulate DC bus voltage in the output end of rectifier and another online training recurrent modified Elman NN controller is developed to regulate AC power in the output end of inverter in order to improve the control performance. Finally, some experimental results are verified to show the effectiveness of the proposed recurrent modified Elman NN controlled PM synchronous generator system based on wind turbine emulator. [ABSTRACT FROM AUTHOR]

Proposes a multisegment sliding mode control in accordance with the trapezoidal velocity profile for a permanent magnet linear synchronous motor (PMLSM). Description of the modeling of PMLSM; Control approach underlying a PMLSM servo drive; Discussion on the incremental motion control of PMLSM; Simulation and experimental results.

Presents information on a study which described an integral-proportional controller with on-line gain-tuning using a recurrent fuzzy neural network for controlling the mover position of a permanent magnet linear synchronous motor (PMLSM) servo drive system. Modeling of PMLSM; Basic control approach of a PMLSM servo drive.

The Editor-in-Chief has retracted this article. [ABSTRACT FROM AUTHOR]

The Editor-in-Chief is issuing an Editorial Expression of Concern for this Article. [ABSTRACT FROM AUTHOR]

This article has been retracted. Please see the retraction notice for more detail: https://doi.org/10.1007/s12206-020-1243-8 [ABSTRACT FROM AUTHOR]

Owing to some nonlinear characteristics in the permanent-magnet synchronous motor (SM), such as nonlinear friction, cogging torque, wind stray torque, external load torque, and unmodeled systems, fine control performances cannot be accomplished by utilizing the general linear controllers. Thereby, the backstepping approach adopting three adaptive rules and a swapping function is brought forward for controlling the rotor motion in the permanent-magnet SM drive system to reduce nonlinear uncertainties effects. To improve the chattering phenomenon, the backstepping control with three adaptive rules using a revised recurring sieved Pollaczek polynomials neural network (RRSPPNN) with reformed grey wolf optimization (RGWO) and a recouped controller is proposed to estimate the internal collection and external collection torque uncertainties, and to recoup the smallest fabricated error of the appraised rule. In the light of the Lyapunov stability, the on-line parametric training method of the RRSPPNN can be derived through an adaptive rule. Furthermore, to obtain a beneficial learning rate and improve the convergence of the weights, the RGWO algorithm adopting two exponential-functional adjustable factors is applied to adjust the two learning rates of the weights. Then, the efficiency of the used controller is validated by test results. [ABSTRACT FROM AUTHOR]

Owing to some nonlinear characteristics in the permanent-magnet synchronous motor (SM), such as nonlinear friction, cogging torque, wind stray torque, external load torque, and unmodeled systems, fine control performances cannot be accomplished by utilizing the general linear controllers. Thereby, the backstepping approach adopting three adaptive rules and a swapping function is brought forward for controlling the rotor motion in the permanent-magnet SM drive system to reduce nonlinear uncertainties effects. To improve the chattering phenomenon, the backstepping control with three adaptive rules using a revised recurring sieved Pollaczek polynomials neural network (RRSPPNN) with reformed grey wolf optimization (RGWO) and a recouped controller is proposed to estimate the internal collection and external collection torque uncertainties, and to recoup the smallest fabricated error of the appraised rule. In the light of the Lyapunov stability, the on-line parametric training method of the RRSPPNN can be derived through an adaptive rule. Furthermore, to obtain a beneficial learning rate and improve the convergence of the weights, the RGWO algorithm adopting two exponential-functional adjustable factors is applied to adjust the two learning rates of the weights. Then, the efficiency of the used controller is validated by test results. [ABSTRACT FROM AUTHOR]

