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• A smith predictor-based delay compensation scheme is proposed for the suppression of the undesired speed overshoot/variation phenomena caused by the speed filter. • The effectiveness and stability of the proposed solution are verified analytically and experimentally. • The robustness of the proposed solution against system parameter mismatch is verified analytically and experimentally. • The proposed structure is simple to implement with a low calculation burden and no parameters need to be tuned. The load disturbance rejection ability of the electrical machine systems is an important consideration factor in many applications, including both power generation (e.g., wind power generator) and consumption (e.g., servo systems such as high-precision machining and continuous motion in manufacturing automation). Existing studies on load disturbance rejection mainly focus on developing disturbance observers with improved steady state and dynamic performance. However, the performance of the disturbance rejection control is not only determined by the performance of the disturbance observers but also influenced by the speed response control during the transient. The latter problem might require more attention, especially due to the fact that speed filter is widely used in many actual systems to suppress the speed ripples or noise. The speed control performance would suffer from the delay caused by the filter and result in an undesired oscillatory speed response. In this paper, load disturbance rejection control based on a sliding mode disturbance observer is considered as an investigation platform, where an adaptive filter is proposed to further improve the performance of the observer. More importantly, a Smith predictor-based speed filter delay compensator is proposed to mitigate the undesired variation in the speed response caused by speed filter, achieving enhanced transient speed response under load disturbance. This structure is simple to implement, and no control parameters need to be tuned. The effectiveness of the proposed solution has been verified on a permanent magnet synchronous machine drive system. [ABSTRACT FROM AUTHOR]