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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]

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]

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]

Because the V-belt continuously variable transmission system spurred by permanent magnet (PM) synchronous motor has much unknown nonlinear and time-varying characteristics, the better control performance design for the linear control design is a time consuming procedure. In order to overcome difficulties for design of the linear controllers, the composite recurrent Laguerre orthogonal polynomials modified p article swarm optimization (PSO) neural network (NN) control system which has online learning capability to come back to the nonlinear and time-varying of system, is developed for controlling PM synchronous motor servo-driven V-belt continuously variable transmission system with the lumped nonlinear load disturbances. The composite recurrent Laguerre orthogonal polynomials NN 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 modified 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]

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 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 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]

The Editor-in-Chief has retracted 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]

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]