A Gain-Adaptive High-Order Terminal Sliding Mode Observer Under SPMSM Sensorless Control

In this paper, a gain-adaptive (GA) high-order terminal sliding mode observer (HOTSMO) is designed for back EMF estimation in the sensorless control of permanent magnet synchronous motors (PMSMs). The proposed observer features an adaptive gain mechanism that dynamically adjusts the sliding mode gain coefficient based on the system state. During the reaching phase with large observation errors, the gain coefficient is elevated to ensure observer stability. As the system approaches the sliding surface, the gain coefficient automatically reduces to suppress chattering while maintaining estimation accuracy. The adaptive mechanism is achieved through real-time coordination between the sliding mode surface function and the gain coefficient. Compared with the conventional HOTSMO, the proposed GA-HOTSMO effectively suppresses chattering and reduces both current and back-EMF estimation errors while maintaining observer stability. The effectiveness of the proposed GA-HOTSMO is validated through comprehensive theoretical analysis and experimental results.