A novel control method, the self-recurrent wavelet neural network super-twisting non-singular fast terminal sliding mode (SRWNN_STNFTSM) control with prescribed performance, is proposed to improve the tracking control performance of the ball and plate system in the presence of dynamic uncertainties and unknown perturbations. The prescribed performance function (PPF) is used to convert the originally constrained position error of the ball and plate system into an unconstrained error model. The non-singular fast terminal sliding mode control (NFTSMC) sliding mode surface is introduced to resolve the singular issue of conventional terminal sliding mode control. Additionally, a compensation term of the tanh function is incorporated to improve the NFTSM sliding mode surface, adjusting the convergence speed and tracking accuracy. Moreover, the SRWNN_ STNFTSM controller is combined with the super-distortion algorithm (STA) to mitigate the effects of chattering and lumped disturbance. To address the lumped disturbance of the system and ensure high tracking accuracy, an adaptive SRWNN compensator is designed in conjunction with the STNFTSM. This compensator is aimed at eliminating disturbances and ensuring robustness. Simulation results compared with existing conventional sliding mode control methods demonstrate that SRWNN_STNFTSM exhibits excellent performance. It accurately tracks the ball and plate system under the influence of lumped disturbances.