Control circuit design and chaos analysis in an ultrasonic machining system

This study aims to investigate the dynamic motion of an ultrasonic machining system comprising two Duffing oscillators, each with a single degree of freedom. After derivation of the differential equations of the system using the Lagrange equations and dimensionless time, numerical analysis was used to observe changes in the system caused by differences in excitation frequency.

To suppress this effect and improve performance, proportional differential (PD) control was used. The integral absolute error was used as the fitness function, and particle swarm optimization was used to find the best value for the gain constant of the PD controller.

The results showed that with specific changes of excitation frequency, the dynamic motion of the system became nonlinear and chaotic behavior resulted. This made the system unstable and affected performance.

A range of methods, including fuzzy control, was used to analyze the results, and exhaustive laboratory work was carried out. Means of control were found that were effective in suppressing the chaotic behavior, and differences in response to control were investigated and verified. The findings of this study can be used as a basis for system parameter settings or control circuit design.