Adaptive Time-Delayed Feedback Control Applied to a Vibro-Impact System

Multi-stable systems can be found in many fields of engineering from vibro-impact energy harvesters to origami structures. They are mainly characterised by the presence of co-existing attractors in their dynamic response. This feature can be beneficial when the system is required to adapt to the environment or unfavourable as the system may diverge from the desired behaviour. Hence, these systems usually require actuation or control that can be activated to maintain the desired response or switch between configurations. Recently, the idea to use the time-delayed feedback method to switch between co-existent attractors was proposed focusing on the controlled system’s ability to exchange between attractors or maintain a specific type of behaviour. However, the control method is still required to have its gains set on a trial and error basis when dealing with stable solutions. Furthermore, it requires a deeper analysis of the system dynamics when dealing with unstable orbits. To address the beforementioned challenges and eliminate requirements of a priori knowledge of the system evolution function, this work uses the adaptive gain time-delayed feedback method to switch between co-existing attractors. Numerical results show that the proposed controller can be a viable low energy control option in multi-stable systems.