In recent years, pneumatic stages have attracted attention as stages for semiconductor manufacturing equipment due to their low cost and minimal maintenance requirements. However, pneumatic stages include nonlinear elements such as friction and air compressibility, making precise control challenging. To address this issue, this paper aims to achieve high-precision positioning by applying a nonlinear position control method to pneumatic stages. To achieve this, we propose a control method that combines filtered right coprime factorization and Prescribed Performance Control–Sliding Mode Control (PPC-SMC). Filtered right coprime factorization not only stabilizes and simplifies the plant but also reduces noise. Furthermore, PPC-SMC enables safer and faster control by constraining the system state within a switching surface that imposes limits on the error range. Through experiments on the actual system, it was confirmed that the proposed method achieves dramatically higher precision and faster tracking compared to conventional methods.