In light of fine learning ability in the existing uncertainties, a sage revised reiterative even Zernike polynomials neural network (SRREZPNN) control with modified fish school search (MFSS) method is proposed to control the six-phase squirrel cage copper rotor induction motor (SSCCRIM) impelled continuously variable transmission assembled system for obtaining the brilliant control performance. This control construction can carry out the SRREZPNN control with the cozy learning law, and the indemnified control with an assessed law. In accordance with the Lyapunov stability theorem, the cozy learning law in the revised reiterative even Zernike polynomials neural network (RREZPNN) control can be extracted, and the assessed law of the indemnified control can be elicited. Besides, the MFSS can find two optimal values to adjust two learning rates with raising convergence. In comparison, experimental results are compared to some control systems and are expressed to confirm that the proposed control system can realize fine control performance. [ABSTRACT FROM AUTHOR]

As the six-phase squirrel cage copper rotor induction motor has some nonlinear characteristics, such as nonlinear friction, nonsymmetric torque, wind stray torque, external load torque, and time-varying uncertainties, better control performances cannot be achieved by utilizing general linear controllers. The snug backstepping control with sliding switching function for controlling the motion of a six-phase squirrel cage copper rotor induction motor drive system is proposed to reduce nonlinear uncertainty effects. However, the previously proposed control results in high chattering on nonlinear system effects and overtorque on matched uncertainties. So as to reduce the immense chattering situation, we then put forward the rectified reiterative sieved-Pollaczek polynomials neural network backstepping control with an improved fish school search method to estimate the external bundled torque uncertainties and to recoup the smallest reorganized error of the evaluated rule. In the light of Lyapunov stability, the online parametric training method of the rectified reiterative sieved-Pollaczek polynomials neural network can be derived by utilizing an adaptive rule. Moreover, to improve convergence and obtain beneficial learning manifestation, the improved fish school search algorithm is made use of to readjust two fickle learning rates of the weights in the rectified reiterative sieved-Pollaczek polynomials neural network. Lastly, the effectuality of the proposed control system is validated by examination results. [ABSTRACT FROM AUTHOR]

This paper presents an altered grey wolf optimization, the Taguchi method, and finite element analysis (FEA) with two-phase multi-objective optimization for the design of a six-phase copper squirrel cage rotor induction motor (SCSCRIM). The multi-objective optimization design with high-performance property aims to achieve lower starting current, lower losses, lower input power, higher efficiency, higher output torque, and higher power factor. The multi-objective optimization design with high-performance property using the altered grey wolf optimization, the Taguchi method, and FEA in the first-phase program is used for minimizing the starting current, stator iron loss, stator copper loss, and input power. The multi-objective optimization design with high-performance property using the altered grey wolf optimization, the Taguchi method, and FEA in the second-phase program is used for maximizing the efficiency, output torque, and power factor. Finally, the proposed skill with higher performances is evaluated and verified via a two-phase program design and some performance tests. [ABSTRACT FROM AUTHOR]

A switched reluctance motor (SRM) circuit drive system caused many nonlinear effects due to convex construction. The linear control methods were hard to achieve good performance for the SRM circuit drive. The adaptive nonlinear backstepping control system using switching function is proposed for controlling the SRM drive system to obtain good performance. To reduce chattering of control effort, the adaptive nonlinear backstepping control system using adaptive law is proposed to estimate the required lumped uncertainty. When the inertia of the counterweight is varying, this proposed method cannot get a satisfactory performance. The adaptive nonlinear backstepping control system using mended recurrent Romanovski polynomials neural network with adaptive law and error‐estimated law is proposed for controlling the SRM drive system to raise robustness of the SRM drive system. Furthermore, two variable learning rates in the mended recurrent Romanovski polynomials neural network are adopted by using mended particle swarm optimization (PSO) algorithm to speed up parameter's convergence. Finally, comparative performances through some experimental results are verified that the proposed control system has better control performances than those of the proposed methods for the SRM drive system. [ABSTRACT FROM AUTHOR]

