| Summary: | Because permanent-magnet synchronous linear motors (SLM) still exhibit nonlinear friction, ending effects and time-varying dynamic uncertainties, better control performances cannot be achieved by using common linear controllers. We propose a backstepping approach with three adaptive laws and a beating function to control the motion of permanent-magnet SLM drive systems that enhance the robustness of the system. In order to reduce greater vibration in situations with uncertainty actions in the aforementioned control systems, we propose an adaptive modified recurrent Rogers–Szego polynomials neural network backstepping (AMRRSPNNB) control system with three adaptive laws and reimbursed controller with decorated gray wolf optimization (DGWO), in order to handle external bunched force uncertainty, including nonlinear friction, ending effects and time-varying dynamic uncertainties, as well as to reimburse the minimal rebuild error of the reckoned law. In accordance with the Lyapunov stability, online parameter training method of the modified recurrent Rogers–Szego polynomials neural network (MRRSPNN) can be derived by utilizing an adaptive law. Furthermore, to help reduce error and better obtain learning fulfillment, the DGWO algorithm was used to change the two learning rates in the weights of the MRRSPNN. Finally, the usefulness of the proposed control system is validated by tested results.
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