To improve the performance of an electro-hydraulic position servo system employed in a blasting demining launcher, a novel nonlinear function—designated the Ifal function—is proposed to resolve the chattering problem caused by the non-smoothness of the conventional extended-state-observer (ESO) fal function around the origin in active-disturbance-rejection control (ADRC). Furthermore, to reduce the large number of manually tuned parameters and simplify the engineering calibration, an adaptive tuning strategy based on a radial-basis-function (RBF) neural network is introduced. Simulation results demonstrate that, compared with the conventional ADRC, the proposed ADRC incorporating the Ifal function and RBF neural network effectively suppresses chattering and delivers superior control performance, significantly enhancing the response speed, tracking accuracy, and disturbance-rejection capability of the electro-hydraulic servo system.