Intelligent backstepping sliding-mode control using RBFN for two-axis motion control system

An intelligent backstepping sliding-mode control system using radial basis function network (RBFN) for a two-axis motion control system using permanent magnet linear synchronous motors (PMLSMs) is proposed. First, single-axis motion dynamics with the introduction of a lumped uncertainty, including cross-coupled interference between the two-axis mechanism, is derived. Then, to improve the control performance in reference contour tracking, a backstepping sliding-mode approach is proposed to compensate for uncertainties occurring in the motion control system. The bound of the lumped uncertainty is necessary in the design of the backstepping sliding-mode control system and is difficult to obtain in advance in practical applications. Therefore, an RBFN uncertainty observer is proposed to estimate the required lumped uncertainty in the backstepping sliding-mode control system. An adaptive learning algorithm, which can learn the parameters of the RBFN online, is derived using Lyapunov stability theorem. The proposed control algorithms are implemented in a TMS320C32 DSP-based control computer, and the motions in the x-axis and y-axis are controlled separately. The simulated and experimental results of circle and four leaves reference contours show that the motion tracking performance is significantly improved and the robustness to parameter variations, external disturbances, cross-coupled interference and frictional forces can also be obtained using the proposed controller.