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Purpose <p>To mitigate the stringent low-frequency micro-vibration requirements of high-precision spacecraft missions and overcome the limitations of conventional linear isolation systems, this paper proposes a novel active isolation system. It integrates a quasi-zero-stiffness (QZS) mechanism into a six-degree-of-freedom (6-DOF) Gough-Stewart (G-S) parallel platform, aiming to combine theultra-low-frequency isolation advantages of QZS with the multi-axis control capabilities of the G-S platform.</p> Methods <p>This paper presents the coupled, nonlinear 6-DOF dynamic model of the QZS G-S platform, elucidating that beneficial QZS behavior occurs strictly at the zero-equilibrium position. To address the system's strong nonlinearity and coupling, a sliding-mode control (SMC) scheme is designed. A saturation function is introduced to replace the traditional discontinuous signum function to effectively mitigate control chattering. Numerical simulations under free vibration, harmonic excitation, and random excitation are conducted to evaluate performance, comparing the proposed active SMC against passive isolation and Proportional-Integral-Derivative (PID) control.</p> Results <p>Static analysis reveals that the platform possesses multiple equilibrium positions, necessitating active control to maintain the QZS operating point. Time-domain simulations demonstrate that the proposed SMC regulates the platform to the QZS equilibrium rapidly with no obvious overshot, while effectively mitigating chattering, whereas passive systems exhibit prolonged residual vibrations. Frequency-domain analysis shows that the active strategy reduces vibration amplitudes by orders of magnitude in the low-frequency band across all 6 DOFs. Furthermore, the SMC demonstrates superior global suppression and robustness compared to PID control, which struggles with multi-axis coupling.</p> Conclusions <p>Numerical results demonstrate that the active QZS G-S platform holds great potential for realizing 6-DOF low-frequency vibration isolation. The proposed saturation-based SMC strategy effectively handles system nonlinearities and coupling while ensuring smooth control forces suitable for limited-output spacecraft actuators. These findings provide a theoretical foundation and a robust control solution for next-generation multi-dimensional space isolation systems.</p>

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Sliding Mode Control of Quasi-zero-stiffness Parallel Platforms

  • 期刊论文

  • 发表日期：

    2026年1月26日

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  • Xiang Fu,
  • Jie Tang,
  • Ke Sun,
  • Yinghui Li,
  • Kun Zhao,
  • Huatao Chen,
  • Dengqing Cao

摘要

Purpose

To mitigate the stringent low-frequency micro-vibration requirements of high-precision spacecraft missions and overcome the limitations of conventional linear isolation systems, this paper proposes a novel active isolation system. It integrates a quasi-zero-stiffness (QZS) mechanism into a six-degree-of-freedom (6-DOF) Gough-Stewart (G-S) parallel platform, aiming to combine theultra-low-frequency isolation advantages of QZS with the multi-axis control capabilities of the G-S platform.

Methods

This paper presents the coupled, nonlinear 6-DOF dynamic model of the QZS G-S platform, elucidating that beneficial QZS behavior occurs strictly at the zero-equilibrium position. To address the system's strong nonlinearity and coupling, a sliding-mode control (SMC) scheme is designed. A saturation function is introduced to replace the traditional discontinuous signum function to effectively mitigate control chattering. Numerical simulations under free vibration, harmonic excitation, and random excitation are conducted to evaluate performance, comparing the proposed active SMC against passive isolation and Proportional-Integral-Derivative (PID) control.

Results

Static analysis reveals that the platform possesses multiple equilibrium positions, necessitating active control to maintain the QZS operating point. Time-domain simulations demonstrate that the proposed SMC regulates the platform to the QZS equilibrium rapidly with no obvious overshot, while effectively mitigating chattering, whereas passive systems exhibit prolonged residual vibrations. Frequency-domain analysis shows that the active strategy reduces vibration amplitudes by orders of magnitude in the low-frequency band across all 6 DOFs. Furthermore, the SMC demonstrates superior global suppression and robustness compared to PID control, which struggles with multi-axis coupling.

Conclusions

Numerical results demonstrate that the active QZS G-S platform holds great potential for realizing 6-DOF low-frequency vibration isolation. The proposed saturation-based SMC strategy effectively handles system nonlinearities and coupling while ensuring smooth control forces suitable for limited-output spacecraft actuators. These findings provide a theoretical foundation and a robust control solution for next-generation multi-dimensional space isolation systems.