LAUSR

In this paper, an intelligent fractional-order backstepping control (IFOBC) method combining fractional-order backstepping control (FOBC) and Takagi–Sugeno–Kang-type fuzzy neural network (TSKFNN) applicable to the permanent magnet linear synchronous motor (PMLSM) is adopted to achieve high-performance servo control fields. First, the global regulation and position tracking of the system are realized by backstepping control (BC). In order to improve the convergence speed and control accuracy of the system, a FOBC which has extra degree of freedom in the control parameters is designed. Second, since the boundary of the uncertainties in the system is difficult to estimate, which makes the switching control gain hard to select, the TSKFNN is introduced to estimate the uncertainties online. By using asymmetric Gaussian function as the membership function, the convergence speed and the accurate approximation capability of TSKFNN are improved greatly. Additionally, a robust compensator is developed to confront the uncertainties such as approximation error, optimal parameter vector and higher Taylor series. Therefore, the robustness of the system is further improved. Finally, the adaptive learning algorithms for the online training of the TSKFNN are derived using the Lyapunov theorem to guarantee the asymptotical stability of the system. The experiments implemented on a digital signal processor (DSP), TMS320F28335, demonstrate that the proposed control method provides a high-performance dynamic characteristics and that is robust with respect to parameter variations, external disturbances and nonlinear friction forces.