Objective Space optical payloads for remote sensing and laser communication increasingly demand large apertures and long focal lengths, making them highly susceptible to micro-vibrations generated by on-board moving components such as reaction wheels and cryocoolers. Although these vibrations typically possess low amplitudes, they significantly degrade Line-of-Sight (LOS) stability and imaging quality due to optical path amplification. To address the dual challenge of high-precision pointing and effective micro-vibration isolation, the voice-coil motor (VCM) driven parallel flexible platform has emerged as a prominent solution. This "active-passive integrated" system utilizes flexure hinges to provide low-stiffness support for high-frequency isolation and VCMs for non-contact precision attitude control. However, a fundamental contradiction exists in the soft-support design: low stiffness, while beneficial for isolation, inevitably introduces low-frequency mechanical resonance modes (typically <10 Hz). In systems with large payload inertia, the prominent resonance peak causes a severe drop in the gain margin, forcing the servo system to operate at a very low open-loop gain. This limitation restricts the closed-loop bandwidth to a level often insufficient for fast maneuvering and precision tracking. This study aimed to resolve this conflict between isolation performance and pointing bandwidth by systematically comparing two distinct resonance suppression strategies—Improved Notch Filter (signal-based) and Skyhook Damping (model-based)—applied to a custom-developed four-leg voice-coil driven platform.

Methods The research utilized a custom-built four-leg parallel platform driven by voice coil motors. The platform featured a differential control architecture where symmetrically arranged legs generated pure torque for pitch and yaw motions, decoupling the multi-degree-of-freedom dynamics. A simplified single-degree-of-freedom rotational dynamic model was established using the Newton-Euler method. System identification experiments revealed a dominant weakly damped mechanical resonance at approximately 7.4 Hz with a peak magnitude of 19 dB, confirming the theoretical model. Two resonance suppression control architectures were designed and implemented. 1) An Improved Notch Filter (NF) strategy was employed as a series compensator within the position loop. Unlike traditional notch filters where depth and width are coupled, the improved structure allowed independent tuning of notch depth, width, and frequency. This flexibility enabled precise "surgical" removal of the resonance energy to recover phase margin without inducing excessive phase lag at the crossover frequency. 2) A Skyhook Damping (SK) strategy was implemented as an active vibration control inner loop. Based on absolute acceleration feedback measured by high-sensitivity accelerometers, this method emulated a virtual damper connected between the payload and the inertial frame ("sky"). The implementation involved integrating the acceleration signal to obtain absolute velocity, which was then multiplied by a skylight gain to generate an active damping force. To validate these strategies, a high-precision optical pointing experimental system was constructed. The setup included a Z-shaped secondary reflection optical path using a high-stability collimator, a fixed primary mirror, a moving secondary mirror mounted on the platform, and a high-resolution CCD camera (1K×1K resolution) as the terminal detector. Control experiments were conducted using both internal sensors (linear grating encoders, 50 nm resolution) and external sensors (CCD camera) to cross-validate performance.

Results and Discussions Frequency domain analysis via sine sweep testing (0.1–25 Hz) characterized the system dynamics. Open-loop results confirmed the rigid-body behavior in the low-frequency range and the sharp resonance peak at 7.4 Hz. A secondary resonance at ~20 Hz was also identified, attributed to the coupling modes of the gravity off-loading suspension system. In closed-loop frequency response tests, the traditional PI controller was severely limited by the resonance, achieving a bandwidth of only ~0.7 Hz. Both the PI+NF and PI+SK strategies successfully suppressed the 7.4 Hz resonance peak, eliminating the gain margin constraint. Consequently, the closed-loop bandwidth was extended significantly from <1 Hz to over 5 Hz (CCD feedback) and over 6 Hz (encoder feedback). Notably, the Skyhook strategy demonstrated additional suppression of the 20 Hz suspension mode due to its broadband damping effect, whereas the Notch Filter, being frequency-specific, only addressed the target mode. Time-domain trajectory tracking experiments were conducted at frequencies of 0.02 Hz, 0.06 Hz, and 0.10 Hz with a reference amplitude of 1.725 mrad. Results showed that tracking errors increased with frequency for all strategies due to physical bandwidth limitations. However, the resonance suppression methods significantly outperformed the baseline PI control. At 0.10 Hz, the baseline PI control yielded a root mean square error (RMSE) of 203.8 µrad. The PI+NF and PI+SK strategies reduced this error to 60.8 µrad and 63.6 µrad respectively, representing a reduction of approximately 70%. A critical performance divergence was observed in the ultra-low frequency regime (0.02 Hz). While the Notch Filter maintained a 64% improvement rate, the Skyhook strategy’s improvement dropped to 48%. Analysis indicated that this degradation stemmed from the physical implementation mechanism of Skyhook: at very low frequencies and small amplitudes, the acceleration signal strength decreased significantly, leading to a low signal-to-noise ratio (SNR) from the accelerometers, thereby weakening the active damping effect.

Conclusions The investigation confirmed that flexible parallel platforms suffer from a critical trade-off between isolation stiffness and control bandwidth, primarily imposed by low-frequency mechanical resonances. Both the improved notch filter and Skyhook damping strategies proved effective in resolving this contradiction, successfully extending the closed-loop bandwidth by a factor of five (from 0.7 Hz to >5 Hz) and reducing dynamic tracking errors by approximately 70% in high-frequency tracking tasks. The comparative analysis highlighted distinct engineering trade-offs. The improved notch filter offered a simpler implementation requiring no additional sensors and excelled in low-frequency tracking where accelerometer noise is problematic. However, it relied heavily on accurate model identification and lacked robustness against parameter drift or unmodeled modes (like the 20 Hz suspension mode). Conversely, Skyhook Damping provided superior robustness against parameter perturbations and broadband suppression of auxiliary modes but incurred higher hardware costs and was limited by sensor noise floors at low frequencies. These findings provide comprehensive engineering guidelines for designing control systems for large-scale space optical payloads. Future iterations will optimize the optical layout for dual-axis coupling control and incorporate an external disturbance platform to validate transmissibility under complex micro-vibration environments.