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.

The three spacecraft of the space gravitational wave antenna employ heterodyne interferometry to mitigate the effects of Doppler shift. Constrained by laser relative intensity noise (RIN) and the sampling frequency constraints of phase readout circuits, the widespread adoption of fixed offset frequencies effectively regulates the frequency of heterodyne interferometric beat notes within a reasonable frequency domain of [5 MHz, 25 MHz]. In this work, a high-precision fitness genetic algorithm for heterodyne interferometry is utilized to generate the initial offset frequency distribution scheme. To address issues with unreasonable switching times and offset frequency settings in the initial scheme for partial frequency domains, optimization strategies are proposed from three aspects: frequency domain selection extension, switch times control, and numerical low frequency. Results demonstrate that the optimization of frequency domain selection extension narrows the reasonable frequency domain to [5 MHz, 15 MHz] and [7 MHz, 17 MHz]. Optimization of switch times control ensures that switching times of offset frequency distribution scheme generated under the settings of [6 MHz, 17 MHz] and wider frequency domains can be controlled within a reasonable range of 6 to 13 times. Fixed offset frequency settings are generally reduced by 24.3% after low-frequency optimization. This methodology and result can provide a reliable reference for Program Taiji and even related space gravitational wave antenna projects.