Resonance frequency tracking method for multi-degree-of-freedom resonant systems based on adaptive extremum seeking control

Abstract

Resonance-based devices are extensively utilized in engineering applications due to their low energy consumption and high energy conversion efficiency. However, fluctuations in resonance frequency caused by variations in stiffness and damping in the system can lead to a mismatch with the excitation frequency, which degrades the performance of the system. To address this issue, real-time resonance frequency tracking (RFT) is crucial. This study proposes a phase-locked loop-based adaptive extremum seeking control (PLL-AESC) method for online RFT, which is demonstrated using a three-degree-of-freedom resonance system. The method employs the response amplitude of the system as a cost function and estimates the local gradient in real time, which enables indirect optimization of the excitation frequency. Compared with conventional direct RFT approaches, PLL-AESC offers reduced computational complexity and improved real-time performance. Furthermore, its learning rate is adaptively adjusted based on the gradient and phase difference signals, which improves the efficiency of the method to various disturbances. The effectiveness of PLL-AESC is validated through simulations and comparative analyses. Results indicate that the proposed method demonstrates a shorter settling time than traditional extremum seeking control methods. Compared with the phase-locked loop method, it successfully maintains RFT performance under damping variation disturbances.

Graphical abstract

Keywords

multi-degree-of-freedom system / resonance frequency tracking / extremum seeking control / data-driven methods

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