Resonance frequency tracking control of a three-degree-of-freedom acoustic resonance system

Abstract

Resonance can enhance energy conversion and transmission efficiency in mechanical systems. However, maintaining effective resonant behavior by tracking the resonant frequency can be challenging due to load fluctuations. This study introduces a software-based phase-locked loop (SPLL) control method for three-degree-of-freedom acoustic resonant systems (3DOFARS). Initially, the dynamic equation governing the behavior of 3DOFARS is provided, followed by a frequency domain analysis based on the amplitude-phase frequency characteristic curve. Subsequently, the SPLL control method is developed by considering the phase relationship between the system’s excitation signal and response signal, and a control model is then established using Simulink. For the step, slope, and sinusoidal disturbances with specific amplitude and frequency variations, the SPLL control method can track the excitation frequency to the resonant frequency in real time. Among these disturbances, step disturbances pose a greater risk of system instability compared to slope and sinusoidal disturbances. Finally, simulation verification and statistical analysis are carried out by introducing quality interferences of varying types, amplitudes, and frequencies to assess the SPLL control method’s impact on different interferences. Under stable conditions, the SPLL method has better control capabilities against low-frequency interference and better robustness against high-frequency interference. In comparison to conventional methods, the SPLL control method effectively maintains real-time tracking of the excitation frequency to the resonant frequency while upholding process flow integrity.