AI Article Synopsis
- A feedforward control technique is introduced that uses a second harmonic component to steer a non-linear system between attractors based on excitation frequency and amplitude.
- The technique applies to the Keller-Miksis equation, which models the dynamics of a gas bubble in a liquid and functions as a non-linear oscillator.
- By carefully selecting frequency ratios and tuning excitation amplitudes, the system’s trajectory can be smoothly altered between different periodic behaviors, such as moving between period-3 and period-5 orbits.
Article Abstract
A feedforward control technique is presented to steer a harmonically driven, non-linear system between attractors in the frequency-amplitude parameter plane of the excitation. The basis of the technique is the temporary addition of a second harmonic component to the driving. To illustrate this approach, it is applied to the Keller-Miksis equation describing the radial dynamics of a single spherical gas bubble placed in an infinite domain of liquid. This model is a second-order, non-linear ordinary differential equation, a non-linear oscillator. With a proper selection of the frequency ratio of the temporary dual-frequency driving and with the appropriate tuning of the excitation amplitudes, the trajectory of the system can be smoothly transformed between specific attractors; for instance, between period-3 and period-5 orbits. The transformation possibilities are discussed and summarized for attractors originating from the subharmonic resonances and the equilibrium state (absence of external driving) of the system.
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| http://dx.doi.org/10.1063/5.0005424 | DOI Listing |
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