Control methods for switching between coexistent attractors of impact oscillator

The idea of taking advantage of nonlinear system dynamics to promote adaptability or improve performance is becoming a popular concept in science and engineering. One way to explore these dynamics is to have the ability to switch between coexisting solutions at will. For example, switching between non-impacting and impacting solutions can enhance drilling processes or avoid chatter in machining. Despite the potential applications, just a few control methods with such an objective are reported in the literature. Recently, two methods were proposed: the intermittent control and the time-delayed feedback control. These methods have completely different strategies to switch between coexistent attractors, and a comparison between them can lead to a deeper understanding of both controllers and guide selecting the adequate controller for an application. This work analyses the advantages and disadvantages of
these methods to switch between stable coexisting solutions. A piecewise linear impact oscillator model is used as a typical multistable system to test controller capabilities. The comparisons are made in a scenario where the exchange is made between impacting and non-impacting solutions where period-1 and period-2 orbits coexist. The properties of the control methods are then analysed and discussed. Results show that, on the one hand, the time-delayed feedback method requires much less knowledge of the system to be applied but cannot perform the switch in some scenarios. On the other hand, intermittent control requires more system knowledge but can succeed in all analysed scenarios.