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The robust nonlinear speed control technique has been proposed for the speed regulation of permanent magnet synchronous motor (PMSM) by adopting a new fast terminal sliding mode control (FTSMC) based on the finite time sliding mode observer (FTSMO). The proposed technique can ensure the robustness against load disturbances, which has the capability of high tracking precision, fast finite time convergence and smooth dynamic operation in both transient and steady state conditions. Moreover, the requirement of high switching gain to reach the upper bound limit of total disturbances may produce the steady state error and chattering. To address this issue, one robust FTSMO based FTSMC is designed to alleviate those limitations aforementioned. The FTSMO can successfully estimate the total disturbances of the system, then the estimated disturbances can be compensated by the feed-forward compensation technique. The FTSMO based FTSMC should require the smaller switching gain to meet upper bound limit of the disturbances compared with the conventional SMC (CSMC) and FTSMC. The stability of the close loop control system is fully verified by the Lyapunov theory. Comprehensive simulation and experimental results have fully demonstrated that the proposed method is robust against load disturbances.