Satellite pointing mechanisms for earth observation require ultra-low speed scanning (approximately ${70}^{″}/\mathrm{s}$) and precise variable-speed compensation. However, traditional Field-Oriented Control (FOC) suffers from significant velocity bias and instability under these conditions. To address these issues, this paper proposes a position-loop-based speed control scheme integrated with a variable structure control strategy. By substituting the speed command with a position loop, the proposed method effectively suppresses steady-state velocity bias, while the variable structure strategy mitigates fluctuations during variable-speed motion. Experimental results indicate that, compared to traditional FOC, the proposed method reduces velocity bias error by over $30\%$ during uniform tracking and decreases the amplitude of velocity fluctuations by more than $40\%$ in variable-speed scenarios. This strategy significantly enhances the control precision of satellite pointing mechanisms and improves on-orbit imaging compensation accuracy.

Low-frequency base vibration transmitted through supporting platforms can degrade the stability of precision payloads, optical instruments, and inertial measurement systems. In velocity-sensor-based active isolation platforms, displacement-related feedback states are unavailable. Direct velocity integration can drift under sensor bias, while raw lower-platform velocity feedforward can introduce measurement noise and out-of-band components. This paper proposes a dual extended state observer (ESO) reconstruction method combining equivalent-displacement feedback and lower-platform feedforward. The upper-platform ESO reconstructs feedback velocity and a bounded equivalent-displacement state, while the lower-platform ESO provides a smoothed velocity reference for feedforward compensation. The method was implemented on a plate-type active vibration isolation platform and evaluated using lower-to-upper-platform acceleration transmissibility over 0.1–10 Hz. Across three repeated 200 s records, the proposed ESO feedback–feedforward condition achieved an integrated input–output suppression ratio of $38.67\pm 0.46$ dB, reduced the upper-platform output acceleration RMS to $(1.31\pm 0.09)\times {10}^{-7}$ g, and provided a $48.92\pm 2.12$ dB RMS reduction relative to the passive baseline. Direct nominal–measured comparisons further showed that the reduced model captured the dominant passive and feedback-controlled dynamics. These results demonstrate that low-frequency active micro-vibration isolation can be achieved using only velocity measurements, without additional displacement sensors.