Abstract: For the high-speed permanent magnet synchronous motor (PMSM) with sensorless rotor position used in hydrogen fuel cell air pumps, it is challenging to obtain accurate information about the motor rotor position and speed within an extremely short time. To address this issue, this paper proposes a design scheme of a predefined time-space super-twisting sliding mode observer (PdT-ST-SMO) based on a barrier function. By adopting a space division strategy, the system states are divided into two regions, the barrier function region and the rapid reaching region. In the rapid reaching region, a predefined-time-space reaching law is employed to accelerate the convergence of errors. In the barrier function region, an improved barrier function is utilized to suppress chattering—a common issue in sliding mode control systems that can degrade control performance and cause mechanical wear. Ultimately, the super-twisting sliding mode algorithm is leveraged to achieve accurate observation of the back electromotive force (bEMF), which is crucial for deriving the rotor position and speed of the PMSM. Design an observer based on the designed predefined time-space reaching law and super-twisting sliding mode algorithm. To verify the stability of the proposed observer, the Lyapunov stability theory is applied. The theoretical analysis demonstrates that the current observation error of the designed observer can converge to the predefined neighborhood of the origin within the predefined time, ensuring the reliability and effectiveness of the observer in practical applications. Simulation results are presented to validate the performance of the proposed approach. When the target speed is , the proposed observer achieves the rotor position observation accuracy ofwithin the different predefined times . Comparative studies are conducted against the traditional sliding mode observer (SMO) and the conventional super-twisting sliding mode observer. The results show that the error accuracy of the observer proposed in this paper is improved by 5.5% and 4.875%, respectively, compared with these two traditional observers. This significant improvement in observation accuracy highlights the superiority of the proposed design in addressing the sensorless control challenge of high-speed PMSMs for hydrogen fuel cell air pumps, laying a solid foundation for enhancing the overall efficiency and stability of hydrogen fuel cell systems.