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Purpose <p>This study aims to develop a robust vibration control strategy for piezoelectric cantilever beams to address the instability and performance degradation caused by uncertain time delays.</p> Methods <p>A novel control approach is proposed using Proximal Policy Optimization (PPO) integrated with a Delay Domain Randomization (DDR) mechanism. By implementing dynamic random sampling within a predefined delay domain during the reinforcement learning training process, the PPO agent learns a generalized control law. A discrete state-space model of the piezoelectric beam is established based on Euler-Bernoulli beam theory and the modal superposition method, with key physical parameters identified through experimental characterization.</p> Results <p>Comparative simulations indicate that while standard PPO controllers outperform conventional proportional-derivative (PD) controllers in delayed environments, agents trained at a single fixed delay suffer from overfitting and limited generalization. Experimental validation demonstrates that the proposed DDR-PPO controller achieves an approximate 20–30 dB reduction in the second-order mode vibration peak compared to the fixed-delay-trained PPO. Furthermore, the DDR mechanism significantly extends the allowable time-delay range while maintaining system stability.</p> Conclusion <p>The integration of Delay Domain Randomization with PPO significantly enhances the robustness of active vibration control systems against uncertain delays. The proposed DDR-PPO controller provides an effective and generalized solution for structural vibration suppression in engineering applications where communication or processing delays are prevalent and variable.</p>

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Active Vibration Control of Piezoelectric Beams under Uncertain Delay via a DDR-PPO Approach

  • 期刊论文

  • 发表日期：

    2026年4月6日

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  • Juncheng Wu,
  • Ting Zhang

摘要

Purpose

This study aims to develop a robust vibration control strategy for piezoelectric cantilever beams to address the instability and performance degradation caused by uncertain time delays.

Methods

A novel control approach is proposed using Proximal Policy Optimization (PPO) integrated with a Delay Domain Randomization (DDR) mechanism. By implementing dynamic random sampling within a predefined delay domain during the reinforcement learning training process, the PPO agent learns a generalized control law. A discrete state-space model of the piezoelectric beam is established based on Euler-Bernoulli beam theory and the modal superposition method, with key physical parameters identified through experimental characterization.

Results

Comparative simulations indicate that while standard PPO controllers outperform conventional proportional-derivative (PD) controllers in delayed environments, agents trained at a single fixed delay suffer from overfitting and limited generalization. Experimental validation demonstrates that the proposed DDR-PPO controller achieves an approximate 20–30 dB reduction in the second-order mode vibration peak compared to the fixed-delay-trained PPO. Furthermore, the DDR mechanism significantly extends the allowable time-delay range while maintaining system stability.

Conclusion

The integration of Delay Domain Randomization with PPO significantly enhances the robustness of active vibration control systems against uncertain delays. The proposed DDR-PPO controller provides an effective and generalized solution for structural vibration suppression in engineering applications where communication or processing delays are prevalent and variable.