In order to cut down influence on the uncertainty disturbances of a linear motion single axis robot machine, such as the external load force, the cogging force, the column friction force, the Stribeck force, and the parameters variations, the micrometer backstepping control system, using an amended recurrent Gottlieb polynomials neural network and altered ant colony optimization (AACO) with the compensated controller, is put forward for a linear motion single axis robot machine drive system mounted on the linear-optical ruler with 1 um resolution. To achieve high-precision control performance, an adaptive law of the amended recurrent Gottlieb polynomials neural network based on the Lyapunov function is proposed to estimate the lumped uncertainty. Besides this, a novel error-estimated law of the compensated controller is also proposed to compensate for the estimated error between the lumped uncertainty and the amended recurrent Gottlieb polynomials neural network with the adaptive law. Meanwhile, the AACO is used to regulate two variable learning rates in the weights of the amended recurrent Gottlieb polynomials neural network to speed up the convergent speed. The main contributions of this paper are: (1) The digital signal processor (DSP)-based current-regulation pulse width modulation (PWM) control scheme being successfully applied to control the linear motion single axis robot machine drive system; (2) the micrometer backstepping control system using an amended recurrent Gottlieb polynomials neural network with the compensated controller being successfully derived according to the Lyapunov function to diminish the lumped uncertainty effect; (3) achieving high-precision control performance, where an adaptive law of the amended recurrent Gottlieb polynomials neural network based on the Lyapunov function is successfully applied to estimate the lumped uncertainty; (4) a novel error-estimated law of the compensated controller being successfully used to compensate for the estimated error; and (5) the AACO being successfully used to regulate two variable learning rates in the weights of the amended recurrent Gottlieb polynomials neural network to speed up the convergent speed. Finally, the effectiveness of the proposed control scheme is also verified by the experimental results. [ABSTRACT FROM AUTHOR]

The linear optical-ruler sensor with 1 μm precision mounted in the linear permanent magnet synchronous machine (LPMSM) is used for measuring the mover position of LPMSM in order to enhance the precision of a measured mover position. Due to nonlinear friction and uncertainty effects, linear controllers are very hard to achieve good mover positioning of LPMSM. The proposed adaptive amended Elman neural network backstepping (AAENNB) control system is adopted for controlling the LPMSM drive system to bring about the mover positioning precision of LPMSM. Firstly, a backstepping scheme is posed for controlling the tracing motion of the LPMSM drive system. The proposed backstepping control system, which is applied in the mover position of the LPMSM drive system, possesses better dynamic control performance and robustness to uncertainties for the tracing trajectories. Because of the LPMSM with nonlinear and time-varying dynamic characteristics, an adaptive amended Elman neural network uncertainty observer (AAENNUO) is posed to estimate the required lumped uncertainty. According to the Lyapunov stability theorem, on-line parameter training methodology of the amended Elman neural network (AENN) can be derived by use of adaptive law. The error estimated law is proposed to compensate for the observed error induced by the AENN with adaptive law. Furthermore, to help improve convergence and to obtain better learning performance, the mended particle swarm optimization (PSO) algorithm is utilized for adjusting the varied learning rate of the weights in the AENN. At last, these experimental results, which show better performance, are verified by the proposed control system. [ABSTRACT FROM AUTHOR]

A two-step optimal design with multi-objective functions by using two kinds of optimization methods for a six-phase synchronous reluctance motor is applied in a centrifugal compressor to achieve minimum cost, lower torque ripple, maximum efficiency and higher power factor. In the first-step procedure, the optimal design with multi-objective functions by use of the altered bee colony optimization (BCO) and the Taguchi method combined with finite element analysis (FEA) is used for optimizing the barrier shape and size in the rotor to reduce torque ripple, raise power factor, maximum efficiency and raise output torque. In the second-step procedure, the optimal design with multi-objective functions by means of the altered BCO and the Taguchi method combined with FEA is applied for optimizing the geometry of stator to reduce manufacturing cost, stator iron weight and stator winding weight. Finally, some experimental results show the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]