Switching between periodic orbits in impact oscillator by time-delayed feedback methods

Abstract

An ability to exchange between different attractors can bring adaptability and new functionalities to an engineering system. While nonlinear controllers are widely used to stabilize on a preferred orbit, there is only a few which can exchange back and forth between two or more stable periodic responses. This work proposes a new variation of the original Time-Delayed Feedback (TDF) control method capable to effectively switch back and forth between periodic orbits having only a limited knowledge of the system dynamics. The stable or unstable periodic responses of the system that are inside or outside a chaotic attractor can be targeted. The proposed control method named here as the Fractional Time-Delayed Feedback Control (FTDF) is tested numerically and experimentally using a newly developed impact oscillator rig. Various responses including impacting and non-impacting orbits, high period attractors and chaos are considered. The main advantages of the FTDF over the TDF are presented by showcase scenarios where the TDF alone cannot safely perform the exchange between orbits.